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Re: [Phys-l] Does COBE data contradict relativty?



On 05/01/2007 03:51 PM, Folkerts, Timothy J wrote:
Data of the cosmic microwave background radiation from COBE (Cosmic
Background Explorer) suggests that we are moving in the general
direction of the constellation Leo. In some sense, the background
radiation defines a preferred reference frame - the rest frame of the
universe if you will.
Doesn't this contradict the principle of relativity (at least the
colloquial expression) - that there is no preferred reference frame?
That there is no way to judge absolute movement?

The short answer is no, there isn't any contradiction.

The longer answer has three parts:

a) In principle, the observations do not contradict
the relativistic symmetry ... /provided/ you state the
symmetry correctly, as we shall see.

By way of analogy: The fundamental laws of physics
are all invariant with respect to rotation ... but
that does not mean that my cat is rotationally
symmetric. What the law says is that if you rotate
/together/ everything that matters, you get back a
physically-equivalent situation. That is, if I
rotate the cat /together/ with the chair he's
sleeping on, the cat-to-chair relationship is
unchanged. Mathematically this can be expressed
in terms of a dot product between the cat orientation
vector and the chair orientation vector ... and the
truly fundamental thing is the rotational invariance
of the dot product.

This is an example of a /broken symmetry/. The cat
is governed by the laws of nature, but the cat is
less symmetric than the laws themselves. It is
common to find equations where any solution to the
equation is less symmetric than the equation itself.
Examples include a particle in a symmetric double-well
potential. A fair coin toss is a sub-example of this.
The potential is the same for heads and tails, but any
particular coin on the table will be heads /or/ tails,
not a symmetric superposition of the two.

What, you may ask, does the cat analogy have to do with
relativity? Well, you asked about velocity, and a
change in velocity (i.e. a boost) is associated with
a /rotation/ in the xt plane in spacetime. So there
is quite a profound analogy to rotating the cat in
the xy plane.
http://www.av8n.com/physics/spacetime-trig.pdf

b) In practice, the microwave background radiation
is not a problem. You can't rotate it arbitrarily
as easily as you can rotate the cat's chair, but
you can screen it out. Tinfoil suffices.

If you're doing a large-scale experiment, you might
need a lot of tinfoil, but that's an engineering
detail, not an issue of principle.

c) To address a question that wasn't quite asked: What
would happen if we had a supposed symmetry that was
badly broken in a way that we couldn't control and
couldn't screen out? Well, that would be a problem.
We would have to do without that symmetry in practice.