# Can two bodies exist in the same space-time position?

## Main Question or Discussion Point

Can two objects overlap in space-time? Why or Why not? If so, what circumstances must exist? If not, by what mechanism are two objects deemed separate?

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I would think at a particular instance one could have two bodies in the same position in space time, but it would simply be an intersection of their world lines? However I would say that they cannot have the exact same coordinates, on the same coordinate system, for it seems then they would have to be inside one another. However, superimposing one of the coordinate systems on the other I would think that you could have the same coordinates, in space and in time. I have limited knowledge in this subject so dont quote it please :P

bcrowell
Staff Emeritus
Gold Member
Can two objects overlap in space-time? Why or Why not? If so, what circumstances must exist? If not, by what mechanism are two objects deemed separate?
Are you talking about actual macroscopic objects, like two rocks? If so, then this isn't really a relativity question, and I think we ought to ask an administrator to move it to a forum like Quantum Physics, which is where you'll be more likely to get good answers.

If you're talking about pointlike particles, then actually I still don't see what's relativistic about the question. Relativity is a classical theory that can accommodate particles and fields, but the particles and fields are just sort of plugged in to the theory. Relativity doesn't say anything about their properties. For instance, if you plug in a theory of pointlike particles with electric charge, then it's going to take infinite energy to get them right on top of each other -- but this is a fact about the theory you plugged in to relativity, not about relativity itself.

This question is better suited for the Quantum Mechanics forum. In 3 dimensions in Quantum Mechanics, we get some restrictions on whether on not identical particles can be at the same point in space and time. (In 2 dimensions, it gets much more complicated)

Identical bosons can be at the same points in space and time (but the wave function of the collection must be unchanged on exchanging any 2 of the particles)
Identical fermions cannot be at the same point in space and time (and the wave function of the collection gains a negative sign on the exchanging of any 2 of the particles)
Non-identical particles (like an electron and a proton) can be at the same point in space and time with no restrictions on the wave function.

I've heard it said that a baseball could "vibrate" itself through a brick wall - so to speak - if it moved slow enough and its energy form (wave-like) would do its thing. It might take three billion years to accomplish this but was do-able.

Waves can pass through the same media at the same time and only affect each other at their common areas or zones of intersection, so if matter really was crystalized energy (waves) I suppose that would be possible.

It certainly has no place in the real world, though.

I have a question now... Is a photon a packet of electromagnetic waves along a "beam?' Like this:

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