Interpretations of Quantum Mechanics (is there a general consensus?)

  1. Hi :)

    I recently read a book that states that most scientists believe the wave function represents a real field (i.e., one that possesses energy and momentum). I think this is part of the transactional interpretation of QM but not sure... can anyone confirm whether the book I read is right about this or not?
     
  2. jcsd
  3. I don't know what most scientists believe, but I find that statement strange. I would have thought that the one thing, about the wave function, they would agree on, is that it doesn't represent a real field.
     
  4. From my experience, I would say there is not a general consensus on this point, and most scientists seem to take the view of SUAC - Shut Up And Calculate - which means they know how to do the calculations and just don't worry too much about the interpretation.
     
  5. You would fill some money refund form :uhh:
     
  6. jtbell

    Staff: Mentor

    Which book?
     
  7. Ken G

    Ken G 3,439
    Gold Member

    Not only don't I think there's a consensus on that, I'm not even sure what the statement means. A field is real if it carries energy and momentum? How does one know if a field carries energy and momentum? I would say that thinking is backward-- we don't ask if it carries energy and momentum, and then decide we think it's real, we ask if we think it's real, and then decide it carries the energy and momentum. In other words, we all know we wish to associate energy and momentum with the wavefunction, whether we regard it as real or not, so we first have to ask if we regard it is real before we can decide whether or not it "carries" that energy and momentum, instead of just "associates with" that energy and momentum. So the field is not real if it carries energy and momentum, the field carries energy and momentum if it is real.
     
  8. Yeah, what you said makes sense, Ken. I would have thought that most scientists don't believe the wave function is real, too, martin. I may have mis-stated the part about the wave function a bit, but here's a quote from the preface of the book:

    "...if someone, not a theoretical physicist and not thoroughly acquainted with modern methods of analysis, were to attempt to digest a current article dealing with nuclear forces or cosmic rays, relying for help on the available books on the subject, he would discover to his dismay that modern quantum mechanics differs radically from that which he finds in the textbooks... More confusing to him is the interpretation of a field in the new mechanics. It seems evident that what is meant is a real field possessing energy and momentum. Yet the textbooks attach a purely symbolic meaning to the wave field of a particle, picturing the field concept merely as a probability function."

    ...and there you have it.

    lol I got it from Borders bookstore before they went out of business, so... :P

    It's called Quantum Mechanics of Particles and Wave Fields, by Arthur March.
     
  9. Try the Book publisher then :uhh:
     
  10. hehe... Do you seriously think I should? :)
     
  11. bhobba

    bhobba 4,209
    Science Advisor
    Gold Member

    Most probably believe it has a real existence like say an electric field does - not as an actual field - but as something that exists out there because they think a wave-function collapse is an issue. The interpretation that probably demands it is one based on quantum decoherence for that collapse and its variants - don't know about the transactional interpretation.

    I personally don't believe it does - I think its like classical probability theory - its simply a device for calculating statistical outcomes. Check out:
    http://arxiv.org/pdf/quant-ph/0111068v1.pdf

    Thanks
    Bill
     
  12. stevendaryl

    stevendaryl 2,802
    Science Advisor

    There is something about the wave function that makes a completely different kettle of fish than fields such as the electric field. That is, that unlike the electric field, the wave function is not a field in the physical world. It's a field in configuration space.

    The distinction is this: In the case of an electric field, I can point to a particular spot, and ask "What is the value of the electric field right there?" You cannot ask the analogous question about the wave function, because it is not a probability amplitude on points in space. To see why not, consider a two-particle wave function. In general, It would be written as (simplifying to the case of 1 spatial dimension): ψ(x1, x2), the square of which gives the probability density of finding the first particle at position x1 and the second particle at position x2. It doesn't make any sense for me to point to a particular point and ask what the value of the wave function is at that point.

    I don't know what the implications of this physical-space versus configuration space distinction is for whether the wave function is "real", but it certainly shows that the wave function cannot be considered an ordinary field like the electric field.
     
  13. Ken G

    Ken G 3,439
    Gold Member

    Yet you can point to a box in real space and ask "what is the probability of finding a particle in that box", even for multiple-particle wave functions (if the particles are distinguishable, you can also specify which type of particle you are asking about). You can also ask about correlations like "what is the probability of finding particles in both of these two boxes", and so on. So it's a more sophisticated kind of field, but it seems to me one can still imagine it "exists" in real space if one wants to. True, it is kind of a "question answering field", but then, so are they all. Does one want to attribute independent existence to question-answering fields? No less so in quantum than classical physics, it was always something of a stretch in my view!
     
  14. @ Ken_G: The point of stevendaryl is that fields are represented by mathematical object that have domain spacetime not configuration space. I thought this was so obvious, that's why I didn't even say in my post!
     
  15. stevendaryl

    stevendaryl 2,802
    Science Advisor

    Yet you can point to a box in real space and ask "what is the probability of finding a particle in that box", even for multiple-particle wave functions (if the particles are distinguishable, you can also specify which type of particle you are asking about). You can also ask about correlations like "what is the probability of finding particles in both of these two boxes", and so on. So it's a more sophisticated kind of field, but it seems to me one can still imagine it "exists" in real space if one wants to. True, it is kind of a "question answering field", but then, so are they all. Does one want to attribute independent existence to question-answering fields? No less so in quantum than classical physics, it was always something of a stretch in my view!​

    Well, I don't think there was ever any question about whether the wave function was useful for answering questions. It certainly provides information about the real world. My point is that it isn't something that resides in the real world. It isn't an object that exists in some location, nor is it a field that varies from location to location.
     
  16. bohm2

    bohm2 793
    Gold Member

    I really like Matt Leifer's suggestion in this post:

    Can the quantum state be interpreted statistically?
    http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/
     
  17. Gell-Mann once wrote, ‘Bohr brainwashed a whole generation of physicists into ‘believing' the Copenhagen interpretation of quantum mechanics'.
     
  18. So a wave function is not a wave and its not a particle, its an entity of some sort in 'superposition' that spreads out in x,y,z and t. We can only find out if its 'there' by decohering it. Otherwise it is not a physical, real entity.

    It behaves as though it were a 'calculation' waiting for its result (at some x,y,z and t) on decoherence. It leaves no track of its path. It simply 'arrives'. We know where it came from but have no idea of its path to its destination.

    So what entity can achieve this? Something superposition is not a 'thing' - its not an object that we cannot enclose or put in a container - unless we decohere. And even then decoherence results in 'values observed'.
     
  19. If it doesn't represent a real field, how can it interfere with itself in the double slit experiment?

    We can't detect gravitational waves right now, but it does not mean they do not exist.
    It just mean our instruments are not sensitive enough to detect them directly right now.
     
    Last edited: Feb 12, 2012
  20. Vectronix:
    There are many interpretations...check here in Wikipedia
    for background and introduction

    http://en.wikipedia.org/wiki/Quantu...ble_functions_-_analytical_calculus_formalism



    It's probably the 'abstract vector space' formulation thats leads to major disagreements.

    Here are a few quotes I saved from QUANTUM MECHANICS by Albert Messiah:

    This first may be the most controversial:

    So some new mathematical models became popular:

    * This is a 'one liner' referring to the Heisenberg uncertainty principle.

    So what we have, in my own words, are models. They provide some great insights, have been shown to offer many experimental predictions which have been verified to great precision, but which still leave remaining interpretational issues.
     
  21. Ken G

    Ken G 3,439
    Gold Member

    My point is that with multiple particles, complete information in quantum mechanics refers not only to the particles themselves, but also to their correlations. The importance of correlations doesn't mean we are not dealing with things that "reside" in 3-space, it just means that correlations are more sophisticated animals. We would face an analogous issue if we were interested in purely classical correlations between density variations between two species in 3 space, like two types of gas. There our density correlation functions would be mathematically dependent on 3X2 space, not 3 space, because we'd be interested in questions like the probability of finding density increases in one gas given that we have nearby density increases in the other. Yet even so, no one would question that the density distributions themselves "reside" in 3 space. The mathematical animal needed to talk about correlations in 3 space is a higher dimensional object, but I don't see why that needs to compromise our sense of where these correlations "reside." It's like how in relativity, we think of events as residing in spacetime, but the fields in relativity are tensors, not vectors that take on values in spacetime. So they are more sophisticated mathematical objects, to maintain the correct invariances, yet we still think of relativistic fields as "residing" in spacetime.
     
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