# If probability wave is true wouldn't there be flickering?

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1. Jun 8, 2015

### deansatch

I've been reading up a lot on the double slit experiment recently (and I'm no physicist at all). Although I haven't really seen the experiment done with my own eyes, from the demonstrations on youtube it seems as though the pattern when shining a laser through the slits is constant and solid.

If this was really probability would a laser shining through onto a screen not be like an extremely fast animated version of watching the single photos building up (but disappearing as fast as they appear)? So would this not make the result appear to flicker...vary in brightness on each line? Unless it is not truly probability and the result is a guaranteed pattern after X amount of photons? Maybe it does flicker if you have seen it yourself but I have yet to get the chance.

2. Jun 8, 2015

### vanhees71

Lasers are not sources of photon-Fock states but of coherent states, which are closer to a classical em. waves. However, there are "quantum fluctuations". In a coherent state the photon number is Poisson distributed, i.e., it's mean is $\langle N \rangle=\lambda$ and it's standard devition $\Delta N^2=\langle N^2 \rangle-\langle N \rangle^2=\lambda$ too. So at high intensities you don't see the fluctuations, but dimming the Laser down you'll see them.

3. Jun 8, 2015

### deansatch

Thanks...I'm not quite advanced enough to follow the maths though, but take your word for it about the low intensity light which answers my question.

Would it be unreasonable to assume that rather than photons being waves that can turn into particles or vice versa, that they really are just particles that "ride" a set atmospheric wave that we have no method of seeing? Like little surfers that join the wave at whatever point they are fired which then determines their final position? Or is that just crazy talk?

4. Jun 8, 2015

### logico

Hmm. The answer that a low intensity beam (modern experiments deliver one photon at a time) would flicker applies to any beam. I'm guessing (?) from your question that you are thinking about a flickering at each of the two slits. That doesn't happen, because to see/detect a photon you have to interrupt its progress. The standard explanation of the two-slit experiment (Copenhagen...) is that that each photon passes throgh both slits; or that a probability-like wave passes through both slits. It's an answer that challenges common sense, and raises problems so severe that Everett and his numerous disciples conjured up (Very) Many Worlds to explain it away - but still in a way that accords ill with common sense. But if you want to sample a novel approach, a Chinese researcher called Shan Gao has published numerous papers propounding his theory that the motion of the photon or other particle is actually in discrete steps, which stochastically generate the probability wave. Interestingly, Aharonov et al have some experimental evidence for such a real wave...

5. Jun 8, 2015

### atyy

Would this be what you mean by flickering?

6. Jun 8, 2015

### Staff: Mentor

That's common in pop sci accounts and beginning texts - but its not what's going on:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

Its really a demonstration of the uncertainty principle and the principle of superposition.

Thanks
Bill

7. Jun 8, 2015

### andresB

That sound a lot like de Broglie-Bohm mechanics

http://en.wikipedia.org/wiki/De_Broglie–Bohm_theory

8. Jun 8, 2015

### logico

bhobba

It's a brave man who can say "it's really... superposition." Nobody doubts that the Schrödinger equation works; but "superposition" implies an ontological commitment to the unobserved states. Personally, since only particles are observed, I don't feel any greater need to regard the wave equation as real than I do to the idea, say, that the Normal Distribution Curve reaches out to govern the positions of bulletholes in a target.

9. Jun 8, 2015

### Staff: Mentor

I would hazard a guess that not everyone accepts that implication... But this thread isn't the right place for that argument conversation.

10. Jun 8, 2015

### Staff: Mentor

It depends. If your screen is something like photographic film that makes a permanent record of each photon impact, then the pattern builds up as in the video that atyy posted. It'll built up quickly if the source is intense so a large number of photons land and make their marks in a short period; it will take longer to build up if the source is less intense, but sooner or later we'll have enough dots on the image to make clear interference pattern.

On the other hand, if the detector is something more like the retina of your eye, which responds to incoming light, holds the impression for a short period of time, and then loses it, you might see the dots coming and going. You won't with a human retina, because it takes at least a few hundreds of photons landing in a short time to provoke one of the light-sensitive cells in our eyes to fire, but you could imagine a detector with more sensitive cells that respond to individual photons. Vanhees was saying that whether this appears as "flicker" or not still depends on the intensity of the light: if the intensity is high all the cells will be more or less continuously triggering, rather like a pouring rainstorm will uniformly drench everything even though the water is being delivered in individual droplets; if the intensity is lower we will detect the individual dots coming and going.

However, this effect depends only on the intensity, so is pretty much the same whether the "probability wave" goes through one slit or two - we have the same considerations any time that we shine a light on a screen. The interference from the two slits just means that the light intensity (probability of photon arrival per unit time) is not uniform across the screen.

11. Jun 8, 2015

### Staff: Mentor

All superposition is, is a reflection of the vector space structure of pure states which follows from the Born Rule which, although its only usually found in more advanced treatments, is basically implied by Gleason. See post 137:

To fully spell it out the Born rule says, given an observable O, a positive operator of unit trace, P, exists such that the expected value of the observation associated with O. E(O), is E(O) = Trace (PO).

By definition P is called the state of the system. States of the form |u><u| are called pure. States of the form ∑pi |ui><ui| are called mixed. It can be shown all states are mixed or pure. Usually we deal with pure states |u><u| so the |u> form a vector space. This is the origin of the principle of superposition.

To return to the double slit behind the two slits the state obviously depends of the state just behind each slit ie is a superposition of those states. But due to the symmetry of the situation its as per equation 9 in the link I gave - and you get the standard double slit interference pattern.

Indeed. What I gave above is the mathematics of the situation, which, generally, everyone accepts. What it means however is another matter and very interpretation dependant.

In discussing interpretations there is no right or wrong view, they are all equally valid. Their value IMHO lies in the light it sheds on what the QM formalism says and what is an assumption - but discussion can, counter-productively, get a bit heated.

Thanks
Bill

Last edited: Jun 8, 2015
12. Jun 9, 2015

### deansatch

Would anyone be able to clarify a few things about the experiment for me?

The firing of photons toward the 2 slits...how accurate is this? i.e. aim? For a single slit I imagine firing them straight through as though there were no obstruction at all. Then for the double slit, do they fire at the blockage in between? Do photons travel in such a way that they don't go straight so randomly miss a slot or go through one or the other? Or do they hunt for a target?

What propels a photon? And at the same time what determines the direction of travel?

And lastly...what's to say that if the direction of travel is so inconsistent that (considering how small they are) when they enter a slit they aren't simply bouncing around the inside walls of the slit before making it all the way through?

Apologies if any of these questions are daft but I'm asking as a laymen, studying QM for pleasure.

Also to clarify what I was asking about the flickering:
What I meant was that if you look at the video posted by atyy - that is single photons hitting and being stored in the seemingly random (but probable) fashion. So if they weren't fired one at a time and were just a constant laser (or relevant lighting device that does fire photons as particles) at a wall...not stored...wouldn't we see a fast version of that video followed by another different version and so on...obviously this would be ridiculously fast but I would expect to see the pattern of light on the wall vary whether it be a flickering or pulsating? Kind of like if you did the single photon experiment millions of times then took printouts of the results as slides and made a flickbook animation - the patterns would differ with each slide enough to see movement?

Last edited: Jun 9, 2015
13. Jun 9, 2015

### Staff: Mentor

First can I suggest you at least glance at the paper I posted? I know it involves math but it does elucidate a number of points you raise.

Because the photon is emmited from a known position that means, as explained in the paper, its direction is unknown, so cant be aimed.

Photons are massless so always move at C.

For various more advanced reasons its best to consider the experiment done with electrons - otherwise you are lead to certain inaccuracies - but I will ignore those here since they are not germane to conceptually what's going on.

The walls in the experiment absorb photons so it will not bounce around.

Sure - if you have a continuous stream not strong enough so you see continuous bands, but not weak enough so you see individual photons one at a time, you will get a flickering effect.

Thanks
Bill

Last edited: Jun 9, 2015
14. Jun 9, 2015

### deansatch

Thanks Bill. I'm reading that paper now but must admit it is a struggle when I have to google half the words :)

15. Jun 9, 2015

### Staff: Mentor

I understand - but hopefully you will get a bit of the drift.

When people post explanations with math and the math is beyond you that's the general way of getting the gist.

Thanks
Bill

16. Jun 9, 2015

### Staff: Mentor

These questions sound as if you are thinking of the photon as a little tiny bullet, a small solid particle that travels through space from the source to the destination, something that can be aimed on a particular path. That's a natural picture to form when you hear the word "particle", but it is very misleading - a photon is nothing like that, and it is a very unfortunate historical accident that physicists use the word "particle" in a way that is so different from the plain English meaning of the word.

A better picture (still not a substitute for doing the math, but close enough to keep you out of trouble) would be: Light propagates as an electromagnetic wave, and this can no more be aimed at a single spot like a slit than you could aim a water wave at a single point on the surface of the water - the best you can do is send the wave in the general direction of the target. Photons only come into the picture when the electromagnetic wave interacts with matter; we find that the wave always delivers its energy in discrete lumps at a single points in the area covered by the electromagnetic wave. Each time that happens, we say that "a photon was detected at that point". In the empty space between source and screen (including the openings that form the slits) there's no matter to interact with, so no way of talking sensibly about photons in that empty space.

17. Jun 9, 2015

### zonde

Take a laser pointer, two pieces of hard paper and experiment a little. Put two pieces of paper together so that they form V type slit with very small angle (you can hold it with one hand) and with second hand aim laser pointer at that slit. As you aim the laser up and down and move it to the left and right you can change the with of the slit. And you will need dark room with smooth white surface as a screen. That way you can observe how diffraction changes with slit size and you will get better idea about beam size vs slit size. And you can observe diffraction fringes btw.

18. Jun 10, 2015

### zonde

Your argument seems faulty to me.
Laser beam can go large distance without widening too much (and widening is linear after waist). When it encounters narrow slit it widens suddenly in direction perpendicular to the slit. If you explain widenig of laser beam after the slit using Huygen's Principle then why it does not apply when laser beam propagates freely?

19. Jun 10, 2015

### Staff: Mentor

Why do you believe Huygens Principle is required for that?

Thanks
Bill

20. Jun 10, 2015

### zonde

Nugatory says (see his post) that viewing light as a wave is less misleading and as I see it Huygens Principle is what makes wave model useful. Don't you agree?

21. Jun 10, 2015

### Staff: Mentor

No.

Read the paper I linked to then we can discuss it:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

BTW I don't disagree with Nugatory - but in reality the least misleading of all is that it is neither particle or wave.

However I have to also mention that we likely spend too much time on this issue and it has been done to death in many threads. So I don't think there is any value rehashing it here.

Thanks
Bill

22. Jun 10, 2015

### Staff: Mentor

Although the model I describe is faulty - of course! it's a heuristic picture whose greatest virtue is that it will set the original poster on the right track! - I must confess that I don't see your particular objection. Both the low divergence of a laser beam and the diffraction when it encounters a slit are easily understood as classical wave phenomena, and that has to be better than trying to model a light beam as a stream of little bullet-light photons travelling on definite trajectories even when they aren't being absorbed at a particular point on teh screen.

23. Jun 10, 2015

### zonde

I understand diffraction as combination of high divergence and interference. There are no questions about interference. What seems counterintuitive is low divergence of freely propagating laser beam and high divergence of laser beam near border of obstacle. If high divergence is explained using Huygen's Principle (high divergence happens at the edge of wave front) then why it does not happen for freely propagating laser beam (obviously there is edge of wave front too).
I see problem with photons being particles at far field only if you model narrow slit as far field. But it does not seem right to view slit as far field. Laser beam has low divergence when it propagates freely and it has high divergence right after the slit (or near border of any barrier). So it seems like the light (whatever wave or particle) that goes through the slit interacts with barrier so it can't be modeled as far field.

24. Jun 10, 2015

### zonde

Thanks for the link but I already have read this paper however I don't want to discuss it right now. And it goes a bit sideways from the point Nugatory was making.

25. Jun 10, 2015

### atyy

Roughly, the single photon is a wave, so it passes through the single slit and the double slit. Then at the screen, each photon makes a mark at a random position on the screen. The randomness is specified by the photon wave. This idea is a bit inaccurate, but it will be ok if one uses electrons instead of photons. The difference between electrons and photons is that the latter are massless and need a more technical treatment.

Another simplification we made above is that the photon has a direction of travel. Let's just say these are given by the initial push that it gets when it is created. The true analysis is very hard, and I have never seen it carried out, so these are the usual simplifications.

They do (essentially because it is a wave).

Yes, the photons are fired one at a time, and each photon causes one mark to appear on the screen.

If you fire a bunch, then you will see a fast version each time you fire a bunch. The pattern will be different for each bunch.