Tunnelling and special relativity

[sj660]

I have an undergraduate minor in astrophysics from a long time ago and have been brushing up to teach my kids, so I'm not an expert or even a great student of these things, but something I thought I'd log in and ask here:

If special relativity stands for the premise that there is no preferred frame of reference under constant velocity, but QM tells us that (1) we're not "really" anywhere, we're just probably at a certain 3-space coordinate, and (2) there is a nonzero chance that at any given instant I (or a particle of me?) could undergo what would amount to extreme (but perhaps not continuous?) acceleration and show up somewhere else entirely I would ask:

(a) Are there *any* frames of reference at all?
(b) Are there any frames of reference where constant velocity isn't just a high probability?
(c) Inasmuch as GR solves the problems for different accelerations,
(c1) how can QFT work without GR and
(c2) how can QFT work *with* SR?

 

[mfb]

(a) Are there *any* frames of reference at all?

Reference frames are mathematical/physical constructions, not objects.

(b) Are there any frames of reference where constant velocity isn't just a high probability?

If you consider quantum mechanics: No. Particles do not have "one" velocity there, they have something which could be considered as velocity distribution.

(c) Inasmuch as GR solves the problems for different accelerations,

Not at all.

(c1) how can QFT work without GR and

Fine. How can it work with GR? (Nobel prize for the answer)

(c2) how can QFT work *with* SR?

QFT uses SR in its construction. It cannot work without.

 

[sj660]

(a) Obviously; but are they constructs that make sense if the notion of "position" isn't real.

(c) Wait, what? GR doesn't generalize SR to different accelerations?

(c1) Maybe the tone of rhetorical/non-rhetorical question isn't coming through in my post. Maybe more clearly: if there is a nonzero chance you are always going to displace, then you, at least, need a theory that accounts for that, no? SR doesn't, right?

(c2) Understood. But my question was, again, if there are no frames of reference as such, how do you even make that construction?

The question isn't some kind of reductio ad absurdum. I understand well these are two of the (if not the) most experimentally verified theories ever. Maybe I just don't have the math to understand SR given the possibility of tunnelling etc.

 

[mfb]

(c) Wait, what? GR doesn't generalize SR to different accelerations?

So what?
I don't even see which "problem" you mean. In any way, GR does not solve problems in quantum mechanics.

if there is a nonzero chance you are always going to displace, then you, at least, need a theory that accounts for that, no? SR doesn't, right?

Quantum mechanics does.

But my question was, again, if there are no frames of reference as such, how do you even make that construction?

There are reference frames.

 

[Bill_K]

Wait, what? GR doesn't generalize SR to different accelerations?

Nope. General Relativity is a theory of gravity and curved space. Special Relativity handles acceleration just fine.

 

[ZapperZ]

I am also rather puzzled what tunneling has anything to do with all this.

Zz.

 

[cosmic dust]

I think that what "sj660" is asking (please tell me if I misunderstood), is if (according to QM) the notion of "exact position" is non-sense, then how can one claims that some coordinate system is “there, at some point in space” ? Well, that depends of your scale of measurement. If you use macroscopic objects to define the coordinate system, then you have no problem, but, if you built a nano-coordinate-system and you set a nano-observer on that, then (because of QM effects on microscopic objects) that observer will not have a definite position. So, you cannot use his/her measurements to describe YOUR reality because you do not know what he/she is really referring to. These information would be useful to you, if you obtained them while you measured successfully his/her position.
Now, about your concern on velocity and acceleration. When QM states that the position of an object is not known before it is measured, but there is a probability of measuring it here or there, it doesn’t mean that that object is rapidly varying it’s position (so it has some velocity and acceleration). It means that it DOES have a fixed position, but we CANNOT know where that is unless we measure it. So there is no need to mention velocity and acceleration, but to reconsider the notion of probability in QM.

 

[mfb]

It means that it DOES have a fixed position, but we CANNOT know where that is unless we measure it.

No - or not in the way you describe it. That would need hidden variables and does not work. The de-Broglie-Bohm theory has individual particles with well-defined positions, but they do not influcence physics - the wavefunction guides those particles, but is not influenced by the particles.