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. — Kenosha Kid
[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. — Kenosha Kid
The true boundary conditions — Kenosha Kid
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. — Kenosha Kid
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.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. — Kenosha Kid
That was a nice presentation and an interesting discussion. Thanks for putting in the effort! — SophistiCat
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. — SophistiCat
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). — SophistiCat
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. — SophistiCat
Anyway, this is probably a diversion (or not - you tell me). — SophistiCat
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. — Harry Hindu
Is quantum theory the "set theory" of physics? Weird at first but providing a foundation? :chin: — jgill
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. — Kenosha Kid
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? — Kenosha Kid
Run that movie backwards and you have exactly the same thing... — Kenosha Kid
The Copenhagen description, though, is irreversible: wavefunction collapse is a loss of information that is not retrieved by simulating the reverse process. — Kenosha Kid
Do you think that a hot object knows that the cooler object is cooler when it radiates heat? — Metaphysician Undercover
And I'm sure you know that the definition of "black-body" is based in thermodynamic equilibrium. — Metaphysician Undercover
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. — Metaphysician Undercover
Emission/absorption is only reversible when an object is at thermodynamic equilibrium, which is when emission will not occur. — Metaphysician Undercover
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. — Metaphysician Undercover
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. — Metaphysician Undercover
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. — Kenosha Kid
Another self indulgent spitball from me. Thank you for the free physics lessons. — fdrake
What stops complex quantities from being physical? — fdrake
It is sufficient that each particle knows where it is going. — Kenosha Kid
No, a blackbody radiator is a non-equilibrium thermodynamic system, that is: it is not in equilibrium with its environment. — Kenosha Kid
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. — Kenosha Kid
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. — Kenosha Kid
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? — Metaphysician Undercover
If a substantive thing, (massive object), is inclined toward temporal continuity (as inertia implies), yet "feels" a force which would impel that object to change, then there are two very distinct forces involved, the force to stay the same, and the force to change. If the object stays the same, despite feeling the force which would impel it to change, doesn't this appear to you like the object has made a choice, and exercised will power to prevent the force of change? — Metaphysician Undercover
Do you get most of your information from Wikipedia? — Metaphysician Undercover
But these aren't physical either. It is simply that complex exponentials are much easier to manipulate than individual sines and cosines. — Kenosha Kid
But no complex quantity can be physical in itself, i.e. we can't observe it in nature. — Kenosha Kid
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. — Kenosha Kid
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. — Kenosha Kid
No, I did something that has apparently never occurred to you: I got an education. — Kenosha Kid
How does your (transactional?) interpretation recover the Born rule? — SophistiCat
How do you get the interference stripes in the double slit experiment? — SophistiCat
Complex quantities are no more and no less physical than real quantities, tensors, vectors, and whatnot. They are all mathematical objects. — SophistiCat
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 — SophistiCat
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. — Kenosha Kid
Yet the screen, double slits and the electron emitter are all macro objects composed of electrons and all have an effect on the outcome of the experiment.The back screen is a macroscopic object that cannot be treated precisely with quantum mechanics — Kenosha Kid
No, I did something that has apparently never occurred to you: I got an education. — Kenosha Kid
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. — Kenosha Kid
From the overlap integral of the retarded wavefunction with the advanced wavefunction:
In transactional QM, this is the very meaning of the Born rule. — Kenosha Kid
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'. — Kenosha Kid
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. — Kenosha Kid
I'm getting confused now between ontologically real and real as in has no imaginary component. — Kenosha Kid
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. — Kenosha Kid
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 — Metaphysician Undercover
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. — SophistiCat
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. — SophistiCat
which is no more than what vanilla QM tells us and doesn't explain the really interesting bit, i.e. the measurement problem. — SophistiCat
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. — SophistiCat
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). — fdrake
This might trivialize C. Here's a quote from the web, from an educational perspective: — jgill
A vector space isomorphism is only defined between two vector spaces over the same field — jgill
It would help if this issue is clarified. — jgill
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? — fdrake
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. — Kenosha Kid
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. — Kenosha Kid
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