# Length Expansion Opposite Direction: SR Simultaneity Explained

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• Nathan123
Yes, it is true that the distance the light covers in both directions is the same in the ship's rest frame, but not in the frame in which the ship is moving. This is because the light has to catch up with one end of the ship (back to front), while it is closing faster with the other end (front to back). This is not something particular to relativity; it is just as true in Newtonian mechanics. (The things that are particular to relativity are the length contraction and the speed of light being the same in all frames.)

#### Nathan123

SR says that there is length contraction in the direction of movement. This works nicely for light going from the back of the ship to the front. From my perspective, the ship is moving away but that is offset by the ship's contraction.

But things get tricky for light going from the front of the ship to the back. From my perspective, it will get to the back of the ship quicker than in its perspective that it is not moving. So SR says that simultaneity is relative.

I don't get it. It seems much more consistent to say that there is length expansion in the
opposite direction. Why isn't this the obvious choice?

Because the speed of light is the same in all frames of reference. The spaceship is contracted by the same factor in your fame of reference regardless of whether it is moving to the left or to the right. Therefore the distance the light covers is the same if the spaceship is traveling in either direction and so is its speed. Therefore, in your frame, light will take the same amount of time regardless of whether it is moving front to back or back to front.

kuruman said:
Because the speed of light is the same in all frames of reference. The spaceship is contracted by the same factor in your fame of reference regardless of whether it is moving to the left or to the right. Therefore the distance the light covers is the same if the spaceship is traveling in either direction and so is its speed. Therefore, in your frame, light will take the same amount of time regardless of whether it is moving front to back or back to front.
I am not sure what you are saying. Length contraction is in the direction of movement. I think it is consistent to say that the ship expands in the opposite direction. This way, when the light goes from the front of the ship to the back, it does not hit the back from my perspective in a shorter time, because the ship expands in that direction.

Nathan123 said:
I am not sure what you are saying. Length contraction is in the direction of movement.

The contraction/dilation effects depend on the *square* of velocity. If the body is moving along z-axis, you could say that its length along the z-axis will be reduced (a stationary observer would measure it as such), but there is no direction in there, its not like the tail of the spaceship stays still whilst the nose is moving towards the tail to ensure shrinkage.

Nathan123 said:
Length contraction is in the direction of movement. I think it is consistent to say that the ship expands in the opposite direction.

No, it isn't. You need to look at the math instead of waving your hands. As @Cryo has pointed out, the math clearly says that length contraction depends on the squared magnitude of the velocity, which means it is the same in both directions.

kuruman said:
The spaceship is contracted by the same factor in your fame of reference regardless of whether it is moving to the left or to the right. Therefore the distance the light covers is the same if the spaceship is traveling in either direction

Careful. The distance the light covers in both directions (back to front of ship, front to back of ship) is the same in the ship's rest frame, but not in the frame in which the ship is moving. This is not because of any anisotropy in the speed of light or length contraction of the ship; it's simply because the light has to catch up with one end of the ship (back to front), while it is closing faster with the other end (front to back). This is not something particular to relativity; it is just as true in Newtonian mechanics. (The things that are particular to relativity are the length contraction and the speed of light being the same in all frames.)

PeterDonis said:
Careful. The distance the light covers in both directions (back to front of ship, front to back of ship) is the same in the ship's rest frame, but not in the frame in which the ship is moving. This is not because of any anisotropy in the speed of light or length contraction of the ship; it's simply because the light has to catch up with one end of the ship (back to front), while it is closing faster with the other end (front to back). This is not something particular to relativity; it is just as true in Newtonian mechanics. (The things that are particular to relativity are the length contraction and the speed of light being the same in all frames.)
Yes of course.

PeterDonis said:
Careful. The distance the light covers in both directions (back to front of ship, front to back of ship) is the same in the ship's rest frame, but not in the frame in which the ship is moving. This is not because of any anisotropy in the speed of light or length contraction of the ship; it's simply because the light has to catch up with one end of the ship (back to front), while it is closing faster with the other end (front to back). This is not something particular to relativity; it is just as true in Newtonian mechanics. (The things that are particular to relativity are the length contraction and the speed of light being the same in all frames.)
Which is why I am trying to propose the concept of length expansion. I see what others are saying that length contraction is not for the front as opposed to the back, but why not propose as such that the front gets condensed to the back, and the back expands out?

Nathan123 said:
Which is why I am trying to propose the concept of length expansion.

And, as has already been pointed out, this concept is not correct. To get the correct answer for the distance light travels from the front to the back of the ship, in the frame in which the ship is moving, you have to take into account that the ship is length contracted. Not length expanded.

Nathan123 said:
why not propose as such that the front gets condensed to the back, and the back expands out?

Because that doesn't give the correct answer. (As you state it, it's not even clear that it makes sense.) Stop waving your hands and do the math.