General Relativity

[sol invictus]

I find it very difficult to accept that the planets do not, in reality, revolve around the center of mass of the solar system, which then revolves around the center of mass of the galaxy, which revolves around some galactic center of mass, etc. etc., with the whole mass of the universe being stationary (on average) in some universal rest frame, which may be demonstrated by the rest frame of the CMB. Does that picture not resonate at all with you?

In GR there are coordinate independent quantities. If you like, those are "reality" according to GR (they're the things that aren't relative, and are therefore important).

One such quantity are the various curvature invariants - and the sun has a much bigger effect on those than the earth or the other planets.

I would be interested to learn how you might respond to my analogy of the Mona Lisa, described above?

I agree that humans prefer certain things. I'm just not sure it's very relevant to physics.

 

[Perpetual Student]

But in reality, the only time the planets actually revolve around the center of mass of the solar system is when they are considered from the rest frame of the center of mass of the solar system.

In any other frame--including the frame of the CMB, the planets are doing something quite different.

Not true.

 

[sol invictus]

Not true.

It is true.

In the rest frame of the CMB, the solar system is hurtling through space at something like 350 km/s. It's orbiting the center of the milky way, and the milky way is moving along with the local group of galaxies.

Since the earth orbits the sun at "only" 30 km/s or so, its motion around the sun is a pretty small perturbation, and its trajectory is some kind of very stretched out helix that circles the center of the milky way, while at the same time drifting along with the local group.

 

[sol invictus]

There's a (literally) bigger issue there. We can only see a finite part of the CMB. As far as we know, our part of the CMB is in motion with respect to the parts we can't see because they're too far away.

Now, you might think that's unlikely - but remember that the part we can see isn't perfectly uniform. It's got fluctuations that mean it doesn't actually have a rest frame. Those fluctuations are small - 1/100,000 on large scales - but it turns out that even in the most vanilla cosmological models they accumulate over distance. So according to the standard cosmological model, our part of the CMB is in very fast relative motion to distant parts of it, and the universe as a whole does not have a CMB rest frame.

Using the visible CMB to define a rest frame isn't much different from using the surface of the earth - it's bigger, but not necessarily better.

 

[Perpetual Student]

It is true.

In the rest frame of the CMB, the solar system is hurtling through space at something like 350 km/s. It's orbiting the center of the milky way, and the milky way is moving along with the local group of galaxies.

Since the earth orbits the sun at "only" 30 km/s or so, its motion around the sun is a pretty small perturbation, and its trajectory is some kind of very stretched out helix that circles the center of the milky way, while at the same time drifting along with the local group.

Isn't that just a quibble? If I have inertial motion relative to something like a carousel, a horse on that carousel will have a helix like motion relative to me, but that does not change the fact that I can continue to regard the horse as revolving around the center of the carousel. I can treat it that way in my inertial frame or any other frame of reference if I choose to do so.
In that same way I can always regard the planets as revolving around the center of mass of the solar system from whatever frame of reference I choose.

 

[Perpetual Student]

You say that we should prefer the original over the copies, but what if all we have are copies? (To use the language analogy: Think of reality as a chair, and the GR descriptions of it as the words for chair in many different languages. No matter what language you use, you're still just dealing with a representation of the chair, not with the actual chair). If the best theory we have doesn't say that one of copies is special, then why should we? Because our intuition tells us that one of them will be more "real" than the others? This would be a bad reason, since science has proved our intuition wrong many times.

In GR there are coordinate independent quantities. If you like, those are "reality" according to GR (they're the things that aren't relative, and are therefore important).

One such quantity are the various curvature invariants - and the sun has a much bigger effect on those than the earth or the other planets.



I agree that humans prefer certain things. I'm just not sure it's very relevant to physics.

There's a (literally) bigger issue there. We can only see a finite part of the CMB. As far as we know, our part of the CMB is in motion with respect to the parts we can't see because they're too far away.

Now, you might think that's unlikely - but remember that the part we can see isn't perfectly uniform. It's got fluctuations that mean it doesn't actually have a rest frame. Those fluctuations are small - 1/100,000 on large scales - but it turns out that even in the most vanilla cosmological models they accumulate over distance. So according to the standard cosmological model, our part of the CMB is in very fast relative motion to distant parts of it, and the universe as a whole does not have a CMB rest frame.

Using the visible CMB to define a rest frame isn't much different from using the surface of the earth - it's bigger, but not necessarily better.

I sense that we have reached the end of the line here. My desire for a universal frame of reference remains but does not appear to have real scientific support. I remain hopeful that some new physics, astronomical observation or cosmological theory will provide some basis for a universal frame of reference just as we have a universal frame of reference for time -- i.e.: the universe is 13.75 or so billion years old and it would be nice to know it's frame of reference is moving at some v relative to our local galaxy cluster (or super cluster or filament or whatever).
It seems to be an odd and interesting fact that this universal asymmetry between time and space exists.

 

[ynot]

I sense that we have reached the end of the line here. My desire for a universal frame of reference remains but does not appear to have real scientific support. I remain hopeful that some new physics, astronomical observation or cosmological theory will provide some basis for a universal frame of reference just as we have a universal frame of reference for time -- i.e.: the universe is 13.75 or so billion years old and it would be nice to know it's frame of reference is moving at some v relative to our local galaxy cluster (or super cluster or filament or whatever).
It seems to be an odd and interesting fact that this universal asymmetry between time and space exists.

I’m pleased that you haven’t been seduced by Matheism.

 

[Perpetual Student]

I’m pleased that you haven’t been seduced by Matheism.

That happened decades ago. For a very long time now, I have regarded the mathematical behavior of the universe with awe and continue to do so.* Again and again, humans have watched, learned, created mathematical equations and discovered that our equations model reality with amazing precision. From time to time, we learn about new behavior and our equations get better and better.
Unfortunately, the problems being discussed here come about because these equations have led us to territory that's beyond our (layman's) intuition (at least, mine). This has created a lot of problems for many people who don't have a lot of training and experience with modern physics -- including me. Nevertheless, we must agree that the fact that GR has been confirmed experimentally trumps all other considerations.
I must admit, however, that as I become more familiar with this stuff, it is beginning to become more plausible. The tensor equation of general relativity is without a doubt the most marvelous thing I have ever come across in science. In low gravity it reduces to Newtonian physics, at high velocities it morphs to accommodate special relativity and it yields the most remarkable information about gravity and spacetime. And -- it seems I've only scratched the surface.

*Recently, I have been studying the Lagrangian and the principle of least action. It amazes that this seemingly abstract (and rather odd) mathematical approach leads to all the laws of classical mechanics (Newton's laws) and has significant utility in relativity. It's just another example of the exactingly mathematical nature of the universe.

 

[Kwalish Kid]

So according to the standard cosmological model, our part of the CMB is in very fast relative motion to distant parts of it, and the universe as a whole does not have a CMB rest frame.

A well-defined foliation of spacetime into spacelike volumes and a single time coordinate that corresponds to the proper time of ideal galaxies (or clusters of galaxies or some slightly larger scale) is assumed by the standard cosmological model.

 

[sol invictus]

A well-defined foliation of spacetime into spacelike volumes and a single time coordinate that corresponds to the proper time of ideal galaxies (or clusters of galaxies or some slightly larger scale) is assumed by the standard cosmological model.

No, not really - today, the standard cosmological model includes a period of inflation as an explanation for that (which indeed used to be an assumption). Several of the predictions of inflation have been confirmed in relatively spectacular fashion by a series of experiments. But inflation makes the predictions I mentioned above.

 

[theprestige]

Isn't that just a quibble?

Is it a quibble, or is it the whole point of the thing?

...I can continue to regard the horse as revolving around the center of the carousel. I can treat it that way in my inertial frame or any other frame of reference if I choose to do so.

Have you actually tried to do this? Have you actually plotted the motion of the horse in the rest frame of the carousel, and then plotted the motion of the horse in the rest frame of the Sun, and then compared the two plots?

ETA: And while we're at it, have you actually plotted the motion of the sun, in a frame where the horse is revolving around the center of the carousel?

 

[H'ethetheth]

Potential technological implications aside, one can ask that question of any knowledge. What does it accomplish to know that the universe is approximately 13.75 years old? If the CMB tells us something about the rest frame of the universe, it contributes to our understanding of reality.

But that's the point, isn't it? In General Relativity, the CMB-rest frame cannot tell us anything that any other frame can't. Preferring this frame literally adds nothing to our understanding of reality.

In the rest frame of the CMB, the solar system is hurtling through space at something like 350 km/s. It's orbiting the center of the milky way, and the milky way is moving along with the local group of galaxies.

Since the earth orbits the sun at "only" 30 km/s or so, its motion around the sun is a pretty small perturbation, and its trajectory is some kind of very stretched out helix that circles the center of the milky way, while at the same time drifting along with the local group.

Isn't that just a quibble? If I have inertial motion relative to something like a carousel, a horse on that carousel will have a helix like motion relative to me, but that does not change the fact that I can continue to regard the horse as revolving around the center of the carousel. I can treat it that way in my inertial frame or any other frame of reference if I choose to do so.
In that same way I can always regard the planets as revolving around the center of mass of the solar system from whatever frame of reference I choose.

Yes you can, but by doing this you're basically describing it in terms of epicycles, which makes it no better (or worse) than describing the universe in terms of, say, Ptolemaic epicycles.