Looking for a hard determinism type of QM interpretation

[bhobba]

and I have some deep doubts about the utility of this approach in an introductory quantum mechanics course.

You would have to have rocks in your head to try this in an introductory course, and even in advanced courses unless the audience has sufficient math background.

But that's not the point I am trying to make here. Its the principles that underlie what QM is about.

Thanks
Bill

 

[Matterwave]

You would have to have rocks in your head to try this in an introductory course, and even in advanced courses unless the audience has sufficient math background.

But that's not the point I am trying to make here. Its the principles that underlie what QM is about.

Thanks
Bill

I was actually referring to Vanhees's statement that he taught a Poisson bracket to commutator relations approach to QM in a quantum 1 course. Rereading his post, I see that Quantum 1 is actually taught to upper level undergrads who I guess *might* understand this approach (maybe German classical mech is taught differently as well?). I thought Quantum 1 was taught to entering undergrads, which I thought was way too early to have anything to do with Poisson brackets.

 

[atyy]

But is it true that QM cannot exist if POR were to fail?

If QM can still exist (say using Sakurai and Napolitano's axioms) in the absence of POR, then POR is not a principle of QM. Rather, POR is a principle that can be consistent with QM.

For example, does QM not work in curved spacetime, where POR does fail?

 

[PhilDSP]

I thought Quantum 1 was taught to entering undergrads, which I thought was way too early to have anything to do with Poisson brackets.

It seems a great shame that things like Poisson brackets and Phase Space aren't introduced early, even in high school. There's obviously no need to go into high technical detail. But a hand-wavy "this is what PB's look like and this is why we use them" type of approach might go a long way towards generating interest, curiosity and familiarity (rather than fright or aversion) early on IMO. Then it is fair to tell students that they will not be tested on those subjects and the situation becomes one of "learning by inspiration".

 

[rubi]

But is it true that QM cannot exist if POR were to fail?

If QM can still exist (say using Sakurai and Napolitano's axioms) in the absence of POR, then POR is not a principle of QM. Rather, POR is a principle that can be consistent with QM.

For example, does QM not work in curved spacetime, where POR does fail?

The Schrödinger equation is actually more fundamental, because it still works in situations that aren't symmetric under time translations. This is the case for time-dependent Hamiltonians for example, which appear in many practical applications. Of course, if the system has a time-translation symmetry, one can typically derive the Schrödinger equation from it.

 

[bhobba]

It seems a great shame that things like Poisson brackets and Phase Space aren't introduced early, even in high school.

Mate that's one of the huge issues with QM.

To really understand it you need the background for something like Ballentine.

Many of the questions I answer for beginning students, or simply those who have only read popularisations, are easily found in Ballentine.

In many ways I consider my posts translations from that text to more accessible language - with varying success I might add.

Thanks
Bill

 

[bhobba]

The Schrödinger equation is actually more fundamental, because it still works in situations that aren't symmetric under time translations. This is the case for time-dependent Hamiltonians for example, which appear in many practical applications. Of course, if the system has a time-translation symmetry, one can typically derive the Schrödinger equation from it.

That's true.

But, as in the case of say what Landau does in Mechanics, the generalisation to those cases aren't hard, even though the laws were only developed for inertial frames.

Some people say that SR can't handle accelerated frames - which isn't true either - generalising it to those cases isn't that hard.

Thanks
Bill

 

[Matterwave]

It seems a great shame that things like Poisson brackets and Phase Space aren't introduced early, even in high school. There's obviously no need to go into high technical detail. But a hand-wavy "this is what PB's look like and this is why we use them" type of approach might go a long way towards generating interest, curiosity and familiarity (rather than fright or aversion) early on IMO. Then it is fair to tell students that they will not be tested on those subjects and the situation becomes one of "learning by inspiration".

The high school level might be asking too much. Even my undergraduate introductory physics classes focused purely on Newtonian mechanics. I don't think that that's necessarily a bad thing either. Newtonian mechanics is far less formal and far easier conceptually to understand because it has a strictly cause and effect structure in my opinion (force causes acceleration, torque causes rotation).

 

[bhobba]

But is it true that QM cannot exist if POR were to fail?

The POR is in fact a meta law ie a law about laws. Physics, in general, would be in deep do do if it failed in a drastic way. What is more likely to happen is it may fail in some 'realm' way beyond everyday experience in which case, like so many things in physics, its simply something applicable only to a well defined 'realm' like classical mechanics is to quantum mechanics, and quantum mechanics is to QFT.

Also by definition it only applies to inertial frames, which don't strictly speaking actually exist - even in intergalactic space. Its very hard for a law to fail in a drastic way for a conceptualisation. If it did fail you simply say that conceptualisation is not applicable here. I would say its of course not impossible, but it would be a pretty unusual thing.

To be clearer the modern definition of an inertial frame is one such that all points are the same, all directions the same, and all instances of time the same - as far as the laws of nature are concerned. Its easy to see all such frames must move wrt each other at constant velocity. All the POR does is adopt the maximum symmetry in such a situation - that not only are the laws of nature the same in each frame - but between frames as well. If, say for example, we find a constant of nature changes with time then that would not violate the POR because we can simply say that it has that value is not a law of nature. That's why the thing is so hard to invalidate - we actually decide on what a law of nature is.

That said - difficult to invalidate does not mean impossible eg if an actual aether was found that would not mean the laws of nature are the same in all inertial frames - it would depend on the direction of the aether wind in your frame.

Most that adhere to an aether are cranks that do not understand the physical implications - but a few aren't and its interesting to see their views eg:
http://ilja-schmelzer.de/glet/

Thanks
Bill

 

[atyy]

The POR is in fact a meta law ie a law about laws. Physics, in general, would be in deep do do if it failed in a drastic way. What is more likely to happen is it may fail in some 'realm' way beyond everyday experience in which case, like so many things in physics, its simply something applicable only to a well defined 'realm' like classical mechanics is to quantum mechanics, and quantum mechanics is to QFT.

Also by definition it only applies to inertial frames, which don't strictly speaking actually exist - even in intergalactic space. Its very hard for a law to fail in a drastic way for a conceptualisation. If it did fail you simply say that conceptualisation is not applicable here. I would say its of course not impossible, but it would be a pretty unusual thing.

To be clearer the modern definition of an inertial frame is one such that all points are the same, all directions the same, and all instances of time the same - as far as the laws of nature are concerned. Its easy to see all such frames must move wrt each other at constant velocity. All the POR does is adopt the maximum symmetry in such a situation - that not only are the laws of nature the same in each frame - but between frames as well. If, say for example, we find a constant of nature changes with time then that would not violate the POR because we can simply say that it has that value is not a law of nature. That's why the thing is so hard to invalidate - we actually decide on what a law of nature is.

That said - difficult to invalidate does not mean impossible eg if an actual aether was found that would not mean the laws of nature are the same in all inertial frames - it would depend on the direction of the aether wind in your frame.

Most that adhere to an aether are cranks that do not understand the physical implications - but a few aren't and its interesting to see their views eg:
http://ilja-schmelzer.de/glet/

Thanks
Bill

But if POR inertial frames don't exist as you say, and as you agreed with rubi that QM works even if POR fails, why should we consider POR an axiom for QM?

 

[bhobba]

But if POR inertial frames don't exist as you say, and as you agreed with rubi that QM works even if POR fails, why should we consider POR an axiom for QM?

A point doesn't exist either - nothing has position and no size - but we use it freely in our models.

Like a point an inertial frame is an abstraction that has proven useful.

Thanks
Bill

 

[atyy]

A point doesn't exist either - nothing has position and no size - but we use it freely in our models.

Like a point an inertial frame is an abstraction that has proven useful.

Thanks
Bill

But back in post #31 you were discussing principles. Doesn't this mean that POR is not a principle of QM, but rather something that can be added to QM?

 

[George Jones]

I hope this isn't too far off topic. Has anyone look at the book "Do We Really Understand Quantum Mechanics?" by Franck Laloe,

https://www.amazon.com/dp/110702501X/?tag=pfamazon01-20

Laloe is co-author of the classic 2-volume set "Quantum Mechaincs", by Claude Cohen-Tannoudji, Bernard Diu and Franck Laloe.

 

[atyy]

I hope this isn't too far off topic. Has anyone look at the book "Do We Really Understand Quantum Mechanics?" by Franck Laloe,

https://www.amazon.com/dp/110702501X/?tag=pfamazon01-20

Laloe is co-author of the classic 2-volume set "Quantum Mechaincs", by Claude Cohen-Tannoudji, Bernard Diu and Franck Laloe.

I don't know if the book is very different, but Laloe has a free article with the same title at http://arxiv.org/abs/quant-ph/0209123.

 

[strangerep]

[...] Doesn't this mean that POR is not a principle of QM, but rather something that can be added to QM?

Absolutely. QM is just a framework for constructing unitary representations of dynamical groups. Different dynamical groups are applicable to different classes of systems, in general.

For non-rel QM, the Galilean group is a subgroup of the larger dynamical groups.

 

[bhobba]

But back in post #31 you were discussing principles. Doesn't this mean that POR is not a principle of QM, but rather something that can be added to QM?

Indeed that's true - it isn't a principle of QM. The principles are the two axioms detailed in Ballentine - or one if you are sneaky like me and express the first axiom in a form you can apply Gleason to.

The POR is a meta law - applying to all physical laws - not just QM.

That said it still is an assumption - but one of a different logical status.

Thanks
Bill

 

[bhobba]

Absolutely. QM is just a framework for constructing unitary representations of dynamical groups. Different dynamical groups are applicable to different classes of systems, in general. For non-rel QM, the Galilean group is a subgroup of the larger dynamical groups.

Drats - what was it meatloaf said - you took the words right out of my mouth - actually you said it better than I would have - nice post.

Thanks
Bill

 

[bhobba]

I hope this isn't too far off topic. Has anyone look at the book "Do We Really Understand Quantum Mechanics?" by Franck Laloe,

No - but it looks REALLY REALLY good - must put it in my wish list at Amazon.

I am itching to get the Kindle version right now - can I resist?

Thanks
Bill