Is Noether's theorem applicable to the expanding universe?

[Cosmo Novice]

One thing that would be cool is "an encyclopedia of failed ideas". That would speed up the "have you thought of... Yes, we thought of that, and here is why it didn't work..."

I have read and respected many of your comments, but i must disagree here. It can actually be educational for people to make the mistake for themselves, and not all discarded ideas are without merit.

 

[JaredJames]

I have read and respected many of your comments, but i must disagree here. It can actually be educational for people to make the mistake for themselves, and not all discarded ideas are without merit.

As much as I agree that making mistakes yourself is a good way to learn, there's just not enough time. And to have too many people working on already failed ideas just wastes even more time.

If an idea is shown to be a complete failure, I don't see what would be wrong with having it listed somewhere for people to 'check on' when they come up with something.

 

[Subluminal]

It's unclear to me on what basis I would use to answer that question, so I'd have to answer with "I don't know."

Aristotle said that a body in motion always eventually comes to rest. It took people like Newton and Galileo to find and convincingly show otherwise. The current belief (I understand not held by all) that photons simply lose energy in extragalactic vacuum reminds me of that time before energy was determined to be a conserved quantity, so I can't see how it's true. I admit this is intuition, and I apologize for that. It just seems to me that we lack the capacity to observe what's really happening, as Aristotle lacked the instruments available to later scientists. Or maybe we can see it but we're not looking in the right place.

If we could integrate all the photon energy lost to expansion redshift within our CMB sphere since decoupling, how would that compare that to WMAP readings of how much dark energy we see now? The Planck spacecraft is due to send us much better data than WMAP next year, the "year that dare not speak its name". The WMAP gave such solid confirmation of BB theory that it's hard to deny (http://map.gsfc.nasa.gov/universe/bb_tests_exp.html). Planck will measure the amount of dark matter & energy 10x more accurately. Are there any theories that predict the ratio of these 2 things?

 

[marcus]

If we could integrate all the photon energy lost to expansion redshift within our CMB sphere since decoupling, how would that compare that to WMAP readings of how much dark energy we see now? ...

I remember making a similar comparison back in 2003-2004, just for fun. It was something like this: we don't know that "dark energy" is actually an energy. It behaves like a constant in the equation, whose dimensions is curvature. Interpreting as energy is optional

but if you do choose to do that the energy density is about 0.6 nanojoules per cubic meter.

And correct me if I am wrong, anybody, but I recall the CMB energy density is about 4.2 x 10^-5 nanojoules per cubic meter. It should be lookable-up somewhere.

Now those CMB photons have "lost" (by a succession of little doppler shifts as they progress from frame to frame--if you choose to think of the expansion process that way) about 1090/1091 of their original energy, so the energy of each photon now in this frame is 1/1091 what it was when it started in its emission frame.

So the energy of those photons used to total about 1000 times larger. that is about
4.2 x 10^-2 nanojoules per cubic meter.

So 0.04 compared with 0.6

It doesn't match. It is nearly within an order of magnitude, which is kind of cute. But it does not match. And there is no physical reason it should.

So Subluminal, to answer your question in a rough sort of way, if you take a cubic meter out in space, if you like to quantify the cosmo constant as an energy density and like to think of it that way, then that cubic meter has 0.6 joules of DE in it. And if you look at all the CMB photons in it, and add up all the energy they have "lost" since they started their travels, then that cubic meter of CMB photons has lost a total of 0.04 joules.

If I recall correctly. It's quite a bit less. You wanted a comparison like that, I think.

 

[marcus]

The concept of energy is meaningful within a given reference frame. I guess most of us, to define energy, would require a Newtonian frame, or the frame of a Special Rel observer.
Just, for instance, to be able to say clearly what "work" is.

Conservation of momentum and energy are proven using time and space translation symmetry. In the real world (where symmetry is only approximate) they are only approximately true. In general, there is no global frame of reference. There is no global definition of energy. You cannot prove conservation globally. There is no reason to believe it in general

We have all met people who suffer from excessive credulousness. They don't critically examine their beliefs. Some one told them "energy is conserved" and "things cannot move faster than c relative to other things". They swallow that naively without asking "in what context?" and "under what assumptions?"

Without assumptions about symmetry you cannot define our motion relative to something that existed in the past. Without a reference frame there is no unambiguous definition of motion or speed. As a general rule, curved spacetimes do not admit global frames.

I'm no great expert or authority in these matters, but I'm pretty sure that over cosmological distances you can't unambiguously say what distance is or motion is without making some explicit definitions first. That would go for energy also, to the extent that it can be defined.

BTW I recall reading years ago that in a curved space an amoeba-like creature could travel by successively changing its shape. I've lost the reference. It was in arxiv.org as I recall, maybe about the same time 2004? Do you happen to remember seeing something like that? It appears to violate intuition---the think is moving without rockets, without any "equal and opposite" reaction mass. Anybody remember seeing that?

I found some links!
Something from Science, February 2003:
http://www.sciencemag.org/content/299/5614/1865
Free article from Physical Review D
http://arXiv.org/pdf/gr-qc/0510054v2
also more recent popularization in Sci Am.
http://www.scientificamerican.com/article.cfm?id=surprises-from-general-relativity&page=2
Some animations (scroll down)
http://physics.technion.ac.il/~avron/

 

[Subluminal]

good stuff marco, thanks.

...quantify the cosmo constant as an energy density and like to think of it that way, then that cubic meter has 0.6 joules of DE in it. And if you look at all the CMB photons in it, and add up all the energy they have "lost" since they started their travels, then that cubic meter of CMB photons has lost a total of 0.04 joules.

It may amount to little, but what about all the other photons besides CMBR? I am picturing an anisotropic homogenous model where baryonic matter has condensed into "few" and far-between photon-producing objects capable of delivering new photons to our extragalactic cubic meter of interest. As an engineer I can only wonder what finite element analysis software might apply to this, you are probably already thinking of a quick hand calculation!

 

[marcus]

Subluminal, thanks for the kind words. You are right that the starlight etc amounts to very little. I remember seeing an "energy inventory" for the cosmos a while back. Some of the others would be better at answering than I.

The CMB energy density is easy to calculate from the Stefan-Boltzmann black body radiation law. Because we know the temperature of the CMB is 2.725 kelvin or some such figure.
Cavity radiation density is proportional to the fourth power of the temp.

There is a factor of 4/c that gets in but otherwise it is just the familiar S-B constant.

About other E-M energy, not from "recombination" Most of it would be within an order of magnitude the same energy as when it was emitted, because the redshift is typically less than 9.

So it isn't very much of the inventory, and it hasn't lost more than about 90% of its energy anyway. Mostly much less.

George Jones, Ben, Brian Powell might know an estimate of the non-CMB EM energy fraction in the inventory. The best I could do is google. I recall there is something on the arxiv from some years back.

Here, I found it!
http://arxiv.org/abs/astro-ph/0406095

 

[Subluminal]

Here, I found it!
http://arxiv.org/abs/astro-ph/0406095

This is a great link to add to this thread, to further summarize the observational data supporting "the BB theory" to the exclusion of other popular ideas. I am one page into the 35-page link here and also have a long way to go on all the other material you referenced, but I wanted to offer a quick comment and another question before I re-sequester my monkey brain's efforts to catch up and better understand current events.

The inventory for primeval thermal remnants, 0.0010 ± 0.0005:
2.1 electromagnetic radiation 10^−4.3±0.0
2.2 neutrinos 10^−2.9±0.1
2.3 prestellar nuclear binding energy −10^−4.1±0.0

Earlier you estimated the original component of the energy density (not sure if that wording makes sense) from electromagnetic radiation, mostly from CMB photons as you've explained, as roughly 0.04 joules/m³, where there are 0.6 joules of DE in that m³. I was thinking about newer photons, but did not think to go backwards and suspect the "CNB" contribution. There is an order of magnitude increase there - cute, no?

My other question belongs in a new thread...

 

[marcus]

Earlier you estimated the original component of the energy density (not sure if that wording makes sense) from electromagnetic radiation, mostly from CMB photons as you've explained, as roughly 0.04 joules/m³, where there are 0.6 joules of DE in that m³. I was thinking about newer photons, but did not think to go backwards and suspect the "CNB" contribution. There is an order of magnitude increase there - cute, no?
...

did I say 0.6 joules/m³?

I meant to say nanojoules. Perhaps (I hope) I did and it didn't come through.
Anyway if DE is really to be considered an energy density, it is estimated at about 0.6 nanojoules per cubic meter.

One way to visualize is to blow that up to a cubic kilometer and then it is 0.6 joules per cubic kilometer. (kilo cubed is nano you're an engineer so this is second nature, but may not be to other readers.) A joule is easy to imagine---just raise a freshman physics textbook a few centimeters off the table. Or drop it, if you want to hear a joule worth of thud. But that is in a cubic kilometer, not a cubic meter.

I don't remember what I calculated for the CMB. In any case each photon had lost about 999/1000 of its original energy by the time we catch it in the antenna.

Good luck with the rest of your question in the other thread! You keep us hopping around here.

 

[Subluminal]

You keep us hopping around here.

I don't mean to cause any extra work, as might be measured in kg*m²/s² (based on what we consider to be meters and seconds in this reference frame anyway). And sorry if I misquoted units, but might the 0.042/0.6 ratio still hold for the discussion? But what do you make of the 25-fold increase in the energy inventory for neutrinos in the primeval thermal remnants, compared to E-M, as a possible contributor to that faint "thud of the physics tome"?

 

[twofish-quant]

I am picturing an anisotropic homogenous model where baryonic matter has condensed into "few" and far-between photon-producing objects capable of delivering new photons to our extragalactic cubic meter of interest.

Then you run into galaxy formation constraints, and CMB issues.

One thing that has to be emphasized is that cosmology is an observational science. We have a ton of data come in.

As an engineer I can only wonder what finite element analysis software might apply to this, you are probably already thinking of a quick hand calculation!

It's been done. What you do is to assume the universe is made of X, Y, and Z materials and then you get correlation coefficients.

 

[twofish-quant]

The current belief (I understand not held by all) that photons simply lose energy in extragalactic vacuum reminds me of that time before energy was determined to be a conserved quantity

That's not the current belief. The issue is that different people will measure and define energy in different ways. Also energy is not a conserved quantity in all situations, and certainly not at cosmological scales.

One of the based theorems is Noether's theorem, which says that for every conserved quantity there is a symmetry and for every symmetry there is a conserved quantity. Conservation of energy comes from time symmetry. If you have rules which are time symmetric, energy will be conserved.

The thing about the expansion of the universe is that it isn't time symmetric so energy isn't conserved.

It just seems to me that we lack the capacity to observe what's really happening, as Aristotle lacked the instruments available to later scientists. Or maybe we can see it but we're not looking in the right place.

So then the question which is what theorist spend time doing is to figure out

1) what should we be looking at that we aren't
2) what instruments should we be building

If you can come up with something that says, to see X, you need to build instrument Y and point it at Z, then people write papers and then you go to Congress for money to build spacecraft .

Part of the reason that WMAP and COBE exists is that people wrote papers back in the late-1980's saying that if there were some inhomogenity, then you should see it in the CMB. We don't, which is sort of a bummer.

The WMAP gave such solid confirmation of BB theory that it's hard to deny (http://map.gsfc.nasa.gov/universe/bb_tests_exp.html). Planck will measure the amount of dark matter & energy 10x more accurately

Are there any theories that predict the ratio of these 2 things?

Lots of them.

There is a bit of a fudge here, and that what is defined as the "standard big bang theory" changes over time. What people say when they mean BB theory in 2010 is a bit different from the term in 1970 or in 2030.

 

[twofish-quant]

I have read and respected many of your comments, but i must disagree here. It can actually be educational for people to make the mistake for themselves, and not all discarded ideas are without merit.

That was my point. We need an encyclopedia of incorrect ideas, because that's more educational than a textbooks that just give received wisdom. It also points out how science is different from a lot of religions (not to say that there is anything wrong with religion).

Also sometimes things change. For about fifty years, the idea that there was a cosmological constant was a failed idea that was obviously wrong. I think it's been called Einstein's biggest blunder.

Then in 1998, people got new data, and then people started looking back at that wrong idea.

 

[bcrowell]

BTW I recall reading years ago that in a curved space an amoeba-like creature could travel by successively changing its shape. I've lost the reference. It was in arxiv.org as I recall, maybe about the same time 2004? Do you happen to remember seeing something like that? It appears to violate intuition---the think is moving without rockets, without any "equal and opposite" reaction mass. Anybody remember seeing that?

I found some links!
Something from Science, February 2003:
http://www.sciencemag.org/content/299/5614/1865
Free article from Physical Review D
http://arXiv.org/pdf/gr-qc/0510054v2
also more recent popularization in Sci Am.
http://www.scientificamerican.com/article.cfm?id=surprises-from-general-relativity&page=2
Some animations (scroll down)
http://physics.technion.ac.il/~avron/

Also:

"Swimming in Spacetime: Motion in Space by Cyclic Changes in Body Shape" Jack Wisdom 2003, Science , 299 , 1865. http://groups.csail.mit.edu/mac/users/wisdom/

"The relativistic glider," Eduardo Gueron and Ricardo A. Mosna, Phys.Rev.D75:081501,2007. http://arxiv.org/abs/gr-qc/0612131

cf. MTW, p. 1120, ex. 40.8

 

[bcrowell]

One of the based theorems is Noether's theorem, which says that for every conserved quantity there is a symmetry and for every symmetry there is a conserved quantity. Conservation of energy comes from time symmetry. If you have rules which are time symmetric, energy will be conserved.

The thing about the expansion of the universe is that it isn't time symmetric so energy isn't conserved.

I don't think this really applies to GR. What physicists refer to as Noether's theorem is really a number of different results that apply under different technical conditions. The two theorems that she originally publisher were very restricted, and then they were generalized from there. The relevant symmetry in GR is invariance under smooth coordinate transformations, but for technical reasons Noether's theorem can't be applied to that symmetry. Also, note that there *are* conserved mass-energy scalars that can be defined in spacetimes that are time-varying, as long as they are asymptotically flat.