About the wavefunction

[akhmeteli]

Apparently, several different questions were raised in this thread.

The original poster, naqo, asked: "couldn't one work from the begining with a real wave?". On the basis of the Schroedinger's article, I gave a (qualified) positive reply in post #3 (mind you, I was not trying to answer the question "shouldn't one...?"). I have not seen an objection to that in this thread.

Then there was a discussion of whether a wave can be represented by one real function. I expressed my point of view (it "can"; whether it "should", is a completely different question). I don't want to speculate whether there is a consensus now.

jtbell asked: "Can you replace the time-dependent Schrödinger Equation with a differential equation that does not have an $i$ in it, has a real (not complex) wave function as its solution, and describes all the phenomena that the SE and its solutions can?" Again, using the results of the Schroedinger's article, I gave a qualified positive reply in post #20 and have not seen an objection to that in this thread. Again, I was not trying to answer the question "Should you...?"

Finally, several knowledgeable people asked just that: Why do you need to replace a complex wavefunction with a real one, although it is much more convenient to work in the complex domain? Let me give my reasons here (the details may be found in my article quoted in my post #7).

I believe this opens a way for a different interpretation of quantum mechanics. Namely, in the Klein-Gordon-Maxwell system of equations you can naturally exclude the wavefunction describing the matter and obtain independent evolution of the electromagnetic field. Therefore, in the Bohmian interpretation of quantum mechanics, the electromagnetic field, not the quantum potential, plays the role of the guiding field (unfortunately, the extension of this conclusion to the Dirac-Maxwell system in the article is not satisfactory, and I hope I'll be able to correct this in a few days). Is this worth the trouble? Is the Bohmian interpretation itself worth the trouble? I think so, but I suspect most people in this forum will disagree

 

[Fra]

Why do you need to replace a complex wavefunction with a real one, although it is much more convenient to work in the complex domain? Let me give my reasons here (the details may be found in my article quoted in my post #7).

I believe this opens a way for a different interpretation of quantum mechanics. Namely, in the Klein-Gordon-Maxwell system of equations you can naturally exclude the wavefunction describing the matter and obtain independent evolution of the electromagnetic field. Therefore, in the Bohmian interpretation of quantum mechanics, the electromagnetic field, not the quantum potential, plays the role of the guiding field (unfortunately, the extension of this conclusion to the Dirac-Maxwell system in the article is not satisfactory, and I hope I'll be able to correct this in a few days). Is this worth the trouble? Is the Bohmian interpretation itself worth the trouble? I think so, but I suspect most people in this forum will disagree

I've got a feeling that once you've got that different interpretation, you also got to have some ideas in your sleeves how to take this beyond "interpretation only" and perhaps give a new angle to solve bigger problems in the context of unifications?

Is that possibly what you are after? :) Assuming your main objective is not just to restore classical realism at all cost, but also to bring the theory forward, I may hint a point and sense a remote connection to my perferred thinking.

Are you trying to restore classical objective realism, like my perception is many bohmians are after? or what is the ultimate purpose of your attention to this?

/Fredrik

 

[akhmeteli]

I've got a feeling that once you've got that different interpretation, you also got to have some ideas in your sleeves how to take this beyond "interpretation only" and perhaps give a new angle to solve bigger problems in the context of unifications?

Is that possibly what you are after? :) Assuming your main objective is not just to restore classical realism at all cost, but also to bring the theory forward, I may hint a point and sense a remote connection to my perferred thinking.

Are you trying to restore classical objective realism, like my perception is many bohmians are after? or what is the ultimate purpose of your attention to this?

/Fredrik

Thank you for your questions.

Initially, I just was not happy with the Copenhagen interpretation. Restoring classical realism at all costs? I don't quite see the point, because, if you ask me, the standard Bohmian interpretation already restored it (few people accept this interpretation, but for those who want realism at all costs it presents a solution). It seems to me that the cost is too high, but that's just my opinion. However, I hope that the interpretation may seem more attractive when it is the electromagnetic field, not the quantum potential, that guides the particle, so you are not "multiplying entities without necessity".

As for "a new angle to solve bigger problems in the context of unifications", actually, it might be possible, although so far this is pure speculation. But I don't know why I should not answer your question.

So it goes like this. What I am doing is only possible because the Klein-Gordon-Maxwell is a gauge-invariant theory. For the Dirac-Maxwell theory you can do pretty much the same by imposing the following constraint: "the axial current is zero". The resulting theory is limited, but meaningful, and you need just Majorana spinors instead of Dirac ones, and Majorana spinors are an analogue of real numbers for spinors. Whether such a theory is enough to describe all experiments, I don't know, but anyway, it is at least an interesting toy model of quantum mechanics, which allows a completely different interpretation, so it may be useful for discussions of interpretations. As for the Standard Model or unification theories, they are also gauge-invariant theories, so one can speculate that a similar mechanism can be applied to them, so real representations of the relevant groups, rather than complex, may be sufficient for fermions. However, I am not sure I am qualified to develop anything like this.

 

[Fra]

Thanks for your response.

To me my personal choice of interpretation is the one who provides me with the best expected stance for extending things, so interpretations are selected by the "power" of extrapolation IMO. If it wasn't for the extensions, a minimalist interpretation would be my choice.

I still don't quite understand your objective, just almost. As for who is qualified to do this or that, I don't know who that would be? I am not sure I am qualified either but I don't think that ever stopped anyone before

/Fredrik

 

[Fra]

However, I hope that the interpretation may seem more attractive when it is the electromagnetic field, not the quantum potential, that guides the particle, so you are not "multiplying entities without necessity".

I see, so electromagnetic field qualifies as a necessity and quantum potential does not?

Do you consider the necessity to be objective? or could it be that what is a necessity to one observer, is not to another? And how are necessities induced from experience? An from the particle view, how does a particle induce this necessity from experience?

If you are into bohm, did you ever try to merge the bohmian view with the subjective bayesian view? Sort of suggesting that the bohmian speculated degrees of freedom rather represents subjective estimates. They aren't real hidden variables in the objective classical sense?

I am not into bohm, but his thinking is not totally off chart IMO. But I think there is another way of seeing the bohm formalism, that does not make use of the deterministic philosophy.

I tried to ask demystifier who has posted alot about bohmian views but it seems he does not acknowledge this association. I would be curious to hear a bohmian view of this, but since it in one sense may have similarities to the bohmian thinking, it is even farther away from it than the copenhagen thinking since it introduces even more fundamental uncertainty.

If I were to induce my thinking onto the bohmian stuff, i would described the bohmian degrees of freedom (here extending it to general degrees of freedem and leave unsaid to interpret as "particles" sets of particles or whatever) as part of the identity of the system, but it determines the expected action relative the system. And I think it's the fact that the expected action relative different systems is different, that gives rise to non-trivial dynamics.

So from outsider, the bohmian degrees of freedom are not hidden variables in the sense of a definite structure with an unknown state, this is wrong because the identification of the microstructure itself! even with a completely unknown (random) state DOES contain information. And this information doesn't exist on the outside.

So IMO, a "bohmian like" interpretation might be kind of possible without the notion of hidden variables.. because it gives the impresion that the varible structure is known it's just that their values are not. I rather see it that the not only is the variable value hidden, the variables themselves re hidden, and effectively doesn't exists - from the outside. which connects to a subjective reality interpretation of QM.

Is this anything in your taste? I ask this out of general curiousity since you are into bohm.

/Fredrik

 

[Fra]

To comment to the expected objection how this subjective reality can be compatible with scientific model, then the answer is that one would still expect the objective reality to be emergent as a collective equilibration and evolution. In line with any learning ideas. We learn and our baseline also evolves along with it.

/Fredrik

 

[akhmeteli]

Fra,

Thank you for your posts and interest.

I am not sure I'll be able to give short answers, and right now I have some deadlines to meet, so I'll try to answer by Monday. Sorry.

Anyway, I am not sure I'll be able to offer anything meaningful on philosophical issues.

 

[Fra]

Fra,

Thank you for your posts and interest.

I am not sure I'll be able to give short answers, and right now I have some deadlines to meet, so I'll try to answer by Monday. Sorry.

Anyway, I am not sure I'll be able to offer anything meaningful on philosophical issues.

I am just curious. Don't waste too much time to make up a response unless you can relate to my questions. Even a lack of response or an unexpected response is a kind of response too.

Good luck with your deadlines.

/Fredrik

 

[akhmeteli]

To me my personal choice of interpretation is the one who provides me with the best expected stance for extending things, so interpretations are selected by the "power" of extrapolation IMO. If it wasn't for the extensions, a minimalist interpretation would be my choice.

I still don't quite understand your objective, just almost. As for who is qualified to do this or that, I don't know who that would be? I am not sure I am qualified either but I don't think that ever stopped anyone before

/Fredrik

I think I already speculated enough on possible extrapolations of what I do

As for my objective... Initially I was motivated by a firm belief that if two similar experiments produce different results, we should be able at least to indicate the difference between them that makes the "mileage vary". May be I just was a fatalist back then While I still keep that belief, I don't feel I'm in the driver's seat any more as far as my research is concerned, I rather tend to follow the logic and the results of that research. For example, I could not even dream that it would be possible to eliminate the wavefunction from the Klein-Gordon-Maxwell theory and have deterministic equations of motion for the electromagnetic field. Applications of this result to an electron in a hydrogen atom or two a two-slit interferometer are fascinating, but I have not had time to study them in more detail.

 

[akhmeteli]

I see, so electromagnetic field qualifies as a necessity and quantum potential does not?

Do you consider the necessity to be objective? or could it be that what is a necessity to one observer, is not to another? And how are necessities induced from experience? An from the particle view, how does a particle induce this necessity from experience?

I guess it's a matter of simplicity. We tend to prefer a simpler theory, all other things being equal. Of course, observers may differ in what they call simple, but there are also objective criteria of simplicity/complexity. As for necessities and experience... If a simpler theory fails to describe the experimental results, we have to look for a more complex one. I like Einstein's "slogan": "as simple as possible, but not simpler". The same about particles, I guess.

If you are into bohm, did you ever try to merge the bohmian view with the subjective bayesian view? Sort of suggesting that the bohmian speculated degrees of freedom rather represents subjective estimates. They aren't real hidden variables in the objective classical sense?

I am not into bohm, but his thinking is not totally off chart IMO. But I think there is another way of seeing the bohm formalism, that does not make use of the deterministic philosophy.

I tried to ask demystifier who has posted alot about bohmian views but it seems he does not acknowledge this association. I would be curious to hear a bohmian view of this, but since it in one sense may have similarities to the bohmian thinking, it is even farther away from it than the copenhagen thinking since it introduces even more fundamental uncertainty.

If I were to induce my thinking onto the bohmian stuff, i would described the bohmian degrees of freedom (here extending it to general degrees of freedem and leave unsaid to interpret as "particles" sets of particles or whatever) as part of the identity of the system, but it determines the expected action relative the system. And I think it's the fact that the expected action relative different systems is different, that gives rise to non-trivial dynamics.

So from outsider, the bohmian degrees of freedom are not hidden variables in the sense of a definite structure with an unknown state, this is wrong because the identification of the microstructure itself! even with a completely unknown (random) state DOES contain information. And this information doesn't exist on the outside.

So IMO, a "bohmian like" interpretation might be kind of possible without the notion of hidden variables.. because it gives the impresion that the varible structure is known it's just that their values are not. I rather see it that the not only is the variable value hidden, the variables themselves re hidden, and effectively doesn't exists - from the outside. which connects to a subjective reality interpretation of QM.

Is this anything in your taste? I ask this out of general curiousity since you are into bohm.

/Fredrik

Very generally speaking, I don't have problems with subjective bayesian view. For example, I very much like Jaynes' information theory approach to statistical physics. It is important to understand, however, whether such an approach is necessary at the fundamental level or at some higher level (statistical physics may be an example of such higher level). As for the fundamental level, I have yet to be convinced that the bayesian view simplifies the matter or, although adding complexity, is just necessary.

 

[Fra]

Very generally speaking, I don't have problems with subjective bayesian view. For example, I very much like Jaynes' information theory approach to statistical physics.

I'm glad to hear this.

It is important to understand, however, whether such an approach is necessary at the fundamental level or at some higher level (statistical physics may be an example of such higher level).

I agree.

As for the fundamental level, I have yet to be convinced that the bayesian view simplifies the matter or, although adding complexity, is just necessary.

I understand your skepsis. I am personally now quite confident that this is the way, but it wasn't straightforward. I've spent some efforts analysing this from the POV of philosophy of science as I prefer it, and I've arrived at a pretty confident personal position of the foundations. I judged this as absolutely necessary as I could not justify the high degree of speculation that I ended up with as a student.

I think the bayesian view alone is insufficient to explain everything, but it is a step in the right direction. I even think that our inability to understand how the "quantum world" scales from an information theoretic point, is correlated to our lack of understanding how QM and GR can be unified. I think separating them, is part of the problems also to understand the QM foundations.

This traces down to the philosophy of science.

IMO statistics, inductive inference and even probability theory really touches the essence of science. What is knowledge? How _confident_ are we in the "knowledge" we think we have? How do we _measure_ confidence? All these questions touches foundations of statistics and probability theory. Many of these things have issues, that are non-trivial, but by tradition are treated as philosophy by many physicists. I could never accept such attitude, but science also has social dimensions. And if this behaviour is accepted in the scientific society, because everybody does it, well then there you go. And from group dynamics it sure is going to take more than one opinion to change the group behaviour. And reflecting over this, I see deep connections to physical interactions and information theory.

This leads me to a new idea of simplity. Risk taking and speculation.

Sometimes you have to speculate and take a risk based in incomplete information, beucause that's life. Because choosing to not take any actions at all may actually be more risky, than taking one of a set of possible smaller risks.

I interpret "as simple as possible, but not simpler" in a more specific interpretation as:

One should not take unjustified risks, and should only take the justified risks necessary to optimise your self-preservation. The "no risk" options usually never exists. When you connect this game thinking, to probability theory and it's foundations many interesting things appear. But I think it would take that someone works out something explicit and applies to to make new predictions and accomplish at least part unification before the collective pays any interest to it. For some reason very few people seems attracted to this.

/Fredrik

 

[Xeinstein]

As I mentioned in some of my earlier posts, quantum mechanics does not necessarily needs complex wavefunctions (real wavefunctions may be enough). This is not just my personal opinion. Shroedinger demonstrated this for a Klein-Gordon field interacting with electromagnetic field. The reasons offered in the preceding post do not work there as the probability density does not equal \psi^2 in that case

Here is a related thread about "complex wavefunctions" that you might be interested

https://www.physicsforums.com/showthread.php?t=207417

 

[akhmeteli]

Here is a related thread about "complex wavefunctions" that you might be interested

https://www.physicsforums.com/showthread.php?t=207417

Thank you,

actually, I follow the thread that you started, but have not had time to participate in the discussion.

I still stand by what I have written in this thread. The arguments to the contrary in your thread did not convince me.

 

[reilly]

Hi there, i have been studying a bit about QM, but ther's one fundamental question
about the wavefunction i can't understand: why is the wavef. defined complex? I mean,
couldn't one work from the begining with a real wave?

Thanks

It all started, in earnest, with Euler's exp(2πi) = 1. (At least I think it was Euler.)The rest is history; practical history. We use complex variables in all manner of sciences, engineering, and, yes, even economics. Why? Complex variables, through contour integration, analytic continuation, conformal mapping, etc. give us enormous mathematical power. (Not much different than the choice of Arabic vs. Roman numerals.)

Why do we let electric current be complex in RLC circuits? Convenience. Nothing more, nothing less. Think about the various phase relationships in circuits -- complex variables allow a particularly simple way of dealing with phases.

It's no big deal. If you don't like it, try QM without i. Why do we use 3 or 99, or x= something?

For the record, when I taught QM I required first that my students knew basic atomic and nuclear physics, particularly the key early experiments -- like Davisson Germer --And I also required students to have at least an undergraduate course in complex variables, and an E&M course that covered basic partial differential equations including special functions, radiation, etc. and advanced mechanics, including contact transformations and the Hamilton -- Jacobi EQ. I thought then, and still do, that without this basic background, it will be agonizingly difficult to understand and cope with QM,
Regards,
Reilly Atkinson

 

[danime]

If the wave-function represent a confined particle, there's allways some way to write it as a real function. See Landau-Lif****z volume 3.

 

[reilly]

Why use Arabic numerals rather than Roman numerals in physics?
Regards,
Reilly Atkinson