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Non-scientist here trying to get my head around the double slit experiment.

If whilst exhibiting wave-like behaviour electrons are potentially in more than one place at once, and if time is a dimension just as the spatial dimensions are dimensions (correct me if I'm wrong), then why whilst exhibiting wave-like behaviour would electrons not also be potentially in more than one time at once? And if they can be, wouldn't that explain the irrelevance of intervals when it comes to the appearance of the interference pattern? They're not only everywhere but everywhen, so to speak. The act of observation would then not only force the electron to be in a particular place but in a particular time. Or am I so far off that I need to go back to school? (Only did science up to GCSE level many years ago.) ;)

Perhaps a clearer way to ask this is: why is uncertainty limited to spatial dimensions, and generally not considered in the time dimension?

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  • $\begingroup$ "the irrelevance of intervals when it comes to the appearance of the interference pattern" - can you clarify? Do you mean the intervals between sending two consecutive electrons? $\endgroup$
    – Filip Milovanović
    Commented Nov 20, 2022 at 1:10
  • $\begingroup$ I guess a good way to think about this is that, very roughly speaking, these sorts of experiments revealed that "particles" are not little balls zooming around as we originally envisioned them, but rather these spatially extended objects that give rise to wave-like fields that somehow have the ability to produce localized phenomena that for the most part look like tiny particles to us, and this ability is controlled by the peaks & troughs of the wave. The irrelevance of the interval is then due to each run of the experiment producing roughly the same wavelike pattern. $\endgroup$
    – Filip Milovanović
    Commented Nov 20, 2022 at 1:11
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    $\begingroup$ Congratulations! You've stumbled across one of the main unsolved problems in physics right now, namely that general relativity and the theory of spacetime just refuses to work alongside our current understanding of quantum mechanics, and vice versa. You just can't treat time as "just another dimension" in quantum mechanics and have predictions match observations, yet having time be just another dimension is crucial to general relativity, and yet both of these theories are independently very well tested and have great predictive power at their relevant scales. $\endgroup$
    – Hearth
    Commented Nov 20, 2022 at 17:06

2 Answers 2

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In quantum mechanics, time is not a dimension, it's a universal parameter (involved in the evolution of states/operators depending upon your so-called picture). Also in quantum mechanics, the electron is a particle described by a wave function. The wave function can go through both slits but what does that mean for a particle? That question is the point of the experiment.

Of course, time is not a parameter. Quantum mechanics is a (mostly) non-relativistic approximation. Incorporating relativity leads to quantum field theory, where there are no particles. Quantum fields permeate space-time, and an electron is quanta of that field.

Since computations are so difficult, we usually think in approximations. There is an initial state: incoming free particle electron, a final state: outgoing free particle electron detected at the screen. The electron takes all possible paths between the two (Feynman's path integral formulation), and we can calculate the scattering matrix describing it.

In that picture, there really is no mystery: beam impinges on target and scatters to a detector.

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  • $\begingroup$ Would you say that QFT still treats time somewhat asymmetrically? I mean that the probabilities are defined at a time point and they add to 1 at a time point. Wavefunctionals also defined at a time, like $\phi [\psi , t]$. Particle states like $|p\rangle$ are de-localised in space but exist at a definite time point. $\endgroup$
    – Ryder Rude
    Commented Nov 19, 2022 at 14:23
  • $\begingroup$ QFT allows particle states to be delocalised in space, but time is always definite as a parameter. And wavefunctionals $\phi [\psi, t]$ have a time parameter but no space parameter. I think QFT treats space and time equally for operators but not for states. $\endgroup$
    – Ryder Rude
    Commented Nov 19, 2022 at 14:31
  • $\begingroup$ @RyderRude You're correct, once you've chosen a reference frame. One can always boost and then $t'$ mixes $t$ and $x$. $\endgroup$
    – JEB
    Commented Nov 19, 2022 at 14:42
  • $\begingroup$ Your answer states time is not a parameter. The other answer appears to disagree. Any idea where the difference comes from? $\endgroup$
    – Mast
    Commented Nov 21, 2022 at 3:05
  • $\begingroup$ @Mast yes: you read my answer incorrectly. $\endgroup$
    – JEB
    Commented Nov 21, 2022 at 3:29
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Electrons are not everywhere at once. All information about the electron is encoded in a function $\psi (x, y, z, t) $. And there is no hidden information about the electron other than this (at least not in the standard interpretation).

$|\psi (x, y, z, t) |^2$ is the probability density of observing the electron at the point $(x, y, z) $ at time $t$. Note that:

$$\int |\psi (x, y, z, t) |^2 dxdydz=1$$

for a fixed time $t$. So if you simultaneously conducted position measurements at all space locations, the probability of you finding the particle would be 1. The information about a particle is uncertain in space, but not uncertain in time.

It is not true that:

$$\int |\psi (x, y, z, t) |^2 dxdydzdt=1$$

If your hypothesis was right, the above equation would have been true. Position is a probabilistic observable in Quantum Mechanics. Time is only a parameter.

if time is a dimension just as the spatial dimensions are dimensions

Time and space should be treated equally in a relativistic theory. The theory I described above is a non-relativistic theory.

In the Relativistic theory, called Quantum Field Theory, both space and time become parameters instead of observables. They appear as parameters of Operator Fields which are mathematical objects defined at every point of spacetime.

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  • $\begingroup$ Thanks for the responses. As I said, I'm a non-scientist, so responses that make assumptions of prior knowledge or use mathematical formulas are only partly helpful. If I understand the first explanation correctly (albeit superficially), we can know that the electron will be somewhere at a given time, but we can't pinpoint precisely where (could be at point x, y or z, for instance). But doesn't this uncertainty work the other way round? We can know that the electron will be at point x, say, but can't pinpoint exactly when. $\endgroup$
    – Endymion
    Commented Nov 19, 2022 at 14:53
  • $\begingroup$ Also, do 'position measurements' count as observations in the double-slit experiment sense, and if so, do they have some similar effect in forcing the electron to 'make a decision'? I know these are naive questions, but everybody's got to start somewhere! $\endgroup$
    – Endymion
    Commented Nov 19, 2022 at 14:53
  • $\begingroup$ "We can know that the electron will be at point x, say, but can't pinpoint exactly when." Not really. For instance, you could keep a position detector at a point for infinite time, and it's possible that the electron will never be detected there. Quantum Mechanics describes nature as a probability distribution in space (or, in general, a Hilbert space), but at a fixed point of time. This is just how nature is. It will become clear after you learn the theory. $\endgroup$
    – Ryder Rude
    Commented Nov 19, 2022 at 15:18
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    $\begingroup$ @Endymion You will be interested in the answer here by Mitchell Porter. It describes an idea like yours. But it's not a standard quantum mechanics interpretation. It is some String Theory hypothesis. $\endgroup$
    – Ryder Rude
    Commented Nov 19, 2022 at 18:27

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