# The Implications of Homogeneity and Isotropy

#### Eugene Shubert

I’m wondering if it’s mathematically permissible, if space is homogeneous and isotropic, for a moving rod to experience a uniform expansion or contraction during the time it’s not in its stationary frame of reference. What’s preventing a moving rod from returning to its point of origin smaller or larger? The expanding or shrinking effect could go like f(v)exp(kt) for as long as the rod maintains a constant velocity v. Conceivably, this might be made to work in 3 spatial dimensions. Every observer could say that every other frame is shrinking uniformly in time and, akin to the twin paradox, all returning twins could end up YOUNGER and smaller.

Can you prove that homogeneity and isotropy alone disallows this possibility?

Eugene Shubert
http://www.everythingimportant.org/relativity/generalized.htm

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#### jcsd

Gold Member
Yes, a rod could return to it's point of origin with it's length dialated, however it would have to be travelling at a different speed than it was when it was originally at it's point of origin as length dialation is dependent on velocity.

In the twin paradox (which is not a paradox as answer shows that it is self consistent) only one twin travels anywhere and the symmetry is broken due to inetria.

#### Eugene Shubert

shrinking uniformly in time

My key words were “shrinking uniformly in time” and “Can you prove that homogeneity and isotropy alone disallows this possibility?”

My question is about geometry and the implications of homogeneity and isotropy.

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#### jcsd

Gold Member
But where on Earth did you get the idea that objects with constant shrink uniformly in time? How do you expect someone to prove a negative, geometry reasonably assumes that objects don't shrink. Your original post is pretty vague.

#### Eugene Shubert

Mathematicians prove negatives all the time

Length contraction is pretty standard stuff in special relativity. My perspective is that of a mathematician, not a physicist. My interest is only in mathematical possibilities, not the way the universe really is. This is the correct forum to discuss motion.

It is often said that the Lorentz transformation can be derived from the homogeneity and isotropy of space alone. I’m looking for a concrete counterexample to this claim. I do have a mathematical curiosity about generalized special relativity.

My question comes from several ideas and facts, one of which is a crazy theory in physics called VSL. I like to make fun of the physicists who have respect for it by saying, “We were giants yesterday and we’ll be Lilliputians tomorrow.”

#### jcsd

Gold Member
Tired light isn't a crazy theory it's one of the best alternatives to conventionial big bang cosmology, however it is still severely deficient at explaining the universe around us.

I think you have your wires crossed, theories on the exapnsion of the universe generally assume that space is roughly homogenous and istropic and that the expansion is therefore uniform. This may be what you're looking for:

http://www.jb.man.ac.uk/~jpl/cosmo/RW.html

http://www.astro.rug.nl/~onderwys/sterIIproject98/wijnholds/mathematics.html [Broken]

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