Shrinking circles

kev

The ratios are the same but the gap behaves differently to the solid rockets.

In the initial frame, the rockets get shorter and the gap stays the same.

In the rocket frame, the rockets stay the same and the gap gets larger.

That is not something you would expect if you take the simplistic attitude that space contracts and solid objects and gaps length contract equally.

It was that misconception, that caused many so called experts to incorrectly assume that the sting joining the two rockets would not snap, in the original Bell's rocket paradox.

Quinzio

Yes, that satisfies me better.
IMO, what expands or contract is the space "under your feet", so lenght changes.
Just like if the floor was made of rubber you can squeeze or stretch. Unity of measure changes, not object.
I know it is not true as well, because moving objects do shrinks.
Cannot think anything else.

Quinzio

Yes, I do.
But let me make a point.
IMO, from the non rotating frame, or from an Earth frame, moving frame space doesn't get denser, but more rarefied, stretched, so objects do measure as shorter.
But the concept is the same.

In the case of two circular rods, one still (my frame), one rotating, the rotating space is rarefied and the rod measure as shorter.
Space would superimpose on itself, but I can see less problems in this case. Space is just what we call our unit of measure.

The whole problem is puzzling, really.

Quinzio

I cut some parts of interest
Does the acceleration of this single particle cause the Earth to physically length contract. ?
Not for us that we live on Earth. We can really ignore what a distant particle is doing and apply our ordinary physical rules.
But from the particles view point things do really change and our Earth is really not as before.
Relativity states that there is not a preferred frame. Each frame is as good as anyone else.
Special relativity doesn't talk about acceleration. It doesn't really matter who accelerates and why.
It matters that in a certain istant, two inertial frames are moving one toward the other.
That's what I think.

That's true. Earth do not lenght contract if you observe the Earth from the Earth, as we all usually do.
But each particle interacts with the Earth as if it was lenght contracted in its direction.
But how it is possible ?
Realtivity talks about moving frames, not objects.
An object doesn't belong to any particular frame.
A particle is a particle, it doesn't belong to frame "A" or to frame "B".
It happends that in a particular frame, that particle is still and you can apply our ordinary Newton laws.
As it happends that in a particular frame, the Earth is still.
But a particle belongs to all the frames you can imagine out there.
I think that relativity is all about "observing" the rest of the world from a particular point of view. Observing and measuring.

A.T.

The gap behaves differently because in that particular setup it changes it's proper length during acceleration. That has nothing to do with length contraction being applied differently to gap vs. rocket. This is just manipulating the proper length to cancel out the length contraction.

You could build extending / telescopic rockets which can change their proper length, and increase it during the acceleration, to cancel out their length contraction too. This is exactly what the extendable circular ruler does. It increases it's own proper length (= what the ruler measures) to keep a constant length in the non-rotating frame (= circumference).

But objects and gaps do length contract equally. The ratios are the same is the key point here. However if one of them changes its proper-length while the other doesn't, they already behave differently in their own frame, without any length contraction. Length contraction in other frames still applies equally to both.

I would agree with you "space contracts" is bad. If you want an alternative to "objects contract" you would rather say rather "space elongates" or "for moving objects space has more capacity ". You get more of the stuff to the same space, if the stuff moves.