Bell's Spaceship Paradox & Length Contraction

[David Lewis]

No. The shape of the molecules plays no role, since, as pointed out in post #55, we are talking about SR, not quantum mechanics.

Then I don't understand how an object can get shorter.

 

[pervect]

Then I don't understand how an object can get shorter. View attachment 243696

If molecules had a shape, they'd get shorter. In the world of quantum mechanics, though, it's not clear if molecules actually have shapes or not, at least not to me. I would say that molecules have wavefunctions which occupy a non-physical "configuration space", with 3 dimensions for every particle in the molecule (presumably these particles are atoms, but you could break the atoms down into more particles). That's not really a "shape" as far as I am concerned.

Most treatments of introductory QM treat single particle systems, where the wavfunction does occupy normal space. It's when one considers multi-particle systems that one gets into the issue of the wavefunctions not occupying physical space.

But it's much simpler to keep the arcane aspects of QM out of the discussion, which is what the original point was.

 

[PeterDonis]

Then I don't understand how an object can get shorter.

Because that's how the geometry of spacetime works. The SR treatment of the Bell spaceship paradox does not make any hypothesis about the internal structure of the object. It just explores the consequences of the stated conditions, given the geometry of Minkowski spacetime. This geometry puts constraints on any model of an object's internal structure; but it doesn't tell you anything specific about that internal structure.

 

[PeterDonis]

I don't understand how an object can get shorter.

As far as an "object" describable by classical physics is concerned, Lorentz showed in the 1890s (IIRC) that any object made of electric charges bound together by electromagnetic fields would exhibit length contraction in a frame in which it was moving.

 

[A.T.]

Then I don't understand how an object can get shorter.

The string in Bell's scenario doesn't get shorter, so the contracted binding EM fields have to span the same distances. Hence the tension. To avoid the complications of QM don't go down to the atomic level, but instead consider the contracting links of a chain that is forced to keep a constant length.

 

[pervect]

The string in Bell's scenario doesn't get shorter, so the contracted binding EM fields have to span the same distances. Hence the tension. To avoid the complications of QM don't go down to the atomic level, but instead consider the contracting links of a chain that is forced to keep a constant length.

I agree. If one has a rod or string which one divide into classical pieces of matter, then, when the rod undergoes length contraction, so does each of the pieces of the rod.

It doesn't matter to the argument how small each of the pieces is.

It does matter to the argument that we consider the pieces to behave classically. It's unclear to me how one rigorously deals with the quantum aspects, but this argument can go in another forum such as the quantum forum. I would guess that there is some sort of classical limit one can take, but I've never seen a serious formal discussion of the issue. This doesn't mean that one may not exist, as I'm not too familiar with the appropriate literature, unfortunately.

 

[PeterDonis]

It's unclear to me how one rigorously deals with the quantum aspects, but this argument can go in another forum such as the quantum forum.

Exactly.