The Uncertainty Principle Uncertainty

[bhobba]

Object is stationary in one inertial system. Photons are not stationary in any inertial system.

Thats not what stationary state means:
http://en.wikipedia.org/wiki/Stationary_state

Thanks
Bill

 

[carllooper]

That's untrue.

Its a statement about non-commuting observables and applies to any state - stationary or otherwise.

The use of non-commuting variables follows from the principle, not the other way around. There's nothing in mathematics that requires that two variables be non-commuting.

I saw the link on "stationary state" so perhaps that's where we are getting our lines crossed once again. By "stationary state" I read the question as meaning "at rest". As many respondents have as well. So it's in that context (as should be obvious, but obviously not) that I am speaking.

C

 

[bhobba]

The use of non-commuting variables follows from the principle, not the other way around. There's nothing in mathematics that requires that two variables be non-commuting.

That also is incorrect.

It is a theorem of non-commuting observables.

Thanks
Bill

 

[carllooper]

It is a theorem of non-commuting observables.

What motivates the use of non-commuting variables? It is the concept of non-commuting observables. This is a limit proposed in QM. It is not a limit that is in any way required in mathematics with respect to two variables used to otherwise represent a particle at rest.

That's the point being made. But more importantly is why this point is being made. It's being made in the context of an assumption (rightly or wrongly) that the question, as well as many of the answers, are intending by "stationary state", or "stationary particle", the concept of a particle at rest.

Have a read of the thread. It becomes obvious from the discussion that by "stationary particle" is meant a particle at rest.

And it is in this context (not some other) that the Uncertainty Principle is being elaborated as ruling out such a proposed particle, ie. where mathematics itself does not.

C

 

[bhobba]

What motivates the use of non-commuting variables? It is the concept of non-commuting observables.

What has motivation got to do with validity? When I muck around investigating a mathematical structure trying to prove something, or simply out of curiosity, all sorts of things motivate me - or maybe nothing at all. Either way its got nothing to do with its implication.

Have a read of the thread. It becomes obvious from the discussion that by "stationary particle" is meant a particle at rest. And it is in this context (not some other) that the Uncertainty Principle is being elaborated as ruling out such a proposed particle, ie. where mathematics itself does not.

In QM words have a definite meaning. Stationary state is entirely different from stationary particle. Indeed a state where a particle is at rest with a definite position is impossible.

Thanks
Bill

 

[carllooper]

What has motivation got to do with validity? When I muck around investigating a mathematical structure trying to prove something, or simply out of curiosity, all sorts of things motivate me - or maybe nothing at all. Either way its got nothing to do with its implication.

I think you'll find the Heisenberg Uncertainty Principle is more than just a mathematical proposition. It has it's origin in experimental physics. Bohr sums it up quite well in this 1949 section of "Discussions with Einstein on Epistemological Problems in Atomic Physics" (highlights mine):

The way to the clarification of the situation was, indeed, first to be paved by the development of a more comprehensive quantum theory. A first step towards this goal was the recognition by de Broglie in 1925 that the wave-corpuscle duality was not confined to the properties of radiation, but was equally unavoidable in accounting for the behaviour of material particles. This idea, which was soon convincingly confirmed by experiments on electron interference phenomena, was at once greeted by Einstein, who had already envisaged the deep-going analogy between the properties of thermal radiation and of gases in the so-called degenerate state. The new line was pursued with the greatest success by Schrödinger (1926) who, in particular, showed how the stationary states of atomic systems could be represented by the proper solutions of a wave-equation to the establishment of which he was led by the formal analogy, originally traced by Hamilton, between mechanical and optical problems. Still, the paradoxical aspects of quantum theory were in no way ameliorated, but even emphasised, by the apparent contradiction between the exigencies of the general superposition principle of the wave description and the feature of individuality of the elementary atomic processes.

At the same time, Heisenberg (1925) had laid the foundation of a rational quantum mechanics, which was rapidly developed through important contributions by Born and Jordan as well as by Dirac. In this theory, a formalism is introduced, in which the kinematical and dynamical variables of classical mechanics are replaced by symbols subjected to a non-commutative algebra. Notwithstanding the renunciation of orbital pictures, Hamilton's canonical equations of mechanics are kept unaltered and Planck's constant enters only in the rules of commutation h

qp - pq = -(h/2p) , (2)


holding for any set of conjugate variables q and p. Through a representation of the symbols by matrices with elements referring to transitions between stationary states, a quantitative formulation of the correspondence principle became for the first time possible. It may here be recalled that an important preliminary step towards this goal was reached through the establishment, especially by contributions of Kramers, of a quantum theory of dispersion making basic use of Einstein's general rules for the probability of the occurrence of absorption and emission processes.

In QM words have a definite meaning. Stationary state is entirely different from stationary particle. Indeed a state where a particle is at rest with a definite position is impossible.

Yes, a particle at rest is impossible. That's the point that was being elaborated.

Regarding semantics, the original question does not use the phrase "stationary state". It uses the phrase "stationary particle". And subsequent elaboration by the author of the question makes it quite clear that by "stationary particle" is not meant "stationary state". And the following comment, does not use "stationary state" either:

"Object is stationary in one inertial system. Photons are not stationary in any inertial system."

And yet, it is precisely in response to the above statement that you make the completely irrelevant point:

"Thats not what stationary state means"

It's obvious throughout the entire discussion that by "stationary" is intended the classical/relativistic use of that term. The discussion on frames of reference and inertial systems and "photons not stationary in any inertial system" make this exceedingly obvious.

I'm the one that actually used the phrase "stationary state" and I'm now very much regretting that I did so.

C

 

[bhobba]

I think you'll find the Heisenberg Uncertainty Principle is more than just a mathematical proposition. It has it's origin in experimental physics. Bohr sums it up quite well in this 1949 section of "Discussions with Einstein on Epistemological Problems in Atomic Physics" (highlights mine):

Things have moved on a lot since then.

In this theory, a formalism is introduced, in which the kinematical and dynamical variables of classical mechanics are replaced by symbols subjected to a non-commutative algebra.

That was all swept away when Dirac developed his transformation theory in December 1926 and generally goes under the name Quantum Mechanics today.

Its a theorem - no ifs or buts about it - see page 223 - Ballentine - Quantum Mechanics - A Modern Development.

Emphasis mine.

QM, as found in Ballentine, is based on two axioms - for an elaboration of that, see post 137:
https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

The KEY axiom is:
'An observation/measurement with possible outcomes i = 1, 2, 3 ... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.'

Observables etc, which may or may not commute, follow from that. For example does the spin observable commute with position? The uncertainty relations is a theorem about observables that do not commute.

Regarding the stationary state thing, you are entitled to use words in anyway you like, but its good practice to use them in the standard way because it makes reading and understanding by others much easier. Even then the standard use of words like observation etc in QM leads to problems - but we are stuck with it.

Thanks
Bill

 

[carllooper]

Things have moved on a lot since the famous, and it must be said magnificent, Einstein Bohr debates where pictorial visualisations were often used. They were mostly incorrect BTW - its really got nothing to do with firing photons at objects etc - that's just for pictorial vividness. But that was the early days of QM - much water has gone under the bridge since then - and wasn't really Einsteins deepest objection to the theory anyway which was detailed in EPR.

While a lot has certainly happened since those days, it's still as relevant today as it was then. The Uncertainty Principle remains the same principle. It hasn't changed. It's been elaborated of course, but the origin of the principle remains the same. You can't just change that because it happened so long ago. Or rather, if you did, you'd probably want to call it something else.

Also, Bohr might have used pictures but he certainly didn't encourage them. Indeed he famously had a go at Feynman for using a pictorial representation of quantum mechanics. But as Feynman demonstrated you can indeed use pictures (or diagrams) to represent a useful concept, ie. as much as any other way. And Feynman's integral path is a very clever way of elaborating the physics in a pictorial way.

The basics of physics is still very much the same as it ever was, ie. elaborating or inventing what can be otherwise demonstrated in a physical experiment. That hasn't changed. Otherwise it's no longer physics. This doesn't preclude a mathematical line of enquiry, but the expectation is still that it can be demonstrated in a physical setup. You may not know that in advance of course. So it's not a pre-requisite. More of "post-requisite". And there's plenty of room for a greater mathematical understanding of the physics we already have. Efforts to build a quantum computer, for example, don't (on the face of it) require the introduction of any new physics (although it might), nor need it involve any physical experiments for that matter, but can still require a significant amount of mathematical work be done to resolve a candidate solution. But the physical solution will involve building it - demonstrating it in practice. Even if, as theorists, we already know it will work.

And as a side project, of course, is always the ongoing fascination with the weirdness - what are we missing? Are we missing anything? The interpretative game.

C

 

[bhobba]

While a lot has certainly happened since those days, it's still as relevant today as it was then. The Uncertainty Principle remains the same principle. It hasn't changed.

Its physical basis has changed - its simply a theroem abnout non-commuting onservables. Observables can be commuting or not - the uncertainly principle applies to non-commuting observables as a general therorem.

Also, Bohr might have used pictures but he certainly didn't encourage them. Indeed he famously had a go at Feynman for using a pictorial representation of quantum mechanics. But as Feynman demonstrated you can indeed use pictures (or diagrams) to represent a useful concept, ie. as much as any other way. And Feynman's integral path is a very clever way of elaborating the physics in a pictorial way.

Pictures are sometimes useful - sometimes not. It is now known those ancient discussions about the uncertainly principle are wrong. Feynman OTOH was simply using pictures to represent terms in a perturbative expansion - which Bohr didn't appreciate at the time.

The basics of physics is still very much the same as it ever was

Actually the basic rock bottom essence of any science, including physics, is its all provisional, subject to one thing, and one thing only - correspondence with experiment. The old ideas of Bohr etc etc have been replaced, as undoubtedly many of our current ideas will be replaced. Some have remained unchanged (eg the Copenhagen interpretation remains basically the same) and some have been swept away (eg those ancient discussions about observation disturbing the system as the basis of the uncertainty principle - it isn't).

And as a side project, of course, is always the ongoing fascination with the weirdness - what are we missing? Are we missing anything? The interpretative game.

Who knows what future progress will bring. If I knew I would be out collecting my Nobel prize.

Interpretations are more a psychological crutch IMHO, but each to their own, preordaining anything is not how science progresses - some interpretation may prove to be of vital importance for the next breakthrough.

Thanks
Bill

 

[carllooper]

Its physical basis has changed - its simply a theroem abnout non-commuting onservables. Observables can be commuting or not - the uncertainly principle applies to non-commuting observables as a general therorem.

Which is how the principle is being used - as a theorem. There is no suggestion whatsoever that it's being used as anything other than a theorem.

I don't know what the fuss is all about. If one is going to use the concept (or theorem, or whatever else one might like to call it) then it's going to conflict with the concept of a particle at rest. Or vice versa. They don't agree with each other. Today or yesterday. In modern times or 'ancient' times.

C

 

[carllooper]

Actually the basic rock bottom essence of any science, including physics, is its all provisional, subject to one thing, and one thing only - correspondence with experiment.

I agree. I don't know how, or in what way, anything I said implies anything different. It's the very same point. So perhaps I'll just take your comment as one being in solidarity with mine, rather than one posed as some objection.

C