CMB and Absolute Rest: Resolving Contradiction

[zadignose]

I'm having trouble resolving the contradiction between theories of the Cosmic Microwave Background, and Special Relativity.

Einstein denied the existence of any absolute standard of rest. As einstein-online.info paraphrases: "In the real world, there exists no such state of absolute rest. That's the content of the so-called principle of relativity, which is one of the basic postulates of the special theory of relativity."

However, there now seems to be the concept of "at rest" with regard to the CMB. This shows that there does exist an experiment that different observers can perform which will give variable results based on their inertial motion. Why doesn't this undermine relativity, which is itself the foundation of most of our cosmological models?

 

[Calimero]

It doesn't undermine relativity in any way. Being in rest with regard to the CMB, simply means being at rest with regard to the bulk of ancient matter.

 

[Chronos]

Relativity assumes there are no PREFERRED reference frames - i.e., the laws of physics are the same regardless of your speed and direction [reference frame]. In the CMB rest frame you measure no velocity with respect to the CMB photons. It is a purely arbitrary, but, convenient way to define a 'rest frame' for the universe. But, the laws of physics are no different from those in any other arbitrarily chosen reference frame. So, the short answer is the CMB rest frame is not 'at rest' in any absolute sense, thus relativity is not threatened.

 

[Zeno Marx]

I'm having trouble resolving the contradiction between theories of the Cosmic Microwave Background, and Special Relativity.

Einstein denied the existence of any absolute standard of rest. As einstein-online.info paraphrases: "In the real world, there exists no such state of absolute rest. That's the content of the so-called principle of relativity, which is one of the basic postulates of the special theory of relativity."

However, there now seems to be the concept of "at rest" with regard to the CMB. This shows that there does exist an experiment that different observers can perform which will give variable results based on their inertial motion. Why doesn't this undermine relativity, which is itself the foundation of most of our cosmological models?

Yes Lee Smolin and the folks at the Perimiter Institute seem to be proposing this is indeed the case

 

[Curtdboy]

The reality of the cosmic reference frame

The concept of an at-rest reference frame comes from a detailed analysis of Einstein's Twins paradox. It is true that whatever speed of motion that twin #1 has (as long as he stays inertial), twin #2 will return from his round-trip younger than twin #1, it is still possible to determine what the at-rest frame is by using atomic clocks. The equation for the time dilation rate is not linear (δ=(1/√(1-v2/c2))-1); the dilation rate is proportional to the velocity squared. One can take 3 synchronized atomic clocks in the inertial frame of twin #1, then slowly displace one of them to a distant location, keeping synchronization. When it arrives, speed the clock up to keep a constant distance from twin #1. Then twin #2 takes one of the clocks and travels rapidly to the distant clock, and checks the synchronization of the clocks, leaving the third with twin #1 for reference. If twin #1 is moving, say 400 km/s relative to the cosmic rest frame (see Wiltshire, 2012 on astro-ph. [Using Sne Ia, he measured expansion velocity vs. distance in spherical annuli out to ~100 Mpc, finding that our motion relative to the true Hubble flow was significant, and not entirely in agreement with the "boost" of the cosmic dipole of the CMB.]) and twin #2 is traveling at 400 km/s in the opposite direction of #1's motion, then #2 will be in the cosmic rest-frame while traveling, and will arrive at the distant location with a clock that reads later than the clock that was slowly displaced to that location. Thus, twin #2 would be able to tell that he was traveling at a rate closer to the cosmic rest frame than #1. The reason for this is that the displaced clock was moving at 400 km/s, and hence has a time dilation relative to #2 while he was moving. However, on the return trip, twin #2 must go faster than twin #1 in order to catch up. If he went 800 km/s relative to the cosmic rest frame (400 km/s relative to twin #1) to catch up, thus taking the same time to return as the first leg of the trip, then the time dilation rate during the return trip would be four times that of twin #1. Thus the average time dilation rate for the total trip of #2 would be twice that of #1.

This explains how, without these atomic clocks, and considering the non-linearity of the dilation rate with velocity, the cosmic rest frame cannot be discovered by the twins..

However, this does not contradict Einstein's (1905) point that physics will be measured by an observer to be identical regardless of his state of motion as long as he is inertial. But by using sophisticated instrumentation, one could tell that there is a cosmic standard of rest -- an at-rest inertial frame, and one could determine what it is by experimenting with the above thought experiment. The at-rest inertial frame is the one in which the time-rate of clocks is maximal.

 

[abitslow]

?
Consider an asteroid moving at 30,000 mph relative to Earth's center. Now which would you rather have happen: collide with the asteroid when you are at rest relative to Earth OR collide with the asteroid when your motion, relative to the asteroid is 0.01 mph? You SEEM to be saying that your understanding of the laws of Physics requires the PHYSICAL results to be the same (otherwise, this would be an experiment to differentiate the two frames). Of course, the flaw here is changing the physics (the motions) rather than just changing the rest frame (accounting).
The CMB is light from the (meaning 'emitted in the') co-moving flow and is expected on average to be "stationary" relative to us...meaning that our velocity (the local cluster's) is, on average, very low relative to the CMB.
Given a bunch of assumptions about the model, what the CMB gives us is a universal standard frame of reference. Its no more absolute than the standard of distance is a mile...or should I have said kilometer? Anyway, it would allow us and an observer a long way from us to agree on assigning a value for the velocities of various astronomical objects we both observe...that's assuming that our averaging techniques are sophisticated enough. (It also assumes that the isotropy and homogeneity of the Universe is fine enough - as I said assumptions about the model).
Let me give you an example (off the top of my head, meaning that its probably got holes in it that I'm too stupid to recognize, but still bear with me). Let's say there IS a absolute reference frame. So, anything at rest wrt this frame will have an absolute (linear) momentum of exactly zero. Will this affect the splat you make with that asteroid? No. As long as its the relative momentum that has to be accounted for, it won't matter. But what if there were some Physical Law that was different for acceleration and deceleration? That is, accelerating (relative to the absolute frame) resulted in (slightly) different results than decelerating (towards absolute motionlessness). Well, suddenly, the Laws of Physics demand an absolute frame. Problem with this idea is that we have seen no indication that its the way our Universe is put together. Of course, we could follow-up and ask:"what if acceleration worked, but changes in acceleration were where this effect showed up?". Or changes of the changes, or... So, you can ask a meaningful question as follows: To what degree of precision have we confirmed that velocity, accleration, and higher time derivatives do not have any inhomogeneity? And now you're talking! (But I have no answer for you, perhaps others here know...)..
This is essentially a Michaelson-Morley type experiment, and they've been done - lots of them. What I DO know is any effect is between zero and a very small number, what I don't know is how small that number is...currently. Our best guess is that its exactly zero, but in the real world, EVERY measured quantity must have a range of values, as well as uncertainty, associated with it. (even things like the inverse square laws, 1/d², how sure are we that the exponent is 2 and not 2.0021? -- guess what? There is research on that!)