Determinism, Reversibility, Decoherence and Transaction

This idea of the absolute square is important. It is how we get from the non-physical wavefunction to a real thing, even as abstract as probability. Why is the wavefunction non-physical? Because it has real and imaginary components: u = Re{u} + i*Im{u}, and nothing observed in nature has this feature. The absolute square of the wavefunction is real, and is obtained by multiplying the wavefunction by its complex conjugate u* = Re{u} - i*Im{u} (note the minus sign). Remembering that i*i = -1, you can see for yourself this is real. We'll come back to this.

The back screen is a macroscopic object that cannot be treated precisely with quantum mechanics.

The back screen is a high-entropy object compared with the electron. That is, at any time, it may occupy one of hundreds of thousands or millions of microstates: particular configurations that are energetically equivalent to one another. At one instant t', a position on the screen r' may not admit an electron because it already has one there. At a subsequent instance t'', it might admit an electron at r'. The screen will explore these microstates in a thermodynamic way. i,e, in the same way that a box of gas will have different but energetically equivalent configurations of gas molecules one instant to the next.

Because the electron's birth and death are the true boundary conditions of its wavefunction!

I can say that the concepts employed here are deficient, showing a lack of understanding of the concepts.

A moving body has velocity, mass, and momentum according to Newtonian principles, but it does not have "energy".

We understand radiant energy, such as radiant heat, through its absorption, not through an understanding of the process of radiation.

I believe the macroscopic/microscopic division is not an adequate representation of the real divide.

Conventional wisdom tells us that the wave formulation is far more advanced, providing a much higher degree of understanding of the reality of the situation, so we ought to dispense this conception of empty space with bodies or particles moving around, and replace it with a consistent wave model.

You cannot represent a photon or electron as being emitted.

If the voltage of the cathode is reduced such that only one electron fires out, say, per ten seconds, eventually the same pattern builds up. From this we deduce that each electron is a wave.

If the pattern is something that "builds up" then the pattern isn't the result of one electron, but many over time. One electron going through every ten seconds makes one dot on the screen every ten seconds that eventually builds up the pattern over time. So each electron behaves like a particle and the relationship between all the electrons is a wave, not that each electron is a wave, or else you'd get the pattern with the first electron. There would be no "building up" if each electron was a wave.

This must be judged from within a quantum theory, with additions and subtractions of course, so I will focus on the parts of your response that fall within that scope.

This is worth treating. In 1900, things were thought to be either particles or waves. The blackbody radiation spectrum and quantised atomic orbitals turned that on its head: waves were behaving like particles; particles were behaving like waves. It was surprising, hence the "wave-particle duality paradox'.

There is no paradox. There is no preferred basis set for describing waves except for that of the operator a particular measurement device is described by. At one extreme, plane waves -- Eigenstates of the momentum operator -- have well defined momentum and no defined position, but occupy all of space. At the other, Eigenstates of the position operator have well-defined position but no defined momentum. Everything else lies in between.

The double-slit experiment begins with an electron with a well-defined position and, after measurement, ends with an electron with a well-defined position. These need not be precise, though they are typically treated as such. In between, the electron spreads out as a wave, but eventually must reduce, either deterministically or spontaneously, to something more localised.

The concept of emission is pretty uncontroversial in quantum mechanics.

The end-game being an attempt to put to bed the 'quantum equals non-determinism' myth.

Since the problems of quantum theory are a manifestation of the conceptualizations employed (as I described above), then we have to step outside quantum theory to get a handle on these problems.

As I stressed in the last post, your claim that there is a particle, called an electron, which exists during the in between period, and "spreads out as a wave", is completely unsupported by the conceptualization of "energy".

It really makes no sense to attempt at a validation of a temporal continuity of a single electron by introducing different forms of the electron , like "stroboscopic wave-packet"

OK, if that's what you want to discuss, then perhaps you can describe how spontaneous emission and random fluctuations are consistent with determinism.

I'm afraid not. If there are no other electrons to interfere with, and the electron does not interfere with itself, there is no possibility of interference effects.

A brief reminder: when a cathode fires electrons at a screen with two slits, beyond which is another screen, the pattern that builds up on the back screen is bands of light and dark, the dark bands being where few or no electrons strike, the light bands being where more strike. From this we deduce that the electron beam coming from the cathode is a wave.

If the voltage of the cathode is reduced such that only one electron fires out, say, per ten seconds, eventually the same pattern builds up. From this we deduce that each electron is a wave.

LOL. Just read what you wrote, bro.

The "beam" is the relationship between the individual electrons and according to you is a wave. If the same pattern is created no matter how long the interval between each electron, then it isnt the electron that is a wave because one electron would create the pattern if it were a wave like the "beam" of electrons.

I dedicated quite a portion of the OP to spontaneous emission

Photon emission/absorption is another example of a reversible process.

The former has a determinate cause, the latter may be spontaneous.

The fact that you can treat the two mathematically as one reversible process does not justify your claim that the two are one reversible process.

The second experiment doesn't show that each electron is a wave. It shows that electrons don't appear to move through, or are governed by, space-time like other particles, or maybe it is our view of space-time that is skewed.

Maybe, but that does not fall within the scope of the OP, which concerns quantum mechanics, not alternative theories to quantum mechanics.

This idea of the absolute square is important. It is how we get from the non-physical wavefunction to a real thing, even as abstract as probability. Why is the wavefunction non-physical? Because it has real and imaginary components: u = Re{u} + i*Im{u}, and nothing observed in nature has this feature.

Sure it does. It shows that your OP is unfounded in asserting that electrons are waves, and is not the rest of your OP built upon that faulty premise?

You propose a complete misrepresentation of the human conceptualization of radiant energy.

Both the retarded wavefunction going from t -> t' and the advanced wave coming from t' -> t may explore whatever places they want, but only in the trajectories where one is the conjugate of the other do their trajectories become real.

Probably a stupid question: if the mapping from a wavefunction to it times its complex conjugate always produces a purely real variable, and that the "advanced wave" is defined by the mapping of this wavefunction to its complex conjugate, how could this be taken as evidence of a coincidence of physical mechanisms (two processes with the same result) when it's actually two names for the same mapping?

Ideas about the nature of radiation that are different to quantum mechanics may well be fascinating, but not relevant.

As stated previously, the OP is regarding QM, and nothing outside that framework. Feel free to start a thread on the subject you'd obviously prefer to discuss.

What is it that i obviously want to discuss, KK?

Something wherein electrons are not waves, i.e. something that is not quantum mechanics. And by all means, but elsewhere.

You're confused. Its your OP that fails to show that electrons are waves. You've only been able to show that the beam is a wave. So if a requirement of QM is a belief that electrons are waves, then your OP isn't about QM either. That's all I'm saying.

Hats off to Kenosha Kid.

This does not put time and space on equal footing. The solution requires knowledge of u at one time and two places. These are generally derived from physical considerations, e.g. where the electron wavefunction must vanish: two positions where the wavefunction is zero at one time: generally the start.

[The relativistic wavefunction] puts time and space on equal footing (both energy and momentum are squared), requiring knowledge of the particle at two times, not just one. This is why in relativistic quantum theories, we do not proceed by specifying an initial state, time-evolving it forward, and asking the probability of spontaneously collapsing to a particular final state. Rather, we have to specify the initial and final states first, then ask what the probability is.

The true boundary conditions

This idea of the absolute square is important. It is how we get from the non-physical wavefunction to a real thing, even as abstract as probability. Why is the wavefunction non-physical? Because it has real and imaginary components: u = Re{u} + i*Im{u}, and nothing observed in nature has this feature. The absolute square of the wavefunction is real, and is obtained by multiplying the wavefunction by its complex conjugate u* = Re{u} - i*Im{u} (note the minus sign). Remembering that i*i = -1, you can see for yourself this is real. We'll come back to this.

The OP is not deriving QM, merely summarising it. Conversation would be pretty limited in scope if you have to re-derive from first principles everything that you intend to discuss every time.

That was a nice presentation and an interesting discussion. Thanks for putting in the effort!

The "trick" of putting some of the boundary conditions ahead in time makes the point a rather trivial one. Another way to state it would be to note that if there is a fact of the matter about the way the world is going to be at some future time, then there is nothing indeterminate about it. Well, of course.

I wouldn't agree with the statement that the wavefunction is non-physical because it has a complex component. We can represent uncontroversially real entities with complex functions, as you are no doubt aware (e.g. the electromagnetic field in classical electrodynamics, and generally any 2D model where complex representation is expedient).

But if only measurements are real, then nothing about the wavefunction as such is real, not even its absolute square: a probability density is not a measurement.

Anyway, this is probably a diversion (or not - you tell me).

Then either QM is flawed in how it goes about showing that an electron is a wave, or your summarization of QM is flawed. I never asserted that electrons are or are not waves, merely that you didn't show that they were.

Is quantum theory the "set theory" of physics? Weird at first but providing a foundation? :chin:

But let's turn the question around. An atom in the oven emits a photon and later another atom absorbs it and re-emits it (more like A below). How does the first atom know to emit a photon such that an even number of its wavelengths will fit in the box? How does either the atom or the photon know how big the box is? Photon emission is just the de-excitation of an atom from one energy level to a lesser one, and the energy of the oven is given by its temperature, which could be anything.

The question becomes less mysterious when we treat time and space equally: the emitted photon doesn't just have a spatial endpoint, but a temporal one, i.e. the photon can only be emitted when it "knows" where and when it will be absorbed. But how could this be?

Run that movie backwards and you have exactly the same thing...

The Copenhagen description, though, is irreversible: wavefunction collapse is a loss of information that is not retrieved by simulating the reverse process.

Do you think that a hot object knows that the cooler object is cooler when it radiates heat?

And I'm sure you know that the definition of "black-body" is based in thermodynamic equilibrium.

Since this idea which you have (I should call it an "ideal") that emission/absorption is reversible, is dependent on black-body conditions, it's practical significance is very limited.

Emission/absorption is only reversible when an object is at thermodynamic equilibrium, which is when emission will not occur.

Clearly you cannot "run the movie backward". The idea that you can take an object's radiation of energy to its surroundings, and turn it around such that you can represent it as it's environment radiating the energy to the object, is completely unjustified, and obviously wrong.

Have you ever heard of "mechanical efficiency"? Mechanical efficiency is always less than 1, because a mechanical system always loses energy to its environment, friction for example.

But these aren't physical either. It is simply that complex exponentials are much easier to manipulate than individual sines and cosines. I'm not trying to do the wavefunction down, though. Whatever its ontology, it is important for predicting experimental outcomes and therefore corresponds to something physical. But no complex quantity can be physical in itself, i.e. we can't observe it in nature.

Another self indulgent spitball from me. Thank you for the free physics lessons.

What stops complex quantities from being physical?

It is sufficient that each particle knows where it is going.

No, a blackbody radiator is a non-equilibrium thermodynamic system, that is: it is not in equilibrium with its environment.

I'll give you a heads up now, since you keep making this error: very little of what I've presented in the OP is original.

Fundamentally, a particle moving from one position to another is reversible for instance, e.g. things are not constrained to move in the same direction along a given axis.

That's nonsense, to say that a particle knows where it's going. Are you suggesting that the particle has a mind of its own?

Do you get most of your information from Wikipedia?

But these aren't physical either. It is simply that complex exponentials are much easier to manipulate than individual sines and cosines.

But no complex quantity can be physical in itself, i.e. we can't observe it in nature.

That's actually not an uncontroversial statement. The wavefunction is frequently referred to epistemologically as the total of our knowledge about a system. The OP basically states that it encoded more ignorance than knowledge.

he wavefunction can be written as a real function multiplied by a complex phase defined everywhere (this is trivial: a complex number has magnitude and phase). The phase is important for interference effects, but makes no difference when it comes to observables. The former is why I believe in an ontic wavefunction, and the latter is why the wavefunction might be considered epistemic.

No, I did something that has apparently never occurred to you: I got an education.

How does your (transactional?) interpretation recover the Born rule?

How do you get the interference stripes in the double slit experiment?

Complex quantities are no more and no less physical than real quantities, tensors, vectors, and whatnot. They are all mathematical objects.

So if that makes the wavefunction real in a broad sense (which is fine by me), then the whole of it has to be real, not just the amplitude

There is no cutoff, which is fine as I am not exploring the realm of the classical limit. It is sufficient to know that a classical limit exists. The relevance of the macroscopic screen is merely that it explores microstates, nothing more.

The back screen is a macroscopic object that cannot be treated precisely with quantum mechanics

No, I did something that has apparently never occurred to you: I got an education.

The OP holds that the complex wavefunction is an ontic description -- or fair approximation to such -- of how particles propagate through space and time as we represent them.

From the overlap integral of the retarded wavefunction with the advanced wavefunction:

In transactional QM, this is the very meaning of the Born rule.

When a particle moves from event (r,t) to (r',t'), it still does so by every possible path (Feynman's sum over histories). If you sum up every possible r' at t' and normalise, you recover the wavefunction at t'.

Ah, I see. This is deeper than I'd realised. Simply multiply whatever complex number by whatever physical unit: we never see that. I see I have 10 fingers and that I'm 5.917 feet tall, but I have never weighed (12 + 2i) stone.

I'm getting confused now between ontologically real and real as in has no imaginary component.

The OP holds that the complex wavefunction is an ontic description -- or fair approximation to such -- of how particles propagate through space and time as we represent them. How we describe the relationship between time and space is intrinsically complex, just from straight relativistic vector calculus, which happens to be the language quantum field theory is written in. There are other languages for describing relativity that can do away with the imaginary number and it may well be that in future we can generalise QFT in a similar way; such an endeavour would be part of a general relativistic quantum mechanics. So I don't hold the complex wavefunction to be an ontic description of the particle itself, rather it encodes the ontology of the wavefunction in our spacetime representations accurately, e.g. encodes information vital for doing the physics.

As evident from the terminology which you use, (described in my reply to jgill above), your education was not in physics. Nor was mine, so we ought to be on par for any approach to this matter of physics

But this only gives the "real paths" of the electron once the "boundary condition" on the other end is fixed, i.e. once the measurement already happened at the back screen.

This doesn't explain any actual data though: we have no independent knowledge of those "real paths" besides what the interpretation tells us. What we have from experimental setup and observation are just the boundary conditions, the origins of the retarded and the advanced wavefunctions.

which is no more than what vanilla QM tells us and doesn't explain the really interesting bit, i.e. the measurement problem.

Well, of course, if you take something that is usually represented by a scalar, such as height or weight, then a real number will be optimal as a mathematical representation.

Complex numbers form a 2D vector space over the reals which is isomorphic to R2 (vectors take the form (Re(z), Im(z), adding real and imaginary parts works just the same as adding x and y components, it's why the plane representation of complex numbers works).

This might trivialize C. Here's a quote from the web, from an educational perspective:

A vector space isomorphism is only defined between two vector spaces over the same field

It would help if this issue is clarified.

If it's impossible for an imaginary quantity to be physical, and it's possible for a real quantity to be physical, why would it be the case that one complex number representation (x+yi) can't be physical, and another (2 by 2 matrices of real numbers) might be physical?

We've never managed to measure anything that is a 2x2 matrix either. We use matrices a lot -- they are useful, but they are constructs. I don't think nature knows about them.

Given the way they enter into the equations, my feeling is that it's the latter, but I'm not trying to make that particular case in the OP. However complex things are at root, empirically they manifest as real.

or take this to PMs

Somehow individual measurements are physical but tabulating them makes them incapable of being physical.

Nature can "know" about the vector elements but not the vector

EG: if the criterion for a theory (as a whole) being physical is successful prediction of experimental results ("manifesting as real"), it's silent on theory elements...

Yes. Vectors are a way of dealing with multiple similar quantities which transform in similar ways. Some of those quantities may be related to one another, but there's nothing I can think of that makes the interpretation of the vector as anything more than a notational convenience.

I won't quote the rest, just sum up. A theory is tested empirically, not it's individual elements. If the theory as a whole (or a subset of elements, catering for irrelevancies to a particular experiment) yields otherwise inexplicable or more accurate predictions for experimental outcomes, it's a good theory.

Nature cannot care that much how we represent it.

Which is why I'm pressing the issue; if nature doesn't care how we represent it, why would whether something could be physical or not vary with an isomorphism of structures? Why would a criterion to decide whether a structure is physical decide differently depending upon which representation of a structure you choose?

Note that electric impedance is a complex variable. So there exist classic physical variables described by complex numbers.

If complex numbers fit the bill better than real numbers to describe a particular phenomenon, maybe it means something...

Well, if complex numbers are nothing more than a mode of computation, there's no reason to worry about their use in the wave function.

it's a wave after all so Fourier's methods must apply?

As intriguing as complex representations in physics, for me, is how linear operators are so effective. One would think nature to be complicated and non-linear; linearity is a very stringent condition, while simplifying the math.

As intriguing as complex representations in physics, for me, is how linear operators are so effective. One would think nature to be complicated and non-linear; linearity is a very stringent condition, while simplifying the math. However, it is a seasoned trick in the profession to approximate the non-linear by linear constructs, and, of course, ordinary differentiation and integration are linear operators.

the square and the circle, are fundamentally incompatible.

Straight lines can never be reconciled with curved lines

I have done quite a few investigations into linear fractional transformations, and one feature that makes them important is they transform Circles into Circles, where the capital C is in recognition of the fact that a straight line is simply a circle with infinite radius. This has to do with the Riemann sphere.

It appears the rest of your post goes into the hyperreals, where others on TPF have greater competence.

Maybe that's the reason they are used in the wave function as well: it's a wave after all so Fourier's methods must apply?

A circle with an infinite radius is an incoherency. This is exactly the problem I am talking about, the faulty attempts by mathematicians to make circles compatible with straight lines. It necessarily results in incoherency. The logical thing to do when faced with this glaring incompatibility is to address the nature of reality, and attempt to determine the reason for that incompatibility, rather than to attempt to veil it, or cover it up with such incoherent principles.

Hey, just to let you know, I want to think on this some more, don't want to reply just for the sake of saying something.

Like the flock of sparrows sitting on your fence, the peanut gallery has no interest in the true nature of space and time.

The truth about reality is just too far removed . . .

I will never reveal such a thing, because it is not understood by anyone.

I already showed you how your thesis, which is a turning away from the vast array of evidence that energy is transmitted as waves, towards a theory which treats this transmission as a movement of particles, is a turn in the wrong direction.

I disagree with your analysis and do not see it as consistent with QM.

Clearly, wavefunctions represent waves, not particles as you insist from your interpretation.

By the way, why do you present this stuff on a philosophy forum when you are completely uninterested in philosophical discussion of it? Why leave your peers? Have you been rejected?

For instance: is the electron wavefunction the only quantity that affects where the electron can be found?

I thought the electron couldn't be 'found' anywhere until it is measured? It is not a discrete entity that exists in some unknown location until such time as it is registered. In fact there really is no such thing as 'an electron' until it is measured, when it manifests as a registration on a plate - which is the basis of 'the measurement problem'.

But your explanation presumes that there is an electron as a discrete existing particle that exists independently of being measured. Whereas, if you are to question the 'Copenhagen Interpretation', isn't that precisely the point at issue?

It referred only to the general ideas of himself and Bohr with respect to what could and could not be stated on the basis of quantum physics. So I hardly think it's 'simplistic'.

However, the 'collapse' of the wave function is actually a metaphor, as there never is an actual wave per se (any more than there is an actual particle).

and as MU observed, this is a philosophy forum, not a physics forum. I do ask questions on that forum also, but they give pretty short shrift to philosophy over there.

If I'm out of line in my OP, can you be a bit more explicit?

In the double slit experiment, the back screen is treated as ideal. This means the only thing that affects where the electron can be measured is the electron wavefunction, which is ambiguous, hence the measurement problem.

The insight drawn from this is that the wavefunction evolves into this ambiguous state and can collapse to any position on the ideal screen. But this holds only for ideal screens.

The measurement problem is that the wavefunction that describes the electron can be in a superposition of observables, but when we measure it it's always in one. It is always a wave.

With the double-slit experiment, you can considerably vary the rate at which particles are fired without effecting the resulting interference pattern. That is, roughly speaking, 24 hours at 1 particle fired per second would give the same pattern as 86,400 particles fired in 1 second (all else being equal).

I know this is one of the strange things about the experiment, and as I understand it, this is the origin of the idea that the particles fired one-at-a-time 'interfere with themselves', which I think seems a very lame idea (but as I said, I'm not a physicist).

However the point which struck me is that if the inteference pattern is not rate-dependent, then it means that time is not a factor in the generation of the interference pattern i.e. if the same pattern can be generated in 1 second as in 24 hours, then 'time' is not a variable (as 'rate' is a function of 'time'). And that struck me as being at least philosophically significant.

The measurement problem is that the wavefunction that describes the electron can be in a superposition of observables, but when we measure it it's always in one. It is always a wave. Even if we managed to measure its position to arbitrary accuracy, it would be a wave in momentum space still. (Likewise if we measure it's momentum exactly it's a wave in space. This is the uncertainty principle.)

But your explanation presumes that there is an electron as a discrete existing particle that exists independently of being measured.

Kenosha Kid likes to waffle.

I generaly find Kenosha's posts a model of clarity. I often don't agree with them but not because I think they're 'waffle'.

Not according to the transactional interpretation of quantum mechanics, which holds that the actual trajectories a particle takes are not just determined by the retarded wavefunction going from time t to t', but also the advanced wavefunction going from time t' to t. (Advanced wavefunctions come up in standard QED as well, to yield the electron self-energy). In this interpretation, the complex conjugate is essentially a message from the future. The electron takes the real trajectories it does in part because it has information about where it's going or, from another viewpoint, where it's conjugate came from.

The true boundary conditions of any particle are its birth and death: where and when it was created, and where and when it will be destroyed. These are facts of each particle. This is the full time-dependent wavefunction of the electron which is, relativistically speaking, equivalent to a static 4D wave.

A good basis set that puts wavelike and particle-like extremes on equal footing is the stroboscopic wave-packet representation, on which I wrote my master's thesis. All of the above still holds: we simply replace Pauli exclusion of two electrons being in one kind of state (position) with that of two electrons being in another kind of state (stroboscopic wave-packet). The exclusion principle holds across all such bases (e.g. you cannot have two like-spin electron plane waves with the same momentum, which is what I had in mind for the states k, j', k" and k"', though these could be position, orbital, Bloch, Wannier or stroboscopic states or anything else you might consider, it makes no difference to the argument).

If you want to know more about why individual electrons are waves, you can Google it.

The new-ish bits are that a) one cannot draw conclusions about where a particle may be found at a given time by considering only that particle at the time, and b) that the birth and death of a particle are its true boundary conditions. Those might be considered novel or controversial.

When a particle moves from event (r,t) to (r',t'), it still does so by every possible path (Feynman's sum over histories). If you sum up every possible r' at t' and normalise, you recover the wavefunction at t'.

The OP holds that the complex wavefunction is an ontic description -- or fair approximation to such -- of how particles propagate through space and time as we represent them.

This is evident in the various interpretations of QM. in Copenhagen, the electron is a complex wave, the field acts linearly, there is one measurement outcome and spontaneous collapse. In MWI, the electron is a complex wave, the field acts linearly, there are an infinity of outcomes and the wave evolves forward in time deterministically. In Bohm, the electron is a real, classical particle, the field is nonlinear, there is one outcome, and the particle evolves forward in time deterministically. In transactional QM without my edits, the electron is a complex wave, the field is linear, there is one outcome, the wave evolves forward and backward in time but probabilistically.

The measurement problem is that the wavefunction that describes the electron can be in a superposition of observables, but when we measure it it's always in one. It is always a wave. Even if we managed to measure its position to arbitrary accuracy, it would be a wave in momentum space still. (Likewise if we measure it's momentum exactly it's a wave in space. This is the uncertainty principle.)

As Heisenberg said 'We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning.'

Disgusting, MU. Whatever happened to you that instead of a reasonable courtesy and the good sense to learn you seem invariably to default to a dogmatic whackdoodleism whose first characteristics are denial of reality and denial of fact in favour of the world as MU thinks it is. What school taught you that?

They all acknowledge that there is a deep philosophical problem sorrounding the ontological status of the wave function - whether it's real, or simply a mathematical device, or an artefact of the understanding. None of that is resolved.

The back screen is physical, it's not 'ideal'. When you run the experiment, the results are recorded on a physical screen.

It referred only to the general ideas of himself and Bohr with respect to what could and could not be stated on the basis of quantum physics. So I hardly think it's 'simplistic'.
— Wayfarer

In truth, it's less the interpretation and how it's applied

But again, the Schrodinger equation is wave-like, but it is an actual wave?

But that got smacked down with: don't be stupid, the particle interferes with itself! (per Dirac).

Kenosha Kid likes to waffle. When it suits Kenosha's purpose, the electron is a particle. When it suits Kenosha's purpose, the electron is a wave. But Kenosha adheres to no concrete principles to distinguish between when the electron is observable as a particle, and when it is observable as a wave. Kenosha Kid will call it a particle, or a wave, depending on what is required at that point in the discussion.

Please point out where you think I failed to understand it [the interpretation of the wave function collapse]

The probability of finding [the object] at a given position is unaffected by this phase. This is not a general feature of wavefunctions.

The particle-like behaviour evident in measurement is not that the electron ceases to be a wave at all, but that the wave somehow reduces to a single Eigenstate of the measurement operator.

If the voltage of the cathode is reduced such that only one electron fires out, say, per ten seconds, eventually the same pattern builds up. From this we deduce that each electron is a wave.

This isn't addressed to you per se, just for general clarity: the concrete principle adhered to is the expansion postulate of QM, which states that the wavefunction is always a linear admixture of one or more Eigenstates of a given operator. After measurement, this is equal to a single Eigenstate of the measurement operator.

QM does not maintain two different types of electron: one wave-like, one particle-like, and swap between them. It is always a wave. That wave can be a position Eigenstate or not. I think I've already addressed this once before.

The particle-like behaviour evident in measurement is not that the electron ceases to be a wave at all, but that the wave somehow reduces to a single Eigenstate of the measurement operator.

Not according to the transactional interpretation of quantum mechanics, which holds that the actual trajectories a particle takes are not just determined by the retarded wavefunction going from time t to t', but also the advanced wavefunction going from time t' to t. (Advanced wavefunctions come up in standard QED as well, to yield the electron self-energy). In this interpretation, the complex conjugate is essentially a message from the future. The electron takes the real trajectories it does in part because it has information about where it's going or, from another viewpoint, where it's conjugate came from.

We would make such a demand of the cathode: for an electron to be emitted at point (r,t) there must be an electron at (r,t). It is only sensible that we do so for the hole the electron will occupy. (It's worth convincing yourself that this hole also has a history. For every electron that vacates position r to occupy position r', it leaves behind a hole and goes to where the hole previously was, describing an electron hole that vacates position r' to occupy position r. We do not need to consider it the same hole throughout, but there must be some conservation of hole-ness.)

The true boundary conditions of any particle are its birth and death: where and when it was created, and where and when it will be destroyed. These are facts of each particle. This is the full time-dependent wavefunction of the electron which is, relativistically speaking, equivalent to a static 4D wave. Unlike in the QM of the Copenhagen interpretation, the conjugate solution (from death to birth) is also a solution when these boundary conditions are applied. This solution eliminates almost all of the trajectories possible (and expected) in Copenhagen QM. And this is just the single-particle picture.

As we expand the picture to include more bodies in the universe, especially the rest of the electronic field, more and more remaining trajectories are removed by things like scattering and Pauli's exclusion principle.

If not, we're left with a solution that looks like a hugely constrained version of the many-worlds interpretation. I name this the not-many-worlds interpretation of quantum mechanics.

Furthermore in the case of atoms the claim that these are “particle trajectories” has been re-examined recently by Flack and Hiley [47] who have concluded that the flow lines, as we shall now call them, are not the trajectories of single atoms but an average momentum flow, the measurements being taken over many individual particle events. In fact they have shown that they represent an average of the ensemble of actual individual stochastic Feynman paths.

And this is a philosophy forum, where [E?V]u=12m[p?A]2u is not, as it were, lingua franca.

Please point out where you think I failed to understand it [the interpretation of the wave function collapse]
— Kenosha Kid

If you posted your OP at physicsforum.com, I'd be interested to see what other physicists say about it. I intuitively feel there's a problem with it, but of course I don't have the skills to say what, exactly.

So the challenge to you is to explain how you manage to reduce the wave transmission of energy to a trajectory.

in relativistic quantum theories, we do not proceed by specifying an initial state, time-evolving it forward, and asking the probability of spontaneously collapsing to a particular final state. Rather, we have to specify the initial and final states first, then ask what the probability is. This is constructed as a Green's function G(r, t; r', t').

So how would you reconcile these two incompatible descriptions of the electron, one in which it has a momentum as a wave packet, and the other within which it has a position with the capacity to leave that position creating a hole there?

In relation to quantum trajectory theory, here's an article (I haven't had time to read completely read it yet) which might interest you, if the link works: https://doi.org/10.3390/e20050353
entropy 2018, 20(5), 353

Interestingly this popped on my radar today, describing something very similar to what the OP describes but with light waves instead of electron waves.

https://scitechdaily.com/scientists-crack-quantum-physics-puzzle/

The genuinely controversial part of the OP is the idea that, if we could solve the many-body wave equation for the whole apparatus, we would find that a given electron does not have the characteristic double-slit band pattern at a given time.

Is there any 'given electron' - prior to it being measured?

Yes, in quantum theory, including quantum field theory, the electron is considered to be there whether it's measured or not.

What is meant by ‘position’ in the quantum realm? Nothing more or less, Heisenberg answered, than the result of a specific experiment designed to measure, say, the ‘position of the electron’ in space at a given moment, ‘otherwise this word has no meaning’. For him there simply is no electron with a well-defined position or a well-defined momentum in the absence of an experiment to measure its position or momentum. A measurement of an electron’s position creates an electron-with-a-position, while a measurement of its momentum creates an electron-with-a-momentum. The very idea of an electron with a definite ‘position’ or ‘momentum’ is meaningless prior to an experiment that measures it.

In perturbation theory and path integral formalisms of relativistic QM, such as quantum electrodynamics, one specifies initial and final states, as per the form of the Dirac equation which is power 2 in space and time (momentum and energy). This is what is meant by a path or trajectory.

If we do this with final position states for all positions on the back screen, we reconstruct the wavefunction defined over all of those points. The wavefunction and the Green's function are highly related.

These descriptions aren't incompatible. Any wavefunction can be written as a superposition of Eigenstates of any measurement operator. If my electron collapses to an exact position state, for instance, and an electron in the screen is a wave-packet spread around that position, either the latter has to be scattered away from that position or the former is blocked from being found there.

The very idea of an electron with a definite ‘position’ or ‘momentum’ is meaningless prior to an experiment that measures it.

And a reconstruction of the wavefunction over all the points produces a map of probabilities, not a description of an actual trajectory.

The problem being that there is a real difference between a spatial separation and a temporal separation, because by the nature of time, a temporal separation is not invertible, while a spatial separation is.

The separation between time1 and time2 cannot be treated in the same way as the separation between spatial point A and point B, because the empirical evidence demonstrates that things only move from time 1 to time 2, and the opposite is impossible.

The power, or force, which causes the material world to be as it is, at each moment as time passes at the present, must be prior to the passing of time at the present, and therefore a cause which is in the future.

When one of them excludes the possibility of the other, this means that the two are incompatible.

Neither in relativity nor relativistic quantum mechanics is there a preferred direction of time. Histories of particle motions constitute worldlines in 4D, with no intrinsic arrow.

Actually the empirical evidence proves that time and space are interchangeable, i.e. those dimensions in one frame of reference get mixed together in another frame of reference. Look up the Lorentz transformations.

Interesting. It sounds a bit similar to the OP, in so far as the physical requirements of the existence of the material world in the future dictate the possible causes in the past. Coherence is very much a wavefunction feature.

See my above response to Wayfarer. A wavefunction can *always* be written as a linear combination of states from any basis set. This is the expansion postulate of QM.

Therefore the theories are deficient with respect to empirical observation, in that sense.

The Lorentz transformations provide mathematical principles for reconciling different frames of reference. They provide no empirical evidence that time and space are interchangeable.

In reality, whatever comes to be at t1, as Q, is caused by something in the future of t1, and whatever comes to be at t2, as R is caused by something in the future of t2. The only true causes are always in the future. and being in the future, they have not material, or physical existence. We know them as the immaterial cause of material existence (immaterial Forms, God).

Sure, just like a quantity of H2O can be expressed as a combination of ice and liquid,

And yet no one has devised an experiment to show that photon emission/absorption is unidirectional, or motion is unidirectional, or matter/antimatter pair creation/annihilation is unidirectional, and these constitute almost all of the elementary phenomena studied by the most empirically-tested theory ever: quantum electrodynamics.

Copenhagen and common sense are at odds with this, which might explain why the pioneers of quantum mechanics had the issues they did.

Meanwhile Dirac was doing it right and seeing reversibility in more accurate equations.

'Position' is a state. All of the possible positions constitute a complete basis set.

the inherent difficulties of the materialist theory of the atom, which had become apparent even in the ancient discussions about smallest particles, have also appeared very clearly in the development of physics during the present [i.e. 20th] century.

This difficulty relates to the question whether the smallest units are ordinary physical objects, whether they exist in the same way as stones or flowers. Here, the development of quantum theory some forty years ago has created a complete change in the situation. The mathematically formulated laws of quantum theory show clearly that our ordinary intuitive concepts [e.g. of ‘existence’] cannot be unambiguously applied to the smallest particles. All the words or concepts we use to describe ordinary physical objects, such as position, velocity, color, size, and so on, become indefinite and problematic if we try to use then of elementary particles. I cannot enter here into the details of this problem, which has been discussed so frequently in recent years. But it is important to realize that, while the behavior of the smallest particles cannot be unambiguously described in ordinary language, the language of mathematics is still adequate for a clear-cut account of what is going on.

During the coming years, the high-energy accelerators will bring to light many further interesting details about the behavior of elementary particles. But I am inclined to think that the answer just considered to the old philosophical problems will turn out to be final. If this is so, does this answer confirm the views of Democritus or Plato?

I think that on this point modern physics has definitely decided for Plato. For the smallest units of matter are, in fact, not physical objects in the ordinary sense of the word; they are forms, structures or—in Plato's sense—Ideas, which can be unambiguously spoken of only in the language of mathematics.

Meanwhile Dirac was doing it right and seeing reversibility in more accurate equations. — Kenosha Kid


OK, you really seem to believe the proposition that time is reversible, and applying this proposition in physics is "doing it right". I sincerely hope that you do not really have a PhD in physics if this is an indication of what is being taught in physics these days.

These are all temporal processes. Time is empirically proven as unidirectional. By simple deduction therefore, these processes are unidirectional. There is no experiment required

That time is unidirectional is the most fundamental and important empirical principle which we have.

If your argument for determinism is simply a denial of the obvious difference between future and past, then this thread is ridiculously pointless.

But it is important to realize that, while the behavior of the smallest particles cannot be unambiguously described in ordinary language, the language of mathematics is still adequate for a clear-cut account of what is going on.

it corresponds to something real.

If the mathematical entity -- the wavefunction -- is doing its job in yielding accurate predictions of statistical outcomes, it corresponds to something real.

Then don't describe it as empirical. What it is is a strongly held belief

Yes, to think that the collective professor-hood of world physics didn't think to come and check what you personally find intuitively plausible before constructing their curricula. What an oversight!

Then don't describe it as empirical. What it is is a strongly held belief.

And yet you just said we don't need empirical evidence because a claim is sufficient.

Fine. If all you have is an insistence to the contrary, your response is ridiculously pointless.

And this is sufficient. If the mathematical entity -- the wavefunction -- is doing its job in yielding accurate predictions of statistical outcomes, it corresponds to something real. It doesn't need to be the case that the epistemic object we deal with be identical to the ontic thing it represents. That's true generally in mathematical physics.

Obviously, it's a strongly held belief because it is empirical. Empirical means based in observation and experience rather than theory. Clearly, the strength in the belief that time is unidirectional is provided for by experience and observation, and therefore it is empirical.

I said deductive logic is sufficient.

What is pointless, is for someone like you, to come into a philosophy forum, and argue determinism based on premises derived from science fiction, produced from the fringes of relativity theory, enabled by the deficiencies of the faulty boundaries of that theory.

Yeah, that's really not how empiricism works. You can't look at a red car and state that your strongly held belief that all cars are red is empirical. If you want to know whether the elementary process of QED are reversible or not, you can't look at thermodynamics and say, "Well, that's irreversible, therefore everything is!" That's just backward thinking.

t's not deductive, it's inductive.

Certain mathematical formulae or processes in physics show a symmetry in the time variable. How this relates to "going back in time" is a reasonable question.

Incidentally, what does QM have in common with a savings account? :cool:

Is making a measurement in QM and getting a specific result time reversible? How much of "time reversibility" might be artifacts of the mathematics that describe phenomena?

I compare the role of the information in classical and quantum dynamics by examining the relation between information flows in measurements and the ability of observers to reverse evolutions. I show that in the Newtonian dynamics reversibility is unaffected by the observer’s retention of the information about the measurement outcome. By contrast—even though quantum dynamics is unitary, hence, reversible—reversing quantum evolution that led to a measurement becomes, in principle, impossible for an observer who keeps the record of its outcome. Thus, quantum irreversibility can result from the information gain rather than just its loss—rather than just an increase of the (von Neumann) entropy. Recording of the outcome of the measurement resets, in effect, initial conditions within the observer’s (branch of) the Universe. Nevertheless, I also show that the observer’s friend—an agent who knows what measurement was successfully carried out and can confirm that the observer knows the outcome but resists his curiosity and does not find out the result—can, in principle, undo the measurement. This relativity of quantum reversibility sheds new light on the origin of the arrow of time and elucidates the role of information in classical and quantum physics. Quantum discord appears as a natural measure of the extent to which dissemination of information about the outcome affects the ability to reverse the measurement.

Time dependent vector fields - like force fields that fluctuate - show symmetry occasionally. Here is an elementary and casual discussion of the subject.

Certain mathematical formulae or processes in physics show a symmetry in the time variable. How this relates to "going back in time" is a reasonable question.

At that point, information is generally lost to the environment due to wavefunction collapse.

They cannot determine from that state what the original state was. But an isolated observer can (in principle).

Incidentally, what does QM have in common with a savings account? :cool:

The frame invariance of relativity suggests that the temporal and spatial aspects of this process should be interchangeable...

If the mathematical entity -- the wavefunction -- is doing its job in yielding accurate predictions of statistical outcomes, it corresponds to something real. It doesn't need to be the case that the epistemic object we deal with be identical to the ontic thing it represents. That's true generally in mathematical physics.

Just a clarification, it is not lost to the environment in the Copenhagen interpretation: it is simply deleted.

Decoherence is the process of information loss to the environment, in which superpositions cannot be sustained by macroscopic objects because of the large number of degrees of freedom. When an electron is found at y, the contribution at y' is dissipated. Last time I checked, consensus was this is real but insufficient to account for apparent wavefunction collapse, although Penrose advocated this view at some point.

https://plato.stanford.edu/entries/qm-decoherence/#ConApp

They cannot determine from that state what the original state was. But an isolated observer can (in principle).
— Andrew M

This is specifically the Von Neumann-Wigner interpretation.

The friend can even tell Wigner that she recorded a definite outcome (without revealing the result), yet Wigner and his friend’s respective descriptions remain unchanged (6). [Deutsch]
...
Another option is to give up observer independence completely by considering facts only relative to observers (24) [Rovelli]

The familiar ‘paradox’ of Wigner’s friend offers an interesting setting for this discussion. Wigner speculated [9] (following to some extent von Neumann [1]) that ‘collapse of the wavepacket’ may be ultimately precipitated by consciousness. The obvious question is, of course, ‘How conscious should the observer be?’

The answer suggested by our discussion is that—if the evidence of collapse is the irreversibility of the evolution that caused it—retention of the information suffices. Thus, there is no need for ‘consciousness’ (whatever that means): The record of the outcome is enough. On the other hand, the observer conscious of the outcome certainly retains its record, hence being conscious of the result suffices to preclude the reversal—to make the ‘collapse’ irreversible. Quantum Darwinism [11,25–34] traces the emergence of the objective classical reality to the proliferation of information throughout the environment.

Anyway, point being that these various interpretations are not interchangeable. The docoherence picture of wavefunction collapse is at odds with Copenhagen, MWI, transactional QM, and Wigner's friend. Likewise Wigner's friend is at odds with Copenhagen, decoherence and transactional.

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 ei?=cos(?)+isin(?)ei?=cos?(?)+isin?(?) works its magic.

Thanks, that's pretty well the only point I was getting at.

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?

This is just unitary QM. For example, MWI and RQM both agree with this prediction and are both referenced in the paper you linked

Zurek is a decoherence guy and he agrees with the Wigner's friend predictions. You seem to be treating decoherence as objective.

Decoherence usually is.

(I know, I've made a mess of the physics!) :gasp:

Start with a very simple version of Schrödinger's equation:

ih???t=H?, ?=?(x,t)ih???t=H?, ?=?(x,t).

So I opened an account at the bank with $100 at an imaginary 3.14% interest rate

• The emitter produces two half-amplitude waves: a retarded wave going in the forward time direction and an advanced wave going in the backwards time direction (with a negative [s]energy[/s] energy eigenvalues and phase-shifted by 180 degrees).
• The absorber is "stimulated" by the retarded wave from the emitter (offer wave) and also produces a pair of half-amplitude waves going in opposite time directions. The advanced wave from the absorber (confirmation wave) reaches back in time towards the emitter.
• When there are multiple potential absorbers, they all produce confirmation waves with amplitudes proportional to the amplitude of the offer wave. The absorber is selected randomly, with the probability of selection weighted by the square of the amplitude - this is where the Born rule comes into play.
• 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.

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.

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.

(I hope I got this right.)

some relativistic formulations of the wavefunction equation have two solutions: w and its complex conjugate w*

But complex conjugation is equivalent to time reversal (although it also implies negative frequency, energy and charge)

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.

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.

(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.)

I still don't see how this can be. Boundary conditions are, by definition, local.

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?

I think it's more economical than parallel universes.

With interest rates for savings where they are one might as well open an account with an imaginary rate. :worry:

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?

some relativistic formulations of the wavefunction equation have two solutions: w and its complex conjugate w*

All, I believe.

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.

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.

I think it's more economical than parallel universes.

there are a number of alternative relativistically invariant wave equations, at least one of which is first order in time

Are there really any absolutely forbidden points of interaction? Instead of being absorbed, can't the electron scatter instead?

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?

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.

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

although it does ditch those advanced solutions. Hm... could you combine the two?

there are a number of alternative relativistically invariant wave equations, at least one of which is first order in time

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).

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.

No, because the probability distribution of the incident electron will still multiply the probability distribution of acceptor sites.

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.

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?

Not if there is only one available site - in this case the electron wavefunction becomes irrelevant.

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?

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.

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.)

Another paper by Cramer (Foundations of Physics, 1973) specifically treating the arrow of time:

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

Cramer:
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.

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

I was just rereading part of the paper on type II emission and absorption events, which are interesting. If we take the emitter to be atom 1, the absorber to be atom 2, and the emission to be a photon, from the lab frame it appears as a photon (its own antiparticle) from the origin is absorbed by atom 1 (the emitter) and then, seemingly unrelatedly, atom 2 emits a photon of the same energy, which continues forever.

If the distance between the two atoms is L, the time between perceived absorption and emission (actually emission and absorption) will be L/c. So if type II is possible, it ought to be detectable experimentally in principle, though in practice it would be hard if the phenomenon is limited to CMB radiation (assuming that's all that could constitute a photon from the origin).

What's more interesting is the idea that causal relationships between events can be apparently unmediated in principle.

I wonder why he thinks that Type II emission is equally possible as Type I. Type I is an interpretation of a well-studied phenomenon (emission/absorption of EM radiation), while it takes work to explain away Type II. What's the rationale in proposing it? Just a general preference for symmetry?

The motivation for the Wheeler-Feynman absorber theory is to have a time-symmetric formulation of classical electrodynamics, right? Both Type I and Type II absorptions are symmetric, but I don't see why you have to have both, and not just Type I. Type I is just an interpretation of classical electrodynamics, since it is formally equivalent to it. Type II constitutes a net new addition to the theory, for which we have no evidence.

Clearly then the true probability of transmission from cathode to any given site A-E is not identical to the absolute square of the wavefunction (denoted by the blue rays coming from the cathode), but also on whether each site has an electron in it or not.

Cramer claims to have mapped the above arrow of time to the cosmological arrow in the paper here:

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


However the more I read it the less compelling I find it. He actually talks about advanced waves going forward in time, which is contrary to what an advanced wave is.

Cramer’s proposal cannot work for EM waves, simply because the early universe was not transparent to EM radiation

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.

But other than terminology, do you see any issues with his proposal?

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

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.

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.)

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?

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.

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.

does not quite hold: we cannot make emissions happen at will (can we?)

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.

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.

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.

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.

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).

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.

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.

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?

(Unless holes and/or emission events conspire to construct the distribution that we expect to see.)

Perhaps the emitter is picky and won't always transact with a hole just because it's available?

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).

(Unless holes and/or emission events conspire to construct the distribution that we expect to see.)

Effectively, yes. TQM is a conspiracy of sorts.

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.

What it represents is our inability to actually understand the true nature of emission and absorption.

Therefore it is simply a vicious circle of misunderstanding, manifesting as the appearance of conspiracy

...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.)

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.

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.

Transmission is emission + absorption.

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?

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.

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.

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.)

I wonder though whether the absorber theory actually rules out, logically or empirically, uncollapsed/unabsorbed waves?

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.

it occurred to me that the mechanism seems to be the same as a lightning strike

...a canny comparison.

The photon shows up as a single speck on the florescent screen, with an interference pattern built up as the statistics of many individual particles?

The original double-slit experiment diffracted a beam of light into a spreading field before it reached the double-slit, so it was most certainly traveling through both slits simultaneously to interfere with itself, but the modern double-slit experiment could be different.

I'm not sure where holography comes into it though.

Maybe a particle is merely a standing wave?

The idea expressed in the OP, and expressed by yourself above, is a 4D generalisation of this. Each particle is a 4D standing wave that can be decomposed into parts moving forward in time (retarded wavefunction) and parts going backward in time (advanced wavefunction). They're not exactly analogous: in Bloch waves the operation is additive, in these they are multiplicative, but they are very similar.

I might go back and edit my embarrassing snapping at MU

Generally that's not a good idea. For instance, if I edited out everything I said that was embarrassing to me, there really wouldn't be much left.

My next lecture will explicate quantum mechanics as the golden path to fourth dimensional world peace! Its the advanced wave of the future man! lol

The erroneously-regarded "interference" pattern on the detector screen will then vary symmetrically in proportion to emitter position, also slit quantity, width and placement, predictable according to some kind of mathematical formula. Is this accurate?

In the textbook example, i.e. in conventional quantum mechanics, each particle goes through every slit, which is why there's an interference pattern. To determine the weighting through each, you'd have to solve the wave equation and take the integral of the absolute square across the area of each slit. It will depend on the distance between the slits.

That interpretation doesn't make sense to me. It fails to account for why a detector at one of the double slits only registers a particle half the time, nor the apparent randomness of localized absorber contact amongst even dozens of particles.

It's easier to see it in the case of photons. The photon must travel through the undetected slit and not be destroyed or the detected one and be destroyed. There's no possibility in that case of interference.

I'm not aware of any direct evidence that the particle travels through both slits simultaneously as a wave, then recombines into a particle. It might be the case for photons while not for much more massive particles

what could possibly be the mechanism?

The interference pattern is the evidence.

What is the evidence that a single emitted electron is a wave spanning multiple slits, and does this evidence obtain for molecules also?

I linked to an article on the paper.

Probably involves mathematical parameters that are difficult to explain in a simple message board post. Not a physicist, but maybe I'll take a look at it.

To get the dark and light bands of the interference pattern, you have to have multiple sources that can reinforce or cancel each other out. You can't get this kind of pattern with a wave and a single slit, and you can't get this pattern with point particles and multiple slits, as these would just produce multiple copies of the same thing you'd get with a single slit.

Putting a detector behind one of the slits basically gets you back to the pattern you'd get with point particles. The wave has to get past the detector or not, so go through one slit or the other. You can't get interference this way. You can only get interference if it goes through one slit *and* the other.

I suggest, if you cannot take my word for it, that you read the article I sent you. It's written more for non-experts.

The key result of the paper is that only one electron is diffracted at a time, meaning that the electron wave must be interfering with itself, meaning it must be going through both slits.

How can a diffuse wave interfere with itself to form a single particle on the screen?

How the electron got from a field to a point is called the measurement problem, and different solutions to the measurement problem have yielded different interpretations of quantum mechanics. The oldest successful interpretation was the Copenhagen interpretation which states that, upon measurement, the electron wavefunction collapses probabilistically to a single position, the probability given by the absolute square of the wavefunction (the Born rule).

This idea of the absolute square is important. It is how we get from the non-physical wavefunction to a real thing, even as abstract as probability. Why is the wavefunction non-physical? Because it has real and imaginary components: u = Re{u} + i*Im{u}, and nothing observed in nature has this feature. The absolute square of the wavefunction is real, and is obtained by multiplying the wavefunction by its complex conjugate u* = Re{u} - i*Im{u} (note the minus sign). Remembering that i*i = -1, you can see for yourself this is real. We'll come back to this.

There are other probabilistic interpretations, and also some deterministic ones, such as Bohmian mechanics, wherein the electron always has a single-valued position and momentum (hidden variables), and Many-worlds interpretation in which the wavefunction does not collapse but, thanks to the mathematical rules of entanglement, you can never have a term in the wavefunction in which the electron hit the screen at position y but you observed it at position y??y.

In the double-slit experiment a wave packet or "wavicle" travels through one or the other slits, but either option is equally probable across many trials, though fundamentally deterministic (thus far immeasurably so) in relation to a single wavicle. An apparent "interference pattern" is not generated by diffraction through the slits but rather produced by peaks of charge distribution along the absorber's surface rendered symmetrical by the slits, which initiate the various trajectories of wave packets in coordination with the emitter charge and determine the statistical range of possibility for endpoints.