# Times less than Planck Time?

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#### Æthelwulf

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##### Times less than Planck Time?
« on: 27/04/2012 02:51:46 »
''Hawking's singularity theorem is for the whole universe, and works backwards-in-time: in Hawking's original formulation, it guaranteed that the Big Bang has infinite density. Hawking later revised his position in A Brief History of Time (1988) where he stated "There was in fact no singularity at the beginning of the universe" (p50). This revision followed from quantum mechanics, in which general relativity must break down at times less than the Planck time. Hence general relativity cannot be used to show a singularity.''

excerpt from the holy book, wiki.

Sure, quantum mechanics doesn't deal with singularities... but I wonder what motivated the above. Saying General Relativity breaks down at times less than the Planck Time, surely is essentially meaningless anyway, since we cannot measure anything which exists below the Planck Time or if we could it would essentially seem not to change at all. Does anyone have an incline to how Hawking is managing that arguement?

#### Æthelwulf

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##### Re: Times less than Planck Time?
« Reply #1 on: 27/04/2012 14:44:53 »
Why has this been moved to new theories?

This isn't a new theory. I am talking about Hawking's own theories, which are usually well-established within maintsream.

#### JP

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##### Re: Times less than Planck Time?
« Reply #2 on: 27/04/2012 16:00:38 »
. . . we cannot measure anything which exists below the Planck Time or if we could it would essentially seem not to change at all. . .

What's the basis for that statement?  I see this get repeated all the time, but no one has ever offered a good reason for it.  To the best of my knowledge, the Planck time is where our theories break down, since we know neither quantum mechanics nor general relativity alone will be sufficient there and we don't yet have a testable theory that ties them together.

My understanding of anti-singularity arguments is that what GR predicts as a singularity is probably going to be a much richer phenomenon when we figure out a way to describe what actually happens on those scales.

#### Æthelwulf

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##### Re: Times less than Planck Time?
« Reply #3 on: 27/04/2012 16:30:28 »
. . . we cannot measure anything which exists below the Planck Time or if we could it would essentially seem not to change at all. . .

What's the basis for that statement?  I see this get repeated all the time, but no one has ever offered a good reason for it.  To the best of my knowledge, the Planck time is where our theories break down, since we know neither quantum mechanics nor general relativity alone will be sufficient there and we don't yet have a testable theory that ties them together.

My understanding of anti-singularity arguments is that what GR predicts as a singularity is probably going to be a much richer phenomenon when we figure out a way to describe what actually happens on those scales.

You know, we only see objects when light bounces off objects yes?

Well, the planck time is the amount of time for a photon to cross a distance of 1 planck length. In light of this, we can be sure that we cannot make any measurements on times smaller than this because light would not be able to travel the distance quick enough.

#### JP

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##### Re: Times less than Planck Time?
« Reply #4 on: 27/04/2012 17:06:46 »
You're assuming the Planck length is some fundamental unit there.  Otherwise, I could insert any other unit of distance and make the same argument.  I could take a light year and say that it takes 1 year for light to travel the distance of a light year.  Therefore I can't measure anything less than a year long.

So that returns us to the same question: what makes the Planck scale the length beyond which we can't measure anything?

#### Æthelwulf

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##### Re: Times less than Planck Time?
« Reply #5 on: 27/04/2012 17:30:34 »
You're assuming the Planck length is some fundamental unit there.  Otherwise, I could insert any other unit of distance and make the same argument.  I could take a light year and say that it takes 1 year for light to travel the distance of a light year.  Therefore I can't measure anything less than a year long.

So that returns us to the same question: what makes the Planck scale the length beyond which we can't measure anything?

It's very technical. Even for my poor brain.

At planck lengths, geometry as it is understood by General Relativity breaks down. So a photon travelling a light year is absolutely fine but we can't infer it to be fundamental. The planck lengths are however and they are derived using dimensional analysis. Another way to state this, is that the Schwartzchild radius of a black hole is equal to the Compton wavelength at the planck scale thus a photon trying to probe this would gain no information at all.

For a quick comparisson, the Classical Electron Radius is in fact $$\frac{1}{137}$$ times larger than the Compton Wavelength. The Compton Wavelength is (h/Mc) where h is Plancks Constant and it has a value of 6.62606957(29) X 10^(−34) j.s. The Compton Wavelength itself has a value for the electron as 2.4263102175 +(-) 33 X 10^(−12) m value varies with different particles) and is a measure itself of the wavelength of a particle being equal to a photon (a particle of light energy) whose energy is the same as the rest-mass energy of the particle.

Basically, all particles have a wavelength. Photon's can never be at rest but the energy of a photon can be low enough to have it's wavelength match any particle who is at rest. It's often seen in the eye's of many scientists as the ''size'' of a particle. Actually, a more accurate representation of the size of an object would be the Reduced Compton Wavelength. This is just when you divide the Compton Wavelength by $$2\pi$$ and it gives a smaller representation for the mass of a system.

Furthermore, if a photon could measure a planckian object, it could actually create a new class of particle called a Planck Particle - it would distort that space so badly that the photon would be gobbled up and no measurement could be performed. This is due to the Uncertainty Principle if my memory serves

http://en.wikipedia.org/wiki/Planck_particle
« Last Edit: 27/04/2012 17:42:34 by Æthelwulf »

#### Æthelwulf

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##### Re: Times less than Planck Time?
« Reply #6 on: 27/04/2012 17:40:06 »
Here is a derivation I quickly looked over and which might help.

#### Æthelwulf

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##### Re: Times less than Planck Time?
« Reply #7 on: 27/04/2012 17:45:37 »
You're assuming the Planck length is some fundamental unit there.  Otherwise, I could insert any other unit of distance and make the same argument.  I could take a light year and say that it takes 1 year for light to travel the distance of a light year.  Therefore I can't measure anything less than a year long.

So that returns us to the same question: what makes the Planck scale the length beyond which we can't measure anything?

It's very technical. Even for my poor brain.

At planck lengths, geometry as it is understood by General Relativity breaks down. So a photon travelling a light year is absolutely fine but we can't infer it to be fundamental. The planck lengths are however and they are derived using dimensional analysis. Another way to state this, is that the Schwartzchild radius of a black hole is equal to the Compton wavelength at the planck scale thus a photon trying to probe this would gain no information at all.

For a quick comparisson, the Classical Electron Radius is in fact $$\frac{1}{137}$$ times larger than the Compton Wavelength. The Compton Wavelength is (h/Mc) where h is Plancks Constant and it has a value of 6.62606957(29) X 10^(−34) j.s. The Compton Wavelength itself has a value for the electron as 2.4263102175 +(-) 33 X 10^(−12) m value varies with different particles) and is a measure itself of the wavelength of a particle being equal to a photon (a particle of light energy) whose energy is the same as the rest-mass energy of the particle.

Basically, all particles have a wavelength. Photon's can never be at rest but the energy of a photon can be low enough to have it's wavelength match any particle who is at rest. It's often seen in the eye's of many scientists as the ''size'' of a particle. Actually, a more accurate representation of the size of an object would be the Reduced Compton Wavelength. This is just when you divide the Compton Wavelength by $$2\pi$$ and it gives a smaller representation for the mass of a system.

Furthermore, if a photon could measure a planckian object, it could actually create a new class of particle called a Planck Particle - it would distort that space so badly that the photon would be gobbled up and no measurement could be performed. This is due to the Uncertainty Principle if my memory serves

http://en.wikipedia.org/wiki/Planck_particle

You know, I remember having a discussion with a string theorist once and he was asbolutely certain that the Planck time did not need to mean the smallest time that could be extrapolated from science. I don't know if his string theory education allowed that possibility... I know minimal about the theory. As far as I can tell however, most physicists seem to agree that the Planck Lengths are fundamental and you can't get anything smaller than this. We've only been able to measure larger times anyway. It will be long time before we can actually attempt to put the Planck time to the experimental physics.

#### Æthelwulf

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##### Re: Times less than Planck Time?
« Reply #8 on: 27/04/2012 18:01:55 »
Here is a derivation I quickly looked over and which might help.

There are a few jumps in these derivations you need to be careful of just looking over it again, it may not seem clear. For instance, when it asks us to take $$\ell$$ as the radius of a sphere... thus

$$m = \frac{\hbar}{2c\ell}$$

Then it asks to consider a special case

$$\frac{1}{2} mc^2 = \frac{Gm^2}{R}$$

a bit of jump without a derivation. I work it out as, multiply both sides of $$m = \frac{\hbar}{2c\ell}$$
with the speed of light squared,

$$mc^2 = \frac{\hbar c}{2\ell}$$

The c in the denominator on the right cancels, a $$c$$ appears besides the reduced planck constant $$\hbar$$. Then one must know that $$\hbar c = Gm^2$$ so

$$mc^2 = \frac{Gm^2}{2\ell}$$

And that looks close to the equation for $$\frac{1}{2} mc^2 = \frac{Gm^2}{R}$$
« Last Edit: 27/04/2012 18:03:46 by Æthelwulf »

#### imatfaal

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##### Re: Times less than Planck Time?
« Reply #9 on: 27/04/2012 18:41:19 »
The Planck Scale

The Planck scale is where one can no longer rely on GR and Quantum Gravity is needed.  Additionally QFTs breakdown because one is no longer able to renormalise out the effects of gravity.  It is beyond the planck scale that we need unified theories - the four forces are no longer separate but are all aspects of a single force (possibly)

The planck scale, the p. time, the p. lenght, and the p. mass do not form a fundamental limit beyond which nature does not pass (as an analogy absolute zero is a fundamental limit); the planck scale is a limit of our current understanding, but we are almost certain that it can be exceeded physically - look at the Planck Epoch aka Planck Era.

Experimentally - we are not even close to the Planck Scale - and we don't have any good ideas of how to get there yet; but that is a technical limit not a fundamental one
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#### Æthelwulf

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##### Re: Times less than Planck Time?
« Reply #10 on: 27/04/2012 18:47:24 »
The Planck Scale

The Planck scale is where one can no longer rely on GR and Quantum Gravity is needed.  Additionally QFTs breakdown because one is no longer able to renormalise out the effects of gravity.  It is beyond the planck scale that we need unified theories - the four forces are no longer separate but are all aspects of a single force (possibly)

The planck scale, the p. time, the p. lenght, and the p. mass do not form a fundamental limit beyond which nature does not pass (as an analogy absolute zero is a fundamental limit); the planck scale is a limit of our current understanding, but we are almost certain that it can be exceeded physically - look at the Planck Epoch aka Planck Era.

Experimentally - we are not even close to the Planck Scale - and we don't have any good ideas of how to get there yet; but that is a technical limit not a fundamental one
Imatfal, could you please return this thread back to the question and answers forum. This is completely in the wrong place. It is not a new theory thread.

#### Æthelwulf

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##### Re: Times less than Planck Time?
« Reply #11 on: 28/04/2012 06:12:08 »
Interestingly, Brian Greene has speculated on sub-Planckian existences. Whilst the Planck lengths could be fundamental, we don't know this for fact. He said:

"the familiar notion of space and time do not extend into the sub-Planckian realm, which suggests that space and time as we currently understand them may be mere approximations to more fundamental concepts that still await our discovery.”

Which is interesting, because if anyone actually follows my own speculations and contentions, I have been wheeling the idea that space and time could certainly not be fundamental since in the very beginning, there was no geometry (space-time) - not in the sense that GR deals with it.

#### yor_on

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##### Re: Times less than Planck Time?
« Reply #12 on: 28/04/2012 06:19:44 »
You know JP, you might be right. Maybe the Planck scale should be seen as a definition we have from the physics and math we know today. But there are so much physics inter-bound, as it seems to me, with that scale. I have this nice historical summary of the development of the Planck scale First Steps of Quantum Gravity and the Planck Values. As in most cases what people thought as they created something helps me immensely to see what they meant, once when it started.

But sure, there might be something else lurking After all, where does it end? 'photons' are dimensionless, aren't they?
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#### yor_on

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##### Re: Times less than Planck Time?
« Reply #13 on: 28/04/2012 06:22:37 »
Well Wulf, Brian has a very fertile mind And.. He.. Will.. speculate..
and as he does, sell books..
==

But yes, he's interesting, and some of his attempts to explain, especially entanglements, was very good. Still I prefer the experiments first. Theory building on that, and I'm not discussing weak measurements when I say experiments.
« Last Edit: 28/04/2012 06:26:34 by yor_on »
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#### Æthelwulf

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##### Re: Times less than Planck Time?
« Reply #14 on: 28/04/2012 06:29:27 »
Well Wulf, Brian has a very fertile mind And.. He.. Will.. speculate..
and as he does, sell books..
==

But yes, he's interesting, and some of his attempts to explain, especially entanglements, was very good. Still I prefer the experiments first. Theory building on that, and I'm not discussing weak measurements when I say experiments.

I do try and speculate myself. I am already trying to write out some kind of unification in my head as well, so I can see why physicists enjoy the speculations so long as there is a real science behind it

Unlike Hawking... who recently advocated M-theory as the theory of everything... I was very disappointed at this.

#### Æthelwulf

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##### Re: Times less than Planck Time?
« Reply #15 on: 28/04/2012 06:35:56 »
I dare say sub-Planck physics might be the right track though.

If spacetime arose from a singularity, a point - in no dimensions, then perhaps this makes sense why spacetime would make no sense below the Planck lengths. Below these lengths, we must assume that space and time are not fundamental. And below this length, the uncertainty principle concerning energy  is very high. Hopefully all these things will lead to some clues in which we can treat the initial conditions with a new type of understanding, or maybe try and understand it with the physics we have - as it may just be a matter of peicing a very complicated jigsaw puzzle together.

#### yor_on

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##### Re: Times less than Planck Time?
« Reply #16 on: 28/04/2012 06:41:16 »
Oh yes, I agree, physics is the best game there is and you're a gamer Wulf.

And I shouldn't be so harsh on Brian, he's a cool guy, although temperamental at times as seen at some blogs
He's doing some pretty impressive speculating, as we all want to do at times

==

As for above and under Planck, it's like you said, most of the physics we use today draw a line there for what we can explain. Maybe we will get a way to prove scales under it too, Smolin had some ideas there, or rather some of his friends? Using astronomical evidence for drawing conclusions of what might be under Planck scale.
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#### Æthelwulf

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##### Re: Times less than Planck Time?
« Reply #17 on: 28/04/2012 06:44:32 »
Oh yes, I agree, physics is the best game there is and you're a gamer Wulf.

And I shouldn't be so harsh on Brian, he's a cool guy, although temperamental at times as seen at some blogs
He's doing some pretty impressive speculating, as we all want to do at times

==

As for above and under Planck, it's like you said, most of the physics we use today draw a line there for what we can explain. Maybe we will get a way to prove scales under it too, Smolin had some ideas there, or rather some of his friends? Using astronomical evidence for drawing conclusions of what might be under Planck scale.

In regards to Smolin, did he? (or his friends)? I haven't seen any of that work, do you know where a link is at?

#### yor_on

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##### Re: Times less than Planck Time?
« Reply #18 on: 28/04/2012 06:53:00 »
I can try to find it, but I think I read it in his (latest(?) book, although I have a memory of seeing it somewhere else too. Give me a minute..
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#### yor_on

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##### Re: Times less than Planck Time?
« Reply #19 on: 28/04/2012 06:54:25 »
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#### yor_on

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##### Re: Times less than Planck Time?
« Reply #20 on: 28/04/2012 06:59:54 »
But there was some others too in the book?
Try this one too 'Can we probe planck-scale physics with quantum optics?' at http://backreaction.blogspot.se/
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#### JP

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##### Re: Times less than Planck Time?
« Reply #21 on: 28/04/2012 18:15:07 »
It looks like all the arguments against making sub-Planck measurements use general relativity + quantum mechanics to "prove" that the energies required to probe sub-Planck lengths will create Planck scale black holes.  But that assumes GR and quantum mechanics both hold at that scale, which we don't expect to be the case...

#### Æthelwulf

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##### Re: Times less than Planck Time?
« Reply #22 on: 28/04/2012 19:09:26 »
That was so weird... a good while ago I couldn't even post here lol

#### syhprum

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##### Re: Times less than Planck Time?
« Reply #23 on: 28/04/2012 19:33:23 »
There is a technical difficulty reading this as it is much tooooooooooooooooooooooooooo wiiiiiiiiiiiiiiiiiiiiiiiiiiide
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#### yor_on

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##### Re: Times less than Planck Time?
« Reply #24 on: 29/04/2012 09:52:54 »
It looks like all the arguments against making sub-Planck measurements use general relativity + quantum mechanics to "prove" that the energies required to probe sub-Planck lengths will create Planck scale black holes.  But that assumes GR and quantum mechanics both hold at that scale, which we don't expect to be the case...

That's the way I think of it too JP. As if we have 'phase transitions' of a sort, describing one thing at the macroscopic scale, another at QM level, a third under it. What will be interesting is the question of 'causality chains' and a 'arrow' there. I don't expect there to be any linear definition as our 'normal arrow' possible myself at/under Planck scale. But then again, what will 'exist' there? Bosons?
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#### yor_on

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##### Re: Times less than Planck Time?
« Reply #25 on: 29/04/2012 10:13:26 »
Although I better point out one thing. As I think of relativity, from a point of 'locality', meaning that all reference frames are locally equivalent. Which simply stated please me by making a Planck length 'invariant' in any local measurement (that is, if we could:) no matter where you do it, or your relative speed. If looked at that way one does not have to consider a relative length of something, depending on mass/motion etc. So a Planck length will then be a Plank length. But I agree fully on that there will be something more after that, although I don't expect our current definitions to cope with describing it.
=

And I can do that by relate a 'arrow' to 'c', as well as define a length to never change for you 'locally'. You may find a twin experiment to be true, But there is no way you will find a 'changed length', as some rulers compared between frames of reference relatively,  to stand the final test of joining 'frames of reference'.

So what is 'real' to me is how you can put it to that test, and from the conclusions you get you will be able to define the 'properties' of whatever concept you're laboring with. Which makes the arrow locally equivalent to 'c', and a 'length' locally invariant.
« Last Edit: 29/04/2012 10:29:46 by yor_on »
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