Did the Particle Go Through the Two Slits, or Did the Wave Function?

I think what they must be referring to is the fact that particles are only rigorously defined in the free theory. When coupling is introduced, how the free theory relates to the coupled theory depends on heuristic/formal assumptions.

We're leaving my area of understanding, but I believe Haag's theorem shows that the naïve approach, where the interacting and free theories share a Hilbert space, completely fails -- even stronger than that, _no_ Hilbert space could even support an interacting QFT (in the ways required by scattering theory). This is a pretty strong argument against the existence of particles except as asymptotic approximations.

Since we don't have consensus on a well-defined, non-perturbative gauge theory, mathematically speaking it's difficult to make any firm statements about what states "exist" in absolute. (I'm certain that people working on the various flavours of non-perturbative (but still heuristic) QFT -- like lattice QFT -- would have more insights about the internal structure of non-asymptotic interactions.)

Perhaps a better way to say it is that particles are not longer small balls of dirt [1], but a mathematical construction that is useful to generate an infinite serie [2] to calculate the results.

Since in some conditions these mathematical tricks behave very similar to small balls of dirt, we reused the word "particle" and even the names we used when we thought they were small balls of dirt.

[11] We probably never thought they were made of dirt, and in any case the magnetic moment is the double of the value of the small ball of dirt model.

[2] That has so many infinites that would make a mathematician cry.

Particles are an approximation to the actual behavior of the field, and are used in perturbation theory to calculate the more complicated field behavior.

This works well when interactions are weak. Electrons do not couple strongly to the electromagnetic field, so it makes sense to view electrons as particles. However, quarks couple very strongly to the strong force (hence the name), so the perturbative approach breaks down, and it makes less sense to view quarks as particles.

My bad; QFT actually postulates locality. I was thinking about the casual set theory which strives to solve some of the QFT's difficulties, and where locality is an emergent / statistical phenomenon rather than a postulated condition.

> Lorentz invariance is also violated in QFT assuming non-zero temperature.

Source: https://en.wikipedia.org/wiki/Lorentz_covariance

The Universe is fundamentally quantum in nature; if anything, we'd need a model that explains why classical physics works so well most of the time.

>In my opinion we still don't have a logical explanation for why the model changes so dramatically from classical to quantum physics.

I think you have this backwards. QM IS the law of the universe and Classical Physics is just a high mass low energy approximation of it. In any case there doesn't need to be a logical explanation at all, the laws of physics are as they are. Why is the value of the fine structure constant what it is?

>You aren't going to find departures just by banging around in your garage

This kind of rhetoric saddens me. Someone says "design an experiment" and you jump to the least charitable conclusion. That people do this is perhaps understandable, but to do it and not get pushback leads to it happening more and more, to the detriment of civil conversation.

No, the experiment I had in mind would take place near the Schwarzchild radius of a black hole. This would require an enormous effort, and (civilizational) luck to defy the expectations set by the Drake equation/Fermi paradox. It's something to look forward to, even if not in our lifetimes!

This is one of the reasons I believe science and technology as a whole are on an S-curve. This is obviously not a precise statement and more of a general observation, but each step on the path is a little harder than the last.

Whenever a physics theory gets replaced it becomes even harder to make an even better theory. In technology low hanging fruit continues to get picked and the next fruit is a little higher up. Of course there are lots of fruits and sometimes you miss one and a solution turns out to be easier than expected but overall every phase of technology is a little harder and more expensive.

This actually coincides with science. Technology is finding useful configurations of science, and practically speaking there are only so many useful configurations for a given level of science. So the technology S-curve is built on the science S-curve.

To be fair quantum mechanics was invented by guessing that energy might be quantized. It just happened to model the universe well.

One particular model: the electron g-factor.

Now go look up how precise a prediction the same model makes for the muon g-factor.

Bell's Theorem disproves local hidden variables.

Reality can be interpreted as non-local. There has been no conclusive proof it isn't.

c isn't a limit on the kind of non-locality that is required, because you can have a mechanism that appears to operate instantaneously - like wavefunction collapse in a huge region of space - but still doesn't allow useful FTL comms.

Bell's Theorem has no problem with this. Some of the Bohmian takes on non-locality have been experimentally disproven, but not all of them.

The Copenhagen POV is that particles do not necessarily exist between observations. Only probabilities exist between observations.

So there has to be some accounting mechanism somewhere which manages the probabilities and makes sure that particle-events are encouraged to happen in certain places/times and discouraged in others, according to what we call the wavefunction.

This mechanism is effectively metaphysical at the moment. It has real consequences and was originally derived by analogy from classical field theory, with a few twists. But it is clearly not the same kind of "object" as either a classical field or particle.

De Broglie and Bohm would like to have a word…

The trouble with QM is with it's interpretations, not with the accuracy of it's predictions. The latter informs interest in the former. QM works, but the models imply that nature is neither "local" - e.g. entanglement experiments undermine hidden-variables, nor "real" - e.g. a particle does not have a momentum (or position) until you measure it. These physical properties are not just hidden, they are undefined. These implications fly in the face of basic macroscale intuitions about what "physical reality" means, which makes it interesting. Inconsistency is a signal that we have discoveries yet to make. Note that "Many worlds people" think there is no inconsistency - my sketch of a model is fully consistent with that interpretation, if you wish, by simply assign a new universe to every child node in which the node is reached.

Doesn't the difference between measurement and observation stem from an extension of the double slit experiment discussed in thus artucle?

It you place a detector on one of the two slits in the prior experiment, (so that you measure which slit each individual photon goes through) the interference pattern disappears.

If you leave the detector in place, but don't record the data that was measured, the interference pattern is back.

> when a water wave gets pushed through two slits, it breaks into two separate water waves, one coming from each slit, and those two waves push the water up and down at the same time at different locations.

What physically observable distinction are you drawing? The points of water on the far sides of the slits will have a certain height at each point at each time, forming the interference pattern you'd expect. You can decompose that function into a sum of two separate waves, if you want, but you don't have to. And exactly the same thing is true of the quantum mechanical wavefunction for a particle passing through a pair of slits.

> A wavefunction amplitude does not represent a displacement in any kind of medium. They represent a measure of the probability that the system being described is in a particular state at a moment in time. That state need not even be a position, it might be a charge, or a spin, or a speed, or any combination of these. Basically quantum systems oscillate between their possible states, they don't oscillate in space-time like matter affected by a wave does.

I don't think that's a real distinction. Water height is a different dimension from (x,y) position and it behaves very differently; that the wave is moving across the surface and that the surface is moving up and down are orthogonal facts, the reason the former is movement isn't that the latter is movement. A classical electromagnetic wave moves even though it isn't in a medium that's moving (and so does e.g. a fir wave).

> You can decompose the system's wavefunction as a sum of multiple wavefunctions corresponding to certain measurables, but this is an arbitrary choice: any such decomposition is exactly as valid. In matter waves, if I drop two stones in water at different locations, the water surface's movements can be described as a single wave, but there is a natural decomposition into two interfering waves each caused by one of the stones. There is no similar natural decomposition that quantum mechanics would suggest for a similar quantum mechanical system.

Again I don't think this is a real distinction. You have exactly that natural decomposition in the QM system - it's not the only valid decomposition, but it is a valid one and it has some properties that make it nice to work with. And similarly for dropping stones in the water, infinitely many other decompositions are possible and equally valid (e.g. decomposing as two copies of a wave where you dropped two half-sized stones into the water).

> The issue here being that if a photon is a minimal quanta of energy, but is just a classical wave, what prevents it from spreading out and having sub-photon energy? Or if indeed it does, how does that sub-photon quantity get measured? -- if these experiments claim to be emitting a time-series of single photons, classical wave interference won't occur (again, being separated in time).

Right, so that part is new and "spooky" - quantum phenomena are quantised (hence the name). The photon does spread out as a wave, there is in a sense half a photon heading towards the top half of the screen and half a photon heading towards the bottom half of the screen - but then when it hits the screen what we see is a single whole photon that hits either the top half or the bottom half (or, perhaps, half of an us sees a photon hit the top half and half of an us sees a photon hit the bottom half). This is the "wave-particle duality" and while it does fall out of the equations, it's definitely unfamiliar compared to classical physics.

If you want to fully understand, all I can suggest is "work your way through a QM textbook" - every popular explanation I've seen has messed it up one way or another. But it sounds like you're understanding correctly, and thinking for yourself as well - you've hit upon the actual essence of it, the kernel that really is hard.

I don't know how fringe this is, but Huygens Optics gives a possible answer here: https://www.youtube.com/watch?v=tMP5Pbx8I4s. TL;DW: if you assume certain non-linear properties of vacuum as a medium, it seems possible for light (EM waves) to self-contain spatially instead of spreading out, and such trapped energy seems, for all intents and purposes, to behave like particles.

Again, IANAPhysicist, so I don't know what to think of that video, but the channel seems legit, and the explanation is beautiful in its simplicity.

I think Craig Bohren wrote in one of his books, that to get anything calculated and done the waves are all you need. Particles are nice for some kind of visualization, but they don't really help getting things done. I liked that.

Instead of particles I like to view the interactions like the forming of a lightning in a thunderstorm. The energy-field builds up, And at some point of contact the energy is being released in a single lightning strike.

What I still wonder is, if the interaction really depletes the energy-field instantly in a single point, or if there is more going on (on different timescales - maybe with speeds not related to the speed of light).

The experiment working on clusters of atoms is news to me and I loved getting to know about that. But the thing that really breaks my mind is the experiment that proves that the behavior depends on the possibility of getting information from which slit the particle went through. So we can rule out the act of measurement itself interfering with the behavior of the particle.

They did it by splitting a beam of particles into a pair of entangled particles and then setting up a way to measure the polarity of one of them after the point in time where it even hits the final screen. If you measure the polarity then, after the other stream of particles from the beam had already had time to make the pattern, the pattern will be two clusters. If you don't, it goes back to an interference pattern.

That one really cemented the notion in my head that this is just how the Universe is and not some local weirdness with particles and measurements.

I would love to try this experiment with something basketball sized out in space. Like we build an enormous basketball detector behind a double slit inside an unobservable black box. If thr basketball started acting like a wave I would be sooo freaked out

Am I misunderstanding the significant of the double slit experiment?

I thought the takeaway wasn’t that the particle comes out both sides, the implication is that the behavior of a single particle is the same as the behavior of multiple particles - that is to say, it appears to be an interference pattern, even when there should be no other particles to interferes with the single one.

One photon hits the slit and one photon comes out. It is only if you repeat the experiment many times that you start to see a strange wawe-like pattern in where the photons hit.

It is as if every photon that went through the slit is somehow aware of all other photons that did so too so each photon can choose the (random) position where it hits on the wall behind the slit such that together they look like as if a WAWE went through the slit.

That is (one reason) why they call it "Quantum Weirdness". God is playing dice with us

Sounds like Einstein's hidden variables theory: below wave function picture there's more fundamental newtonian reality that produces the higher level wave function behavior, but is itself inaccessible due to insufficiently fine instruments, aka hidden variables. "God doesn't throw dice" is about that.

> Wave functions are just a mathematical representation of a physical property that are (only?) ever operated on using quantum operators which result in a statistical distribution.

It is not correct— at least not unless you subscribe to the Copenhagen interpretation. Yet, while this interpretation is a simple heuristic for interaction with big systems (e.g., a photon hits a CCD array), none of the quantum physicists I know treat it seriously (for that matter, I have a PhD in quantum optics theory).

I mean, at some certain level, everything is "just a mathematical representation" - in the spirit of "all models are wrong but some are useful". But the wavefunction is more fundamental than measurement. The other can be thought of as a particle entangling with a system so large that, for statistical reasons, it becomes irreversible - because of chaos, not fundamental rules.

For some materials, I recommend materials on decoherence by WH Zurek, e.g. https://arxiv.org/pdf/quant-ph/0105127. Some other references (here a shameless self ad) in https://www.spiedigitallibrary.org/journals/optical-engineer... - mostly in the introduction and, speaking about interpretations, section 3.7.

EDIT: or actually even simpler toy model of measurement, look at the Schrodinger cat in this one: https://arxiv.org/abs/2312.07840

You're partially correct, but describing it in that way makes it sound like if you could "just look a little bit closer" the statistics would disappear, which doesn't happen. So it's more subtle than this. Fundamentally it's because QM doesn't use additive probabilities, but rather additive amplitudes which are complex numbers, and the probability is the square of the sum of these, so you can get interference between amplitudes. You can never get interference by adding probabilities.

In the dual slit experiment this is visible as you can't get the interference effects by summing the probabilities for "particle through slit 1" and "particle through slit 2" but rather you need to sum the amplitudes of the processes.

Working physicists (since 100 years) just do this, there is no practical need to interpret it further, but it would be cool if someone could figure out some prediction/experiment mismatch that does indeed require tweaking this!

>there is only one model

There is one set of observations, and many many models to describe them: Schrödinger equation formulation, matrix mechanics (Heisenberg, Born, and Jordan), path integral formulation (Feynman), phase space formulation, density matrix formulation, QFT or second quantization, variational formulation, pilot wave theory aka de Broglie-Bohm theory, Hamilton-Jacobi formulation, PT-symmetric quantum mechanics, Dirac equation formulation (well, not really independent, just for spin 1/2 particles).

They all give the same results, and are therefore mathematically equivalent, but different models tend to be associated with different interpretations:

   Schrödinger Equation : Copenhagen, Bohmian Mechanics, Many-Worlds
   Matrix Mechanics : Copenhagen
   Path Integral : Many-Worlds, Stochastic
   Density Matrix: Ensemble, Decoherence-based
   Second Quantization : Many-Worlds
   Pilot Wave Theory : Bohmian Mechanics
   Consistent Histories : Decoherence-based
   Relational QM : Relational Interpretation
   Stochastic Models : Stochastic Interpretations, GRW (Ghirardi–Rimini–Weber) Collapse

What is the name of the better model which you are talking about?

You can explain the photoelectric effect with classical light (i.e. as EM waves) as long as you properly quantize the atomic energy levels. This is often called s semi-classical model.

However, photo-detections with sub-poissonian statistics cannot be explained under this semi-classical model, but it can be explained with properly quantized EM field (i.e. with photons).

For reference, see Mandel and Wolf's Quantum Optics textbook.

If I emit a bass signal at a low amplitude, but then emit it at a higher amplitude, I can see the effect on a glass of water on the table. What’s happening here if amplitude does not carry power?

My understanding is that theoretically energy transfer is a function of wavelength.

OK - a bit like the fairground game of trying to knock coconuts off a stand by throwing a wooden ball at them. It doesn't matter how many balls you are throwing per minute (total energy being delivered) if the energy of each ball doesn't cross the threshold to knock the coconut off.

OTOH, the energy of a photon is such an abstract concept (not like the kinetic energy of a ball) that I'm not sure it really helps explain it.

Particles aren't necessary for it, any quantization is sufficient.

I trust the physics works out.

The problem in these discussions is how to build an intuition about the underlying physical model.

I fail to have an intuition of how can a quantized unit of wave propagate through both slits.

I know that the equations say that the probability of finding the particle at a given location is given by the amplitude squared of the wave function (Born rule).

The image that a "quantized unit of wave propagates through two slits simultaneously" doesn't help me build any further intuition.

Do the two parts going through the two different paths carry half the unit? Clearly that's not the case otherwise they wouldn't be quanta anymore. So does it mean that the entire wavefront is "one unit" no matter how spread out? But in that case, "one unit" of what?

Decoherence is the process that makes it impractically difficult for an experiment to be designed that makes your observations the two interfering possibilities in some kind of double-slit experiment.

Interpreting this in the many-particle case is more difficult, but the basic idea is that due to single-particle uncertainty, you can't have a definite number of particles indexed by momentum and a definite number of particles indexed by position at the same time. If I had 100 particles that were definitely at x=0, in terms of momentum they'd be spread out over the range of possibilities unpredictably.

How frequently a wave would go through just 1 of the slits. If you threw a baseball at a wall with two baseball sized slits it would basically always go through just one of the slits. You would never see an interference pattern.

This is because a baseball is interacting with other matter on the way to the slit. A photon on the other hand might not interact with any matter and it stays as a wave and you can see an interference pattern on the other side.

But if you aren't trying to map the wave function to physical space somehow you are essentially saying that the central construct of your theory has no direct relation to the actual physical processes happening "underneath".

This reduces to a kind of "shut up and calculate" attitude, so it seems poor starting point from which to write an interpretation text.

That's true, but it's also true of the classical probability distribution p(t,x1,x2).

His point from the beginning is this: the particle described by the wavefunction can't be said to move through both slits at once, because ψ(t, x, y) has a single value for a particular x and y at a particular time. The particle has non-0 probability for both x, y1, t and for x, y2, t, of course - but that just means the particle has non-0 probability to pass through either slit.

And as for saying that the wave moves through both slits, that also doesn't make sense, by the very definition of the wave function - it's a wave in probability space, not in space, so it just doesn't move through space.