Reconciling Simultaneity & Relativity: Navigating the Spacetime Maze

[nomadreid]

Oops, forgot to finish the title, but don't see how I can edit it. Sorry.

How does one reconcile the idea that, according to relativity, one cannot talk of simultaneity, yet one can talk of a slice of spacetime to be space where all the points are at the same time?

That is my main question. While I am at it, can one say that a particle could stop existing at one point and instantaneously (?) start appearing at another (not constrained by causality) ? Not only does the problem of "instantaneous" appear again, but since the only thing that is going to distinguish one particle (OK, excitation of the field) from another with otherwise identical characteristics (Energy, charge, spin, etc.) is going to be its positions in spacetime, but if now that changes, how can one say that this is the same particle that reappeared?

 

[mfb]

What did you want as title? I can edit it.

according to relativity, one cannot talk of simultaneity

Of course you can. It just depends on your reference frame.

While I am at it, can one say that a particle could stop existing at one point and instantaneously (?) start appearing at another (not constrained by causality) ?

No, that would violate causality (and local energy conservation).

 

[Nugatory]

one cannot talk of simultaneity,

Two events are simultaneous in a given frame if they have the same $t$ coordinate using inertial coordinates assigned by that frame That's a definition. It works just fine in special relativity (although It needs some rephrasing in terms of "simultaneity conventions" before it will work with general relativity).

Thus, there is no reason why one "cannot talk of simultaneity". You just have to understand that events may be simultaneous on one frame but not in another, because the two frames assign $t$ coordinates differently.

 

[nomadreid]

Thank you, mfb and Nugatory.

The title was meant to be "simultaneity: forbidden by relativity but referred to anyway". Although your answers show that the title expresses a mistaken notion, nonetheless it might be useful for others who are looking through the forum with the same mistaken notion. So, mfb, if you could edit it, that would be appreciated.

So: about the simultaneity, I now understand. (Nugatory: I have looked up the simultaneity conventions you mentioned.) Many thanks to both of you.

As far as something stopping to exist in one place and reappearing in another, Nugatory says that this is impossible. But I thought that this was the whole point of tunneling (which does not involve causality). For example, when an electron changes orbit (or, phrased differently, when there is a shift in the statistical distribution that we call the electron ), we say that it is the same electron, no?

 

[mfb]

To have tunneling, the particles cannot have a single well-defined position to start with. All changes to the wave function in quantum mechanics can be expressed as continuous and local transformations.

 

[nomadreid]

To have tunneling, the particles cannot have a single well-defined position to start with. .

Thanks, this is starting to make sense.

All changes to the wave function in quantum mechanics can be expressed as continuous and local transformations..

Even wave function collapse? Or should that be replaced by a smooth decoherence or a many-worlds interpretation to make it smooth?

 

[mfb]

Collapses are a weird feature of some interpretations of quantum mechanics. There is no equation for the evolution of wave functions that would include anything like a collapse. Just keep applying quantum mechanics and you get smooth decoherence, and MWI if you don't add anything else.

 

[ZapperZ]

As far as something stopping to exist in one place and reappearing in another, Nugatory says that this is impossible. But I thought that this was the whole point of tunneling (which does not involve causality).

Whoa! Back up a bit. What is it about "tunneling" that doesn't involve causality?

Is this another one of those myths that tunneling is when a particle disappears from existence on one side of the barrier, and then pops back into existence on the other side? If it is, then this is wrong!

Zz.

 

[nomadreid]

Is this another one of those myths that tunneling is when a particle disappears from existence on one side of the barrier, and then pops back into existence on the other side? If it is, then this is wrong!

Correct, it is wrong. I think mfb put this to rest when he replied

To have tunneling, the particles cannot have a single well-defined position to start with.

So, to answer

What is it about "tunneling" that doesn't involve causality?

the reply is: nothing. Mea culpa.

But putting up my false conception did lead to these replies which pushed me to look up the relevant facts, so I do not regret posting them, and I thank you both for putting me straight.