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Lately, I was thinking about the one-particle version of the double slit experiment, e.g. in which an electron or a buckyball is emmited. The precise description of what I mean can be found here.

This experiment clearly shows the wave-particle duality of electrons. But I am concerned in something a little bit different, that is, is every particle emmited in such an experiment identical to another ones? If that is the case, then I guess we can say, that there actually is some randomness hidden in the act of measurement and things start to be really interesting.

But I think, that emitting these identical particles is extremely hard to achieve from an experimental point of view (mainly due to the Heisenberg uncertanty principle, decoherence and noise related to the experiment itself). So, if we are in fact unable to reproduce the same initial conditions for each of the consecutive experients, can we still talk about randomness hidden in quantum physics?

If on the other hand we would be able to reproduce these initial conditions with perfect precission, maybe we would observe each particle in the same place on the screen every time? This place of observation could still prove the wave-particle duality nature of an electron (that is, it could be different from only two possible locations guaranteed by the only-particle nature of electrons), but I guess we couldn't still talk about the probability associated with the act of measurement.

What do you think about this?

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  • $\begingroup$ So you are asking if all electrons are, well, electrons? $\endgroup$ – Jon Custer Oct 23 '19 at 12:39
  • $\begingroup$ I am asking if these electrons have for example the same momentum $\endgroup$ – brzepkowski Oct 23 '19 at 13:31
  • $\begingroup$ For an electron source, there is a slight energy dispersion caused by the electron source (cold cathode vs hot filament) which can be important in achieving maximum resolution in imaging applications. This energy variation of several eV should be compared with the electron energy of 10's to 100's of keV after acceleration in the electron gun. Not that different from the photon energy range of a good laser. $\endgroup$ – Jon Custer Oct 23 '19 at 13:52
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You are basically asking two questions:

  1. Is every single electron the same that is emitted one by one in the slit experiment?

I actually asked a question about this:

When an electron changes its spin, or any other intrinsic property, is it still the same electron?

It is about spin and all other intrinsic properties. You are basically asking whether the electrons that are emitted one by one have all the same intrinsic properties and if they are identical.

You started with some state of the electron quantum field and now have a different one; whether some parts of it are the "same" as before are really up to how you define the word "same". Absolutely nothing within the theory itself cares about this distinction.

Now the word identical is the confusing here. The correct word is indistinguishable.

That view goes well with the indistinguishable particle problem in QED scattering: if there are 2 electrons in the final state, it's not that they are identical, it's that they are indistinguishable, meaning they don't really have an identity as different particles, and you have to consider both (or all) paths that lead to the final observed state of the electron field.

So these electrons that are shot one by one, are all indistinguishable. Yet they land on different places on the screen. This is really QM. It is all probabilities.

  1. Can we make somehow sure that each particle that is shot will land on the same spot on the screen?

In the slit experiment we cannot. The interference (and decoherence) is something that is really QM. In QM it is the probability distribution that is determined and the individual photons will be in line with that. The direction (after the slit) of the emitted electron will be random, but it will obey energy and momentum conservation and when the experiment is repeated many times, the electrons will follow the distribution.

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  • $\begingroup$ That's a great answer! But I have a follow up question about the measuring apparatus itself. If every emmited electron is indisinguishable with any other, I guess we should also make sure, that the measuring device is the same every time we conduct an experiment. But I believe this is impossible, because e.g. of the noise of the environment. Can we despite that fact still talk about randomness in QM? Or do you think, that these small changes in the measuring apparatus can influence the results of measruement? [...] $\endgroup$ – brzepkowski Oct 24 '19 at 11:47
  • $\begingroup$ [...] That is, if we would be in possesion of a "perfect" measuring device, would it be possible to see an electron at only one position allowed by the interference of the wavefunction after condcuting multiple experiments? Or would we still see the distribution of measured electrons? $\endgroup$ – brzepkowski Oct 24 '19 at 11:49
  • $\begingroup$ @brzepkowski in reality it is not possible to create a perfect device. But the reality of QM is that it does count for the error. The randomness is not because of the kown error of the device (because it is accounted for in the theory and the experiment) but the QM of the universe itself. $\endgroup$ – Árpád Szendrei Oct 24 '19 at 15:27

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