Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Johann Mahne on 28/07/2011 15:12:06
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I've always wondered how the value of -273 deg c was discovered as the coldest possible temperature.
Was it through experiment or from astronomical measurements (spectrometers) or calculated theoretically?
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It's a theoretical idea.
Temperature is defined as the average kinetic energy of particles making up matter. Kinetic energy is energy of motion, so it's a measurement of the average motion of a lot of particles. It makes sense that the lowest possible temperature is when that motion stops. This was the original idea of absolute zero.
More recently, scientists have learned that small particles can never stop moving because of the rules of quantum mechanics. Absolute zero can still defined as the temperature where they're moving the least amount possible.
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It was discovered by graphing the relationship among temperature, pressure and volume of gasses. For a constant volume of most gases, the pressure to temperature graph follows a straight line which reaches zero pressure at -273.15°C.
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It's a theoretical idea.
Temperature is defined as the average kinetic energy of particles making up matter. Kinetic energy is energy of motion, so it's a measurement of the average motion of a lot of particles. It makes sense that the lowest possible temperature is when that motion stops. This was the original idea of absolute zero.
More recently, scientists have learned that small particles can never stop moving because of the rules of quantum mechanics. Absolute zero can still defined as the temperature where they're moving the least amount possible.
It was first proposed by Einstein, it has a value of 1/2 \hbar ω. It not a theoretical idea, it's a proven limit on temperatures of systems, free and bound.
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I've always wondered how the value of -273 deg c was discovered as the coldest possible temperature.
Was it through experiment or from astronomical measurements (spectrometers) or calculated theoretically?
It was proposed in 1913 using a formula that was develeoped by Max Planck. Einstein used it to describe vibrational energy, and was given as
ε = (hv/ehv/kT-1) + hv/2
hv/2 can be thought of an existing kinetic energy for a system, which means that -273 can never be accomplished. This also means the zero point energy does not actually exist! I've even proposed that Fermi energy equations propose a faulty premise as it requires the idea that the ZP-energy is a real value.
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from wikipedia
http://en.wikipedia.org/wiki/Absolute_zero
Limit to the 'degree of cold'
The question whether there is a limit to the degree of cold possible, and, if so, where the zero must be placed, was first attacked by the French physicist Guillaume Amontons in 1702, in connection with his improvements in the air thermometer. In his instrument, temperatures were indicated by the height at which a column of mercury was sustained by a certain mass of air, the volume or "spring" which varied with the heat to which it was exposed. Amontons therefore argued that the zero of his thermometer would be that temperature at which the spring of the air in it was reduced to nothing. On the scale he used, the boiling-point of water was marked at +73 and the melting-point of ice at 51, so that the zero of his scale was equivalent to about −240 on the Celsius scale.
and from the 1911 (ie before the the planck formula you mention) encyclopedia britannica
http://www.1911encyclopedia.org/Cold
After J. P. Joule had determined the mechanical equivalent of heat, Lord Kelvin approached the question from an entirely different point of view, and in 1848 devised a scale of absolute temperature which was independent of the properties of any particular substance and was based solely on the fundamental laws of thermodynamics (see Heat and Thermodynamics). It followed from the principles on which this scale was constructed that its zero was placed at - 273°, at almost precisely the same point as the zero of the air-thermometer.
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There is no question that the equation and experimental evidence implies the zero point energy limit is not attainable. The reason why is because of:
E = ∫ (Th/Tc - 1) C dT
If the integral here is taken to the Th to Tc, (hot and cold temperatures) then if C is a constant and as Th approaches Tc, E tends to infinity.
This means that it will take an infinite amount of energy to reach T=0. This is along the same idea's as a system requiring an infinite amount of energy to reach speeds equalling c.
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Mr Data could you also explain your variables and notation a bit as well so that those not versed in quantum mechanics can attempt to follow the equations and thus your argument.
As an example
ε = (hv/ehv/kT-1) + hv/2
This looks similar to the average value of a planck oscilator - but it should normally be in terms of Ehat rather than epsilon. And if we are using greek script then the nu should be a nu
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Mr Data could you also explain your variables and notation a bit as well so that those not versed in quantum mechanics can attempt to follow the equations and thus your argument.
As an example
ε = (hv/ehv/kT-1) + hv/2
This looks similar to the average value of a planck oscilator - but it should normally be in terms of Ehat rather than epsilon. And if we are using greek script then the nu should be a nu
You want me to describe this equation for you? Epsilon is a small number, and refers to a small energy contribution. So let ε=Ef where Ef is zero energy field. Let hv/2 = KE where KE is the kinetic energy wherre h is planks constant and v is the frequency. We have expression here (hv/ehv/kT-1) which just looks like a mess of things, including an ugly exponential that non-mathematicians cannot appreciate easily. Just let this equal an energy, but look at it as an energy that equals zero. However, whilst that is a general limit on the system, the system does not actually have a non-zero energy because hv/2 is not equal to zero. So all in all, the equation above really reads
E = KE = 1/2hv
For an existing energy, and will always exist. It cannot reach zero because it would, again, require an infinite amount of energy.
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You can even set v = ω so that
hbar ω/2 = E for a ZP-field fluctuation.
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It's a theoretical idea.
Temperature is defined as the average kinetic energy of particles making up matter. Kinetic energy is energy of motion, so it's a measurement of the average motion of a lot of particles. It makes sense that the lowest possible temperature is when that motion stops. This was the original idea of absolute zero.
More recently, scientists have learned that small particles can never stop moving because of the rules of quantum mechanics. Absolute zero can still defined as the temperature where they're moving the least amount possible.
It was first proposed by Einstein, it has a value of 1/2 \hbar ω. It not a theoretical idea, it's a proven limit on temperatures of systems, free and bound.
Maybe you misunderstood what I mean by theoretical. Absolute zero is theoretical because no one has ever seen it, nor will they, so it's based on theory work, not on observation or experiment. But it's on solid foundation, as we know exactly what it means in terms of measurable quantities (energy).
Phractality and Matthew's points are good ones. The original definition of absolute zero was based on extrapolating from a thermometer. Modern understanding of it is based on the idea of energy in a system.
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It's funny you ask what you did though, because I think
ε = (hv/ehv/kT-1) + hv/2
Is an ugly equation anyway, and does not really explain why ε is small, or even should contribute hv/2 (the existing energy). This is why the limit
E = ∫ (Th/Tc - 1) C dT
Is much more appropriate, because it is devised under the impression that it is
E = W = ∫ (Th/Tc - 1) C dT
meaning it is the ''work'' of the system. The work required to reach the limit is unattainable. It would require more energy than in the observable universe!
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It's a theoretical idea.
Temperature is defined as the average kinetic energy of particles making up matter. Kinetic energy is energy of motion, so it's a measurement of the average motion of a lot of particles. It makes sense that the lowest possible temperature is when that motion stops. This was the original idea of absolute zero.
More recently, scientists have learned that small particles can never stop moving because of the rules of quantum mechanics. Absolute zero can still defined as the temperature where they're moving the least amount possible.
It was first proposed by Einstein, it has a value of 1/2 \hbar ω. It not a theoretical idea, it's a proven limit on temperatures of systems, free and bound.
Maybe you misunderstood what I mean by theoretical. Absolute zero is theoretical because no one has ever seen it, nor will they, so it's based on theory work, not on observation or experiment. But it's on solid foundation, as we know exactly what it means in terms of measurable quantities (energy).
Oh right, well... Let zero point energy equal any definition that makes sense in this case. It is still an experimental fact of a temperature we cannot reach rather than a postulation, it is an axiom.
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Mr Data - your use of terms is confusing me and I would hazard a guess others as well.
1. You say firmly that this is not a postulate - but it is an axiom. In my dictionary they are the same thing - they are the unproven basis of the logical progression from which the argument moves forward.
2. An experimental fact that we cannot do something?
3. Please spell out the variables/constants you are using - I know it is a pain but it really helps understanding
4. you say epsilon is a very small number - which I agree is how it is normally used in this area as a dimensionless increment. However in your equation it clearly must have the same units as energy through dimensional analysis. And what is omega etc? BTW we do have greek letters available (click preview to get full editor) and the nu is nice and distinct
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Don't hazard a guess for anyone else, unless they speak up. If anyone says to me that the zero-point energy is attainable, I would almost certainly disagree with the lack of experimental evidence. No matter how cold we set our instruments to, one will see that T=0 is very unrealistic. Can you proove this wrong? If you can, I will take back what I said, until then I hope you can appreciate that whatever is confusing you on this, will not naturally imply anyone else.
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Mr D - experiments failing to reach absolute zero do not show that it is unreachable - merely that we havent reached it yet - it is theory that determines that abs zero is unattainable.
If anyone says to me that the zero-point energy is attainable, I would almost certainly disagree with the lack of experimental evidence.
You are using zero-point energy and abs zero as interchangeable terms - they are not. zero-point energy is the prime candidate for the casimir effect, which can be demonstrated in a lab - so there is experimental evidence. Abs zero was and can still be seen as a classical limit - zpe is a non-classical quantum effect; whilst there are significant links they are not the same thing at all.
you never did explain any of your equations or why you felt they were relevant to the discussion.
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I agree that Mr Data's use of symbols is confusing, but it's hardly the point.
He claims that absolute zero is based on some complicated equation drawn up in 1913 but there is documentation to show that it was known about earlier than that. In addition, the equation it framed in terms of the thermodynamic temperature. You can't define that unless you already know about absolute zero.
In short, Mr Data is wrong.
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To sum it up:
1) In 1702, absolute zero was defined as the lower limit of a thermometer that worked by the expansion or contraction of a volume of air.
2) In 1848, Lord Kelvin came up with a definition from theory based on the motion of molecules (thermodynamics). Absolute zero would be the point where all motion stopped.
3) In 1913, Einstein and Otto Stern came up with the idea that particle motion can't stop entirely due to quantum mechanics. This changed the definition of absolute zero slightly to be the point at which the energy of motion of the particles is at a minimum.
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I agree that Mr Data's use of symbols is confusing, but it's hardly the point.
He claims that absolute zero is based on some complicated equation drawn up in 1913 but there is documentation to show that it was known about earlier than that. In addition, the equation it framed in terms of the thermodynamic temperature. You can't define that unless you already know about absolute zero.
In short, Mr Data is wrong.
That will be because I've never heard of the other sources.
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Then "Don't hazard a guess ".
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I was perfectly right in what I said though. Zero Point energy is not a theoretical idea. It's a scientific principle. You cannot reach zero momentum; that would directly violate the UP.
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You were "perfectly right" in that you said "It was proposed in 1913", but it was documented nearly half a century earlier and follows from work done in the 1780s.
http://en.wikipedia.org/wiki/Charles's_law
and also from even earlier work going back at least to the work in 1702 by Amontons.
I agree that you can't reach absolute zero.
Nernst pointed that out.
http://en.wikipedia.org/wiki/Third_law_of_thermodynamics
Interestingly, he did so just before 1913.
Zero point energies do exist and, for some systems they are a requirement of the UP.
However, while that's true for a vibrating molecule, it's not true for a lot of particles.
If they are stationary then the uncertainty of the momentum is zero, but, provided that you don't know where they are (ie the uncertainty of the position is infinite), that's not a violation. It applies to the much loved "particle in a box" but not to a free particle.
(if the vibrating molecule stopped vibrating the position of one atom WRT the others would be fixed, and so would its momentum. That's forbidden.)
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Stop, stop stop!
Who said zero-point energies where a fundamental principle? Anything which imposes zero momentum implies an exact spacial coordinate... This is ALWAYS forbidden... who you reading from, englighten me please.
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The concept and workable mechanism behind the experimental evidence behind the zero-point field should be no more complicated than excepting that spacetime, and every planck unit which occupies it, is constantly fuelled with a smallest unit of energy. This energy will at it's lowest energy refer to the kinetic energy of a vibrating energy 1/2 hbar \omega. You cannot have a unit of spacetime reach T=0 as much as you cannot accelerate it to c. Notice that the lowest speed possible will not equal v=0, as much as it's maximum speed will never reach c... everything is always in motion.
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"who you reading from, englighten me please."
My old University notes; probably Atkins or Richards. Anyway, whoever it was I think they had the advantage over you of not saying both
"Zero Point energy is not a theoretical idea. "
implying that it's real and
"This also means the zero point energy does not actually exist! "
saying that it's not.
Perhaps, when you have made up your mind,...
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Ask yourself this. How can the zero point even exist, if no one can ever reach that state? Zero point energy is a real unnattainable limit. It is not an idea, it is a measure of experimental fact.
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Ask yourself this. How can the zero point even exist, if no one can ever reach that state? Zero point energy is a real unnattainable limit. It is not an idea, it is a measure of experimental fact.
You still don't seem sure if it's experimentally real or purely hypothetical.
Incidentally, a good fraction of the nitrogen molecules I am breathing are in the bottom excited vibrational state. Their properties are dependent on the existence of zpe.
You don't have to get to absolute zero to achieve that.
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No, I'm quite sure of what I have said. You simply are not understanding what I telling you. Again, how can a real T=0 (as a temperature exsit) when T=0 cannot be reached? No matter how much cooling energy you pump into your apparatus, there is no way you can ever reach ZPE. There is always energy, always heat attributed to any vibrating energy.
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Try reading this.
As I said before, many or most of the nitrogen molecules I am breathing are in the vibrational ground state.
The only vibrational energy they have is zero point energy.
That's the real world, yet you seem to wan to insist it's not possible.
You seem not to have noticed that, at normal temperatures, most energy is translational.
That's why it's wrong to say "There is always energy, always heat attributed to any vibrating energy."
If it's zpe there's no heat associated with it.
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Lol... are you trying to joke this?
You do realize that the terminology zero point energy is misleading? Ground state energy is something far different than a system achieving zero point energy. It is not called a [zero point] for nothing you know. Zero, the non-existing of temperatures... energy, just as it says on the tin. Except T=0 is never accomplished, and what you have left over is a system with 1/2 hbar omega. You are not gaining energy from a zero point field, it is the energy you have left over when you reach this value of 1/2 hbar omega. It is not caused by a system reaching zero point energy (or by definition T=0) but is caused by the lack of it's ability or work to reach T=0.
Why can't you understand this? Indeed, why does anyone treat the zero point field as something a particle can reach? You don't freeze an electron down to zero temperature, then expect energy to be left over. You try and make the system reach zero point energy, but as I have shown countless and countless time before, this is impossible.
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If it's zpe there's no heat associated with it.
Which is exactly my point bored chemist. If there is no heat, there is no ZPE. But in all cases, there is an energy and momentum associated to every particle in the universe, so by logical deduction, ZPE is non-existant. You just proved my own case.
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From WIKI
" the energy of the ground state is known as the zero-point energy of the system."
From Mr Data
"Ground state energy is something far different than a system achieving zero point energy."
From Mr Data
"You try and make the system reach zero point energy, but as I have shown countless and countless time before, this is impossible."
In reality, most of the molecules in the air around you are in their vibrational ground states and have the ZPE which you need to account for if you want to explain their spectra.
"You don't freeze an electron down to zero temperature, then expect energy to be left over. "
Ignoring the fact that the first half is impossible, actually I do. Once you get cold (and room temperature will be quite cold enough for a lot of cases) there's not enough energy (on average) to get something out of the ground state. So it sits in the ground state, but as we both agree, it has to be moving in order to comply with the UP. The energy associated with that movement is the ZPE.
I'm sure anyone reading this will come rapidly to their own conclusion
For those who care,
The vibrational frequency of nitrogen is 2331 cm^-1
Equivalent to about 0.29eV
At room temp the mean energy is about 0.026 eV
Boltzmann's law gives n/n(o)= e^-(0.29/0.026)
So about 14 molecules in each million are in the first excited vibrational state.
The rest are in the ground state.
99.985 % are in the state Mr Data says you can't reach.
"You try and make the system reach zero point energy, but as I have shown countless and countless time before, this is impossible."
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You are implying zero point energy is real; this would mean you can freeze your system to absolute temperatures!!!!! This is impossible!
The ground state is simply the lowest energy state for any system, like a longitudinal photon is to mexican hat potential.
In reality, most of the molecules in the air around you are in their vibrational ground states and have the ZPE which you need to account for if you want to explain their spectra.
In what sense? Are you saying molecular objects which perhaps absorb zero point flucuations? This I would agree with. Fluctuations of the zero point energy field however, are not borne from systems which reach zero temperatures.
Ignoring the fact that the first half is impossible, actually I do.
Now you are confusing me!
Yes, the first half is impossible, and this is because no system, no molecular, no atomic, no subatomic system can be frozen to zero temperatures, so explain to me how your sentance makes more sense, than saying a particle does not reach zero temperatures because of the energy left over?
Yes... anyone reading this should come to their own conclusions. It makes absolutely no sense to speak of a zero point energy as an ''existing'' temperature. It is a limit, an unnatainable limit, because:
A) It will require an infinite amount of energy for a system to reach T=0
B) Every particle in the universe always has a momentum (and this is attributed directly to ZPE) - except it is an energy which will stop a system reaching T=0 - the system never actually reaches this mythical limit!!
So perhaps any confusions will be settled on this part:
Once you get cold (and room temperature will be quite cold enough for a lot of cases) there's not enough energy (on average) to get something out of the ground state. So it sits in the ground state, but as we both agree, it has to be moving in order to comply with the UP. The energy associated with that movement is the ZPE.
Right, except the energy associated to the ZPE is nothing but an intrinsic momentum inherent in aboslutely every system! It is just another fancy word, for yet another deceiving model of physics. ZPE does not exist, and can never be reached. Any energy in a system is not a contribution of ZPE in many cases - it is simply a part of the momentum of the system. If you could, however, freeze an object to asbolute zero temperatures first, then somehow revive that particle to some mometum through a contribution of some field, then yes... this would be an energy associated from the movement of a zero point field, keeping in mind a zero point field is exactly how I defined it earlier: It is the zero temperature associated to freezing a quantum system.
But dare I say anymore... such systems being frozen is impossible, because as you said, we seem to agree this would violate the Uncertainty Principle.
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You keep talking about fields.
Are you referring to this sort of thing?
"Vacuum energy is the zero-point energy of all the fields in space"
(from http://en.wikipedia.org/wiki/Zero-point_energy )
If you are talking about the zero point energy of a vacuum then it's clearly not the same as talking about the zero point energy of something concrete- like the nitrogen molecules which are (practically) all in the vibrational ground state.
A vacuum doesn't have a temperature so it's clearly got little or nothing to do with the topic.
Why did you bring it up?
Never mind.
No matter how cold you get a nitrogen molecule, it will vibrate at just the same frequency, and with just the same energy as the ones you are breathing.
That energy- the energy associated with the ground state isn't zero. The atoms have potential and/ or kinetic energy.
They are (as we agree) moving.
The vibrational ground state of a nitrogen molecule has has got energy. It has about 0.15 eV of energy
It will continue to do so no matter what you say in reply to this.
It will also remain the case that you said "Ground state energy is something far different than a system achieving zero point energy." in direct contradiction of the received wisdom.
You also said "No matter how much cooling energy you pump into your apparatus, there is no way you can ever reach ZPE. "
which is nonsense- you just breathed in billions of billions of counter-examples.
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A vacuum doesn't have a temperature so it's clearly got little or nothing to do with the topic.
A vacuum does have a temperature - temperature is measured by the energy which fills the space you measure. There is no such thing as an ''empty space'' in physics, every small part of spacetime is filled with energy. In fact, relativity determines that the vacuum is a physical sheet and that the seperation of energy from any part of spacetime is impossible. So yes, a vacuum does contain a temperature.
I have heard people state that the vacuum does not technically have a temperature because it implies energy, but anyone with a deep understanding of relativity will know that the vacuum is a physical dynamical sheet of bubbling quantum particles - spacetime is the appearance of matter-energy. The two cannot be seperated.
Indeed, the vacuum temperature is best known as the Microwave background temperature also, the left over remnant of the big bang http://arxiv.org/abs/astro-ph/0012222
No matter how cold you get a nitrogen molecule, it will vibrate at just the same frequency
Actually, you cannot make a molecule reach zero temperatures. This would mean the absence of movement, I thought we covered this.
That energy- the energy associated with the ground state isn't zero. The atoms have potential and/ or kinetic energy.
They are (as we agree) moving
Right. The system never reaches zero temperature as this would imply zero momentum. Hence why a zero point energy (zero implying zero temperatures) is just nonesense.
The vibrational ground state of a nitrogen molecule has has got energy. It has about 0.15 eV of energy
I won't deny this. In fact, whatever energy is there, is part of the dynamical system itself. It is the instinsic energy of the system, not something borne from absolute zero temperatures.
You also said "No matter how much cooling energy you pump into your apparatus, there is no way you can ever reach ZPE. "
which is nonsense- you just breathed in billions of billions of counter-examples.
This part is troubling you the most. What is it which makes my statement unclear when I explain this? Zero point energy is the zero point temperatures at which motion should cease to exist. But since energy cannot be frozen to absolute values, then the particle can never reach zero point energy. Zero point energy is just a refusal to be frozen! It doesn't reach T=0, it keeps on trucking because of the UP.
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Sorry for my poor use of language there.
I should have said that a vacuum doesn't have a temperature that we can set to absolute zero, so it has little or nothing to do with the topic.
"Actually, you cannot make a molecule reach zero temperatures. This would mean the absence of movement, I thought we covered this."
Strawman; since I never said you could.
I said "No matter how cold you get a nitrogen molecule, it will vibrate at just the same frequency" which is true.
"Right. The system never reaches zero temperature as this would imply zero momentum. Hence why a zero point energy (zero implying zero temperatures) is just nonesense. "
You keep missing the point.
Even if we could get it to zero it would continue to vibrate with ZPE.
Re, The vibrational ground state of a nitrogen molecule has has got energy. It has about 0.15 eV of energy
you said
"I won't deny this."
I think you already did.
"No matter how much cooling energy you pump into your apparatus, there is no way you can ever reach ZPE"
And, as another example,
"Zero-point energy is the energy that remains when all other energy is removed from a system. This behaviour is demonstrated by, for example, liquid helium. As the temperature is lowered to absolute zero, helium remains a liquid, rather than freezing to a solid, owing to the irremovable zero-point energy of its atomic motions. (Increasing the pressure to 25 atmospheres will cause helium to freeze.)" from
http://www.calphysics.org/zpe.html
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Strawman; since I never said you could.
I said "No matter how cold you get a nitrogen molecule, it will vibrate at just the same frequency" which is true.
When you said no matter how cold we make a nitrogen molecule, I thought you were implying our limit of T=0. Of course, this is impossible.
Even if we could get it to zero it would continue to vibrate with ZPE.
But we can't which is my point in its entirity. So how do we destinguish vibrational energy from zero point energy? To know the latter, surely a system first needs to reach T=0?
"Zero-point energy is the energy that remains when all other energy is removed from a system.
What?
If you remove the energy system in question, then what are you cooling down to T=0? By remove, what is meant here? You remove a peice of energy (or simply move it from one place to another) vacuum fluctuations take its place; that isn't zero point energy as we are taught by the reasoning of a zero temperature... Though that seems to be a popular answer. By effect, that is simply just another kinetic system which has taken the place of our previous system. No need for superfluous names like zero point energy, or temperatures.
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You're link says this:
Quantum mechanics predicts the existence of what are usually called ''zero-point'' energies for the strong, the weak and the electromagnetic interactions, where ''zero-point'' refers to the energy of the system at temperature T=0
I thought me and you covered this has to be fundamentally incorrect?
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Due to quantum fluctuations there can be no 'zero point' for anything. And that one is also Heisenberg's uncertainty principle as far as I know. 'Space' from a QM point of view is in a constant 'shivering', never at rest as the Casimir effect show us.
What we call 'zero' is a place where I expect everything to be at rest, and?
That doesn't seem to exist. Which is weird.
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As it actually, if lifted up to a principle, states.
There is no universal 'ground state'.
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Although, locally we have one, 'c'.
And if 'chopped up', we come to the Plank scale in where we can't chop it up any more, as far as I understand :) as that is where the distance travelled by light in one Planck time becomes one Planck length. And we can't make it any better than that.
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Yor_on, the term zero-point energy is a technical term referring to the energy of the ground state of a quantum mechanical system. As you say, in most cases it can't be at zero energy. It's called zero-point because it's as close as you can get.
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""Zero-point energy is the energy that remains when all other energy is removed from a system.
What?
If you remove the energy system in question, then what are you cooling down to T=0? By remove, what is meant here?"
You didn't spot the word "other" there did you?
It's the energy left behind because you can't remove it from the system even at absolute zero (it doesn't matter that you can't get there. The ZPE would still be present if you did).
Can I ask you why you think that you need to compress liquid helium before it will solidify?
The textbooks all say it's down to ZPE; but you don't believe in that.
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In which cases can it be in a 'zero ground state' JP?
How is that defined.
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If you refer to T=0 then it's not possible.
Well, as far as I know?
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Yor_on, you're looking at it backwards. Temperature is not a fundamental property. It's something that emerges when you look at the average kinetic energy of many particles. It doesn't make sense to talk about fundamental properties of a single particle in terms of average values of many.
Zero-point energy is a fundamental property of a single particle or quantum system. Zero-point energy of a quantum system is the lower limit on the energy it can have. This may or may not be easily achievable, but it exists, and you can achieve it in certain cases. The classic example is a simple harmonic oscillator. Classically, it behaves like a spring: if you give it energy it oscillates, but if it has zero energy it remains stationary. Quantum mechanically it's always oscillating a little, no matter how much energy you take out.
If you build your way back up to temperature, not reaching absolute zero tells you that if you have many such particles, they can't all be at their zero-point energy at once. One of them might be, but all of them can't be.
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Yor_on, the term zero-point energy is a technical term referring to the energy of the ground state of a quantum mechanical system. As you say, in most cases it can't be at zero energy. It's called zero-point because it's as close as you can get.
Exactly. It is the closest we can get to zero temperatures, hence zero point energy is a misnomer - a great misunderstanding is applied to this, as we can see, Bored Chemist seems confident that I have somehow a misunderstanding.
I understand exactly what zero point temperatures imply, and I know fine well that reaching T=0 is impossible, so zero point energy as it is defined is never actually reached. It is a mythology.
As I said, zero point energy is just a fancy name for a refusal to reach T=0, so zero point temperatures do not really exist.
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In which cases can it be in a 'zero ground state' JP?
How is that defined.
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If you refer to T=0 then it's not possible.
Well, as far as I know?
In which cases can it be in a 'zero ground state' JP?
How is that defined.
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If you refer to T=0 then it's not possible.
Well, as far as I know?
Ground state is the lowest energy state - note also that this implies by the UP that T does not equal 0. Never does. Hence zero point temperatures does not exist.
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""Zero-point energy is the energy that remains when all other energy is removed from a system.
What?
If you remove the energy system in question, then what are you cooling down to T=0? By remove, what is meant here?"
You didn't spot the word "other" there did you?
It's the energy left behind because you can't remove it from the system even at absolute zero (it doesn't matter that you can't get there. The ZPE would still be present if you did).
Can I ask you why you think that you need to compress liquid helium before it will solidify?
The textbooks all say it's down to ZPE; but you don't believe in that.
I never made any statements on compressing liquid helium. Did I?
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Bored, you said ZPE would still be presentt if I did remove all energy from a peice of spacetime, but I think this is a speculation at best, since there is no experimental evidence to varify that. As I said, you cannot make a bit of spacetime suit the idea of an ''empty space'' - all of it is filled with quantum fluctuations.
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I'm not looking at it any specific way JP, more than saying that there is no ground state that I know of. But you state that there is, if I got you right? Maybe you are referring to defining a system as being in arbitrarily defined 'ground state'? Or maybe it is a theoretical definition of some other kind. What I did reading you was to go out on the net trying to find such a state in our universe? But it wasn't there :) But just as you can define space as a macroscopic ground state I presume that you can do so with a lot of other 'states' too.
That is, if you don't know that 'state' to exist, and can show me how to see it?
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A harmonic oscillator can not be at absolute zero, as far as I know, other than theoretically.
We will never reach that state. To me 'c', and absolute zero, is a symmetry of kind, defining boundaries of our universe. It also has to do with 'scales' of other kinds, as the Planck scale, which to me also becomes boundaries defining where our limit of knowing goes. We know they should 'exist', but just as we won't pass, or even reach, 'c', not by normal motion of invariant mass anyway, so we won't get to absolute zero. They remind me very much of constants' all of them. Well, I suppose they are constants too :)
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I'm not looking at it any specific way JP, more than saying that there is no ground state that I know of. But you state that there is, if I got you right? Maybe you are referring to defining a system as being in arbitrarily defined 'ground state'? Or maybe it is a theoretical definition of some other kind. What I did reading you was to go out on the net trying to find such a state in our universe? But it wasn't there :) But just as you can define space as a macroscopic ground state I presume that you can do so with a lot of other 'states' too.
That is, if you don't know that 'state' to exist, and can show me how to see it?
I think you've hit it on the button. No states can be made to reach T=0, so saying it should exist even when energy is not present seems decieving. I think I make a good arguement to say zero point temperatures don't actually exist. Also you are right about ground state, that can even apply to a macroscopic system, it could even apply to the universe as a whole! In fact, the entire universe according to current belief, is very much in a ground state.
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If we assume that gravity is connected to energy, then if you empty 'space' of its energy there should be no gravity, without its metric I would expect 'space' to cease to exist, as far as we are concerned, and is able to measure. Also the Heisenberg Uncertainty Principle forbids it
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heh FTL.
Just empty 'space' of its energy, then refill as needed, behind your 'propagation' :)
And remember, forgetting this you might just 'run out of space'
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Yor_on, each cell of space should have a ZPE associated with it. This is what gives rise to the casimir force, in theory. The ZPE allowed between two nearby conducting plates is less than outside, so there's a pressure. As for gravity, ZPE is a quantum effect and there is no quantum theory of gravity, so who knows!
Mr. Data, you're confusing ZPE of a single state with T=0, which is only meaningful for many particles. Certainly you can't reach T=0, which would mean putting all particles in a many-particle system in their ZPE states at the same time. But some of those particles will be at ZPE without violating any physical laws. It's kind of like rolling millions of dice. You'll never get them all to come up 1's, but some of them certainly will in any given roll...
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You will certainly get all ones rolling your millions of dice, all ones is no less probable then any other number but you will have to be patient it will take a lot of rolls!
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You will certainly get all ones rolling your millions of dice, all ones is no less probable then any other number but you will have to be patient it will take a lot of rolls!
Sure you can, if you're immortal.
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Yor_on, each cell of space should have a ZPE associated with it. This is what gives rise to the casimir force, in theory. The ZPE allowed between two nearby conducting plates is less than outside, so there's a pressure. As for gravity, ZPE is a quantum effect and there is no quantum theory of gravity, so who knows!
Mr. Data, you're confusing ZPE of a single state with T=0, which is only meaningful for many particles. Certainly you can't reach T=0, which would mean putting all particles in a many-particle system in their ZPE states at the same time. But some of those particles will be at ZPE without violating any physical laws. It's kind of like rolling millions of dice. You'll never get them all to come up 1's, but some of them certainly will in any given roll...
Well, fundamentally-speaking, this is all that counts. You can measure the mass of the universe in a single proton!
What do you mean, some of those particles will have ZPE without violating any laws? You do understand yourself that you surely that ZPE by definition is a system which is at T=0. These are by another name ''absolute temperatures''. Nothing can reach this. If it was T=0 then it must violate the Uncertainty Principle. NOT even a collection of particles, with a small sum of them will reach T=0. None of them by definition have actually reached zero temperatures.
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Bored, you said ZPE would still be presentt if I did remove all energy from a peice of spacetime, but I think this is a speculation at best, since there is no experimental evidence to varify that. As I said, you cannot make a bit of spacetime suit the idea of an ''empty space'' - all of it is filled with quantum fluctuations.
Another strawman.
I never said anything about removing energy from spacetime. I asked about removing it from a nitrogen molecule.
The fact that you have to keep saying things that I didn't is very telling.
You seem steadfast in your decision not to address the evidence so, for the third time of asking,
why doesn't helium freeze unless you apply about 25 bar pressure?
All the textbooks say it's down to ZPE. What's your explanation?
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Indeed I remain steadfast - now you ask me this in the appearance of a question.
You seem steadfast in your decision not to address the evidence so, for the third time of asking,
why doesn't helium freeze unless you apply about 25 bar pressure?
All the textbooks say it's down to ZPE. What's your explanation?
If zero point energy, is by definition:
where ''zero-point'' refers to the energy of the system at temperature T=0, or the lowest quantized energy level of a quantum mechanical system.
(From your link by calphysics) - then my explanation is more logical; that being systems have energy close to T=0 but can never be T=0 (and T=0 being where zero point truely exists), then in this case the energy we are really dealing with is the intrinsic energy of the particle. Note then energy remains as a stubborn refusal to reach zero point because this would directly violate the UP - so temperature arises in systems due to obiding by this principle, also meaning that zero point temperatures have never really been reached.
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Well JP I've seen two definitions there. Either the 'Casimir force' belongs to matter itself, or to space. As for zero point energy, sure it exists, at least I expect it to do so. As for it needs absolute zero? That I don't think myself, if it did the Casimir effect should be a effect of the matter, not space, as at that 'energy scale' there can be no 'energy' 'jiggling' at all. And after all, explaining it in terms of frequency's/wavelengths presume something 'jiggling' as far as I can see? That's another way to look at the idea of absolute zero.
Or how would you define it, as something 'jiggling'? Then we have a ground state of energy where it won't be 'still', but fluctuating. You might argue that HUP takes care of that though, maybe? But then I doubt it to be a 'constant', and it should be, as I see it.
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Simply expressed if you want zero point energy to 'fluctuate' or 'jiggle' at the same time you define it as being at absolute zero then I think you're wrong.
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Turn it around, if we define absolute zero as where nothing 'jiggles' then if we also define vacuum fluctuations to it I now will state that there must be a state beyond what we call 'absolute zero' in where what you see as the 'fluctuations' disappear, theoretically that is. Or we have to define it as there is no ground state of 'non moving' in which case the opposite definition of absolute zero loses all coherence.
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A third way to define it, that I like, is to place quantum fluctuations outside of Planck scale. Doing so we still have to explain how it can influence 'SpaceTime', but that becomes no stranger than how to define the 'expansion' we believe us to see. And placing it 'outside' all discussions about 'absolute zero' lose its relevance as we use temperature as definitions inside Planck scales, SpaceTime that is. To use it for something we won't be able to measure except third hand, so to speak, may make some sense theoretically as we want our ideas to stretch as far as possible. But if you look at Einstein's definition of gravity that pipe dream already has gone broke once, and will probably do it again.
I don't expect SpaceTime to adapt to our ideas, to me it's the other way around.
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One might want to look at in terms of it not being the vacuum 'fluctuating' possibly? Instead, maybe, as a property of 'times arrow' fluctuating at very small scales, and that has to be a very weird idea, hasn't it :) But they all seem to come together at that plane to me.
So 'chopping it up', you end up with Planck scale, and that is the smallest measurable (not really measurable, but theoretically 'understandable') 'bits' we have, as I see it? So when you're at that scale everything will be 'frozen' to me, and from there you might argue that this is 'absolute zero', but then we also are on the threshold of reality, and as I said 'frozen in state'.
Beyond that there might be thygers :)
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Turn it around, if we define absolute zero as where nothing 'jiggles' then if we also define vacuum fluctuations to it I now will state that there must be a state beyond what we call 'absolute zero' in where what you see as the 'fluctuations' disappear, theoretically that is. Or we have to define it as there is no ground state of 'non moving' in which case the opposite definition of absolute zero loses all coherence.
Nope - the realisation of Planck et al was that there is no point at which all fluctuations disappear - the lowest energy/ground state of any quantum oscillator is the zero-point energy (even at absolute zero the simplest system retains an energy of 1/2hν). You are setting in opposition classical definitions and quantum mechanical ideas - and you will nearly always get a clash; you cannot slide seamlessly between the macro-scales of the macro-aggregation (that makes up temperature) to the micro-scales of quantum oscillations without a great deal of care.
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Let us not stray from the proposition being made. Zero point energy, the point at which motion should cease, does not. It is evidence enough to state that the definition of zero point energy is misunderstood.
It seems to be a strongly held belief that zero temperatures are reached, but there still remains a motion. This is an oxymoron.
Motion gives rise to temperature, so if there is no ceasing of motion, then how can your system really be called a zero point? In logical conclusion, zero point motion or temperatures (call it what you will) are never achieved.
If anyone can prove this wrong, I welcome them.
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Mr D - you really need to understand that absolute zero and zero-point energy are not the same thing.
The fact that zero-point energy is the energy remaining in a system at the limit T=0 does not logically imply, nor practically lead to the claim that zpe can only be observed at absolute zero. ZPE is clearly demonstrated in the experimental world through many effects. Abs Zero is the theoretical limit where entropy is minimized and all oscillators within a system will be at zpe - this does not preclude a situation where some oscillators are at ground state and others are not.
It seems to be a strongly held belief that zero temperatures are reached, but there still remains a motion. This is an oxymoron.
I don't recall any post claiming that the limit T=0 can be reached. But whilst we cannot practically reach it - we state with certainty that at T=0 there is still a ground-state oscillation ie the zero point energy.
Motion gives rise to temperature, so if there is no ceasing of motion, then how can your system really be called a zero point?
It is called zero-point energy because i) it would still be there at T=0 ii) you cannot go any lower.
If anyone can prove this wrong, I welcome them.
Liquid helium will not solidify (unless pressurized) even as limit of T=0 is reached
http://en.wikipedia.org/wiki/Liquid_helium
Casimir plates feel a force
http://en.wikipedia.org/wiki/Casimir_effect
The lamb shift of energies of orbitals in hydrogen atom
http://en.wikipedia.org/wiki/Lamb_shift
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Mr D - you really need to understand that absolute zero and zero-point energy are not the same thing.
I use zero temperatures, or absolute temperatures interchangeably.
http://en.wikipedia.org/wiki/Thermodynamic_temperature
The fact that zero-point energy is the energy remaining in a system at the limit T=0 does not logically imply, nor practically lead to the claim that zpe can only be observed at absolute zero.
Definition of the ZPE -
''where ''zero-point'' refers to the energy of the system at temperature T=0, or the lowest quantized energy level of a quantum mechanical system.''
So it is stating that energy remains at T=0. You can use temperature interchangeably with energy or motion. As far as the definition is concerned, zero point energy is when temperatures are zero, and motion should no longer exist. It is entirely logical to assume that the zero point is not a factual temperature, since motion is never erradicated. So long as you have motion, your system cannot be said to be absolutely frozen, hence there is a temperature which cannot be quelled.
I don't recall any post claiming that the limit T=0 can be reached. But whilst we cannot practically reach it - we state with certainty that at T=0 there is still a ground-state oscillation ie the zero point energy.
By what reasoning? If T=0 is never reached, how can speculations be given it is a true ground state? It seems outside the realm of testable physics.
It seems strange one can state with certainty that at T=0 there is still a ground state, if T=0 is never acheived.... think about it.
It is called zero-point energy because i) it would still be there at T=0 ii) you cannot go any lower.
Who says it would still be there, what evidence do you have that reaching T=0 reveals this prediction? Since we cannot reach the state T=0, then it seems redundant to make the speculation energy would still exist. Energy only exists because it cannot reach this state, not the other way around.
Liquid helium will not solidify (unless pressurized) even as limit of T=0 is reached
http://en.wikipedia.org/wiki/Liquid_helium
Casimir plates feel a force
http://en.wikipedia.org/wiki/Casimir_effect
The lamb shift of energies of orbitals in hydrogen atom
http://en.wikipedia.org/wiki/Lamb_shift
I don't see this as a proof. The articles will naturally not take into account the arguements I have given.
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Noting also:
''Absolute zero is the theoretical temperature'' - so absolute zero temperature is absolutely fine when speaking about the ZPE -
http://en.wikipedia.org/wiki/Absolute_zero
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The article is also the closest thing I would agree with, it states:
''A system at absolute zero still possesses quantum mechanical zero-point energy, the energy of its ground state. The kinetic energy of the ground state cannot be removed. However, in the classical interpretation it is zero and the thermal energy of matter vanishes.''
As I said, the energy left over is not really anything special in the sense it is a ZPE - it is merely a kinetic energy of our system which refuses to vanish. T=0 will not imply a freezing of the system, hence T=0 is never acheived.
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This discussion is quite fascinating but I'm not a scientist so i'm not sure that i understand the implications of absolute zero and kinetic energy of molecules.
We are told that the universe has an average temperature of 2.7 k.But now i'm confused.Does this average only apply to matter and not space itself?
If a space probe measures the temperature in space somewhere between our local group of galaxies and the virgo group then what kinetic energy are we taking about? Photons have no mass so they cannot have any kinetic energy?The Cosmic Background radiation cannot have any kinetic energy either.Does this mean that it's not valid to speak of a temperature and that the space probe is returning only the temperature of it's probe?
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It has the homogenous appearance that the Background temperature is even to about 10,000th of an error. Quite a room for error.
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Anyway, mass does not imply kinetic energy. A mass does have a kinetic energy, but kinetic energy is simply the energy of a moving particle. So a photon is simply a packet of kinetic energy.
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So a photon has no mass but has kinetic energy?
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It might be more accurate to say that a photon is kinetic energy purely.
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But yes... no mass.
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Ok mr Data,i'll accept that.
So you are saying the average temperature of the universe includes empty space itself?
So what would the temperature read in the location i was speaking of?
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Careful my friend, there is no such thing as an empty space in physics. All of spacetime is occupied by quantum flucuations. Many of these flucuations only last a fraction of a second, but some are longer lived.
Anyway... temperature is valued in the cold of space where temperatures can vary to 10,000th degrees of an error. Since matter in the universe only occupies 1% of all spacetime, then it makes little justice to measure temperature in our daily acttivities. It makes more sense to measure temperatures in the deep of space where it is more or less homogenous.
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It seems as though you are saying that temperature is really kinetic energy,and that there is no place where there is no kinetic energy?Ok i'll accept that, since as you say radiation has kinetic energy.
What do you mean by 10000th of a degree of error?
What do you mean by quantum fluctuations in space,is this a theory only or has it been measured?
I agree that space cannot be empty as all space has radiation in it.I just meant space without molecules.
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It seems as though you are saying that temperature is really kinetic energy,and that there is no place where there is no kinetic energy?Ok i'll accept that, since as you say radiation has kinetic energy.
What do you mean by 10000th of a degree of error?
What do you mean by quantum fluctuations in space,is this a theory only or has it been measured?
I agree that space cannot be empty as all space has radiation in it.I just meant space without molecules.
By 10,000th of an error, this simply gives us a degree of freedom to allow certain parts of space to be slightly warmer than let us say the X-directionality. It is a smudge-factor.
Now, temperature can be thought of as a kinetic energy, or even the sum of the kinetic energy of the constituents of a macroscopic object. For instance, by theory it is said that a metal becomes hotter when the particles it is made of increase in kinetic energy. The faster they move, the hotter the object becomes.
As for quantum fluctuations, you may want to read this: http://arxiv.org/abs/gr-qc/0401082 - it is our best understanding of the vacuum in context of quantum mechanics.
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This is all detracting from the OP,but anyway...
It seems as though the link you gave is saying that the fluctuations can add energy to particles (cosmic rays),but not detract from them?Seems strange to me because if a particle moves through a zone that has a lower energy then it should suck energy away from the particle.Do the fluctuations not average zero?Seems like perpetual motion?
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Well JP I've seen two definitions there. Either the 'Casimir force' belongs to matter itself, or to space. As for zero point energy, sure it exists, at least I expect it to do so. As for it needs absolute zero?
Yor_on, what is the meaning of defining absolute zero for a single particle? Zero-point energy is meaningful and achievable for a single particle, temperature is not.
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Well JP I've seen two definitions there. Either the 'Casimir force' belongs to matter itself, or to space. As for zero point energy, sure it exists, at least I expect it to do so. As for it needs absolute zero?
Yor_on, what is the meaning of defining absolute zero for a single particle? Zero-point energy is meaningful and achievable for a single particle, temperature is not.
Well, zero point energy for a particle would be a particle which ceases to exist strictly by the classical definition. Of course, quantum mechanics has something else to say. Even if T=0, a particle will still move. Indeed, large collections of particles will move. Speaking of one particle, is just as rewarding if not simpler than speaking or concentrating on a system with a large amount of particles.
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This is all detracting from the OP,but anyway...
It seems as though the link you gave is saying that the fluctuations can add energy to particles (cosmic rays),but not detract from them?Seems strange to me because if a particle moves through a zone that has a lower energy then it should suck energy away from the particle.Do the fluctuations not average zero?Seems like perpetual motion?
Take out some qoutations which highlight your incongruities, and we can analyze them.
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Of course, quantum mechanics has something else to say. Even if T=0, a particle will still move. Indeed, large collections of particles will move. Speaking of one particle, is just as rewarding if not simpler than speaking or concentrating on a system with a large amount of particles.
Nope, you can't talk meaningfully about temperature of a single particle. Temperature is defined for an ensemble of particles and it's properties (such as never reaching T=0) rely on the statistics of many particles. That's where you keep going wrong when you say you can't reach T=0 for a single particle. Such a phrase is meaningless.
Here's a paper on reaching ZPE for a single molecule:
http://prl.aps.org/pdf/PRL/v62/i4/p403_1
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I don't know if I agree with you. Temperature is part of the equation which describes the ZPE for a single quantum oscillator:
ε = hv/(ehv/kT-1) + hv/2
If temperature cannot be defined for a single oscillator, how does it enter the equation?
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That's not the equation that described ZPE for a single quantum oscillator. That's a thermodynamic equation for a collection of them. The single quantum harmonic oscillator energy is:
E=(N+1/2)hbar*omega, where N=0,1,2,3,4,...
When N=0, you're at the ZPE, which has energy hbar*omega/2.
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Not according to this:
http://en.wikipedia.org/wiki/Zero-point_energy
''Then in 1913, using this formula as a basis, Albert Einstein and Otto Stern published a paper of great significance in which they suggested for the first time the existence of a residual energy that all oscillators have at absolute zero.''
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Or maybe I picked it up wrong...
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''the most famous such example of zero-point energy is E={\hbar\omega / 2} associated with the ground state of the quantum harmonic oscillator.''
From the same link. E={\hbar\omega / 2} is just the part of the remaining kinetic energy in the equation given.
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Mr D - please learn to read your own sources before contradicting others. We know you picked it up wrong. Why are you persisting to try and "answer" these questions when it is quite clear that you haven't even read up to a wikipedia level?
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Mr D - please learn to read your own sources before contradicting others. We know you picked it up wrong. Why are you persisting to try and "answer" these questions when it is quite clear that you haven't even read up to a wikipedia level?
The speculations from the equations match those of JP's... after the equation given (which I presented) it simply states that
''According to this expression, an atomic system at absolute zero retains an energy of ½hν.''
Now, I don't see a great difference here. If you set N = hv/(ehv/kT -1) = 0 then you still end up with the same result.
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And I think it a bit sanctimonious of you to suddenly challenge my ability to read something. It's a common frequent thing here to see that kind of behaviour - we are all fallible, prone to mistakes. But I don't see you coming down on other people. Perhaps I left a mark with you?
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This discussion is quite fascinating but I'm not a scientist so i'm not sure that i understand the implications of absolute zero and kinetic energy of molecules.
We are told that the universe has an average temperature of 2.7 k.But now i'm confused.Does this average only apply to matter and not space itself?
If a space probe measures the temperature in space somewhere between our local group of galaxies and the virgo group then what kinetic energy are we taking about? Photons have no mass so they cannot have any kinetic energy?The Cosmic Background radiation cannot have any kinetic energy either.Does this mean that it's not valid to speak of a temperature and that the space probe is returning only the temperature of it's probe?
Johann - the whole of the universe is full of thermal radiation (ie radiation given off by hot objects) that is a relic of three hundred years or so after the big bang. This radiation, which when emitted by hot hydrogen ions was ultraviolet, has been stretched by the expanding universal so that it has been red-shifted to the microwave band. All bodies above absolute zero will give off black body radiation - the spectrum they emit is related to the temperature of the the black body; the wavelength of the CMBR is that of a body at 2.75K.
What that means is that any object colder that 2.75K will on average absorb radiation and warm up (ignore black holes they are weird) and any object warmer than 2.75K will on average emit radiation and cool down; ie the two systems will tend towards equilibrium. As the entire universe is homogeneously full of this radiation it makes sense to talk of a temperature.
A probe always measures the temperature of the probe - but we hope that by clever engineering we can ensure that the probe will be in equilibrium with the surroundings. Other ways to measure temperature rely on the spectrum of radiation the object is emitting and use the black body equation to find the temperature.
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Zero point energy is the zero point temperatures at which motion should cease to exist.
Hence why a zero point energy (zero implying zero temperatures) is just nonesense.
You are implying zero point energy is real; this would mean you can freeze your system to absolute temperatures!!!!! This is impossible!
But in all cases, there is an energy and momentum associated to every particle in the universe, so by logical deduction, ZPE is non-existant.
The reason I have asked you to be more careful is the comments you have made so far in this thread - you will note they are in direct contradiction to what you are now seem to be agreeing with.
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Zero point energy is the zero point temperatures at which motion should cease to exist.
Hence why a zero point energy (zero implying zero temperatures) is just nonesense.
You are implying zero point energy is real; this would mean you can freeze your system to absolute temperatures!!!!! This is impossible!
But in all cases, there is an energy and momentum associated to every particle in the universe, so by logical deduction, ZPE is non-existant.
The reason I have asked you to be more careful is the comments you have made so far in this thread - you will note they are in direct contradiction to what you are now seem to be agreeing with.
Elaborate. And note I will be away for the next hour or so, so make it good for my return.
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Now, I don't see a great difference here. If you set N = hv/(ehv/kT -1) = 0 then you still end up with the same result.
The derivation of the ZPE of a single quantum harmonic oscillator is here: http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator
There is a huge difference because: 1) N is an integer for the harmonic oscillator, while N in your above equation isn't, and 2) these are completely different physical situations. Yours is, from what I recall, an expression for the energy density of a black body radiator. A quantum harmonic oscillator is completely different.
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Mr D - you really need to understand that absolute zero and zero-point energy are not the same thing.
I use zero temperatures, or absolute temperatures interchangeably.
http://en.wikipedia.org/wiki/Thermodynamic_temperature
The fact that zero-point energy is the energy remaining in a system at the limit T=0 does not logically imply, nor practically lead to the claim that zpe can only be observed at absolute zero.
Definition of the ZPE -
''where ''zero-point'' refers to the energy of the system at temperature T=0, or the lowest quantized energy level of a quantum mechanical system.''
So it is stating that energy remains at T=0. You can use temperature interchangeably with energy or motion. As far as the definition is concerned, zero point energy is when temperatures are zero, and motion should no longer exist. It is entirely logical to assume that the zero point is not a factual temperature, since motion is never erradicated. So long as you have motion, your system cannot be said to be absolutely frozen, hence there is a temperature which cannot be quelled.
I don't recall any post claiming that the limit T=0 can be reached. But whilst we cannot practically reach it - we state with certainty that at T=0 there is still a ground-state oscillation ie the zero point energy.
By what reasoning? If T=0 is never reached, how can speculations be given it is a true ground state? It seems outside the realm of testable physics.
It seems strange one can state with certainty that at T=0 there is still a ground state, if T=0 is never acheived.... think about it.
It is called zero-point energy because i) it would still be there at T=0 ii) you cannot go any lower.
Who says it would still be there, what evidence do you have that reaching T=0 reveals this prediction? Since we cannot reach the state T=0, then it seems redundant to make the speculation energy would still exist. Energy only exists because it cannot reach this state, not the other way around.
Note you never answered any of this. I will also remind you of my conjecture:
Let us not stray from the proposition being made. Zero point energy, the point at which motion should cease, does not. It is evidence enough to state that the definition of zero point energy is misunderstood.
It seems to be a strongly held belief that zero temperatures are reached, but there still remains a motion. This is an oxymoron.
Motion gives rise to temperature, so if there is no ceasing of motion, then how can your system really be called a zero point? In logical conclusion, zero point motion or temperatures (call it what you will) are never achieved.
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Now, I don't see a great difference here. If you set N = hv/(ehv/kT -1) = 0 then you still end up with the same result.
The derivation of the ZPE of a single quantum harmonic oscillator is here: http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator
There is a huge difference because: 1) N is an integer for the harmonic oscillator, while N in your above equation isn't, and 2) these are completely different physical situations. Yours is, from what I recall, an expression for the energy density of a black body radiator. A quantum harmonic oscillator is completely different.
Thank you for the link. I will take back what I said about the equation. I admit it is based on a flaw, an incorrect application.
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Zero point energy is the zero point temperatures at which motion should cease to exist.
Hence why a zero point energy (zero implying zero temperatures) is just nonesense.
You are implying zero point energy is real; this would mean you can freeze your system to absolute temperatures!!!!! This is impossible!
But in all cases, there is an energy and momentum associated to every particle in the universe, so by logical deduction, ZPE is non-existant.
The reason I have asked you to be more careful is the comments you have made so far in this thread - you will note they are in direct contradiction to what you are now seem to be agreeing with.
Elaborate. And note I will be away for the next hour or so, so make it good for my return.
Oh, you'll be away for more than an hour, I think, as this response makes it clear you don't have any desire to be civil on this forum: something you've been warned about in the past.
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You really do keep missing the point.
You say "It seems to be a strongly held belief that zero temperatures are reached, but there still remains a motion. This is an oxymoron."
Nope, it's the truth.
You can't remove the vibrational energy from a nitrogen molecule. It's not that you can't get it cold enough, it's that there is no lower energy state for it to be in.
The ground state is the lowest you can get. There's still energy associated with it.
Cooling it further doesn't make sense ( all you could do would be to reduce the fraction of molecules in any excited state.)
Once you get a nitrogen molecule into the vibrational ground state (as most of them are).
1 you cannot take any more vibrational energy out of it because, to do that you would have to move it to a lower energy state and, since it's in the ground state, there isn't one.
2 It will therefore stay in that ground state no matter how far you cool it (including, in principle, to zero)
Yet, because the ground state has a vibrational energy of about 0.15 eV, it still has quite a lot of energy. (Very roughly, the same energy as something glowing red hot)
That energy is the zero point energy of the system.
It's prefectly real.
It's the sort of thing that stops helium freezing unless you compress it.
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BC one thing that this discussion shows how many people do not understand that we live in a dynamic universe and it is this residual vibrational energy that actually holds the atoms in molecules together. Also this dynamic energy gets greater as you look further inside the atom the electrons in atoms have much greater energies corresponding to optical to x ray frequencies and the quarks inside the neucleons have so much energy that there is more energy in their motion than their rest masses.
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To an extent SoulSurfer - but the fact that the bound system has a lower energy than its constituent parts, ie that energy is needed to separate the stable system (the binding energy), does not logically entail the fact that the lowest energy is not zero. In other words it is not obvious from the fact that energy is required to break either molecular or nuclear bonding that these systems must have a ground state that is not zero. Strong bonds are the lowest energy state - not an energy rich state. Whether you can make the connexion between vibrational energy and the quantum chromodynamic binding energy of quarks and gluons is beyond me - but it seems to be explaining non-classical matters in a far too classical a manner
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My personal opinion is that this thread largely shows that Mr data doesn't know what he is talking about to an extent that is verging on trolling.
I cite this excerpt as evidence for that opinion
"Let us not stray from the proposition being made. Zero point energy, the point at which motion should cease, does not. It is evidence enough to state that the definition of zero point energy is misunderstood.
It seems to be a strongly held belief that zero temperatures are reached, but there still remains a motion. This is an oxymoron.
Motion gives rise to temperature, so if there is no ceasing of motion, then how can your system really be called a zero point? In logical conclusion, zero point motion or temperatures (call it what you will) are never achieved."
Other evidence is plentiful, as cited by Imatfaal earlier
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I don't think Mr. Data will be joining us again, as he couldn't engage in debate without being rude to other forum members.
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Look, all of this is just irritating to me :)
I gave two simple definitions that clash with each other. Trying to mumble that there is such a thing as absolute zero, except in theory, also will mean that there is no 'motion'. If so there can be no fluctuations, as long as you find fluctuations inside our arrow of time you also have something that is in motion. the simple solution to this problem as I see it is to define it as such as it is outside Planck time. And that is a simple solution. Not doing so will get you into a place between a rock and a hard place.
As I see it, temperature is all about measuring motion, if that motion would exist inside Planck time I will expect a temperature.
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Maybe we need to define it as collisions?
Kinetic energy released in radiation?
But if we do so, what would then then our virtual 'radiation' be?
A 'not radiation' :)
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I gave two simple definitions that clash with each other.
struggling to find the two simple definitions - can you requote them - they got lost in the melee.
Trying to mumble that there is such a thing as absolute zero, except in theory, also will mean that there is no 'motion'. If so there can be no fluctuations, as long as you find fluctuations inside our arrow of time you also have something that is in motion.
Your problem is that the definition of absolute zero is the theoretical temperature when entropy reaches zero - in the 19th century it was thought this would mean absolute stillness and lack of movement, it has not meant that for almost 100 years.
the simple solution to this problem as I see it is to define it as such as it is outside Planck time. And that is a simple solution. Not doing so will get you into a place between a rock and a hard place.
no; that solution is neither easy nor a solution. Absolute zero and the zero point energy are connected - but you are continuing Mr D fallacy if you insist they are the same. Abs Zero is a temperature theorised over a system that is at its lowest entropy. ZPE is a characteristic of individual entities and redefines the ground state as a state of motion. The fact that Abs Zero is theoretical does NOT imply that ZPE is theoretical - we have good evidence of ZPE occurring in the lab.
Maybe we need to define it as collisions?
Kinetic energy released in radiation?
But if we do so, what would then then our virtual 'radiation' be?
A 'not radiation' :)
There isn't really a problem with the definitions - nor is there a contradiction. It isn't collisions; ZPE cannot be radiated away; and we don't need virtual radiation.
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Trying to mumble that there is such a thing as absolute zero, except in theory, also will mean that there is no 'motion'. If so there can be no fluctuations, as long as you find fluctuations inside our arrow of time you also have something that is in motion.
Your problem is that the definition of absolute zero is the theoretical temperature when entropy reaches zero - in the 19th century it was thought this would mean absolute stillness and lack of movement, it has not meant that for almost 100 years.
the simple solution to this problem as I see it is to define it as such as it is outside Planck time. And that is a simple solution. Not doing so will get you into a place between a rock and a hard place.
no; that solution is neither easy nor a solution. Absolute zero and the zero point energy are connected - but you are continuing Mr D fallacy if you insist they are the same. Abs Zero is a temperature theorised over a system that is at its lowest entropy. ZPE is a characteristic of individual entities and redefines the ground state as a state of motion. The fact that Abs Zero is theoretical does NOT imply that ZPE is theoretical - we have good evidence of ZPE occurring in the lab.
Yor_on, this is the point I was trying to make. Details like Planck scale effects are interesting, but they're just minor tweaks to the physics, and they don't really help with understanding the differences between ZPE and absolute zero, and why ZPE is achievable and absolute zero is not.
I still think the dice analogy is the simplest way of getting at it. You can imagine the dice represent a very low-energy particle. If you roll a die, the 1 represents it being in the ZPE state, while the 2-6 represent higher energy states that it might end up in due to quantum fluctuations.
If all you care about is the state of one particle, you roll one die. There's a 1/6 chance in this case of it coming up a 1. If you look at 100 particles, odds are that one of them will be in the ZPE state.
Temperature is only meaningful for a lot of particles. I'm not sure on the technical definition of "a lot," but you're usually talking about a 1 with 20 or more zeros after it. It's an average of the kinetic energy of the particles, so it can be represented as the average of all the numbers rolled on your dice. Absolute zero in our dice case only happens when all the dice come up 1 at the same time. If even a single die comes up 2, the temperature is slightly above absolute zero. Imagine the odds against rolling all 1s on 100000000000000000000 dice! In reality, you also have heat leaking into the system, so you can imagine someone constantly reaching in and turning one of your dice to a higher number, which obviously makes it impossible to stay at all 1's, even if you happen to somehow roll them.
Now, imagine that you've rolled those 100000000000000000000 dice. Some of them are bound to be 1's, so even in a system whose temperature is above absolute zero, you have some particles in their ZPE states.
Of course, there's always the argument that dice aren't quantum particles, which is completely true. You could apply quantum field theory to this problem as well, and include virtual particles, Planck-scales and many other fun things, but I don't see how it's any more enlightening than the dice example about why ZPE is achievable and T=0 K isn't.
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It's not like zpe is rare.
The (admittedly classical) KE of the electrons round an atom or molecule in the ground state are zpe.
The vibrational energy of most of the molecules you are breathing is zpe.
The obscure cases like liquid helium show it too.
All this stuff about quantum fields just makes it more complicated than it needs to be.
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The vibrational energy of most of the molecules you are breathing is zpe.
BoredChemist,
I'm lost here.Totally.
Do you mean by this that zpe ("zero point energy") is a minimum state of energy of a molecule and that this can be achieved at ambient temperatures and not near zero kelvin?
If a nitrogen molecule is at ambient temperature then at what state are the electrons in?I thought they would be in a higher state than if the molecule was frozen?
Or are you saying that the electrons are in zpe because the molecules are in motion so that the kinetic energy is not appearing in the orbits of the electrons or nuclei vibrating?
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To get nitrogen into the first vibrational excited state you have to add quite a lot of energy. As I said, it is the equivalent of getting it very hot.
To get it into the first excited electronic state you have to get it very hot- say 10,000 degrees.
Most nitrogen molecules at normal temps only have rotational and translational energy.
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Yes, as long as we define it as two different states I have no real problem with ZPE. If we define it as the same as 'absolute zero' it got to be wrong.
Absolute zero is to my eyes where there can be no 'jiggling'. And that is to me the same as no longer being 'here'. Whatever we see is defined by its ability of interacting. If something interacts you will have to assume that there is something that allows it to do so. In my eyes that will be the 'vibrational energy' intrinsic to whatever you observe. As you say JP any temperature must be the result of something interacting, and if what (absurdity ad infinitum) 'interacts' would be at 'absolute zero' I would be wrong in my assumptions.
But I don't think I am.
As for Planck size, it's what defines what we can make sense of as I see it. That doesn't say that you can't have a mylliard bylliard different 'states' existing outside what we can observe, it just states that ''There there might be thygers' as there is no way we ever are going to observe them directly. And that's also why I prefer to place 'virtual particles' outside Planck size myself.
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What everyone seem to miss in this discussion is time. Whatever you observe is a direct result of you being inside a arrow of time, only delivering you in one direction, to your death. As long as nobody can prove me wrong in that assumption, and you can't :), then everything you define, whatever temporal direction, or no direction at all, is a direct result of observations made under that arrow. Only delivering you, and your experiment, one way. It constantly surprises me reading of diffuse definitions of systems being 2-dimensional and 'time reversible' as if this was a defined truth. Symmetry is a truth, but time reversibility have still to be proven, and that goes directly to the truth that there can be no observations ever being able to be defined if we didn't have our arrow. People seem to miss that this is what makes all definitions able to stand the test of time :) If they're not constant under our arrow then they are no repeatable.
So times arrow has a lot to do with anything defined as 'vibrating', as I see it.
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As you say JP any temperature must be the result of something interacting, and if what (absurdity ad infinitum) 'interacts' would be at 'absolute zero' I would be wrong in my assumptions.
I don't think I said that, and if I put it that way, I made a mistake. Although one reason you can never measure absolute zero is the uncertainty principle--that if you measure it, you inject some energy.
What everyone seem to miss in this discussion is time. Whatever you observe is a direct result of you being inside a arrow of time, only delivering you in one direction, to your death. As long as nobody can prove me wrong in that assumption, and you can't :), then everything you define, whatever temporal direction, or no direction at all, is a direct result of observations made under that arrow. Only delivering you, and your experiment, one way. It constantly surprises me reading of diffuse definitions of systems being 2-dimensional and 'time reversible' as if this was a defined truth. Symmetry is a truth, but time reversibility have still to be proven, and that goes directly to the truth that there can be no observations ever being able to be defined if we didn't have our arrow. People seem to miss that this is what makes all definitions able to stand the test of time :) If they're not constant under our arrow then they are no repeatable.
Well, according to all experimental evidence, most quantum mechanics is time-reversible. There's a possible exception for certain interactions involving the production of antimatter, which might explain why it's uncommon, but those interactions are rare and not really relevant to the features of temperature that we're discussing. As you know, you can't prove a that any theory (time-reversibility, in this case) is absolutely correct in science, but you can show a lot of evidence for it, which is what's been done.
Also, time's arrow seems to arise from thermodynamics, which is the same place we get a definition of temperature. If you needed time's arrow to define temperature, you'd be in trouble, since you'd have a circular definition.
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Yes, as long as we define it as two different states I have no real problem with ZPE. If we define it as the same as 'absolute zero' it got to be wrong.
But Yoron - no one does! (apart from dear old late lamented MrD)
Absolute zero is to my eyes where there can be no 'jiggling'. And that is to me the same as no longer being 'here'. Whatever we see is defined by its ability of interacting. If something interacts you will have to assume that there is something that allows it to do so. In my eyes that will be the 'vibrational energy' intrinsic to whatever you observe. As you say JP any temperature must be the result of something interacting, and if what (absurdity ad infinitum) 'interacts' would be at 'absolute zero' I would be wrong in my assumptions.
Yoron - but since the early 20th century we haven't defined it as "no jiggling" we have defined it as the lowest entropy state
As for Planck size, it's what defines what we can make sense of as I see it. That doesn't say that you can't have a mylliard bylliard different 'states' existing outside what we can observe, it just states that ''There there might be thygers' as there is no way we ever are going to observe them directly. And that's also why I prefer to place 'virtual particles' outside Planck size myself.
planck SIZE? - you can view things of planck mass with a decent magnifying glass, the planck length and time are were things get small and high energy. Not sure what you mean.
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To get nitrogen into the first vibrational excited state you have to add quite a lot of energy. As I said, it is the equivalent of getting it very hot.
To get it into the first excited electronic state you have to get it very hot- say 10,000 degrees.
Most nitrogen molecules at normal temps only have rotational and translational energy.
Thanks very much.That is actually quite amazing!
What kind of speeds and rotations do you get?
What happens with helium and hydrogen?
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Planck scale is the smallest definable quantities we have. Beyond that you find a lot of absurdities and infinities, making no sense to us Imatfaal. "Planck units may sometimes be semi-humorously referred to by physicists as "God's units". They eliminate anthropocentric arbitrariness from the system of units: some physicists argue that communication with extraterrestrial intelligence would have to use such a system of units to make common reference to scale. Unlike the meter and second, which exist as fundamental units in the SI system for historical reasons (in human history), the Planck length and Planck time are conceptually linked at a fundamental physical level." Planck units. (http://en.wikipedia.org/wiki/Planck_units) I'm surprised that you want to argue this?
As for arguing that time is reversible. No, it is not as far as I know, but in QM you can find processes that you can play forth and back being equivalent as I understands it. And you can also use it mathematically, but any process you observe JP, you observe under our macroscopic arrow, so as long as you don't want to argue that you observe 'time ticking' as some atmospheric strata being able to wander in different directions depending on 'size of observation' I would expect time to have only one direction.
As for time being a thermodynamic phenomena, thats a theory, or just a hypothesis as far as I know. My death though, is not.
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A simple way to define what time is under Einstein's definitions is to ask yourself if you think you will get a longer life measure by travelling close to light for an extended period of time.
Do you expect that to be true?
Why?
It's not, what you have is one measured life span, intrinsically the same no matter what you plan to do in form of travel etc. That the universe might die under that travel does not give you a longer life span. It's strange how many that miss that, assuming that because a relation might change they now have become 'immortal'. Time will 'tick' for you as long as you live, giving you the exact same treatment as if you had stayed at home. You might want to define it such as 'times arrow' do need some 'stuff' to exist, like a SpaceTime. Also that it have to be interactions following a linear chain of logic to make sense.
You living inside a thought up 'quantum computer' though, then 'time' as such has no meaning as everything already is 'there'. But if you're the operator of said quantum computer lifting out answers from it, then you live under a arrow.
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If this how you think of it being thermo dynamical JP, you do have a point. But to me it's about interactions arranged in a logically explainable causality chain. And to be absolutely tru they do need to be experimentally defined and proven. Our macroscopic arrow is that. Any definitions discussing time reversibility under QM must be defined by observations under that arrow, and so I can see no possibility of proving that concept, other than as a mathematical equivalence of outcomes depending on how you play the movie. In reality, under those observations you really make though, 'times arrow' pointed only one way for anything you did and observed. if it didn't all definitions would become questionable and we would have to lift in new ways of defining 'clocks' as I see it.
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As for time being a thermodynamic phenomena, thats a theory, or just a hypothesis as far as I know.
But "it's just a theory" isn't a valid argument against a scientific theory. Everything in science is "just a theory" on some level.
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Planck scale is the smallest definable quantities we have. Beyond that you find a lot of absurdities and infinities, making no sense to us Imatfaal. "Planck units may sometimes be semi-humorously referred to by physicists as "God's units". They eliminate anthropocentric arbitrariness from the system of units: some physicists argue that communication with extraterrestrial intelligence would have to use such a system of units to make common reference to scale. Unlike the meter and second, which exist as fundamental units in the SI system for historical reasons (in human history), the Planck length and Planck time are conceptually linked at a fundamental physical level." Planck units. (http://en.wikipedia.org/wiki/Planck_units) I'm surprised that you want to argue this?
If you had said beyond the planck scale- it would have made more sense, you said size so I was asking what you meant. There are easily measurable objects that are below the planck mass - the planck scale is so highly energetic 10^27 eV because the planck mass is so big. It is just not necessary to probe at the planck scale of energies to investigate ZPE. To investigate at the planck scale requires such energy that quantum field theory breaks down - and as ZPE is an integral part of that you are not gonna have much joy.
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I don't know what you mean Imatfaal? You were the one questioning my definitions. Maybe you interpreted it differently than me? If so I hope you see what I mean now. And yes JP, I agree, everything is ultimately questionable, except some few things. My death is not, and so I will assume a arrow to exist, having a same 'ground state' in everything we can observe. That one has to be true.
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As for me defining it as 'jiggling' :)
Something being in 'motion' relative you.
Entropy, does that have this definition, think about it :)
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Yoron - you said we had to go beyond the planck size to probe ZPE . The planck size is not a recognized term - it could mean either mass or length . Thus it makes no sense because the planck length is unbelievably small and the planck mass is actually quite a normal size (you can see a planck mass object with a decent magnifying glass). Your second message moved onto the planck scale - now that is well defined - it is an energy scale at which photon have a mass equivalence energy of the planck mass, this is absolutely enormous. Neither of these bear on the ZPE question.
On the jiggling - classical thermodynamical entropy certainly has that in the definition. however the modern statistical mechanics definitions talks of the sum of probabilities over all possible microstates and involves neither temperature nor energy.
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Well Imfatfaal. My definitions were not to your taste then :)
As for me using 'size', scale is about 'size' as I see it.
As for statistical definitions, I agree that those are very useful, but what I refer to when speaking of 'jiggling' is a single object. And I actually knew that already, so I'm not sure why you are mixing that with this?
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"Absolute zero is to my eyes where there can be no 'jiggling'. "
Perhaps, but to other people's eyes it's not that at all.
It's where everything is in the ground state.
The ground states are not stationary because, if they were, they would breach the uncertainty principle (in most cases).
However the ground states are perfectly accessible.
You keep breathing them.
Johann,
The speeds are roughly the speed of sound (which is why sound travels roughly that fast)
There's more about it here
http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution
The rotation rates are roughly speaking in the microwave region.
http://en.wikipedia.org/wiki/Rotational_spectroscopy
For what it's worth, the vibrational energy levels are in the infra red.
http://en.wikipedia.org/wiki/Infrared_spectroscopy
But if you want to talk about them it's probably best to find another thread.
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Yep, that's another way of defining it that makes sense. But I will stand with that to me 'absolute zero' is where there can be nothing happening, as observed by us. And also that this state is unreachable by us, much by the same reasons you give BC. And I define it as over 'Planck scale' being what belongs under our arrow. Outside that scale I don't think we have the right definitions yet, I mean, how could we? If it's not observable?
This universe is mighty strange.
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Just as a bypass, sometimes I think of this universe as being only one thing, energy. And conservation of energy defines it as nothing gets really 'lost' in here, it just 'moves' into another 'position/state' whatever. Which means that all we ever do here is to shuffle energy :) from one 'position/state' to another. And that's also a weird thought, isn't it?
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Yep, that's another way of defining it that makes sense. But I will stand with that to me 'absolute zero' is where there can be nothing happening, as observed by us.
BC's definition isn't "another way of defining it," it's the actual definition.
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"But I will stand with that to me 'absolute zero' is where there can be nothing happening,"
FFS! Why?
Why do you persist with a definition that makes no sense- for example, it fails to explain the freezing of helium.
"as observed by us."
I presume that's the "Royal We" because nobody else here is claiming to have seen absolute zero.
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BC humor is not needed for this:)
As for the 'we' it's the way I write it, take it or leave it.
And absolute zero will be a state of no motion to me, whether you like it or not.
That simple.
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We can formulate it two ways. Assuming that motion exist then I will define Absolute zero as where that motion cease. That is what sometimes seem to be called a 'classical approach'. Then we have HUP Heisenberg's Uncertainty Principle where we find that if applied to the definition of absolute zero there still will exist an uncertainty, making it possible to define it as the 'vibrational energy' of whatever kind, still must have an existence. But that's, to me that is, also a measure of something 'fluctuating' under Planck scale. And to prove your thesis here you will have to probe that 'state' of absolute zero, interacting with it, and so transferring 'new energy' to it. Which doesn't mean that I expect this definition to be wrong, just that to me it's also a function of time, as I wrote earlier, above. And time and its arrow is one of the most fundamental things we have in this cosmos, doesn't really matter if you're observing QM systems or macroscopic. You're still doing inside this arrow doing so, and all conclusions you draw is a function of what you see under that arrow. The laws of thermodynamics state that absolute zero can't be reached as I understands it?
Anyway, when I define it as no motion I'm doing it in from a classical approach. When it comes to QM oscillators at 'absolute zero' I assume the same as you BC, that there still will be a possibility of 'energy' according to HUP, but both assumptions fails in that there is no way we can probe this situation, as far as I know it's an unattainable proposition to ever reach 'absolute zero'. And that's also why I'm as free as you in defining it my way, it's after all a state that doesn't 'exist' to us, experimentally.
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And yet I can show you the effect of zero point energy at temperatures above absolute zero which are quite accessible to experimentation.
Removing the last of the vibrational energy from a nitrogen molecule should be easy (classically), yet it is, experimentally, impossible
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I'm talking about 'absolute zero' here, you're talking about 'zero point energy'. Are you defining it as they are the same BC?
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Let's put it on a understandable spectrum.
Assume that I ask you to measure the 'temperature' of vacuum fluctuations, could you do that? Not their secondary effects, but the actual 'fluctuations'? Not as I know. Why? Because they're out of our range of measuring. You are still free to interpret this as they could be inside Planck scale, although too 'small' to be measured by us, or as I do, assume that they actually is outside Planck scale, and therefore forever unmeasurable as I see it.
'Absolute zero' is to me a definition made from temperatures measured inside our SpaceTime. If you assume that there is a temperature scale, ending in 'zero' K, or whatever other type of measure you use, then my interpretation is that this stage can't be reached classically. As you say, from a classical point of view it should be reachable, but it's not, as proven in those experiments that tries to reach those states.
From a QM point of view there is always a uncertainty in the measurements and, loosely speaking here, the better you define one variable the more uncertain the rest becomes. So from that point of view you might assume that there is no such thing as a 'absolute zero'. And as thermodynamics needs 'temperature' to wander from hot to cold in a mixed system, you meet a paradox in that the last remains of 'heat' in that thought up system will need a colder than 'absolute zero' to wander to, making 'absolute zero' as a definition wrong, as it now would exist another 'colder' stage beyond that 'zero', if that would be possible.
Temperature is to me a classical definition, defined inside a arrow. Zero point energy (vacuum fluctuations) is something else, just as 'virtual particles'. The only thing I'm reasonably sure of it that we won't tap any energy from it. If that was possible I'm sure Nature already would have taken advantage of it. And there is no phenomena I know of that gains 'energy' from a classical 'nothing'. That is if we not are going to discuss how to see & define gravity :)
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"Let's put it on a understandable spectrum.
Assume that I ask you to measure the 'temperature' of vacuum fluctuations,"
Make up your mind.
Do you really think that vacuum fluctuations are more understandable than, for example, the vibrations of a nitrogen molecule?
It has already been pointed out that such minutiae don't actually help.
You seem to hold this odd idea that, at absolute zero, everything stops moving.
Do you realise that nobody else seems to think that way?
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I said classically, and you come on as increasingly rude BC?
Is that because you know that your way must be the only way?
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I have asked why you persist in believing that absolute zero is defined by the absence of motion.
You have not answered that.
I also asked if you think that vacuum fluctuations are more readily understood than the vibrations of a nitrogen molecule.
Again, you have not seen fit to answer.
I asked about the freezing behaviour of helium.
Once again, I got not reply.
I have made it clear all along that the "way" I am describing is not "My way", but the orthodox way.
It falls to you to back your extraordinary claim with extraordinary evidence.
Instead you say I'm rude.
Perhaps you would care to explain why you think everyone else is wrong?
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You are rude alright.
As for the rest of, you may think that you've asked those questions, but I didn't see it.
And comparing the theoretical behavior of 'vacuum fluctuations' to nitrogen molecules? As for me defining it as 'no motion'. It's my choice, not yours, and if you had read what I wrote you might have seen how I looked at it? there are other definitions too, but classically I find it possible to define it as I do, as far as I'm concerned.
As for your behavior though.
Getting to be a 'thought police' are we?
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Yor_on, BC might not be terribly diplomatic, but he has a good point. Coming up with a new definition of temperature isn't inventing a new physical theory. Temperature is a tool for approximating values of things, and redefining it is breaking it's ability to make useful approximations.
Temperature is not a fundamental property of matter. It's an average value (of kinetic energy) that's useful because when you're dealing with billions upon billions of particles, you can't hope to solve the equations of motion of each particle to describe how the system changes in time. Instead, you write a theory in terms of average values, which is much easier. This is essentially the entire point of temperature: it's the average kinetic energy you'd get if you solved the equations of motion for all the particles in your system, and therefore the definition of temperature and it's properties are derived from the equations of motion for those particles.
Dealing with sub-Planck length temperature effects is pointless, since there are no valid sub-Planck length equations of motion (yet). As the laws of motion are extended to to sub-Planck lengths, temperature will follow. But temperature can't go there first, since it's defined from the laws of motion.
The same goes for the arrow of time: fundamental laws of motion don't care about the arrow of time*, so temperature can't depend on them. If you want to include the arrow of time in the definition of temperature, you first have to show that the fundamental laws of motion depend on it.
Absolute zero is also not a special, fundamental property of matter. It's a name we have for the case where all the particles being averaged over are in their lowest possible energy states. If you're averaging over classical mechanics, this means nothing is moving at all. If you're averaging over quantum mechanics, there's the possibility that things are still moving, since the lowest possible energy for quantum particles is sometimes not actually zero-energy.
Zero point energy, again, isn't anything special, nor it it related at all to the definition of temperature. It's just the name for the lowest energy state of a quantum particle, which often has non-zero energy.
Again, to reiterate: temperature is a tool that's designed to simplify solving the equations of motion. Temperature's definition will change as the laws of motion change, not the other way around. If you change the definition of temperature without changing the laws of motion, then temperature becomes useless: it can't simplify your calculations anymore, and it is no longer related to the laws of motion or physics going on.
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* With the possible exception of CPT violation...
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"Definition of Absolute Zero
Absolute zero is the temperature at which all classical motion stops.
Although temperature has no maximum value, absolute zero, at 0 Kelvin (K) or -273.15 degrees Celsius (°C), is the lowest temperature possible. At this temperature, no energy can be transferred out to another body. A common misconception is that all motion stops at 0 K, but quantum mechanics states that some molecular motion must always exist, as having no motion whatsoever would violate the Heisenberg uncertainty principle. Even at 0 K the atoms in molecules continue to oscillate (atomic bonds stretch and contract), giving them a minimum non-zero amount of energy, called the zero-point energy. The coldest temperature ever achieved in a laboratory was 100 pK, or 0.0000000001 K."
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And even if BC had been right it doesn't make being rude any better.
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And as I said, there are several ways too see it. I look at it as where 'classically' all motion should cease, quantum mechanically as where Heisenberg's Uncertainty Principle rules.
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Also, we will never reach absolute zero. And that is because of HUP, classically we might assume it a reachable state. But it isn't, so from that point of view I have no problems with it. But I still expect there to exist a state of no motion, even though then defined as some constituent of time.
Because to me it's all about time :)
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Every experiment we do, we do under the arrow. Every definition we have we get from there. Does that mean that the arrow is a must? That there can be no state where the arrow disappear. We can't reach that state where our macroscopic arrow 'breaks down', but we assume that this might be possible at very small scales. Still, as long as you have a motion you must have a duration, you can't presume a motion without it. But if assuming no duration, then that also should be a state where noting 'moves'.
All as I see it. And that might be seen as my very own definition, but, it wasn't what we discussed with 'Absolute Zero', although it has a relevance to my thinking.
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As for the rest of, you may think that you've asked those questions, but I didn't see it.
Getting to be a 'thought police' are we?
There is none so blind as him who will not see.
and I'm not the thought police; reality does that. If your ideas are wrong, reality makes it clear by, for example, not letting helium freeze at absolute zero.
I may be rude, but I'm in good company; it's not polite to simply ignore questions people put to you.
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Every experiment we do, we do under the arrow. Every definition we have we get from there. Does that mean that the arrow is a must? That there can be no state where the arrow disappear. We can't reach that state where our macroscopic arrow 'breaks down', but we assume that this might be possible at very small scales. Still, as long as you have a motion you must have a duration, you can't presume a motion without it. But if assuming no duration, then that also should be a state where noting 'moves'.
All as I see it. And that might be seen as my very own definition, but, it wasn't what we discussed with 'Absolute Zero', although it has a relevance to my thinking.
Well, you know, yor_on, we can't live in a state where we experience quantum effects first hand, but we know they exist. We don't experience relativistic effects by flying in a spaceship at nearly the speed of light. But by setting up careful experiments, we can find that these effects exist. In the same way, we can check if the arrow of time is important for the laws of motion of particles, and it isn't! Time is important, obviously, but there's no fundamental reason why time goes in one direction.
Since temperature is based on these laws of motion, it doesn't depend on the arrow of time, either. It can't, unless you invent new laws of motion which need the arrow.
Anyway, from what you're describing now, it seems you agree with the mainstream definitions of temperature, ZPE and absolute zero.
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That is the Quantum realm you discuss JP, as defined from macroscopically. Assume a stone rolling down a hill, there you have a 'process'. Now tell me if it's enough calling that process for the sole reason to the 'rolling downhill' or if we need something more to define it by. When people use definitions that's 'rolled up in themselves' more or less, thinking they describe the sole reason for there existing a arrow, then I think they're wrong.
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It's as with everything else we see. We have definitions that works 'perfectly' inside SpaceTime. But we also seem to have something that's more or less 'unmeasurable'. And that you can look at as either existing 'inside' SpaceTime in some manner, although unmeasurable, or define it as being outside the borders that defines it (SpaceTime) to us, and by that I also mean what's measurable.
We use what we can measure to define what we can't. And that makes for some remarkable ideas.
But 'time' is duration. Without 'duration' you can't define it as a 'motion'. Statistically you may discuss it as a 'probable motion' but that's not a motion. That's a probability of motion, and it will be the arrow that defines if it was.
And ahem yes :) I'm discussing QM there, not relativistic effects from macroscopic viewpoints. But I agree that they still have a relevance for 'time' those definitions we use macroscopically. The question of what 'motion' really is for example, as in 'uniform motion'.
But we do assume that 'motion' exist. We also define from it distance and 'clocks'. The clocks use a linear causality chain that makes it possible for us to define a beginning, middle, and possible end, to what we observe. We also see that processes is reversible in some circumstances. From that we get an idea of 'time' being reversible. But macroscopically it never was, as any repeatable experiment will show you. Because if it was there would be no guarantee of their repeatability. So we ground our experiment on the assumption that repeatability is the key to what makes the cosmos 'tick', and so also a arrow.
Maybe 'time' is 'rolled up' in some manner, but it's not 'rolled up' in here. Here it seems a function of the room, and 'frames of reference', having one direction macroscopically.
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Yor_on, you keep talking about your opinion of the definitions. Your opinion happens to contradict experimental fact, which shows that microscopic interactions don't have a preferred arrow of time. It doesn't matter that we as humans happen to always experience an arrow of time. Part of modern science is learning how to do experiments that go beyond our everyday scales and viewpoints of the universe. If we could only do experiments that are limited by our particular viewpoint of the universe, we'd not have relativity or quantum mechanics, since we generally don't directly experience either.
Your opinion isn't going to be valid science as long as it contradicts experimental evidence.
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Well, I don't see where it 'contradicts'?
What I'm saying is that all definitions you use is grounded on assumptions, one of them is the arrow and repeatability.
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I also pointed out that this is mine own view on it, didn't I?
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Tell me JP, how can there be statistics without a defined arrow of time?
Isn't that a necessary presumption for it?
Or could you expect it possible to beget statistics without a arrow too?
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"I also pointed out that this is mine own view on it, didn't I?"
Yes, and I repeatedly asked why you keep believing it.
Just so you don't miss it this time,
Why do you keep defining it in a way that doesn't make sense and which is at odds with reality?
Are you just trolling?
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Yor_on, this is the same thing we say to everyone posting new theories: you're welcome to your opinion, but it isn't science.
I suggest you check out the laws of classical mechanics and quantum mechanics and convince yourself that there is no arrow of time in those cases:
By contrast, all physical processes occurring at the microscopic level, such as mechanics, do not pick out an arrow of time. Going forward in time, an atom might move to the left, whereas going backward in time the same atom might move to the right; the behavior of the atom is not qualitatively different in either case.
[ http://en.wikipedia.org/wiki/Entropy_(arrow_of_time) ]
You can argue all you want, but until you overturn the laws of classical and quantum mechanics, you're wrong about the arrow of time being fundamental.
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You can argue all you want, but until you overturn the laws of classical and quantum mechanics
It seems as though the laws of classical mechanics are already overturned.
Are there any that have survived quantum mechanics?
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You can argue all you want, but until you overturn the laws of classical and quantum mechanics
It seems as though the laws of classical mechanics are already overturned.
Are there any that have survived quantum mechanics?
As I've said above, temperature is a tool used to predict average values of kinetic energy in some pre-existing model. So temperature doesn't tell you what you need in an underlying model. The problem at hand places requirements on whether you use classical or quantum mechanics to model the situation.
There are times when classical mechanics works very well, so you don't need the more accurate quantum theory. In these cases, a classical mechanical temperature definition is fine. If you need to worry about quantum effects, you can base a temperature definition on quantum mechanics.
There's always the tendency to say "but that theory isn't 100% accurate in all cases," which is true of every theory, since no theory describes everything in the universe perfectly accurately. The trick in physics and engineering is to know which model is accurate to the case at hand.
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Well, it depends from where you look I would say. The best theory still is Einsteins relativity, in where time is a function of the room. As for the quality of BC:s comments?
Seems the standard is sinking here.
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Seems the standard is sinking here.
Too right. There was a time when someone who asked a question could reasonable expect an answer.
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Okdoky!
Well, it looks like this horse has been well and truly flogged, so I think it's best to lock the thread for a bit.