# Length contraction of distant objects/space, etc

1. Aug 29, 2012

### coktail

If I am moving through space at a velocity that is a significant fraction of c, are all objects ahead of me in my path contracted in the direction of my travel for an infinite distance? In other words, are planets and stars from right in front of me to the edge of the known universe contracted as I move towards them?

What about once I'm past them? Do they remained contracted until I slow down?

Does this contraction decrease if an object is not directly in front of me, but off to the side a bit?

As always, thank you.

2. Aug 29, 2012

### Muphrid

The Lorentz transformation is the equivalent of a rotation in ordinary space. It does not propagate at the speed of light; it is "instantaneous."

Compare, for example, this scenario: you are moving in a 2d plane that has no absolute coordinate system (no notion of north, south, east, or west) just what's ahead of you, what's behind, what's left and what's right. When you turn, all objects on this plane rotate as well, instantaneously as you do. If you have an object 5 miles ahead of you and you turn 45 degrees to the right, the object is then ~3.5 miles ahead of you and ~3.5 miles to your left.

3. Aug 29, 2012

### HallsofIvy

Staff Emeritus
Yes.

Yes.

It contracts along the axis parallel to your velocity vector.

4. Aug 29, 2012

### coktail

Thanks!

Does the entire universe (including space itself) in my path contract, or just objects?

Can someone please elaborate on "it contracts along the axis parallel to your velocity vector" for me? What I take this to mean is that an item at an angle to me would contract at an angle, but that may be totally wrong.

5. Aug 29, 2012

### Muphrid

If you're pointing in the x-direction, other objects will contract in the x-direction regardless of where they are.

6. Aug 30, 2012

### HallsofIvy

Staff Emeritus
Yes, that is the crucial difference between Einstein's theory and Lorentz's theory: the distance between two objects contracts as well as the objects.

I'm not sure what you mean by "contract at an angle". If you are at (0,0) in some coordinate system moving in the positive y direction, an object that, to a stationary observor, is a rectangle with vertices at (1, 1), (2, 1), (1, 4), and (2, 4), it will appear to you to occupy $(1, 1- \beta), (2, 1- \beta), (1, 4- \beta), (2, 4- \beta)$.