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Say it's a normal double slit experiment, and the particle is detected on some position on a wall after the slits. How much info could be deduced from the position?

I know it's not exactly a path per se in a classical sense, but, based on the position of detection on the wall, how much info could be known about how the particle interferes with itself crossing the double slits?

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    $\begingroup$ In this ecperiment, the position of detection on the screen provides information about the probability distribution of the particle's position, it does not provide information about the specific path or interference pattern that the particle exhibited as it passed through the double slits $\endgroup$
    – user391340
    Jan 27 at 14:04
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    $\begingroup$ A path is multiple consecutive measurements on the same object. Since quanta are not objects but only small amounts of energy, and since energy can only be measured once, the concept of a path does not make sense in quantum mechanics. $\endgroup$ Jan 27 at 14:04
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    $\begingroup$ @frt132 The path integral is not a description of an imaginary particle moving around on some very complicated paths sampling all possibilities. It is an ensemble description that predicts the probability of finding the ensemble in a certain state assuming that it was in another certain state at a previous time. An electron does not "interfere with itself". Interference is the absence of self-interaction in linear systems. That quantum mechanics is linear is not a physical property of quantum systems. It's the consequence of QM being a theory of statistically independent experiments. $\endgroup$ Jan 27 at 15:22
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    $\begingroup$ @frt123 The theory doesn't say anything about a single system. It always talks about expectation values, in every possible mathematical form. A path can simply not be measured for the reason I gave. As soon as we detect a quantum of energy that energy is lost to the quantum system. It can never be measured again. The path integral does not talk about paths of individual quanta. It's not what I would call "a Santa Claus sled" interpretation. $\endgroup$ Jan 27 at 15:43
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    $\begingroup$ photons are quantum mechanical particles in the mainstream standard model, and only the probability of being measured at a particular (x,y,z,t) can be predicted by the mainstream theory. This means that an individual photon, a point particle, does not interfere with itself, it interacts with the boundary conditions, slits and screen, as a point particle. See this answer of mine fpr single photon at a time double slit physics.stackexchange.com/questions/90646/… $\endgroup$
    – anna v
    Jan 27 at 18:23

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This might be better answered with a different situation. A distant star emits light in all directions. As part of all this, a photon is emitted. What path is it on?

There is no way to tell while it is in flight. It spreads out in all directions like a wave. It might wind up anywhere.

Eventually it hits your eye. Now you know where it wound up. Can you say it followed a straight path?

You can collect a lot of photons that enter your eye. You can try things out. Put an object between your eye and the star. It blocks all photons. Put it somewhere else. It doesn't block photons from the star. You conclude that photons travels in straight lines and hits a receptor in your eye like a particle.

Try some more. Put a wall between you and the star. Put a hole in it. If the hole is big, you get particle-like results as before. If you shrink the hole, you find that some of the photons miss your eye and hit a receptor in the eye of a person next to you.

Now they are acting a little like a particle and a little like a wave. You know they wound up at the hole, but you can't say where in the hole. You might think that limits any path they took. They don't hit the wall, but continuing that path doesn't predict which eye they hit. You need to use waves to make a prediction of where they might hit. But when they do hit, they only hit one receptor in one eye.

Put two slits in the wall, so that you are between them and neither aligns with the star. Some photons hit you. None hit the person next to you. Some hit the next person over.

Photons don't change back and forth between a particle and a wave. They are kind of like both. See How can a red light photon be different from a blue light photon?. Sometimes a particle following a path is a good approximation to what they do, and sometimes not.

Ray optics treats them like straight line particles. It works very well, but not perfectly. When light from a distant star hits a camera, it passes through a large hole. The lens focuses all rays onto a single receptor. But passing through a hole introduces a tiny uncertainty in which receptor will be hit. This is called diffraction. It is the wave like nature of light limiting how well ray optics works. A perfectly designed and manufactured lens is said to be diffraction limited.

So sometimes light travels in a straight line, sometimes almost in a straight line, and sometimes not much at all like a straight line. You can derive all of these behaviors from wave properties of light. See Explanation of diffraction of a single light ray by Huygens' principle.

This tells you that light has a spread out nature. You have to add up contributions from everywhere that light is to find out where it will be next. If light is widely spread out, like a plane wave from a distant star, the prediction is that it will continue in the same direction.

Then light hits a hole in a wall. Now it fills the hole, but no farther. If you add up just that much, the wave largely continues straight but spreads out. For a small hole, it spreads out a lot.

But this wave is not a classical wave. It doesn't tell you where the light is. It tells you where you might find light if you measure it. This spread out wave can hit a single receptor. It is something like a particle.

Also you should not think of the particle like nature as a classical particle. In particular, it does not have a size. It can fit a hole or a receptor.

The important particle like property is that the energy of light comes in lumps. When a photon hits a receptor, one lump of energy hits. Nearby receptors get no energy. When a photon passes through a hole or double slits, either all the energy passes through, or none.

The wave tells you where the energy is likely to wind up, but not which receptor will be hit.

This is one of the central counter intuitive parts of quantum mechanics. It is so unlike the cause and effect we are used to from classical physics, that we struggle to make sense out of it. The immediate question is "If a spread out wave arrives at a bunch of sensors, what causes it to pick just one?"

The answer is that cause and effect does not work this way. You just have to get used to it. Nothing travels from distant points of the wave to the lucky receptor. Nothing travels from the lucky receptor to other receptors. It just turns out that one receptor is lucky and all the others are not. All cause and effect has to say is the if a photon arrives, it will arrive somewhere. The wave tells you the probability of where.

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  • $\begingroup$ Thank you for the answer! One thing remains unclear to me, I was asking about deducting "going back in time", and not deducting "going forward in time", which you seemd to focus on. "this wave is not a classical wave. It doesn't tell you where the light is. It tells you where you might find light if you measure it" Yes, we are on the same page on this. But I wanted to know, given the measured location, what can you deduct about its past, (In the double slit experiment you also know its initial state.) So like what scenarios were most likely among those in feynman diagram or etc? $\endgroup$
    – frt132
    Jan 27 at 16:42
  • $\begingroup$ Physics is timer reversal invariant (There are exceptions. It is CPT invariant.). If you know the wave function you can predict its future. Or you can reverse time and play it back to find its past. However, the interference pattern is a measurement of position, not a wave function. You can make a lot of measurements of position to get the magnitude of the wave function at a lot of positions. That still isn't the wave function. You would have to make lots of phase measurements to reconstruct the full wave function. $\endgroup$
    – mmesser314
    Jan 27 at 17:01
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    $\begingroup$ @frt132 One can not extract information from these measurements that nature does not have. That quanta have a path is merely a failed mental model. You can ask a rational question like "Why is nature uncertain?". The reason for that is fairly straight forward: in a relativistic universe the local state is always entangled with the state on the forward light cone. The forward light cone is the future of the local observer. Since the future is unknown, we can't be fully certain about the present, either. $\endgroup$ Jan 27 at 18:28
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    $\begingroup$ @frt132 Feynman's path integral is a mathematical formalism. It does not represent physical dynamics in classical or semi-classical form. That doesn't make it wrong. It simply does not have a physical interpretation in form of traveling objects. $\endgroup$ Jan 27 at 19:47
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    $\begingroup$ @frt132 In quantum mechanics the energy is initially in a source system. It gets transferred to the quantum system ("preparation") and then that energy gets transferred to the measurement system. The practical procedure in the lab is usually called "spectroscopy" and it is literally an energy measurement. That the energy did not take some sort of path follows immediately from the classical definition of energy as a system property. Energy flows (from system to system), but it does not move from place to place. This is not just language. It's what we observe. $\endgroup$ Jan 27 at 20:02
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...how much info could be known about how the particle interferes with itself crossing the double slits?

A useful version of this setup is to consider one in which individual photons are passing through a double slit on their way to a screen (or other detector type). Because the photons go through one at a time, any interference pattern on the screen will be built up strictly as a result of self-interference. Self-interference only occurs when there are 2 (or more) indistinguishable paths from the source to the screen, and at least one of those paths go through each slit. You probably know this much already.

It is possible to estimate the odds of the light hitting spots on the screen. Usually, that is done by considering the pattern of bars that result. The pattern of course changes when interference is possible versus when interference is not possible (such as when one slit is blocked).

There is only interference to the extent that there is indistinguishability between photon paths going through the Left slit, versus going through the Right slit. So to answer your question:

In principle: No "which-slit" information (i.e. information about self-interference) can be gained at all from the location of any individual photon's mark on the screen. Otherwise there would be distinguishability, and then there is no interference. You just get a single crested pattern on the screen, which is the indication that you could (in principle at least) determine the photon path through one slit or the other.

In practice: Being able to distinguish the path through one slit or the other is not an all-or-nothing proposition. You could, for example, have it such that you are 60% sure the photon went through the Left slit, and 40% sure the photon went through the Right slit. In such cases, the patterns become more blurry. There are specific experiments in which this has been accomplished (see second reference below). Further, no experiment is ideal, so there are always some photons that are distinguishable regardless. The resulting pattern is never perfect.

Young’s Double-Slit Interference Demonstration with Single Photons (2024) Note: This paper covers both theory and experiment, and is relatively straight-forward and fully up-to-date.

"The interference of single photons going through a double slit is a compelling demonstration of the wave and particle nature of light in the same experiment."

Young's double-slit experiment with single photons and quantum eraser (2012) Note: this is a more advanced version of the double slit, but a lot of good stuff is presented.

"An apparatus for a double-slit interference experiment in the single-photon regime is described. The apparatus includes a which-path marker that destroys the interference as well as a quantum eraser that restores it."

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    $\begingroup$ Quanta are not objects. They are the amounts of energy that get emitted by the source into the field and that get absorbed by the screen from the field. There is no known experiment that can detect the location of energy before an irreversible transfer of this kind has taken place. The double slit (or any of its many variations) is not even a quantum mechanical experiment. It does not depend on Planck's constant and we aren't measuring correlations between multiple quanta (like in an entanglement experiment). The relative detection frequencies are proportional to classical intensity. $\endgroup$ Jan 27 at 18:15
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    $\begingroup$ @FlatterMann We were not talking about "detect the location of energy before" it hitting the screen. But as there's a set of infinite Feynman paths, en.wikipedia.org/wiki/Path_integral_formulation#/media/…, if one has info about the start and the end (hitting the screen), some of the said paths, which is "locations", can be eliminated. $\endgroup$
    – frt132
    Jan 27 at 18:26
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    $\begingroup$ @frt132 Feynman paths aren't describing the classical motion of an object. They are a way to calculate the propagator of the ensemble. More precisely, the path integral is a quantization procedure that translates a classical dynamic into a quantum mechanical formalism. And no offense to Wikipedia, but not all of their articles represent good physics. $\endgroup$ Jan 27 at 18:32
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    $\begingroup$ That quanta are small amounts of energy is mainstream physics. What we measure in our quantum detectors is always energy. Non-relativistic QM makes this a little opaque because somewhere between the matrix mechanics papers of Heisenberg and von Neumann's "Mathematical Foundations of Quantum Mechanics" the identification of a quantum with energy got lost and we began talking about "state" in an abstract manner. As an experimentalist I can assure you that there is nothing abstract about it. Unless there is an energy difference between initial and final state, there is no measurement. $\endgroup$ Jan 27 at 19:43
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    $\begingroup$ @frt132 There simply is no "photon" in the free field. "The photon" is the amount of energy that gets emitted into the field by the source and then it's the amount of energy that gets taken out of the field by the detector. For low energy processes nature plays a cruel joke on us because the energy seems to be "the same photon all the way". That's a mirage. At LHC they are colliding two protons (more precisely the quarks and gluons inside) and what comes out are not two protons but a totally different mix of quanta with different quantum numbers. $\endgroup$ Jan 27 at 20:16

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