Can anyone explain the physical meaning of spin in QM?

[Hurkyl]

Of course if what you mean is that ``This isn't an issue of of "present theory" because you agree that the present theory can not answer such questions, and is an accepted deficiency (which all professors immediately tell there newbie physics students not to look for such answers) then I would agree.

Of course present theory gives answers such questions. And sometimes, the answer to a question like "what is a photon?" is simply "a photon." To call that a deficiency is to be ignorant of the regress argument, as applied to 'is-ness'.

The relevant question here we are to use science to answer our questions about the nature of nature. If your answer is yes, then present theory does answer "what is" questions. If your answer is no, then this "isn't an issue of 'present theory'".

Of course, all too often this question is simply a smokescreen for prejudice or unrealistic expectations. e.g. accusations that present theory cannot answer "what is" questions are often levied when a person requires that everything should be reduced to Newtonian concepts, or 'intuitive' ideas.

 

[AEM]

I am having trouble wrapping my head around statements that seem to imply that complete physical understanding is only to be found in the mathematics used. To illustrate my difficulty let me pose the following examples:

(1) The heat equation (or, if you prefer, the diffusion equation). The heat equation has been in use for years and many many solutions have been found for many different applications ( See Carslaw and Jaeger, Conduction of Heat in Solids for a few examples), yet I doubt that any of us believe that the continuous function solved for is anything more than a convenient representation for what's going on at a microscopic level.

(2) Now, consider quantum mechanics. I'm sure that most readers of this thread have learned their quantum mechanics from books similar to what I used (Merzbacher, Messiah, Bohm) However there is a hydrodynamic formulation of quantum mechanics based on work by Madelung (1926) and Bohm (1952) that chemical physicists have used quite successfully for solving the time dependent Schrodinger equation. (See Wyatt, "Quantum Dynamics with Trajectories").

(3) We are all familiar with the Pauli spin matrices. But less familiar may be the fact that the algebra of the Pauli matrices is just that of a set of three orthonormal vectors in space under Clifford's geometric product. From what I've read ( Bayliss, "Clifford (Geometric) Algebras"; Doran and Lasenby, "Geometric Algebra for Physicists"), it seems that Dirac theory can be obtained in a very smooth and elegant way through Clifford algebra.

So with these three examples in mind, particularly the last two where different mathematical schemes have been used successfully, shouldn't one be just a bit skeptical that every last word is to be gleaned from the mathematics --particularly if one's knowledge, like mine, isn't exhaustive?

However, "What is ____ really" questions are fraught with unwanted overtones, such as "the asker is a crank, or stupid, or woefully ignorant." I would suggest that a given "What is " question may be appropriate within the context of one mathematical formulation, but not another. I would also argue that it is important to once in a while ask "What is" questions even if it's only in the privacy of our office with the door carefully locked. After all, our experimental technique is improving each year and This year's dumb "What is" question might be entirely appropriate 5 years from now. 40 years ago if one asked "What is the speed of entanglement?" he would have been shown the door. Last summer the results of such a measurement were reported in Nature.

 

[jtbell]

I wouldn't say that the mathematics encodes the complete physical understanding of QM. The problem is that there are several competing "physical understandings" (interpretations) of QM and no way as yet to choose among them experimentally.

 

[Fredrik]

The concept of a photon is defined by QED, so it doesn't make sense to say that "present theory" can't explain what a photon is.

 

[Demystifier]

You cannot understand what spin "really" is without understanding what PARTICLE "really" is. Unfortunately, standard quantum mechanics (QM) does not say what particles and other objects "really" are. Instead, it merely gives mathematical prescriptions to calculate their manifestations in experiments. If you want to understand what things "really" are, it is necessary to go beyond standard QM, to speak in terms of specific interpretations of QM.

The most intuitive interpretation of QM is probably provided by the Bohmian interpretation. So let us see what answer is provided by this particular interpretation. In this interpretation particle is a pointlike object moving along a deterministic trajectory. This object (the particle) is separated from the wave function. Still, the wave function influences the motion of the particle; it acts as an external potential in which the particle moves. According to this interpretation, the particle does not have spin at all. Instead, the spin is a mathematical property of the wave function. Wave functions (spinors) corresponding to different "spins" mean different potentials, which imply different motions of particles. In experiments we observe this or that position of the particle, which was caused by this or that spinor wave function.

 

[Naty1]

I am having trouble wrapping my head around statements that seem to imply that complete physical understanding is only to be found in the mathematics used.

Good...don't accept that. The first section of post #40 is a good enough explanation for me. While I accept that QM has concepts that are perhaps "unknowable" in classical terms today, there is no reason whatsoever to think that a thousand years from now man will not have superior insights...maybe even a "complete" understanding.


While mathematics plays an increasingly important role in physics today relative to a hundred years ago, intuition, persistance and a belief in what you are doing remains paramount. Einstein's ten year struggle with GR is as good an illustration as any: he did not start from pure mathematics, in fact spent years searching for the right formulations to express his ideas...his friend Grossman finally led him to Riemann curvature mathematics...yet others have started with math and then discovered the application: string theory and Bessel functions are examples...physics can work both ways...


How many times in history has a brilliant scientist thought that "the end of physics is near" (or something similar) since we have withour grasp evertyhing that can be known...and then BANG somebody discovers another particle or another theory of a new experimental result...and physics is thrown for a loop...of discovery...

 

[granpa]

as I just said on another forum, maybe we shouldn't even be asking what the fundamental nature of reality 'really' is. maybe we should just ask how we would program a computer to simulate the universe. if it always gives the right answer then what difference does it make what things 'really' are?

after we figure out 'how' things work then we can argue all we want over 'what' things are.

 

[ThomasT]

Thanks for the answers, but they're way too deep and mathematical. Again, I've seen the derivations, presence in the wave function, etc. What I'm looking for is a physical explanation of what spin is.

I'm an assistant in a certain course and a student asked me how he can imagine spin in QM and i didn't really know how to explain it because i don't know myself. I know that it's not the same as spin in "a spinning toll", but somehow related still. I told him that it is an inherent quantity "baked in" to particles, but i couldn't really give a satisfying answer on the physical meaning of spin.

A summary of the replies in this thread should, at least, set your students on a path toward refining and answering your (and their) question(s) about the nature of quantum spin. Anyway, they helped me.

You cannot understand what spin "really" is without understanding what PARTICLE "really" is. Unfortunately, standard quantum mechanics (QM) does not say what particles and other objects "really" are. Instead, it merely gives mathematical prescriptions to calculate their manifestations in experiments. If you want to understand what things "really" are, it is necessary to go beyond standard QM, to speak in terms of specific interpretations of QM.

The most intuitive interpretation of QM is probably provided by the Bohmian interpretation. So let us see what answer is provided by this particular interpretation. In this interpretation particle is a pointlike object moving along a deterministic trajectory. This object (the particle) is separated from the wave function. Still, the wave function influences the motion of the particle; it acts as an external potential in which the particle moves. According to this interpretation, the particle does not have spin at all. Instead, the spin is a mathematical property of the wave function. Wave functions (spinors) corresponding to different "spins" mean different potentials, which imply different motions of particles. In experiments we observe this or that position of the particle, which was caused by this or that spinor wave function.

I don't know Bohmian Mechanics, though I did study some of Bohms quantum theory textbook.

From what you said above, can the "pointlike object moving along a deterministic trajectory" be thought of 'realistically' as a location on an expanding wave shell?

 

[Demystifier]

I don't know Bohmian Mechanics, though I did study some of Bohms quantum theory textbook.

Bohmian mechanics has been developed AFTER the Bohm's quantum theory textbook.

From what you said above, can the "pointlike object moving along a deterministic trajectory" be thought of 'realistically' as a location on an expanding wave shell?

Yes, if wave has the shape of a shell in the first place.

 

[AEM]

A summary of the replies in this thread should, at least, set your students on a path toward refining and answering your (and their) question(s) about the nature of quantum spin. Anyway, they helped me.


I don't know Bohmian Mechanics, though I did study some of Bohms quantum theory textbook.

From what you said above, can the "pointlike object moving along a deterministic trajectory" be thought of 'realistically' as a location on an expanding wave shell?

Bohm's Quantum Theory does not discuss Bohmian mechanics. The standard text on Bohmian mechanics is Holland's The Quantum Theory of Motion . The book by Wyatt I mentioned in my previous post is a nice introduction and section 4.2 of Tonnor's Introduction to Quantum Mechanics, A Time Dependent Approach is very readable. Note the last two authors are interested in actually calculating things like electron dynamics in molecular reactions and stay away from the briar patch of interpretation.

 

[enotstrebor]

Of course present theory gives answers such questions. And sometimes, the answer to a question like "what is a photon?" is simply "a photon."

You must go back to the beginning. You missed the point. The present theory can not tell us if we are modelling the photon or the reaction of the particle to the photon.

Why do you keep avoiding this?

If the theory is the model of the reation to the photon then it is not a model of the photon and thus in no way shape or form (does not) gives an answers to such questions as "what is a photon?"

 

[ZapperZ]

You must go back to the beginning. You missed the point. The present theory can not tell us if we are modelling the photon or the reaction of the particle to the photon.

Why do you keep avoiding this?

If the theory is the model of the reation to the photon then it is not a model of the photon and thus in no way shape or form (does not) gives an answers to such questions as "what is a photon?"

Can you tell me what in this universe that you are living in is NOT based on how one entity is reacting with another? How do you think you are able to SEE with your "eyes", for example? Or what about the description for other entities such as electron, proton, a tree, that pain in your back, etc?

Zz.

 

[enotstrebor]

Can you tell me what in this universe that you are living in is NOT based on how one entity is reacting with another? How do you think you are able to SEE with your "eyes", for example? Or what about the description for other entities such as electron, proton, a tree, that pain in your back, etc?

Zz.

It is not a question of what one observes (what behavior is), it is a question of how the model produces the observed behavior.

Modeling behavior has two basic approaches. One approach is to produce the behavior (get the correct mathematical results) the other is, from a postulated model of the underlying fundamentals by combining the effects of the fundamentals to result in the observed behavior.

For example, one can develop a mathematical model to produce human behavior and given the set of stimuli this psychological attribute based model produces the observed human behaviors. This model does not require neurons to exist.

One can also, produce a model of behavior based on the postulate (theory) that it is the result of neurons (underlying fundamentals). This neuron based model also produces the correct human behavior.

The first psychological model does not address the source elements, the second model does. (This does not mean that the neural hypothsis is correct but it says something about the fundamental nature of the source of behavior rather than just producing the correct results.)

The first model does not distinguish between the behavior coming from the medulla, pons, cerebellum or neocortex not does it destinguish between the reaction of the neocortex to the cerebellum and thus does not destiguish between the source(s) of the behavior (just as the present model doen't destinguish between the source of the behavior, i.e the photon or the reaction of the particle to the photon but only the resultant behavior.).

In QM, QED, QFT, there are not underlying fundamentals postulated (separate photon model elements and massed particle model elements were the interaction between the elements are the source) from which the behavior results. In fact many believe there can be no underlying elements (``hidden variables''?).

Note, it has six differnet views of the nature of Nature (Copehagen, Stochastic, Many Worlds, etc.) where if it answered the question "What is the electron", "What is the photon", etc. there can only be a single answer, not multiple answers ("what the electron is" deliniates the nature of Nature).

Note, it is a wave particle duality while the actual entity by the first law of logic (either something is A or not A) must be wave particle unity. (Actually the SM is a spread out over all of space wave point particle duality, i.e. conflicting behavior duality if it represents the particle! While if it does not represent the particle only requires the underlying fundamentals to be a particle with point effective behavior and wave effective behavior.)

Note, it is called the Standard Model, not standard theory. (Theories addresses the underlying elements, models may or may not. If there is a theory as the source/origin of the model then it will, if the ``theory'' (incorrectly used, correct use is ``interpretation'' or ``view'') is post model as is the case for the SM then it does not)

Is this evidence of my original postulate, that because one can do the mathematics means you know, it doesn't mean you understand?

If you would like, there is suggestive evidence which points to the fact that it is the reaction to the photon that is modeled by the present theory.

I welcome your response.

 

[daschaich]

...

Note, it is called the Standard Model, not standard theory. (Theories addresses the underlying elements, models may or may not. If there is a theory as the source/origin of the model then it will, if the ``theory'' (incorrectly used, correct use is ``interpretation'' or ``view'') is post model as is the case for the SM then it does not)

...

The irony, of course, is that the Standard Model is the best-tested and most fundamental theory of nature in existence. In contrast, "String Theory" and its relatives are a large collection of relatively loosely related models. The Standard Model's name, of course, comes from its historical development. I would recommend learning more about the Standard Model itself than just its name before trying to argue that it somehow fails to be a bona fide theory.

 

[enotstrebor]

The irony, of course, is that the Standard Model is the best-tested and most fundamental theory of nature in existence. ... The Standard Model's name, of course, comes from its historical development. I would recommend learning more about the Standard Model itself than just its name before trying to argue that it somehow fails to be a bona fide theory.

``I would recommend learning'' the difference between a model and a theory. There is no Standard Theory of the Standard Model. There is the Stochastic theory of the standard model, the Copenhagen theory of the standard model, the Many Worlds theory of the standard model, etc, etc. (yes and the afore mentioned Bohmian theory) (As there is a plethera I do believe views is a more relavant word, but they are, in effect, theories of the nature of Nature. )

A plethera of theories is not a fundamental (singular) theory of nature!

There is a difference between the accuracy of a model and its representation as fundamental to the nature of Nature.
(What makes a good model vs what makes a fundamental theory?)

There is a difference between the behavior and the particle.
(How does it inter-act [inter->between multi-object effect] vs What is a photon [singular].)

There is a difference between mathematics and physics.
(How is behavior termed spin modeled vs What is spin?)

There is a difference between knowledge and understanding.
(What it means if I can do the math vs what can be infered or not from the math.)

``and words have grown so false I loath prove reason with them.''

 

[ZapperZ]

``I would recommend learning'' the difference between a model and a theory. There is no Standard Theory of the Standard Model. There is the Stochastic theory of the standard model, the Copenhagen theory of the standard model, the Many Worlds theory of the standard model, etc, etc. (yes and the afore mentioned Bohmian theory) (As there is a plethera I do believe views is a more relavant word, but they are, in effect, theories of the nature of Nature. )

A plethera of theories is not a fundamental (singular) theory of nature!

There is a difference between the accuracy of a model and its representation as fundamental to the nature of Nature.
(What makes a good model vs what makes a fundamental theory?)

There is a difference between the behavior and the particle.
(How does it inter-act [inter->between multi-object effect] vs What is a photon [singular].)

There is a difference between mathematics and physics.
(How is behavior termed spin modeled vs What is spin?)

There is a difference between knowledge and understanding.
(What it means if I can do the math vs what can be infered or not from the math.)

``and words have grown so false I loath prove reason with them.''

Let's not get into semantics here. In many cases, "model" and "theory" in physics is the same thing. If you are arguing about the usage of the label, it tends to indicate that you do not understand the physics. Since this is in the physics section of PF and not, say, the philosophy forum, pay attention to the physics and not the English label being used as the "placecard" for the physics.

If this line of discussion continues, this thread will be locked.

Zz.