Interference pattern, one particle at a time

[MindWalk]

[Mentor's note: Split off from another thread because it's a different question]
I have a question about the single-photon double-slit experiment's results that isn't about the role of consciousness. Should I go ahead and ask it here or ask it elsewhere? (Briefly: If the results are lots of dots accumulating into what looks for all the world like an interference pattern, how is that equivalent to our seeing a lot of tiny individual interference patterns, which is what I'd expect were individual photons interfering with themselves?)

 

[phinds]

[Mentor's note: Split off from another thread because it's a different question]
I have a question about the single-photon double-slit experiment's results that isn't about the role of consciousness. Should I go ahead and ask it here or ask it elsewhere? (Briefly: If the results are lots of dots accumulating into what looks for all the world like an interference pattern, how is that equivalent to our seeing a lot of tiny individual interference patterns, which is what I'd expect were individual photons interfering with themselves?)

? What does that mean? How would these "tiny individual ... " be arranged?

 

[m k]

If the results are lots of dots accumulating into what looks for all the world like an interference pattern, how is that equivalent to our seeing a lot of tiny individual interference patterns, which is what I'd expect were individual photons interfering with themselves?

It isn't.
You can't see individual photons interfering only calculate.

And you do it by adding waves, single also, sort of.
That's the only way to get the answer as you see it, lots of dots as they appear.

 

[MindWalk]

OK, here's my question. I frequently hear or read physicists say that the individual photons in the double-slit experiment interfere with themselves. But the individual photons strike the screen as individual dots, not as tiny interference patterns, don't they? And that means that what we see is an accumulation of dots that builds up a pattern looking for all the world like an interference pattern. That doesn't look the same as what I'd expect to see were the individual photons' interfering with themselves, which would be not dots but tiny interference patterns (one for each photon). Now, it may well be that a mathematical description of those dots' building up into what looks for all the world like an interference pattern and a mathematical description of photons' interfering with themselves would look the same--possibly because a probabilistic description of an ensemble and a probabilistic description applied to individuals looks the same?--but when it comes to interpreting what is happening, the "interfering with themselves" view sure looks unjustified, from my admittedly limited knowledge. Why is this said so often, then?

 

[Nugatory]

I frequently hear or read physicists say that the individual photons in the double-slit experiment interfere with themselves. But the individual photons strike the screen as individual dots, not as tiny interference patterns, don't they?

Yes and yes... But a photon has no position at all (that's "no position"! Not "it has a position but we don't know what it is", but "has no position" the same way that I have no lap when I'm not sitting down) until it interacts with the grain of light-sensitive material at a particular spot on the screen; and when it does that grain and only that grain will be affected. That's why you get individual dots on the screen even though the entire screen is being illuminated. The photon always delivers all of its energy to a single point, namely the point where it was detected.

To reconcile this picture with the notion that the photon "interferes with itself", you will want to read Richard Feynman's (math-free, layman-friendly) book "QED: The strange theory of light and matter".

 

[MindWalk]

As to a photon's "having no position" (I'll get to the rest after this is cleared up)... It is unclear to me what you mean. Here's my guess as to what you mean: the photon is a *something*--wavicle, vibrating string, something not well described as a particle but which, when observed, sometimes yields results suggesting waveness and sometimes yields results suggesting particleness--but when whatever it is interacts with the grain of light-sensitive material at a particular spot on the screen, then you get a dot.

 

[Mentz114]

As to a photon's "having no position" (I'll get to the rest after this is cleared up)... It is unclear to me what you mean. Here's my guess as to what you mean: the photon is a *something*--wavicle, vibrating string, something not well described as a particle but which, when observed, sometimes yields results suggesting waveness and sometimes yields results suggesting particleness--but when whatever it is interacts with the grain of light-sensitive material at a particular spot on the screen, then you get a dot.

In QFT one speaks of a beam of photons with occupation $1..n$ photons. What makes it a beam is that the photon(s) have momentum $\vec{{k}}$.
In no sense is anything moving, but in an interaction energy $\hbar \omega$ and momentum $\vec{{k}}$ is available. This is an oversimplification, it could be more subtle ...

 

[m k]

As to a photon's "having no position" (I'll get to the rest after this is cleared up)... It is unclear to me what you mean. Here's my guess as to what you mean: the photon is a *something*--wavicle, vibrating string, something not well described as a particle but which, when observed, sometimes yields results suggesting waveness and sometimes yields results suggesting particleness--but when whatever it is interacts with the grain of light-sensitive material at a particular spot on the screen, then you get a dot.

No, there is no "sometimes."
It's always a dot.

Problem was the combination of those dots.
You can't handle that without waves.

Other thing is that between start and end you can't get anything out of those dots but at the same time you know it is more than nothing.
Some(many) call that no position, others(same) superposition and so on.
But for what ever you still need those waves.
And get dots.

 

[bhobba]

As to a photon's "having no position" (I'll get to the rest after this is cleared up)... It is unclear to me what you mean. t a dot.

QM is a theory about observations (with observation having a very general meaning that can be made precise in QM - it does not, repeat does not, require a conscious observer) that occur in an assumed common sense classical world.

What's going on when not observed the theory is silent about. And that silence includes if the particle has position or not.

If you want a much better explanation of the double slit see:
http://cds.cern.ch/record/1024152/files/0703126.pdf

Thanks
Bill

 

[bhobba]

You can't handle that without waves.

Wrong.

See the link I gave previously.

What the double slit demonstrates is two basic principles of QM:

1. The Heisenberg uncertainty principle.

2. The practical application of the principle of superposition.

The wave-particle duality usually invoked to explain it is seen as not correct as you get more advanced. Its OK to start with, but strictly speaking its wrong.

Even the explanation in the paper I gave above is wrong:
https://arxiv.org/pdf/1009.2408.pdf

But slowly grasshopper, slowly - full understanding of QM is a slow step by step process with many things at the start changed as you progress. QM is bad like that, but QFT is even worse - so bad we have professors that teach QFT, post here with the correct answers, and they are not believed because some pop-sci or beginner text says otherwise - even professionals can get a bit confused about it (but they have the excuse they write for other professionals who know what they mean) - amazing but true.

Thanks
Bill

 

[m k]

Wrong.

My bad.
Never thought OP as a student.

 

[MindWalk]

No, there is no "sometimes."
It's always a dot.

Problem was the combination of those dots.
You can't handle that without waves.

Other thing is that between start and end you can't get anything out of those dots but at the same time you know it is more than nothing.
Some(many) call that no position, others(same) superposition and so on.
But for what ever you still need those waves.
And get dots.

Of course "sometimes." You run one kind of experiment, you get results that look like the results you'd expect were photons particles. You run another kind of experiment, you get results that look like the results you'd expect were photons waves. That's where the particle-wave duality originates.

 

[phinds]

...That's where the particle-wave duality originates.

As bhobba has already pointed out to you, "wave particle duality" is the wrong way to look at things, really. It's still used in pop-sci presentations but not in actual physics texts. It was dropped about 90 years ago.

 

[MindWalk]

<Sigh> Are you saying that the results of experiments involving photons never appear as one would expect were photons particles (like, say, dots on a screen) and never appear as one would expect were photons waves (like, say, diffraction patterns)?
By "wave/particle duality," I do not have in mind that the photon *is* a particle and *is* a wave. I only have in mind the dual sorts of experimental results, so that the photon must be something that can result in such observations.

 

[MindWalk]

Anyway, I'm just trying to understand Nugatory's meaning when he says the photon has no position. Clearly, it has position when it interacts with the grain of light-sensitive material at a particular location on the screen. I do not mean to say that it has a definite position before then. It is possible that what Nugatory intends is that the photon, *whatever kind of thing it is*, is capable of somehow delivering all of its energy to a specific location, just as though it were a particle interacting with another particle at that location, even though before that, its energy cannot be assigned a specific location (as a particle's could). Is that what you mean, Nugatory?
Then my question remains that of how this counts as "interfering with itself." If it is necessary to look up the Feynman book, I will. Can this be explained in a forum like this one?

 

[rootone]

... photon must be something that can result in such observations.

It is, it's a quantum object.

 

[phinds]

By "wave/particle duality," I do not have in mind that the photon *is* a particle and *is* a wave. I only have in mind the dual sorts of experimental results, so that the photon must be something that can result in such observations.

Unfortunately for you then, "wave particle duality" has a very specific meaning in physics and it's not your self-made definition so using it to communicate with other is not a good idea.

 

[phinds]

... Clearly, it has position when it interacts with the grain of light-sensitive material at a particular location on the screen. I do not mean to say that it has a definite position before then.

Then you are not in conflict. He's just saying that absent any interaction, it has no specified location.

 

[PeterDonis]

Clearly, it has position when it interacts with the grain of light-sensitive material at a particular location on the screen

Not really, because this interaction destroys the photon. What has position is the grain of light-sensitive material.

 

[PeterDonis]

"has no position" the same way that I have no lap when I'm not sitting down) until it interacts with the grain of light-sensitive material at a particular spot on the screen

I think you have to be careful here. As I noted in my previous post just now, this interaction destroys the photon (it is absorbed by the light-sensitive material), so I don't think it's correct to attribute the position of the light flash to the photon; it's the position of the grain that absorbs the photon.

The photon always delivers all of its energy to a single point

This is a better way to say it, because it doesn't require you to say that this point is "the position of the photon". It's just the position at which the energy is delivered (by the photon being absorbed and therefore destroyed).

 

[m k]

And that means that what we see is an accumulation of dots that builds up a pattern looking for all the world like an interference pattern.

What area gets most hits?

 

[phinds]

What area gets most hits?

It's a wave interference pattern. The peak constructive interference area gets the most hits just like any other interference pattern has the constructive interference area being the strongest.

EDIT: This is such an obvious answer I'm wondering if perhaps I don't understand the intent of your question.

 

[bhobba]

That's where the particle-wave duality originates.

No. It actually originated very early on in the development of QM and appears in beginner texts/popularisations because of the semi historical way they explain it. It was done away with by Dirac at the end of 1926 with his transformation theory - probably sooner - but most certainly by then:
http://www.lajpe.org/may08/09_Carlos_Madrid.pdf

That did away with such ideas completely.

A much better way to view QM that avoids such confusion is the following:
http://www.scottaaronson.com/democritus/lec9.html

Its part of a number of very common QM myths:
https://arxiv.org/abs/quant-ph/0609163

Note - you may spot an inconsistency in what I said. I won't tell you what it is, read the paper and see if you can spot it - even more points for thinking about how this seeming inconsistency is resolved. Of course if you don't see how its resolved I will tell you - but please have a go first and see if you can find it.

Thanks
Bill

 

[MindWalk]

Not really, because this interaction destroys the photon. What has position is the grain of light-sensitive material.

Well, OK, but the interaction has definite location, which means when the photon hit, it had definite location.

 

[rootone]

Well, OK, but the interaction has definite location, which means when the photon hit, it had definite location.

After which the particle no longer exists and never did.
https://en.wikipedia.org/wiki/Quantum_decoherence

 

[bhobba]

Well, OK, but the interaction has definite location, which means when the photon hit, it had definite location.

The interaction had definite location - the photon - well that's another matter:
http://arnold-neumaier.at/physfaq/topics/localization

Of course a beginner would never be expected to understand that. Just take away the idea defining the position of a photon is problematical.

That's why its better to discuss the double slit with electrons - you don't run into subtleties like photons don't actually have a position operator or actual position.

Thanks
Bill