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Consider the image below. It shows a double slit experiment but with a single photon at a time. My question is as follows:

Why is it that the photons always take a different path when shot at the same target? Where does the uncertainty lie? If we shoot it in exactly the middle of the two slits, why does it have a 50-50 chance of going into either slit? And why is the amount of diffraction for a single photon always different?

I know that people will say that the photon enters both the slits at the same time and things like that. But does anyone have an intuitive explanation as to why this happens? Why does a photon, shot with the same frequency and exactly in the same direction, still have the probability of entering either slit. Why is it that the diffraction of a single photon is different for the same wavelength?

So in brief, why does a single photon which is shot in an exactly the same why as the previous one, end up being in a different place. I am looking forward to an answer with the least possible math (if any). Or is it that a photon cannot be shot in the exact same way as the previous one?

enter image description here

Image source: http://abyss.uoregon.edu/~js/images/photon_double_slit2.gif

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The photons do not have a well defined trajectory. The diagram shows them as if they were little balls travelling along a well defined path, however the photons are delocalised and don't have a specific position or direction of motion. The photon is basically a fuzzy sphere expanding away from the source and overlapping both slits. That's why it goes through both slits.

The photon position is only well defined when we interact with it and collapse its wave function. This interaction would normally be with the detector. If we interact with the photon, to define its position, before it reaches the slits then the diffraction pattern disappears.

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  • $\begingroup$ I agree, but isn't it always first shot as a photon? And doesn't it seem very counter intuitive that it can go through both slits at the same time? Can we say that it is impossible to shoot a photon at the exact position we aimed? $\endgroup$
    – rahulgarg12342
    Sep 4, 2014 at 9:55
  • $\begingroup$ @rahulgarg12342: At the moment of emission the magnitude of the photon's momentum is reasonably well defined but the direction of the momentum is not. That's why the photon has no well defined position as it propagates. If you define the momentum precisely enough to be sure the photon goes through one of the slits you will not get a diffraction pattern. $\endgroup$
    – John Rennie
    Sep 4, 2014 at 9:58
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The problem with the picture (and probably with your understanding of the physical process) is that it assumes photons as classical particles on well-defined trajectories. If this were a true picture of reality, your objection would be justified. This, however, is not so.

In order to describe the process properly, one has to acknowledge the quantum nature of the photon. Quantum mechanics tells us that particles do not have well-defined trajectories, one can only make statements about probabilities, which in turn can be calculated from their wave function. So if you have a system like the double slit where probabilities for the photon going through each slit are equal, one cannot make a definite statement about what will happen, not even if you have just a single particle.

To clarify this even further, one can also think think about it in terms of the Heisenberg uncertainty principle: it is not possible to determine momentum and position simultaneously. A well-defined momentum implies large uncertainty in position.

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  • $\begingroup$ I am aware of the QM and wave particle duality. All I want to ask is that can you you shoot a photon towards a single target which probably is not possible. $\endgroup$
    – rahulgarg12342
    Sep 4, 2014 at 10:11
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    $\begingroup$ @rahulgarg12342 - There should be no expectation that your innate intuition of Newtonian mechanics (the world we see around us) applies to the quantum world of photons (or relativity for that matter). While you say you are 'aware' of QM and the wave-particle duality, you have not yet internalized it, and remain stuck on your (flawed) intuition. $\endgroup$
    – Jon Custer
    Sep 4, 2014 at 12:58
  • $\begingroup$ @JonCuster I understand your point and thanks for the advice. Just one last bit. Can I therefore say that it is impossible to shoot a photon at the exact same point as the previous one? $\endgroup$
    – rahulgarg12342
    Sep 5, 2014 at 6:03
  • $\begingroup$ @rahulgarg12342: that is true, a priori you only know about the probability of it being at a definite point, not that it is there for certain. $\endgroup$
    – Frederic Brünner
    Sep 5, 2014 at 9:14
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"I am aware of the QM and wave particle duality. All I want to ask is that can you you shoot a photon towards a single target which probably is not possible."

And

"@JonCuster I understand your point and thanks for the advice. Just one last bit. Can I therefore say that it is impossible to shoot a photon at the exact same point as the previous one?"

Ok, so this is the real question. And the answer is yes, you can fire two photons at the same point. It's trivial. Point a laser pointing at the wall. However, using a laser pointing you can't reproduce the experiment that you mentioned.

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An old post I know but this is the best answer I have found after an hour of searching. So it is impossible to fire a single particle toward a slit with accuracy (but the slits have to be very close to each other - how close and why)? The particle is less likely to appear 90 degrees away from the point of aim. 180 degrees away? If so there must be an an equation that describes this? A simple answer to this sort of question would help the layman.

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