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Author Topic: How does E=mc2 conserve mass?  (Read 12884 times)

Offline JP

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How does E=mc2 conserve mass?
« Reply #25 on: 05/10/2011 05:20:00 »
It all goes back to 'energy' doesn't it, and as 'gravity' is coupled to mass and then those photons can be defined to have a mass, we now have a circumstantial chain pointing to 'energy' as the origin of 'gravity' too, which makes sense. With the exception of me thinking of it as coupled, not generated as in 'created' by mass. to me it's more of something 'sticking' to 'it all' SpaceTime that is, including 'energy' :) As a geometry defining energy relative the observer sort of, and always local. Even though intrinsically invariant those light quanta's then can be seen as a summation of 'gravity', changing relative the observers position in SpaceTime.

Well, just as "mass" isn't sufficient to describe physics in special relativity (you need the 4-vector), it isn't sufficient in general relativity.  But in GR you need the stress-energy tensor, not just the 4-vector!  This is a 4x4 tensor, and to pull a single number out of it as "mass" is a way of reducing 16 numbers to only 1 (though only 10 of those numbers are unique).  Anyway, it's probably best not to go there for now.

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But what do you mean by "If you compute the invariant mass including the atoms which will emit the photons, then invariant mass has one value at all times, no matter what reference frame you're in."?
Well, Pmb's pointed out a problem with invariant mass.  Let's say you have two photons being emitted in a box and you compute the invariant mass of those two photons.  In your initial reference frame, both photons are emitted at the same time.  You go from zero invariant mass when no photons are there to some non-zero value when both photons suddenly appear.  If instead, you are in a moving frame, you no longer see both photons being emitted at the same time, so you compute 3 values for invariant mass: no particles, 1 photon, 2 photons. 

The fix to this is that invariant mass is conserved in both cases if you include contributions from the particles that emit the photons to begin with.  Those particles had energy and momentum, and when emitting the photon, they had to recoil to conserve energy and momentum.  If you include them in the calculation, there is only on value of invariant mass for the whole system of emitters+photons, no matter which frame you're in.


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That if we redefine the closed system to also in-cooperate the 'photons' sources, the atoms, you will find a same invariant mass, no matter the 'rotations' you apply on them by your position relative them? And then it is the observer too, he must always be included right?
The observer is included because the observer's motion with respect to the system of particles defines the reference frame being considered.  The point is invariant mass is the length of an energy-momentum 4-vector.  By the rules of SR, a change in inertial frame of the observer is a rotation of the 4-vector, which doesn't change it's length, so the invariant mass is invariant in all inertial reference frames.

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So in that case, there is no difference between that system and a planet?
The mass (of the two photon system) will now be invariant, no matter what rotations you apply on it.
Uh... I'm not sure what a planet has to do with a two photon system...  This idea should work to any system of objects which can be considered as the sum of point particles, I believe.
 

Offline JP

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How does E=mc2 conserve mass?
« Reply #26 on: 05/10/2011 14:43:02 »
What I really mean here is that it is the observer that defines the result. And that without the observer those two photons should have only one path. Would you agree to that or do you see it differently? As I see it all such descriptions always include a observer, and it is that thought up observer that will define the outcome. And this is more of philosophy possibly, but it is a 'presumption' for describing anything, and very important in SpaceTime, well, as I see it. Weird stuff :)
==

Philosophy aside, what SR tells us is that there is no absolute measure of distance or time.  There are events in space-time, but the distances or times between those events can vary depending on the motion of the observer relative to the events. 

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It's not a perfect description, you might assume that SpaceTime, even without observers, will have a independent 'reality', a little as I did with those photons path, relative each other. And if you do you define SpaceTime as being of a 'objective quality', independent from any observer, simultaneously with it being described from observer frames of reference. If you do that you introduce one 'SpaceTime background' that we might call 'original', but invincible to us, as what SpaceTime we see always will be defined from our 'rotation' / 'frame of reference'. But it is about what SpaceTime really 'is', as I see it.
You might assume that, but you'd be wrong.  :p  The problem is that events in space-time are specified by points with space and time coordinates.  But motion of an observer moves these points around.  There is no universal reference frame with "correct" values for these results.

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Either all things in SpaceTime is 'observers', observing SpaceTime differently from their own frame of reference, all of it locally. Or we have a SpaceTime that has a 'objective reality', hidden from our observations. It's hard to see how it can be both to me. In the first case we have radiation and gravity keeping it together, presenting us the 'wholeness' that we all think us to see when looking out in the universe. But all of it defined locally. In the second? What is HUP? Is that a sign of how QM defines a universe, and, why do statistics work?
All distance and time measurements are based on observers.

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This one seems interesting.
Yeah, it's interesting, but it's important to understand that the observer in relativity and the observer in QM aren't doing the same thing.  In SR, the observer's motion changes measurements of distance and time, but the measurement doesn't have to influence the object being measured.  In QM, the observer's measurements must physically change the object being measured.
« Last Edit: 05/10/2011 15:34:41 by JP »
 

Offline Pmb

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How does E=mc2 conserve mass?
« Reply #27 on: 05/10/2011 15:30:06 »
And that brings me to a disagreement with Pmb's point above and a defense of invariant mass.  Pmb said that if you have two photons being emitted, then the invariant mass takes on three values in some reference frames due to the photons not being simultaneously emitted.  This is true because it's not a closed system over time.
You're quite right JP.  I forgot to mention that, for a closed system, energy is a constant.
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If you compute the invariant mass including the atoms which will emit the photons, then invariant mass has one value at all times, no matter what reference frame you're in.
I agree. The purpose of my post was merely that you have to be careful when you add 4-vectors. E.g. supposed you had system of charged particles which are close enough to interact with each other. If we take a surface which is large enough to enclose all particles and where the EM field is too small to make a difference in your calculations then if you add the 4-momenta of all particles in the system then the total 4-momentum is not invariant, nor is it constant. You have to calculate the mass contribution that comes from the EM field.
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And this is why invariant mass is particularly useful.
Yes. You are absolutely correct. The proper (i.e. invariant) mass of a system is quite important in particle physics. However it's relativistic mass that is important in, say, cosmology. There just more people who do particle physics than cosmology and there's people here who are more  interested in particle physics than cosmology. For example, if you come across the text Principles of Physical Cosmology by Peebles, turn to page 63 and see how you have to take account of the effects of pressure on active gravitational mass density (see Eq. 4.21). This quantity is not proportional to energy density. See also page 453, Eq. 18.11
« Last Edit: 05/10/2011 15:39:00 by Pmb »
 

Offline simplified

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How does E=mc2 conserve mass?
« Reply #28 on: 05/10/2011 17:53:54 »
The concept of invariant mass from the Einstein equation is really just for people who are fixated on mass as something important.  mass is best viewed as "trapped energy" and the amount of energy that is trapped defines its gravitational mass.  The same is true for space and time, these are a function of energy and momentum via the main fixed constant which is accepted as the speed of light.  In reality we should always use dimensions of energy and momentum.  but these are not very easy to use in our normal world of space time.
If a trapped kinetic energy is gravitational mass then this trap is time.
« Last Edit: 05/10/2011 17:55:34 by simplified »
 

Offline yor_on

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How does E=mc2 conserve mass?
« Reply #29 on: 05/10/2011 19:14:04 »
It's nice reading this :)

But what is a distance, and what is 'time'. You need the arrow to get a 'distance', and then you need 'statistics' to prove a 'motion'. Or you can exchange 'statistics' for 'history'. So I'm not sure if there is so much differing QM from macroscopic phenomena. If the 'distance' mesaured is a result of the observer relative SpaceTime, and the 'time' he measures for other frames also is a result of his 'motion/mass/energy/gravity'?

We take too much for granted I think.
 

Offline yor_on

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How does E=mc2 conserve mass?
« Reply #30 on: 05/10/2011 19:19:59 »
"In QM, the observer's measurements must physically change the object being measured."

Is that the way you see HUP JP?
That it is the 'physical' interference that creates it?
 

Offline JP

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How does E=mc2 conserve mass?
« Reply #31 on: 05/10/2011 19:50:05 »
"In QM, the observer's measurements must physically change the object being measured."

Is that the way you see HUP JP?
That it is the 'physical' interference that creates it?


Uh oh... I sense a detour into metaphysical implications of QM here.  In the Copenhagen interpretation, at least, the measurement process "collapses the wave function" which generally causes the object being measured to change.  The physical description of the object before the measurement does not equal the description after the measurement.  (The HUP is a consequence of this.)
 

Offline yor_on

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How does E=mc2 conserve mass?
« Reply #32 on: 05/10/2011 20:00:39 »
Well, any 'wave function' has to be metaphysical :)

You can't 'measure' on that and define it 'unchanged'. But I wondered as you wrote physical change :) And that sounded as a 'physical chain reaction' I measure and my measurement change its state by 'interfering' physically with what I try to observe. It's a question of indeterminacy isn't it?
 

Offline JP

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How does E=mc2 conserve mass?
« Reply #33 on: 05/10/2011 22:42:45 »
Well, any 'wave function' has to be metaphysical :)
Metaphysical is a bit of a nebulous term, but I'd say it doesn't have to be, since it has a precise mathematical meaning in terms of the theory and measurable quantities.  If you want to ask how "reality" relates to these mathematical quantities, I'd agree that's metaphysics.

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You can't 'measure' on that and define it 'unchanged'. But I wondered as you wrote physical change :) And that sounded as a 'physical chain reaction' I measure and my measurement change its state by 'interfering' physically with what I try to observe. It's a question of indeterminacy isn't it?
Do you really mean "chain reaction"?  That has to do with processes that self-amplify as they do.  I'm not sure what it has to do with the question of observation.  (http://en.wikipedia.org/wiki/Chain_reaction)

Anyway, my point was that observation in QM implies that you're somehow influencing the state and you've changed it's future.

Observation in SR is all relative, but can be done without influencing the state.
 

Offline yor_on

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How does E=mc2 conserve mass?
« Reply #34 on: 06/10/2011 03:07:17 »
No, I didn't mean it to be taken that way, I was thinking of in terms of 'one thing leading to another', a causality chain. But you're right, in nuclear terms it surely amplifies. And yes, it's tricky defining it. Mathematics may have it defined but a wave function is, as I know it, a 'superposition' of all states possible for whatever it is you're observing, as defined through statistics. And all statistics are built on histories, aren't they?

That's actually a question I wonder about. Can statistics be used without histories to define it from?
 

Offline JP

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How does E=mc2 conserve mass?
« Reply #35 on: 06/10/2011 17:03:40 »
Statistics and probability are different things.  Statistics is the analysis of data or some characteristics of a set of data that's been analyzed.  Probability is the likeliness of different events occurring.

In other words, probability is loosely predicting outcomes in the future, and statistics is inferring something about a process from the past.  In QM, you're really dealing with probabilities, determined by physical laws.  You can infer something by looking at statistics (which is what they're doing in the LHC, for example) and comparing that to the predicted probabilities.

Anyway, neither field requires looking at things over time.  You can have statistics of stationary processes (those that don't change over time), or you can have randomness in some other variable than time: for example you could measure things or ask about the probability of finding something somewhere in space.  However, since we move forward through time, it's usually most useful to take a series of measurements in time or ask what will happen in a future measurement.
 

Offline simplified

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How does E=mc2 conserve mass?
« Reply #36 on: 06/10/2011 19:06:27 »
It's nice reading this :)

But what is a distance, and what is 'time'. You need the arrow to get a 'distance', and then you need 'statistics' to prove a 'motion'. Or you can exchange 'statistics' for 'history'. So I'm not sure if there is so much differing QM from macroscopic phenomena. If the 'distance' mesaured is a result of the observer relative SpaceTime, and the 'time' he measures for other frames also is a result of his 'motion/mass/energy/gravity'?

We take too much for granted I think.
Mass has time,but free time can be around of squeezed mass,it can catch a photon,then the photon turns into mass. 
« Last Edit: 06/10/2011 19:16:06 by simplified »
 

Offline yor_on

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How does E=mc2 conserve mass?
« Reply #37 on: 06/10/2011 21:12:53 »
Yes, the point I was wondering about was if not all statistics needs a 'history'. Even when you do not build one I would say that you build your probability on what have happened before. That is for example the statement that a coin thrown long enough will have a probability of 50/50 head/tail. Or would you say that we can get to such a statement without having experience teaching us?

Assume some other universe for this, and some other 'constants' etc. Because, maybe my question is more of the universality of mathematics than of if being possible to have other ways, and other answers to our coin throwing. That is, are there principles of probability that can guarantee a correct answer under all circumstances? (Without statistics gathered about this new 'place')

Somewhere, some time, somebody must have thrown that coin and noticed that it came out certain ways depending on how long, and from that made a proposition/assumption? It's very vague this one, but I can't help wondering about it.
« Last Edit: 06/10/2011 21:17:46 by yor_on »
 

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How does E=mc2 conserve mass?
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