Relative Endings?

[ydoaPs]

Energy is conserved in a reference frame, but the amount of energy is not necessarily the same for each frame. One can see this with a simple thought experiment. There are three balls(one red, one blue, and one yellow). The red and blue balls are at rest with respect to each other, but moving with respect to the yellow ball. From a reference frame in which the yellow ball is at rest, the red ball has the energy from mass, but since the red ball is moving, it also has kinetic energy. Now, let's move our reference frame to one in which the blue ball is at rest. The red ball still has the same energy due to mass, but, since it is at rest relative to the blue ball, has no kinetic energy. The red ball has more energy in the reference frame of the yellow ball than it does in the reference frame of the blue ball. Thus energy is dependent on the reference frame and is not conserved from frame to frame. Mass, however is the same in every frame of reference. If we consider the three balls as a system and use the same reference frames, we get different values for the total energy of the system. In the reference frame in which the yellow ball is at rest, there is a certain amount of energy in the system from the mass of all three balls and the kinetic energy of the red ball and the blue ball. In our other reference frame, we have the energy from the mass of all three balls and the kinetic energy of just the yellow ball. If these three balls were are that the universe consisted of, the universe would have different amounts of energy depending on which reference frame you are in.

 

I've read in pop-sci books that there is a delicate balance of energy which decides the fate of the universe. If the total energy of the universe is above a certain value, gravity beats the expansion in the long run and the universe contracts to a big crunch. If the total energy of the universe is less than this critical value, then the expansion beats gravity and the universe expands forever.

 

Is it possible that in one reference frame the total energy of the universe is above the critical value, but in another reference frame, the total energy of the universe is below this value? In effect, I'm asking if there could exist two different reference frames in which each has a different ending for the same universe?

[Mr Skeptic]

That does seem troubling. I'll add another, what is seen as a neutron star in one frame might be seen as having enough matter density to be a black hole in a different frame.

 

I think this is evidence that while all frames of reference are created equal, some may be more equal than others And yes, I know this violates the fundamental principle of relativity.

 

There is one specific frame of reference that always seems to be more important: the center of mass reference frame of a system. Which I think also minimizes the energy of that system. Perhaps the center of mass frame of the universe is somehow special?

[timo]

There is a standard frame in cosmology. I would assume that statements about critical energies are to be understood to be meant in this frame. It's not too uncommon for physical values to be meant in a certain frame (e.g. the lifetime of the neutron).

[Martin]

 

I've read in pop-sci books that there is a delicate balance of energy which decides the fate of the universe. If the total energy of the universe is above a certain value, gravity beats the expansion in the long run and the universe contracts to a big crunch. If the total energy of the universe is less than this critical value, then the expansion beats gravity and the universe expands forever.

Is it possible that in one reference frame the total energy of the universe is above the critical value, but in another reference frame, the total energy of the universe is below this value? In effect, I'm asking if there could exist two different reference frames in which each has a different ending for the same universe?

 

Atheist already answered this but I want to confirm what he said.

 

That business about the critical energy density in cosmology refers to the standard frame of something at rest with respect to the CMB (no doppler dipole) or equivalently at rest with respect to the "Hubble flow" another name for the expansion of the universe.

Solar system is going about 370 km per second in the direction of constellation Leo, with respect to cosmological rest frame.

So this has to be factored out of certain observations to compensate.

 

I have to go, just wanted to say that one thing, be back later.

 

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this may not be an adequate response yet

 

It may sound too technical, but I think that conceptually it is basically simple.

If you look at Wikipedia

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

you see three temperature maps of CMB made by the COBE satellite in the 1990s.

The top one looks like the oriental yang-yin symbol---it is raw uncorrected.

 

So all it shows is the dipole, caused by the solarsystem's own motion relative to the universe.

That is so strong that it drowns out all the other fine detail.

So they have to remove the dipole effect in order to reveal the detailed temperature fluctuations.

When you look at the raw uncorrected map you see the red half is the doppler hot spot centered around the constellation Leo which marks the direction we are going

the microwave is hotter, shorterwavelength, higherfrequency in that direction because we are going in that direction

 

the blue half is the doppler cold spot, opposite from Leo, which we are going away from.

 

the constellation Leo is meaningless, just a way to designate the direction---without having to say coordinates like latitude and longitude

 

the middle temperature map is what you get when you SUBTRACT OUT the doppler effect on temperature due to the solarsystem's own motion

 

in the caption, in Wiki, they call the solarsytem's own motion relative to the universe (i.e. to cosmic rest frame) by the techncial term "solarsystem peculiar motion". That just means its own personal motion, there is nothing peculiar or odd about it.

 

It is just the straight line resultant of all the various motions (the galaxy, our circulation within the galaxy...) added up

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George Smoot, who got the Nobel last year, published a paper in mid 1990s where he gave the exact coordinates and speed of the solarsystem motion. The speed was about 370 km/sec and the direction I already told you (but he and his co-authors gave it in coordinates and with errorbars.

 

All cosmologists know that the universe has a rest frame and they use it constantly-----e.g. in correcting that map, to go from the top one to the middle one. the funny thing is that they don't TALK about it very much.

 

You learn about it in a beginning cosmology course, or in a freshman general astronomy course. But I can find hardly anything about it in Wikipedia.

 

I think it is because of cognitive dissonance. In pop sci the public is told there is no absolute reference frame----this is the message of 1905 SPECIAL relativity. And then when you go to 1915 GENERAL relativity you get solutions to the Einstein equation like the Friedmann model which is basically what they use and this DOES have an absolute reference frame. So then the popularizers are stuck. They can't be forthright with the public because it would be too complicated to explain how there really is no contradictions. So they keep quiet about it.

 

Same thing about recession speeds being faster than c. The 1905 theory says speed cannot be faster than c. But solving the 1915 theory we get the usual Friedmann model and its variants, and there the recession speeds MUST be faster than c for much of the universe. And there is no contradiction but it would take too much time to explain. So they don't talk about it in most popularization.

 

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My understanding is that Hubble himself already in the 1930s knew about the universe rest frame and the solarsytem peculiar motion (relative to it). He just didnt know it as accurately as Smoot et al got it from the CMB.

 

Hubble could tell it just by looking at redshifts. Galaxies on the Leo half of the sky were not receding as fast (statistically) as they were on the other half.

The redshift distance relation that Hubble discovered predicted that in the Leo direction there should be more redshift than he actually observed and he figured out that this was because the solarsystem was moving relative to the whole expansion process

 

so that we were, in a sense, trying to "catch up" with those galaxies and it caused a doppler discount of their redshift----by what we now know was 370 km/second.

 

and in the other direction our motion was adding to the recession speed and increasing the observed redshift, by the same amount.

 

Even though it is only a small difference, I am told that Hubble figured out it was there and estimated it.

 

I've been talking informally and oversimplifying, so may be adding to the confusion.

 

the crux, I think, is that 1915 Gen Rel is consistent with 1905 special relativity and the general theory itself has no preferred frame. BUT THERE IS A BUT.

But our universe is just one particular solution of the GR equations. It has its own distinctive distribution of matter and radiation and its own expansion history. A particular solution, like our universe, does not have to exhibit the same degree of symmetry as the general theory. It CAN have a distinguished frame of reference---without this being a contradiction.

 

Something like that.

 

Or another way to reconcile the apparent contradiction is to talk about global asymmetry versus local symmetry. If you just look at local coordinate patches there is all the symmetry you could ask for and 1905 special rel is obeyed. But you can't extend that local frame of reference to cover the whole universe. As you go out, the local projections gets less and less accurate---and finally useless.

There is a larger geometry which is only perceived over very large distances, and this geometry does NOT have the simple symmetry one might expect from just looking at a local patch. So the 1905 rules don't apply at very large scale.

[ydoaPs]

So, you're saying there is a preferred reference frame?

[Klaynos]

So, you're saying there is a preferred reference frame?

 

Nearly always, whether to make comparisons easier, or to make the maths easier to start with...

[timo]

So, you're saying there is a preferred reference frame?

Preferred by the people doing calculations, not by nature.

[ydoaPs]

Preferred by the people doing calculations, not by nature.

I'm guessing that since the motion would be different for each frame, the critical energy level would also be different. So, would the different values of energy in different reference frames necessarily be exactly offset by the difference in expansion in the different frames, or is there a possibility that two reference frames could have two endings for the same universe?

[Martin]

There is a standard frame in cosmology. I would assume that statements about critical energies are to be understood to be meant in this frame...

 

Yourdad, Atheist already answered this.

when they talk about a critical energy density, they mean the energy density measured in the standard frame.

 

so you can't use a different frame and expect the energy density you measure to have implications about the end of the universe, or the expansion history or all that.

 

the equations, like the Friedmann equations of cosmology, are derived for that standard frame

 

So in classic cosmology the answer to your question (can there be two endings for the same universe) is no.

[ydoaPs]

Martin, why wouldn't other frames have similar concepts? Can you not derive those equations for other frames and get similar concepts?

[swansont]

Martin, why wouldn't other frames have similar concepts? Can you not derive those equations for other frames and get similar concepts?

 

Similar concepts, sure. But the value will be different; one would expect it to transform exactly like the terms that comprise it.