# Lorentz contraction

by matheinste
Tags: contraction, lorentz
P: 687
 Quote by kev Nope, to one of the rocket observers the gap between the rockets is getting larger and the other rocket is getting further away, so the two rockets do not regard themselves as being at rest with respect to each other.
OK, so the rockets see themselves as getting further apart.

Yet, the launch frame does not see it this way. It sees the distance as constant.

How is this so?
P: 3,967
 Quote by cfrogue OK, so the rockets see themselves as getting further apart. Yet, the launch frame does not see it this way. It sees the distance as constant. How is this so?
The launch frame is using rulers that are not length contracted, while the rocket observers are measuring the gap using rulers that are gettting progressively shorter so to them the gap appears to be expanding.
P: 687
 Quote by kev The launch frame is using rulers that are not length contracted, while the rocket observers are measuring the gap using rulers that are gettting progressively shorter so to them the gap appears to be expanding.
Is there evidence that length actually contracts within a frame, I mean within the internals of a frame?

Isn't length contraction a phenomena of the "at rest" frame when viewing the moving frame?
P: 3,967
 Quote by cfrogue OK, does this imply space does not contract only rods?
Let's try a slightly modified experiment, to try and shed light on your question.

We have four rockets all with identical solid fuel propellants that burn at a fixed rate for a fixed length of time. Rocket A and B are joined by a tough cable of length d and rockets C and D are separated by a distance of d but not physically connected. All 4 rockets launch simultaneously in the launch frame. When they have exhausted their fuel rockets C and D are still a distance d apart, but rockets A and B are less than d apart. Rockets A and B have been physically pulled closer together by the length contraction of the cable.

If a fifth rocket and observer was introduced and this time only the fifth observer accelerated, then distances between the unconnected and connected rocket pairs would appear to length contract equally, but the apparent length contraction of the gap between the unconnected rockets is not physical. The changes in the clock rates and ruler lengths of the fifth observer makes the gap appear to contract.
P: 3,967
 Quote by cfrogue Is there evidence that length actually contracts within a frame, I mean within the internals of a frame? Isn't length contraction a phenomena of the "at rest" frame when viewing the moving frame?
You can not actually observe length contraction if you are in the frame moving with the object. In the case of Bell's rocket observers they do not see the string as shrinking, but rather see it being stretched across a larger gap.
P: 687
 Quote by kev You can not actually observe length contraction if you are in the frame moving with the object. In the case of Bell's rocket observers they do not see the string as shrinking, but rather see it being stretched across a larger gap.
But why?

The rest frame does not see the gap getting wider.
P: 687
 Quote by kev Let's try a slightly modified experiment, to try and shed light on your question. We have four rockets all with identical solid fuel propellants that burn at a fixed rate for a fixed length of time. Rocket A and B are joined by a tough cable of length d and rockets C and D are separated by a distance of d but not physically connected. All 4 rockets launch simultaneously in the launch frame. When they have exhausted their fuel rockets C and D are still a distance d apart, but rockets A and B are less than d apart. Rockets A and B have been physically pulled closer together by the length contraction of the cable. If a fifth rocket and observer was introduced and this time only the fifth observer accelerated, then distances between the unconnected and connected rocket pairs would appear to length contract equally, but the apparent length contraction of the gap between the unconnected rockets is not physical, but brought about by changes in the clock rates and ruler lengths of the fifth observer who has undergone acceleration. .

This thought experiment changes the game.

It should be solvable in the context we were in.

If the string contracts from the rest observer and the distance does not change, does this imply space does not contract but rods do?
PF Gold
P: 1,847
 Quote by cfrogue If the string contracts from the rest observer and the distance does not change, does this imply space does not contract but rods do?
With the rapid pace of this thread, I think my post #38 may have been overlooked. I think it might be relevant to the difficulty you are having.
P: 687
 Quote by DrGreg With the rapid pace of this thread, I think my post #38 may have been overlooked. I think it might be relevant to the difficulty you are having.
I read this and thought to ask you how you did those perfect graphics. I really mean this.

Assuming your post though, how do you explain this?

We have the rest frame not seeing any distance differentials. We have the accelerating frames getting further apart in their context.

How do you reconcile this?
PF Gold
P: 1,847
 Quote by cfrogue I read this and thought to ask you how you did those perfect graphics. I really mean this.
I used Microsoft Powerpoint to draw the pictures. The latest version has an option to save as a PNG file.
 Quote by cfrogue We have the rest frame not seeing any distance differentials. We have the accelerating frames getting further apart in their context. How do you reconcile this?
Using the notation of my diagram. "Alice" is the launch frame. "Bob" is a frame in which one of the rockets is momentarily at rest (some time later). P & Q are the two rockets.

We know y < z. That is Lorentz contraction.

We also know x = y. ("We have the rest frame not seeing any distance differentials. ")

Therefore z > x. ("We have the accelerating frames getting further apart in their context.")
P: 687
 Quote by DrGreg I used Microsoft Powerpoint to draw the pictures. The latest version has an option to save as a PNG file. Using the notation of my diagram. "Alice" is the launch frame. "Bob" is a frame in which one of the rockets is momentarily at rest (some time later). P & Q are the two rockets. We know y < z. That is Lorentz contraction. We also know x = y. ("We have the rest frame not seeing any distance differentials. ") Therefore z > x. ("We have the accelerating frames getting further apart in their context.")

In order to compare these like this, you must have a uniform space.

You are depending on the trichotomy of the real numbers but the spaces are not the same in the frame to frame analysis.

Do you compare these another way I am not seeing?
P: 4,058
 Quote by cfrogue You are depending on the trichotomy of the real numbers
x,y,z are just real numbers here.
 Quote by cfrogue but the spaces are not the same in the frame to frame analysis.
The frame to frame part is handled by:
 We know y < z. That is Lorentz contraction.
P: 4,058
 Quote by cfrogue We have the rest frame not seeing any distance differentials. We have the accelerating frames getting further apart in their context. How do you reconcile this?
Actually you answer it yourself:
 Quote by cfrogue but the spaces are not the same in the frame to frame analysis.
PF Gold
P: 1,847
 Quote by cfrogue In order to compare these like this, you must have a uniform space. You are depending on the trichotomy of the real numbers but the spaces are not the same in the frame to frame analysis.
I've no idea what any of that means.
P: 687
 Quote by DrGreg I've no idea what any of that means.
OK, sorry, when you have some time, I am not seeing your explanation.

1) One solution suggests there exists length contraction for the string.
2) One solution suggests the ships get further apart.
3) The rest frame concludes the distance remains constant between the ships and the v and any time t is the same.

Actually, if you look from the rest frame, a reaction may be that as v increases, length contraction for the string should increase.

Yet, the SR acceleration equations do not predict this and predict a constant distance between the ships.

How is this worked out?
P: 8,470
 Quote by cfrogue Actually, if you look from the rest frame, a reaction may be that as v increases, length contraction for the string should increase.
That would be wrong, you can only use the length contraction equation for an object with a constant length in its rest frame, but the string's length in its rest frame is changing because its ends are attached to the ships.
 Quote by cfrogue Yet, the SR acceleration equations do not predict this and predict a constant distance between the ships.
Well, only in the launch frame, not in other frames.
P: 687
 Quote by JesseM That would be wrong, you can only use the length contraction equation for an object with a constant length in its rest frame, but the string's length in its rest frame is changing because its ends are attached to the ships..
Yes, but the ships are changing also. This would mean the space between the ships does not contract but the string does. Is this correct?

So, how would the launch frame conclude the string contracts when the launch frame concludes the distance between the ships does not change?

 Quote by JesseM Well, only in the launch frame, not in other frames.
Understood