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Does the conservation law prove that energy is eternal?

by 8LAK
Tags: conservation, energy, eternal, prove
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8LAK
#1
Aug19-09, 05:14 PM
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I've heard many people claim that the first law of thermodynamics proves that the energy/matter must always exist in some form or another, since it cannot be created or destroyed. This would mean that energy/matter had no beginning, and will have no end. Is this a valid claim? Or is there something I'm misunderstand about the conservation law?

And while I'm on the subject, I'd like to ask a few semi-related questions about the Many World's Interpretation of Quantum Mechanics. From what I understand, the MWI says that the random events of quantum mechanics "splits" the universe into different realities, one with each respective outcome of the random quantum event. My questions are:

1. Do physicists take the MWI seriously? Or is it just an imaginative hypothesis that probably isn't true?

2. Would the "universe splitting" of the MWI violate the energy conservation? Does it really create a new universe for each random outcome?

3. If the MWI is in fact true, could we then conclude that there exists an infinite amount of universes? Would it be true infinity, or just a really large number?

Thanks.
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marcus
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Aug19-09, 08:54 PM
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Quote Quote by 8LAK View Post
I've heard many people claim that the first law of thermodynamics proves that the energy/matter must always exist in some form or another, since it cannot be created or destroyed. This would mean that energy/matter had no beginning, and will have no end. Is this a valid claim? Or is there something I'm misunderstand about the conservation law?
...
The idea of energy conservation is questionable outside of the situations where it can be applied in a mathematically rigorous way. We think the universe is governed largescale by General Relativity. Energy conservation is not proven to hold globally in GR.

If you can isolate a subsystem, enclose something in a box, and give meaning to all the relevant types of energy in the box, then you can apply the law. But on large scale in cosmology there are processes which apparently to not obey the local restricted law. Yet they are accepted by the community because they agree with observation and because there is no logical reason to suppose that energy conservation is true for the system as a whole.

There is an FAQ about this that people recommend sometimes. Maybe someone will offer URLs. I realize this is a vague unsatisfactory answer. There are plenty of unanswered questions in science and maybe this is one. Wish I could be more helpful. Good luck pursuing this!
Chalnoth
#3
Aug20-09, 04:41 AM
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This essay is good on the subject:
http://www.math.ucr.edu/home/baez/ph...energy_gr.html

Austin0
#4
Aug20-09, 05:23 AM
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Does the conservation law prove that energy is eternal?

=marcus;2314742]The idea of energy conservation is questionable outside of the situations where it can be applied in a mathematically rigorous way. We think the universe is governed largescale by General Relativity. Energy conservation is not proven to hold globally in GR.
Hi Just a clarification. Does this mean it has been proven not to hold?? Or that within the mathematical structure it is not an inevitable neccessity??

If
you can isolate a subsystem, enclose something in a box, and give meaning to all the relevant types of energy in the box, then you can apply the law. But on large scale in cosmology there are processes which apparently to not obey the local restricted law. Yet they are accepted by the community because they agree with observation and because there is no logical reason to suppose that energy conservation is true for the system as a whole
.

Is this in regard to the apparent motion or related to the energy loss through expansion and photon frequency reduction?? Other???


Thanks
Chalnoth
#5
Aug20-09, 05:46 AM
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Quote Quote by Austin0 View Post
Hi Just a clarification. Does this mean it has been proven not to hold?? Or that within the mathematical structure it is not an inevitable neccessity??
It holds only in special cases.

Quote Quote by Austin0 View Post
Is this in regard to the apparent motion or related to the energy loss through expansion and photon frequency reduction?? Other???
That's one way of looking at it. In general, though, it stems from Noether's theorem, where we find that energy conservation comes about if certain properties of the system are independent of time. In this case, energy will be conserved within General Relativity if we have a space-time geometry that is independent of time.

This is a problematic statement in GR, however, as a space-time geometry that is independent of time for one observer will not be independent of time for some other observers. But in any case energy won't be conserved in an expanding universe because of the expansion.
apeiron
#6
Aug20-09, 05:34 PM
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Quote Quote by Chalnoth View Post
But in any case energy won't be conserved in an expanding universe because of the expansion.
What do you mean here? Do you say this because of dark energy/cosmological constant? Accelerated expansion?

The old style inertial expansion assumption was a closed system description wasn't it?

*****

On the general issue raised by 8lak, MWI is a surprisingly popular interpretation of QM among professionals. There are those who say it is the only choice left to them.

But its radical violation of energy conservation is only one of its many obvious holes. I have always taken MWI as evidence that it is faulty metaphysical principles which have led to such a patently unnatural view of quantum cosmology.
Chalnoth
#7
Aug20-09, 07:23 PM
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Quote Quote by apeiron View Post
What do you mean here? Do you say this because of dark energy/cosmological constant? Accelerated expansion?
Any form of matter that experiences pressure will experience a change in energy per comoving volume due to expansion. Normal and dark matter are generally considered pressureless, and so don't factor into this at late times. But photons have pressure, as do dark energy and the inflaton field. And they therefore do change in energy per comoving volume.

Edit: I should mention that this does depend upon what you mean by "energy". If you include gravitational potential energy into the mix, then energy is always conserved in GR by definition. With dark energy and inflation the increase in energy in the dark energy/inflaton field is understood as coming from an increase in negative gravitational potential energy, just as with the perhaps more understandable case of two rocks falling towards one another (if they start at rest far away, then their kinetic energy is zero and potential energy nearly so. As they fall towards one another, their kinetic energy increases, and their potential energy also increases in the negative direction, leaving the sum constant).

Quote Quote by apeiron View Post
On the general issue raised by 8lak, MWI is a surprisingly popular interpretation of QM among professionals. There are those who say it is the only choice left to them.

But its radical violation of energy conservation is only one of its many obvious holes. I have always taken MWI as evidence that it is faulty metaphysical principles which have led to such a patently unnatural view of quantum cosmology.
It's not a radical violation of energy conservation, though. There is nothing "new" being created when two worlds in the many worlds interpretation diverge. You just have different components of the same wavefunction that don't interfere effectively with one another any more. They're still components of the same wavefunction, so there's no additional energy.
apeiron
#8
Aug20-09, 07:46 PM
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Quote Quote by Chalnoth View Post
If you include gravitational potential energy into the mix, then energy is always conserved in GR by definition.
.
Thanks. Good explanation.

Quote Quote by Chalnoth View Post
It's not a radical violation of energy conservation, though. There is nothing "new" being created when two worlds in the many worlds interpretation diverge. You just have different components of the same wavefunction that don't interfere effectively with one another any more. They're still components of the same wavefunction, so there's no additional energy.
Naively, a whole new world full of stuff appears "somewhere", even if in some QM configuration space or Hilbert-verse.

But this would the view that would come from taking QM as essentially an open thermodynamic story? Uncertainty would be something that can be endlessly borrowed from?
Chalnoth
#9
Aug20-09, 07:57 PM
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Quote Quote by apeiron View Post
Naively, a whole new world full of stuff appears "somewhere", even if in some QM configuration space or Hilbert-verse.

But this would the view that would come from taking QM as essentially an open thermodynamic story? Uncertainty would be something that can be endlessly borrowed from?
Well, again, there's no new energy being created. This should be most clear if one considers that the number of components of the wavefunction that describe a given system actually are somewhat arbitrary: it depends upon what representation you are talking about.

Because the number of components of the wavefunction depends upon what you take the wavefunction in terms of, it wouldn't ever make any sense for there to be conservation of a sum of some physical quantity over the many wavefunction components: the sum would vary just by changing the representation!

Instead, there are two operations in quantum mechanics that correspond to determining the energy. One is to ask the question, "What is the expected value of the energy?" and the other is to ask, "If I make a measurement of energy, what value will the measurement produce?" In the first case, you take a weighted average over the many components, not a sum. In the second, the outcome of your measurement will be one of the components of the wavefunction with a probability given by the square of its amplitude.

So instead of thinking of it as a 'whole new world full of stuff,' perhaps a better way of thinking of it is as just a different configuration of our world coexisting with ours, rather like how an electron can be in two states at once.
apeiron
#10
Aug20-09, 08:21 PM
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Quote Quote by Chalnoth View Post

So instead of thinking of it as a 'whole new world full of stuff,' perhaps a better way of thinking of it is as just a different configuration of our world coexisting with ours, rather like how an electron can be in two states at once.
So in thermodynamic terms, the same ensemble of microstates in different configurations. And if we are counting just microstates, then everything looks conserved.

This is either bogus or subtle.

I guess I am reacting against it because I take the enlarged thermodynamic view where there is top-down causality, global constraints, etc. So that is the framework I'm trying to fit this into.

In this light, I would still feel that the QM uncertainty is like a bottomless well. Then the questions you say are asked - "What is the expected value of the energy?", "If I make a measurement of energy, what value will the measurement produce?" - are the kind of top-down constraints which closes matters to produce the coherence of a "GR system".

Not asking you to agree but you have helped sharpen up the questions for me.
Chalnoth
#11
Aug20-09, 08:49 PM
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Quote Quote by apeiron View Post
So in thermodynamic terms, the same ensemble of microstates in different configurations. And if we are counting just microstates, then everything looks conserved.
It's not that everything looks conserved, but it actually is.

Quote Quote by apeiron View Post
I guess I am reacting against it because I take the enlarged thermodynamic view where there is top-down causality, global constraints, etc. So that is the framework I'm trying to fit this into.
I don't know what you mean by "top-down causality" or "global constraints", but in any case, there is nothing about quantum mechanics that in any way contradicts thermodynamics. Thermodynamics had to be modified somewhat to accord with the statistical properties of quantum mechanics, but for the most part that's a small effect (it has some interesting consequences like superfluidity and superconductivity, but it doesn't affect the overall picture of thermodynamics).

Quote Quote by apeiron View Post
So in thermodynamic terms, the same ensemble of microstates in different configurations. And if we are counting just microstates, then everything looks conserved.
It's not that everything looks conserved, but it actually is.

Quote Quote by apeiron View Post
In this light, I would still feel that the QM uncertainty is like a bottomless well.
A bottomless well in what sense?
apeiron
#12
Aug20-09, 09:32 PM
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Quote Quote by Chalnoth View Post

A bottomless well in what sense?
As naked potential, it would be infinite.

Quote Quote by Chalnoth View Post
It's not that everything looks conserved, but it actually is.
Yes, but in a systems perspective the "everything" also includes the macrostate, so to speak. In conventional views, a system just is the sum of its microstates (a macrostate emerges "for free"). In a systems view - arguably - the macrostate is causally active, a source of action or "energy", and so its cost must be counted as well.

In this line of thought, many worlds seem a violation of conservation as macrostates are being freely created (even if microstates are conserved).

It is like if we were talking about the usual ideal gas model. Conventional approach is to take the flask that contains the gas as read. The thermodynamics is the collection of microstates inside. But in a wider view - as would have to be taken in cosmology - we then have to factor in the issue of who made and paid for the flask, the boundary conditions.

MWI would be like saying you can make new and differently shaped flasks freely.
Chalnoth
#13
Aug20-09, 09:55 PM
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Quote Quote by apeiron View Post
As naked potential, it would be infinite.
Yes, but infinite in what sense?

Quote Quote by apeiron View Post
Yes, but in a systems perspective the "everything" also includes the macrostate, so to speak. In conventional views, a system just is the sum of its microstates (a macrostate emerges "for free"). In a systems view - arguably - the macrostate is causally active, a source of action or "energy", and so its cost must be counted as well.
Fine, but the many worlds of the MWI would be a superposition of different macrostates, not wholly different entities.

Quote Quote by apeiron View Post
MWI would be like saying you can make new and differently shaped flasks freely.
No, it's just saying that it isn't any problem to have a superposition of two different states of the same flask, and there is also the possibility that the interference between those states may be low enough that information isn't communicated between them at any meaningful level.
apeiron
#14
Aug20-09, 10:12 PM
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Quote Quote by Chalnoth View Post
Yes, but infinite in what sense?
Unlimited or boundless would be better terms in my book.

Regular notions of infinity would rely on the image of infinite extension - keep on adding forever. But I am thinking more in terms of the magic pudding - the infinitely divisible.

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

Quote Quote by Chalnoth View Post

No, it's just saying that it isn't any problem to have a superposition of two different states of the same flask, and there is also the possibility that the interference between those states may be low enough that information isn't communicated between them.
Here I don't see how it is legitimate to treat a superposition as an actual macrostate. The superposition has to be decohered to be a definite something. A superposition is the before, not the after.

I can see that you are arguing that all that is happening is a multiplication of the complexity of the superposition state to become an ever more massive MWI agglomeration. And it would be correct in so far as the formalisms of QM superposition are concerned.

But the big QM issue here is the placing of the epistemic cut, the collapse of superposed states. And the MWI just ducks the issue by saying it never has to happen. There is no place the critical questions you mention actually get asked.

Edit: Although the escape clause may be that, as you say, the presumption a lack of interference and so a quasi-separation of some kind. Yet this too must be vulnerable to the criticism it is unrealistic when it looks collapse does generally happen at quite small scales.
Chalnoth
#15
Aug20-09, 11:20 PM
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Quote Quote by apeiron View Post
Unlimited or boundless would be better terms in my book.

Regular notions of infinity would rely on the image of infinite extension - keep on adding forever. But I am thinking more in terms of the magic pudding - the infinitely divisible.

http://en.wikipedia.org/wiki/The_Magic_Pudding
Except it's nothing like that. As I've been saying, nothing "new" is being created.

Quote Quote by apeiron View Post
Here I don't see how it is legitimate to treat a superposition as an actual macrostate. The superposition has to be decohered to be a definite something. A superposition is the before, not the after.
I think you're confusing the MWI interpretation with other interpretations that have wave function collapse. In the MWI, there is no collapse at all. There is only the appearance of collapse. The system is always in a superposition of many states. It's just that if certain interactions have occurred, then the different elements of the superposition cannot communicate effectively. That is all.

As for it not being legitimate to treat it as a macrostate in the thermodynamic sense, well, that's fine. A macrostate in thermodynamics is the set of macroscopic variables that are needed to fully-describe the macroscopic behavior of the system. Because different components of the wavefunction aren't observable in macroscopic systems, they don't belong in a consideration of thermodynamic macrostates. This doesn't mean that the MWI is wrong, just that the word "macrostate" is a poor word to use to describe the entire ensemble of configurations of the system.

Quote Quote by apeiron View Post
But the big QM issue here is the placing of the epistemic cut, the collapse of superposed states. And the MWI just ducks the issue by saying it never has to happen. There is no place the critical questions you mention actually get asked.
That's not ducking the issue. It's solving the problem of wavefunction collapse in an extraordinarily simple and elegant manner. And given the difficulty in demonstrating precisely how the appearance of collapse arises from the MWI, I would consider a claim that it's "ducking the issue" to be an admission of ignorance of the difficulties involved.

Quote Quote by apeiron View Post
Edit: Although the escape clause may be that, as you say, the presumption a lack of interference and so a quasi-separation of some kind. Yet this too must be vulnerable to the criticism it is unrealistic when it looks collapse does generally happen at quite small scales.
And at small scales you can actually calculate how effective the collapse should be, and therefore compare the prediction of the MWI against observation. So far observations match the predictions.
kote
#16
Aug21-09, 12:45 PM
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Quote Quote by 8LAK View Post
I've heard many people claim that the first law of thermodynamics proves that the energy/matter must always exist in some form or another, since it cannot be created or destroyed. This would mean that energy/matter had no beginning, and will have no end. Is this a valid claim? Or is there something I'm misunderstand about the conservation law?
Conservation laws are assumed. They cannot prove anything since it is impossible to verify a scientific theory (you can only prove it wrong, not right). Conservation laws, or symmetry, are about the last assumption we will throw out in developing theories in physics. They are too central to our dependence on the belief that things should exist and be describable in rational intelligible terms. Ex nihilo nihil fit. Nothing comes from nothing.

Of course, assuming conservation laws, something will always exist and something has always existed. But this argument is circular. Welcome to philosophy . It's all about the assumptions, and sometimes the higher level theories (QM, thermodynamics) can just be obfuscating noise.
Chalnoth
#17
Aug21-09, 02:20 PM
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Quote Quote by kote View Post
Conservation laws are assumed.
And then tested and verified. They aren't simply assumed by fiat, but people actually go out and test to see whether or not they are true.

Of course, one cannot prove in a strict, mathematical sense that a conservation law always holds. But one can place reasonable limits upon them.
kote
#18
Aug21-09, 02:24 PM
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Quote Quote by Chalnoth View Post
And then tested and verified. They aren't simply assumed by fiat, but people actually go out and test to see whether or not they are true.

Of course, one cannot prove in a strict, mathematical sense that a conservation law always holds. But one can place reasonable limits upon them.
Of course there is a strong basis for the assumption, which I mentioned. I don't agree that laws can be tested for truth or that they can be verified. Those ideas fly in the face of Popper's generally accepted notion of falsifiability. In science we do falsification, not verification. It seems that you just said that though, so I'm not sure there's any real disagreement.


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