Underlying both DEs is the fundamental relationship: The instantaneous rate of change of something is proportional to the amount at that time. The first DE has the imaginary i in its "constant", and eiθ=cos(θ)+isin(θ)eiθ=cos(θ)+isin(θ) works its magic. — jgill
Thanks, that's pretty well the only point I was getting at. — Wayfarer
I'm not sure I follow your last sentence (and I read the SEP section). If, on measurement, the superposition state information is lost to the environment (apart from the measured value) then what else could be required for apparent collapse to have occurred? — Andrew M
This is just unitary QM. For example, MWI and RQM both agree with this prediction and are both referenced in the paper you linked — Andrew M
Zurek is a decoherence guy and he agrees with the Wigner's friend predictions. You seem to be treating decoherence as objective. — Andrew M
Decoherence usually is. — Kenosha Kid
Because the electron's birth and death are the true boundary conditions of its wavefunction! And here we turn to relativity. The relativistic wavefunction is of the form [E−V]2=[p−A]2+m2. This puts time and space on equal footing (both energy and momentum are squared), requiring knowledge of the particle at two times, not just one. — Kenosha Kid
There is no guarantee here that this will eventually reduce the number of intersections with the screen to 1. But we are a long way from the original Copenhagen picture of an electron that might be found anywhere. I expect that, if we could solve the many-body Dirac equation for the universe (well, it would have to be some cosmologically-consistent generalisation of it), it probably would resolve to 1 intersection. — Kenosha Kid
(I hope I got this right.) — SophistiCat
some relativistic formulations of the wavefunction equation have two solutions: w and its complex conjugate w* — SophistiCat
But complex conjugation is equivalent to time reversal (although it also implies negative frequency, energy and charge) — SophistiCat
To me it seems like TI goes further out on a limb than MWI. I am uncomfortable about the pseudo-causal narrative of the "transaction." But perhaps the more profound aspects of the interpretation escape me. — SophistiCat
Whether it's the non-relativistic Schrodinger equation (which has only a retarded solution) or a suitable relativistic equation (which has both), the equation alone does not determine where and how the absorption/measurement will happen - hence the "measurement problem." I am not sure what point is being made here specifically about the relativistic equation. — SophistiCat
(The Schrodinger equation can be produced as a non-relativistic limit of a more general relativistic formulation. How then do two solutions reduce to one? Turns out that two versions of the Schrodinger equation are equally valid reductions: the other one has only an advanced solution.) — SophistiCat
I still don't see how this can be. Boundary conditions are, by definition, local. — SophistiCat
And yet when we do experiments like quantum interference, we find that the measurements depend mainly on the incident wave. Why aren't results confounded by such strong dependence on the boundary conditions? — SophistiCat
I think it's more economical than parallel universes. — Kenosha Kid
So I opened an account at the bank with $100 at an imaginary 314% interest rate. A year later, the bank claims I owe them $100! They say that if I keep my account open for another year, I'll get my $100 back. Should I trust them, or just pay the $100 and close the account? — Andrew M
some relativistic formulations of the wavefunction equation have two solutions: w and its complex conjugate w* — SophistiCat
All, I believe. — Kenosha Kid
The advanced wave must be similarly causal but in reverse. For an advanced wave to be emitted from a particular point on the screen (describing an electron hole in reverse), that point must be capable of doing so. Otherwise the retarded wavefunction depiction of the electron leaving the cathode is unjustified in the first place. — Kenosha Kid
In the case of both microstate exploration and decoherence, the precise state changes constantly. An electron on the screen which might forbid an incident electron at time t might not be present at time t'. A particular configuration of scatterers that would destroy the wavefunction at time t might permit it at time t'.
The signature pattern of the double slit experiment is not one event but many thousands. What we see then is not just the value of the probability density of the electron, but also the statistical behaviour of the macroscopic screen. Over a statistical number of events, the pattern must be independent of changes in the precise microstate of the screen. — Kenosha Kid
I think it's more economical than parallel universes. — Kenosha Kid
there are a number of alternative relativistically invariant wave equations, at least one of which is first order in time — SophistiCat
Are there really any absolutely forbidden points of interaction? Instead of being absorbed, can't the electron scatter instead? — SophistiCat
So let's consider a limiting case where exactly one spot on the screen is available for interaction at any one time - an advance electron hole, as it were. This is what you hypothesize might indeed be the case, right? — SophistiCat
If the availability of electron holes imposes an absolute constraint on where an interaction can occur, then instead of the interference pattern we should see just that - a uniform distribution. — SophistiCat
Well, if I understand correctly, the Everett interpretation is characterized more by what it doesn't do - arbitrarily impose a collapse - than by what it does, so in a way it's hard to be more economical than that — SophistiCat
although it does ditch those advanced solutions. Hm... could you combine the two? — SophistiCat
there are a number of alternative relativistically invariant wave equations, at least one of which is first order in time — SophistiCat
But also first order in space, I think? So the four solutions (advanced spin up, advanced spin down, retarded spin up, retarded spin down) reduce to two (advanced and retarded). — Kenosha Kid
Sure, but scattering also obeys the Pauli exclusion principle, so there must be two holes: one for the scattering electron to go to, and one for the scattered electron to go to (see the Feynman diagram in the OP). And those scattered electrons can scatter again, each requiring two holes, and so on and so forth. So it's a proliferation of backwards hole emission and transmission events. — Kenosha Kid
No, because the probability distribution of the incident electron will still multiply the probability distribution of acceptor sites. — Kenosha Kid
Once the emitter and the absorber "handshake" (which is sometimes described by another pseudo-process, which I haven't investigated), the "tails" of the wavefunctions going back in time from the emitter and forward in time from the absorber cancel out, as are the imaginary parts of the waves between them, leaving only the superposed real parts of the offer and confirmation waves. To any observer this will look as if a wave traveled from the emitter to the absorber. — SophistiCat
In the double-slit experiment, does the electron follow a definite, albeit unknown, trajectory through one and only one of the slits, similar to pilot wave theory? Or does an electron essentially just disappear from the source and appear at the destination a short time later (a kind of non-local electron/hole exchange)? Or does it travel all possible paths to the destination as a wave? — Andrew M
Not if there is only one available site - in this case the electron wavefunction becomes irrelevant. — SophistiCat
So that is how it appears to an observer. What actually happens once a handshake has occurred, and thus a single destination has been determined? — Andrew M
So the best strategy is to borrow lots of money at an imaginary interest rate, wait until it becomes positive (a 180° rotation), and then withdraw it. — Andrew M
So I went back to Cramer's papers from 1980s onward in an attempt to gain a better understanding of the transactional interpretation. I think I managed to unconfuse myself a bit regarding the "orthodox" TI, but I am still not sure about your take on it.
The core of the theory is an emission-absorption process, such as when two atoms exchange energy or (as in your presentation) an electron is emitted and later absorbed by a solid. (I think scattering is handled similarly, but I haven't looked into it yet. There is also an issue of weakly-absorbed particles, such as neutrinos, which may not have a future boundary; I know that Cramer has looked into this, but I haven't.) — SophistiCat
Another paper by Cramer (Foundations of Physics, 1973) specifically treating the arrow of time: — Kenosha Kid
However, there is an alternative approach which, while not in the mainstream
of contemporary theory, represents an effective way of preserving the intrinsic
time symmetry of the relativistically invariant wave equations and thereby
avoiding the ad hoc insertion of an arrow of time into the formalism. — John Cramer
Not sure this should really be up there, but a copy of the entirety of Cramer's book The Transactional Interpretation of Quantum Mechanics is on my alma mater's website: https://www-users.york.ac.uk/~mijp1/transaction/TI_toc.html — Kenosha Kid
However, the careful reader will perceive that there is a more subtle time asymmetry implicit in the TI description of the quantum event which is implicit in TI2. There the probability of a quantum event with emission from (R1,T1) to an absorber at (R2,T2) is assumed to be:
P12 = |Psi1(R2,T2)|2 [12]
rather than:
P12 = |Psi2(R1,T1)|2 [13]
i.e., in the TI the emitter is given a privileged role because it is the echo received by the emitter which precipitates the transaction rather than that received by the absorber. Thus the past determines the future (in a statistical way) rather than the future determining the past. — Cramer
Another paper by Cramer (Foundations of Physics, 1973) specifically treating the arrow of time: http://faculty.washington.edu/jcramer/TI/The_Arrow_of_EM_Time.pdf — Kenosha Kid
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