A Relativistic Symmetrical Interpretation of the Dirac Equation in (1+1) D (online 7/9 @ 11pm UTC-7)

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This topic contains 8 replies, has 2 voices, and was last updated by Avatar Michael B. Heaney 5 years ago.

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  • #2382
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    Michael B. Heaney
    Participant

    Hello All,

    This is a time-symmetric theory of relativistic quantum mechanics that I’ve been working on the past several years. Your input is invited.

    Thanks,

    Michael
    —————————-
    Abstract:
    This paper presents a new Relativistic Symmetrical Interpretation (RSI) of the Dirac equation in (1+1)D which postulates: quantum mechanics has no arrow of time, and is intrinsically time-symmetric; the fundamental objects of quantum mechanics are transitions; a transition is fully described by a complex transition amplitude density with specified initial and final boundary conditions; and transition amplitude densities never collapse. This RSI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein’s bubble experiment with a spin- 1/2 particle. This RSI can predict the future and retrodict the past, has no zitterbewegung, resolves some inconsistencies of the CI, and eliminates some of the conceptual problems of the CI.

    #2593
    Ken Wharton
    Ken Wharton
    Member

    Hi Michael,

    Thanks for your paper… I’m a bit confused about the proposed ontology; what’s really happening between the measurements, in this account? Aharonov’s take on the two-state-vector formalism seems to be that both the pre-selected wavefunction and the post-selected wavefunction are “really there”. But you don’t seem to be saying the same thing, despite a similar starting point…?

    I guess I’m particularly confused about the phrase “complex transition amplitude density”. Can you unpack exactly what you mean by this? Are these “densities” part of the ontology of what’s really happening between measurements, or just a representation of a lack of knowledge about the eventual outcome?

    Best, Ken

    #2600
    Avatar
    Michael B. Heaney
    Participant

    Hi Ken,

    Thanks for your question!
    Let us first review the Conventional Interpretation (CI) of QM: Consider an electron that is localized as a gaussian wavefunction psi(x,0) around x=0cm at t=0s. What is the probability that this electron will later be found localized as a gaussian wavefunction phi(x,10) around x= 25cm at t=10s? The CI calculates this probability by first multiplying phi*(x,10) by psi(x,10) to get the “complex transition amplitude density,” then integrating this complex transition amplitude density phi*(x,10)psi(x,10) over all space to get the complex transition amplitude A, then multiplying A by A* to get the transition probability.

    In my interpretation of QM, I allow the “complex transition amplitude density” to vary with time: phi*(x,t)psi(x,t). Integrating this over all space and then multiplying the result by its complex conjugate gives exactly the same result as the CI. I interpret phi*(x,t)psi(x,t) as what is really happening between measurements.

    Does this clear up your confusion?

    Regards,

    Michael

    #2604
    Avatar
    Michael B. Heaney
    Participant

    Hi All,

    I am online for the next hour. Hope to hear from you!

    Michael

    #2625
    Ken Wharton
    Ken Wharton
    Member

    Hi Michael; Thanks for your response, but I’m not sure how to interpret a probability for an experiment after it already has a known outcome.

    Let me ask it this way. Suppose the experiment is *complete*, in that I know the precise outcome, and I’m looking back on the whole transaction and doing my best to describe what really happened. At this point, presumably, my description would not be probabilistic, right? So if (phi* psi) is the description of what just happened, why call this a probability density?

    The other part of the question is that if (phi* psi) is the best description of reality, and the only way to determine what that product looks like is to separately calculate psi and phi, then why wouldn’t you go so far as to say that “phi and psi are both real” between the measurements? That would put you squarely in Aharonov’s take on the two-state-vector formalism, I would think.

    #2626
    Avatar
    Michael B. Heaney
    Participant

    Ken,

    My Relativistic Symmetrical Interpretation (RSI) never defines or uses a probability for an experiment after it already has a known outcome! That would make no sense.

    Suppose the experiment has been completed. Then the RSI postulates that the complex transition amplitude density phi*(x,t)psi(x,t) is the complete description of what happened. Note that the RSI does NOT call this a probability density!

    Phi*(x,t) and psi(x,t) are (in general) complex, and not real. This is why I do not say they are both real between the measurements.

    Does this clear up the confusion?

    Regards,

    Michael

    #2650
    Ken Wharton
    Ken Wharton
    Member

    Hmmm… You *are* using this (phi* psi ) to generate probabilities, right? After all , that’s generally what one does with “amplitudes”; squares them and turns them into probabilities. Maybe you need a different terminology if that’s not what you’re going for.

    As for “reality”, I meant “ontic”; complex/real is a totally different issue from ontic/epistemic. After all, Im(phi), Re(phi), Im(psi) and Re(psi) are all “mathematically real” fields. Are *those* fields ontic? If you’re not familiar with the ontic/epistemic distinction in this context, perhaps start here: http://arxiv.org/abs/0706.2661 .

    #2656
    Avatar
    Michael B. Heaney
    Participant

    Consider the classical case of Alice flipping a coin, letting it fall into a box without looking at it, then closing the box. Alice can assign probabilities of 50% it is heads and 50% it is tails. Then Alice opens the box and sees heads. She can now assign a probability of 100% heads for the entire time it was in the box. The same logic applies to phi*psi. It can be used to generate probabilities for arriving at different detectors. But once we detect it at one detector, we know it was in the associated phi*psi the entire time. What would you suggest for terminology?

    I’ll look at the paper you referenced.

    #2657
    Avatar
    Michael B. Heaney
    Participant

    Based on a look at the paper you reference, I think the entire 4D phi*psi object is a complete description of reality. Either phi* alone or psi alone are incomplete descriptions of reality.

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