Lorentz contraction

Oh, the d's are measured in the moving frame and are initially known in the rest frame.

Say that the string is very weak and brittle.

OK, does this imply space does not contract only rods?

Next, at any instant t in the two rocket and string frame, all three are at rest?

Next, at any instant t in the two rocket and string frame, all three are at rest?

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?

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.

OK, does this imply space does not contract only rods?

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.

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.
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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.

I read this and thought to ask you how you did those perfect graphics. I really mean 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?

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.")

You are depending on the trichotomy of the real numbers

but the spaces are not the same in the frame to frame analysis.

We know y < z. That is Lorentz contraction.

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?

but the spaces are not the same in the frame to frame analysis.

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.