We do, of course, observe that the cumulative distribution of impacts on the back screen is in line with the square of the wavefunction from the emitter. If emission occurs whenever, while the distribution of available absorbers on the screen is constrained by external factors, then we won't recover the expected distribution. — SophistiCat
But other than terminology, do you see any issues with his proposal? — SophistiCat
Instead of that, they should interact with the ordinary dense matter, at least 380,000 years old, as shown in Figure 2 from my recent paper on the problem of the direction of the electromagnetic arrow of time: http://philsci-archive.pitt.edu/13505 — Darko B
That this doesn't hold true is precisely my point. While an individual transmission may depend on the precise microstate of the screen, the screen explores these microstates continuously. A statistical number of transmission events will take place over a period of time, during which one will have a statistical spread across the precise microstates explored during that time, a spread which looks like the probability of finding a given electron at a given position depends principally on the wavefunction. — Kenosha Kid
The cancellation depends on both waves being advanced waves, so it's not purely terminological. (Advanced waves cannot cancel retarded waves in Cramer's formulation.) — Kenosha Kid
The cancellation depends on both waves being advanced waves, so it's not purely terminological. (Advanced waves cannot cancel retarded waves in Cramer's formulation.)
— Kenosha Kid
Why not? — SophistiCat
But even if an absorber is available, the cumulative distribution of impacts will be defined only by the distribution of the available absorbers on the screen over time. — SophistiCat
And at the same time, in order for the Born rule to hold, that distribution has to match the impacting wavefunction - whatever it happens to be. If we can contrive to emit a particle that hits the screen at times (t1, t2, ...), the screen had better supply us absorbers at such locations ri that (r1, r2, ...) form the distribution that we expect to see. — SophistiCat
does not quite hold: we cannot make emissions happen at will (can we?) — SophistiCat
Here's an illustration that contains the main point. Current (in natural units) here flows left to right not because the system exhibits an electric field across itself but purely because of the *chemical potential difference* between the source and sink. The electron source on the left has electrons filling energy levels higher than on the right, thus electrons move to the right, thus a current. If the source and sink levels were equalised, no current would flow (or, as is described by quantum transport theory, no *net* current will flow). If the sink level was higher than the source, electrons would move from right to left. — Kenosha Kid
Not *only*: the wavefunction of the emitted electron still natters; my point was rather that it can't be the *only* thing that matters.
In TQM itself, the probability of a transaction causing absorption at (r, t) is the amplitude of the retarded wavefunction arriving at (r, t) times the amplitude of the advanced wave travelling backward from (r, t). So it depends on the probability amplitude of *both* waves. — Kenosha Kid
In your example of a screen that has only one absorption site at any one time, only this site can backwards-emit a hole wave. In the language of TQM, only this wave can handshake with the retarded wave, since the amplitude coming from all other sites is everywhere zero.
However, that single hole will move around the screen and, on average, should be smeared out such that the probability distribution we see forming is given only by the retarded wave. — Kenosha Kid
If the hole moves around independently of the impacting wave, while emissions are a Markov process, i.e. a transaction is established whenever a hole is available (as you explain below), with no "knowledge" of what comes before or after, then the resulting distribution of impacts will be independent of the impacting wave. It will only depend on the entropic movement of the hole - most likely just a uniform distribution. — SophistiCat
I'm not sure why you think so. The electron doesn't have to be transmitted at all. In fact, wherever the hole is located, we expect no electron to be transmitted most of the time. Any time the hole is at a site where the probability of finding the electron (as given by its wavefunction) is zero, then no transmission event will occur at all, for instance (i.e. you cannot slow the rate down to 0.001 Hz and get an event every 1 ms if the only available hole is sometimes inaccessible). — Kenosha Kid
Similarly if the probability of finding the electron at a given site is 0.2, you would expect an electron to transmit there when there is a hole there at most 20% of the time. — Kenosha Kid
In reality, the screen is more complex, and electrons will usually be able to squeeze in somewhere. But there should, as per Pauli, always be places it cannot squeeze, and that is neglected in ideal treatments. — Kenosha Kid
If an electron is ready to fire, and there is (in the edge case) just one hole that it can fill, then it will go there almost always, because where else would it go? — SophistiCat
(Unless holes and/or emission events conspire to construct the distribution that we expect to see.) — SophistiCat
Perhaps the emitter is picky and won't always transact with a hole just because it's available? — SophistiCat
Yes, but in order to explain experiments where we see nice diffraction patterns, we must conclude that the number of holes available at any given time is not too few, or else we would be seeing something different (or we need to modify the theory). — SophistiCat
(Unless holes and/or emission events conspire to construct the distribution that we expect to see.) — SophistiCat
Effectively, yes. TQM is a conspiracy of sorts. — Kenosha Kid
Well, as I said, so long as, over the lifetime of the experiment, the holes on average occupy a uniform distribution, we will obtain the characteristic banded pattern. — Kenosha Kid
What it represents is our inability to actually understand the true nature of emission and absorption. — Metaphysician Undercover
Therefore it is simply a vicious circle of misunderstanding, manifesting as the appearance of conspiracy — Metaphysician Undercover
...To show a certain sequence converges one needs to show it is bounded, but the prove it is bounded reflects back to its convergence behavior. It looks like a step-by-step argument alternating between the two will be the ticket.) — jgill
So if the holes (at the screen and elsewhere downstream) don't participate in the conspiracy (indeed, such an extended conspiracy would seem problematic), and there aren't many holes available at any one time, then the emitter has to time its transactions so as to build up the right pattern over time. — SophistiCat
Is it plausible? I suppose the bare-bones theory (not including a specific mechanism for the Born rule) does not rule it out, and neither does its empirical basis, which consists of just such accumulation over time of apparently probabilistic events. — SophistiCat
Transmission is emission + absorption. — Kenosha Kid
Pardon my interjection, but could you guys briefly outline the properties of wave motion? How does the velocity or oscillation of an electron in an atom vary from one traveling in a beam or current, and how does this compare to electromagnetic radiation in various contexts? — Enrique
Well, I'm being careful to distinguish between transmission and emission. Emission can be described as the spread of a single electron wavefunction from the tip of the cathode. Transmission is emission + absorption. In standard QM, transmission has occurred when we detect an electron on the screen. Emission by itself cannot, as MU keeps saying, be observed directly and independently (well, it can, but not without destroying the interference pattern).
So the electron wavefunction may well continue to evolve but simply not collapse. In TQM, the same holds: the retarded wavefunction can evolve indefinitely; it is only when the transaction with the advanced wave occurs that transmission occurs. As per the OP, the emission occurs precisely because the transmission occurs, i.e. it is simply one of the boundary conditions of a process that is agnostic about any arrow of time. — Kenosha Kid
True, hence my interest in Type II transactions, which, if they existed, should be empirically observable and presumably would differentiate TQM-like interpretations from others empirically. — Kenosha Kid
As per Cramer (and his predecessors), there can be no emission without transmission in the absorber theory, whether classical or quantum. "Absorber theory, unlike conventional quantum mechanics, predicts that in a situation where there is a deficiency of future absorption in a particular spatial direction, there will be a corresponding decrease in emission in that direction." (I don't think you disagree, since that is also the premise of your hypothesis - just pointing this out, because what you wrote might suggest otherwise.) — SophistiCat
I wonder though whether the absorber theory actually rules out, logically or empirically, uncollapsed/unabsorbed waves? — SophistiCat
By the way, in the 1980 paper Cramer wrote: "Davies argues that the most general test of absorber theory would include the possibility of type II transactions." This refers to a 1975 paper by Paul Davies: On recent experiments to detect advanced radiation. — SophistiCat
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