# Length contraction and the expansion of the universe.

1. Sep 20, 2011

### mrspeedybob

1. If I were traveling through the cosmos at high velocity relative to the CMB I should observe the distances between stars and galaxies to be length contracted in the direction of my motion, but not in directions perpendicular to my travel.

2. The same laws of physics apply in all non-accelerating frames of reference

3. The universe, on large scales, in homogeneous (cosmological principal)

How can all 3 of these statements be true? Any 2 are compatible, but I can't see how all 3 can be true at the same time?

Secondly, I understand there is a limit to the size of our observable universe caused by the expansion of space. Objects further away are causally disconnected from us because they are receding from us at superluminal velocity. If I am traveling at high relativistic speed would I measure a different Hubble constant in my direction of travel then I would perpendicular to my direction of travel, essentially flattening my observable universe into a squished sphere? Or, would my universe still be spherical and regions which would otherwise be causally disconnected become connected due to my velocity?

2. Sep 24, 2011

### Bill_K

The laws of physics are the same in all inertial frames, but the objects you see may appear different. The big bang cosmology we live in defines a unique rest frame at each point, namely the frame in which the cosmic microwave background is the same in all directions. An observer moving with respect to this frame will see the background redshifted in one direction and blueshifted in the other. When we say the universe is homogeneous, we mean it is homogeneous on a slice of constant time in this rest frame. Since it is expanding, it is obviously not homogeneous in time. Nor is it homogeneous in any other rest frame.

3. Sep 24, 2011

### Staff: Mentor

The causal structure of spacetime (which events are causally connected or disconnected to which other events) is invariant; it does not depend on your state of motion. The universe would *appear* to you to be squashed if you were traveling at high relativistic speed relative to the CMBR, but that would not change which parts of the universe could send signals to you and which could not. (The signals might appear redshifted or blueshifted relative to what they would look like if you were at rest relative to the CMBR.)