A Question about the Particle-Wave Duality in QM

Wayfarer

Some time back, I posted a question on Physics Forum, and a similar one on Physics Stack Exchange.

Basically the question comes out of discussions I had here about the famous double-slit experiment, and the implications of the so-called 'interference pattern' (a primer can be found on Youtube.)

The question was about the fact that the interference pattern that appears on the screen in the double-slit experiment is rate-independent. That is: up to a certain point, regardless of at what rate particles are fired, the interference pattern will be the same. Given an identical set-up, it could not be determined at what rate the particles had been fired in order to produce two observed interference patterns. So I am interested in the implications of the fact of this 'rate independence'

Now in the first of the two Forum responses above, the initial point - about the identity of the results - was acknowledged without any objections.

But I then introduced the argument that this shows that the 'wave equation' is independent of time (and therefore space, as I had understood these two to be related as 'space-time' in relativistic physics). I said, in particular, that 'what is causing the interference pattern is outside, or not a function of, space-time'.

But as soon as I said that, my argument was designated as 'gobbledegook' on Physics Forum. The objection was that 'The fact that time is not a factor has no relation to the fact that space is a factor', and also that 'The particles move in space-time. The double slit and the detector are in space-time. There is nothing outside of space-time.'

But what I'm arguing is 'outside space time' is the cause which actually produces the interference pattern. It is a real 'distribution of probabilities', but it's not 'in' some medium. It is an attribute of reality itself, like a pattern of tendencies. This is unlike the 'pilot wave' theory, because Bohm's 'pilot wave' is proposed to be physical. Whereas the so-called 'probability wave' is not actually physical - hence my argument that it is outside space and time. (It's literally meta-physical - hence the sharp reaction from the physicist, in my opinion.)

After a bit of to-and-fro, it was agreed that 'the pattern is not dependent on the rate', which is really what I wanted to establish.

The response on Physics Stack Exchange was that:

'The independence of an interference pattern produced by a given number of photons from the time required for those photons to be registered is simply further confirmation of the assertion that each "interferes with itself" ' - which personally I find an absurd explanation, even though it is one of the expressions that is commonly used.

Since posing these questions, I have found another OP - Quantum mysteries dissolve if possibilities are realities: Spacetime events and objects aren’t all that exists, new interpretation suggests. This OP says:

“This new ontological picture requires that we expand our concept of ‘what is real’ to include an extraspatiotemporal domain of quantum possibility,” write Ruth Kastner, Stuart Kauffman and Michael Epperson.

Now, you see, I think they're talking about exactly what I was getting at in my post - they are saying 'extraspatiotemporal', I simply said 'outside space and time'. But it means the same.

I think what it signifies is that 'potentia' are real, but they're not actualised. Whereas, modern philosophy tends to regards 'existence' as having a binary value - something either exists, or it doesn't; something can't be 'potentially real' anywhere outside the mind. Possibilities don't actually exist, we would say; but, think again!

But I would deeply appreciate some feedback by the more physics-educated contributors, such as @Apokrisis and @AndrewK, on such points.

__//|\\__

Wayfarer

View Answer

apokrisis

↪Wayfarer

Each particle "interferes with itself" in the sense that it interacts with the apparatus in every way that it can. It takes every possible path, the combination yielding some sum of probabilities. So some paths add, some cancel. And that results in the "interference pattern" - even if one event could hardly show that by itself.

So it is the fact that the entire apparatus is kept constant over space and time that roots the interference pattern in space and time. If you fire enough identical particles at the slits, the same interaction between particle and path will be repeated. And so the interference pattern this will cumulative generate will slowly be revealed.

Rich

For the non-scientists who do get the gist of the issue, one really can't speak of non-local, spooky action at a distance (now confirmed at the molecular level) and still have any hope for space-time, now can we?

Space-time metaphysics (that all it is) is irrelevant to quantum and current quantum scientific activity is working to replace it, so why lose any sleep over it? As it turns out, Bohm mechanics reconciles the wave patterns without resorting to "wave collapses" in space-time.

andrewk

↪Wayfarer

'The independence of an interference pattern produced by a given number of photons from the time required for those photons to be registered is simply further confirmation of the assertion that each "interferes with itself" ' - which personally I find an absurd explanation, even though it is one of the expressions that is commonly used.

I agree with you. I don't find the phrase 'interferes with itself' meaningful or helpful.

My current way of looking at it (it has changed in the past, and likely will again in the future) is that the wave part is a probability field for a photon striking the screen. With one slit, that probability field is strongest in the centre of the screen and decreases as we move away from there. With two slits, the field strength has an undulating profile as we move across the screen, with peaks and troughs. We call the peaks 'bars'.

If we dim the light, the probabilities decrease, but the fields retain their shape - single blotch or series of bars according to whether there is one or two slits. The blotch or bars are just weaker.

In any given small region Photon strikes appear by a random process (a Poisson process) whose frequency parameter ('probability') is the average field strength in that region. This builds up the pattern over time - quickly if the light is strong and slowly if it is weak ('slow photon rate'). There is no expected difference between the pattern built up from a constant light source over period of length T and that built up from a light source one millionth as strong over a period of one million times T.

This explanation satisfies me, without having to introduce any notion of photons interfering with one another, let alone with themselves. The interference is between the probability fields of the two slits - the 'waves' as some might put it.

Wayfarer

↪andrewk

Thanks, that is pretty much how I would have understood it. What seems to be the challenging philosophical issue is, however, the ontological status of the probability field. Your reply implicitly accepts that the probability field is something real i.e. causal. But it is not in itself something physical - it doesn’t inhere in a medium. So it’s not actually a wave, but rather, something that emulates a wave, or can be described by the wave equation.

apokrisis

:-} It's the paths that "interfere". They either add or cancel to create the interference pattern. It's a thing even in the classical wave mechanics view - https://en.wikipedia.org/wiki/Multipath_interference

andrewk

What seems to be the challenging philosophical issue is, however, the ontological status of the probability field — Wayfarer

Indeed. I approach this by regarding 'laws of nature' as descriptive rather than prescriptive. That way they do not need ontological classification. They are a just a tool we use to visualise what is going on and to make predictions. I accept that many, possibly most, people find that unsatisfying.

If one wanted to attribute an ontological status to the probability field, what do you think of regarding it as some sort of Kantian noumenon? We can never observe the probability field itself, only phenomena that arise from it (photon strikes). That sounds a bit noumenish to me, but I'm a bit of a noumenon newbie (just had to find a way to get that phrase in there).

Wayfarer

↪andrewk

It sounds very near to my understanding of it, also. I think it's an admirable way of seeing it.

What struck me about the fact of 'rate independence' is that it shows the idea of 'the wave' is actually a metaphor - it's not as if the probability wave is an actual wave, because it is not defined by time. What other waves are there, that are not time-related? And yet, it appears to have actual consequences. That's what is interesting about it.

Here is an exchange from the Stack Exchange post about this:

It's the fact that it is not time-dependent which is of interest. I don't think you could replicate this outcome using a physical medium like water waves in a tank, because in that situation, 'time' would be a boundary condition. That is the sense in which 'waves' and 'interference' might actually be only a metaphor for the effect; the effect is not the consequence of actual waves, but of the interaction of probabilities only. The interpretive challenge is then that it appears to demonstrate 'real possibilities' i.e. possibilities that have physical consequences. – Wayfarer Dec 5 '16 at 2:29

It is not time-dependent because the boundary conditions, which in the end define the probabilities, are not time dependent is what I am saying. It is the particular use of wave equations. with operators on psi, that makes the difference between material waves or energy waves and probability waves. – anna v Dec 5 '16 at 4:49

Are there many other types of waves for which time is not a boundary condition, or is this the only example? – Wayfarer Dec 5 '16 at 10:15

f one wanted to attribute an ontological status to the probability field, what do you think of regarding it as some sort of Kantian noumenon? — andrewk

Are you familiar with D'Espagnat?

What quantum mechanics tells us, I believe, is surprising to say the least. It tells us that the basic components of objects – the particles, electrons, quarks etc. – cannot be thought of as "self-existent". The reality that they, and hence all objects, are components of is merely "empirical reality".

This reality is something that, while not a purely mind-made construct as radical idealism would have it, can be but the picture our mind forces us to form of ... Of what ? The only answer I am able to provide is that underlying this empirical reality is a mysterious, non-conceptualisable "ultimate reality", not embedded in space and (presumably) not in time either
1. — Bernard D'Espagnat

It's significant that he uses this term 'self-existent', as that is actually from Buddhism, which says that all phenomenal entities (this would include 'atoms') are not self-existent but are produced.

D'Espagnat's books on Physics and Philosophy go into these questions in a lot of depth - more than I can understand, unfortunately.

The other interesting person is Ruth Kastner, who I mentioned above. She is developing an idea of Heisenberg's, that 'the real' includes entities which exist only as 'potentia'.

Wayfarer

It's the paths that "interfere". — apokrisis

Thanks for your suggestions here, but not really what I was trying to understand. I mean, the fact of there being paths and interference is not at issue, what I am interested in is the nature of the so-called 'probability wave'. I do understand this to be an outstanding issue in current philosophy of physics. I think actually it's a pointer to the interface between physics and metaphysics, but I'm pretty hazy on a lot of the detail.

apokrisis

...what I am interested in is the nature of the so-called 'probability wave'. — Wayfarer

It is not some actual material wave hitting the screen. It is a description of predictable observables with a "wave-like" evolution in time.

In the same way, a quantum field is not a material field. It is a field-like description of observables.

Of course we then want to impute some kind of underlying reality that generates these observables. That is where all the interpretive machinery comes in, like physical pilot waves or spooky non-local connections.

So we can interpret the formalism in all sorts of metaphysical ways, the majority of which are then "bad" metaphysics. We would criticise them on grounds like that they are too profligate (many worlds), or too concrete (Bohmian mechanics).

It is fair enough to seek some kind of mental picture of what is "really going" on underneath the covers. However calling the evolution of a set of observables a "probability wave" is misleading as there is no actual wave in a material sense. It is just the pattern we see in our abstract model of how the probabilities of the situation will unfold.

Rich

However calling the evolution of a set of observables a "probability wave" is misleading as there is no actual wave in a material sense — apokrisis

Well that's your metaphysics and can be rejected for being too "nothing".

Bohmian Mechanics is real. The quantum potential wave field is real. The "particles" (actually field wave perturbations) are real. Action at a distance is built-in and predicted by the model. The delayed choice is easily explained without resorting to "going back in time". The only thing going for Copenhagen is that it v is so embedded into quantum textbooks that it would be an embarrassment for scientists when it is finally tossed out. And tossed out it will be, because unlike the West, China is not married to an antiquated model and is streaming full speed ahead into all types of quantum technology that will leave the Western nations in the dust. Recently they measured that action at a distance is at b least 10,000 times the speed of light and may very well be instantaneous as predicted by the Bohmian model. They have also successfully b verified entanglement from a satellite which b is the basis for a new encryption technology they are building.

andrewk

↪Wayfarer

What struck me about the fact of 'rate independence' is that it shows the idea of 'the wave' is actually a metaphor - it's not as if the probability wave is an actual wave, because it is not defined by time.

Yes, it's a bit like if we snap-froze the ocean while it was wavy. Then we'd have a physical wave shape, but one that was constant across time.

I think one source of the confusion that often arises here is that we can predict the interference pattern using classical wave theory, ie avoiding QM altogether. In that case we are using actual electromagnetic waves emanating through the two slits. Then at each point on the screen the wave manifests as complementary sinusoidal variations in electric and magnetic potential over time. The result of the two waves interfering is that the amplitude of those variations on the screen varies as we move across the screen, giving high amplitude in the middle of the light bars and low amplitude in the dark bars. In that analysis the EM waves are moving in both time and space. But the static 'probability wave' of QM plays no part in this calculation, even though they give the same results.

It is often forgotten that the double-slit experiment is entirely explainable using classical electromagnetic wave theory. QM is only needed to explain various tricky variations of the experiment, such as the one you describe where photons may appear at the screen a rate of only one per second.

apokrisis

Well that's your metaphysics and can be rejected for being too "nothing". — Rich

Coming from you, that's rich.

Bohmian Mechanics is real. — Rich

So reality is both fully deterministic and fundamentally tychic in your book? An interesting twist on quantum crackpottery.

Rich

So reality is both fully deterministic and fundamentally tychic in your book — apokrisis

Nope. Totally 100% wrong again.

apokrisis

Totally 100% wrong again. — Rich

The expert speaks.

Rich

The expert speaks. — apokrisis

The thing is the self-proclaimed expert is 100% wrong. Not even a modicum of study or understanding of Bohm's works. How did you put it? Too concrete. No where near the flights of imagination like other theories?

WISDOMfromPO-MO

But then one reads that physicists are saying that time is an illusion and that we live in a static universe.

Therefore, maybe the observation in the OP confirms the latter rather than invites speculation about anything metaphysical.

Metaphysician Undercover

What seems to be the challenging philosophical issue is, however, the ontological status of the probability field. — Wayfarer

I really don't think that physics has an adequate concept of time. We know that the past consists of events which have already occurred, and the future consists of things which may happen (possibilities), while activity occurs at the present. Physics doesn't seem to have any principles which make sense of these facts.

Wayfarer

So we can interpret the formalism in all sorts of metaphysical ways, the majority of which are then "bad" metaphysics. — apokrisis

it's a bit like if we snap-froze the ocean while it was wavy. Then we'd have a physical wave shape, but one that was constant across time. — andrewk

Well, my question is quite specific. To recap, on the Physics forum, this was the sequence of questions I asked:

Q: So you could set up the [double-slit] experiment at various rates, and produce the 'interference pattern', and then send a copy of the patterns to a physicist, and the physicist wouldn't be able to deduce the rate at which the particles were fired?

A To get the an interference pattern that builds up the individual objects in the 'ensemble' must be identically prepared. A different ensemble, for instance having higher energies per particle, will give a different interference pattern. The gaps/bands will be smaller.

Q: But you could prepare it in such a way that the interference pattern would remain the same regardless of the rate at which the particles are fired?

A: Yes. 24 hours at 1 per second would give the same pattern as 1 second of 86400.

Q: Interesting! So energy is a significant variable - if you vary the energy, you vary the resulting pattern - but rate is not. Would that be a valid conclusion, all else being equal?

A : Yes, but only up to the point where the rate is so high that the interaction between different electrons can no longer be neglected.

Q: The argument that started this was about whether this means that time (being 'rate') is not a factor; which also that means that space (i.e. proximity of particles) is not a factor (as proximity is an aspect of space-time.) So, what is causing the interference pattern is outside, or not a function of, space-time.

A: Sorry, but this is gobbledygook.

So my question to you is: do you think my inference that 'what is causing the interference pattern is outside, or not a function of, space-time' is indeed 'gobbledygook'? Or do you think it's a valid inference?

apokrisis

So my question to you is: do you think my inference that 'what is causing the interference pattern is outside, or not a function of, space-time' is indeed 'gobbledygook'? Or do you think it's a valid inference? — Wayfarer

Your approach is confusing as you start off suggesting that rate ought to matter. So your mental picture seems to be that each event has to be "close enough" in spacetime for interference to occur ... between individual events. Distant events - distant in space or time would not "feel the force". But events happening close together, would.

But that is not what it is about. It is about the interaction between the measuring apparatus and the individual event. Every particle is travelling in an identical fashion down the same apparatus. So - if the slits are not being observed - every particle will show the same probabilistic result. It is the two slits which are constantly in interaction if you like. If both slits are always "open" and free from measurement, then every particle running the gauntlet will behave in wave-like fashion.

So the statistics reflect the shape of the path. The same path is always going to give the same result for every identically prepared particle, regardless of the rate of their release (so long as they don't come so thick and fast they do physically interfere with each other!).

Rich

what is causing the interference pattern is outside, or not a function of, space-time' is indeed 'gobbledygook'? Or do you think it's a valid inference? — Wayfarer

Of course you are correct. There is no space-time under quantum physics. That is why the latest theoretical physicists are abandoning it and apparently treating quantum as purely information and gravity as a product of information entanglement. When Bohm wrote about the quantum potential in his equations 60 years ago, he stated quite emphatically that it acted instantaneously because the field was everywhere (now being discussed as a holographic field) and it relied wholely in the form of information anticipating today's research direction. He also wrote that space-time would have to be reworked, again anticipating the latest direction of theory physics.

apokrisis

↪Rich

Post that on Physics Forum I dare you. :)

Rich

Post that on Physics Forum I dare you — apokrisis

Don't want to upset too many of them during their fund raising efforts. You think I take them any more seriously than the average myth maker. Rather than read the actual works they read Wikipedia (like others who say Bohmian Mechanics is deterministic).

Wayfarer

Your approach is confusing as you start off suggesting that rate ought to matter. — apokrisis

But if it's a wave, how can the rate NOT matter? Remember, the phenomenon at issue is interference. And interference implies interaction. You're prepared to say that 'particles interfere with themselves', but how is that any less confusing?

Furthermore, what is 'the path' defined by? There is no actual 'path' in reality, unless you accept the pilot-wave theory, which you have said you don't. So they follow 'a path' - what is the path defined by? I am saying, it's not defined by something in time.

So - I don't see my approach as 'confusing'. As far as I'm concerned, I have asked a novel question.

Rich

So - I don't see my approach as 'confusing'. As far as I'm concerned, I have asked a novel question. — Wayfarer

It's a great observation, and when the experts are embarrassed (because they really don't get it), they call it gobblygook. Bohm agrees with you. What matters is the form for the information. For further reading I recommend Science, Order, Creativity by Bohm, Hiley.

Wayfarer

↪Rich

That's how it struck me. If you look at the thread, you will notice I chose not to argue the case. But what it seems to me is that, as soon as I ventured something beyond the physics - i.e. into a meta-physical observation - then there's an instant red flag.

The girl on the Physics Stack exchange explicitly said, well, time is not a boundary factor in this experiment. And I asked: this means, it's a timeless wave? Where else in physics would you see something analogous? I didn't get an answer, but for all I know, there might be a quotidian answer to that question.

But I still think I'm onto something novel, here. :-)

WISDOMfromPO-MO

"Our illusion of the past arises because each Now in Platonia contains objects that appear as "records" in Barbour's language. "The only evidence you have of last week is your memory. But memory comes from a stable structure of neurons in your brain now. The only evidence we have of the Earth's past is rocks and fossils. But these are just stable structures in the form of an arrangement of minerals we examine in the present. The point is, all we have are these records and you only have them in this Now." Barbour's theory explains the existence of these records through relationships between the Nows in Platonia. Some Nows are linked to others in Platonia's landscape even though they all exist simultaneously. Those links give the appearance of records lining up in sequence from past to future. In spite of that appearance, the actual flow of time from one Now to another is nowhere to be found.

"Think of the integers," he explains. "Every integer exists simultaneously. But some of the integers are linked in structures, like the set of all primes or the numbers you get from the Fibonacci series." The number 3 does not occur in the past of the number 5, just as the Now of the cat jumping off the table does not occur in the past of the Now wherein the cat lands on the floor." (emphasise mine) -- "There Is No Such Thing As Time"

Rich

The girl on the Physics Stack exchange explicitly said, well, time is not a boundary factor in this experiment. And I asked, this means, it's a timeless wave. Where else in physics would you see something analogous? I didn't get an answer, but for all I know, there might be a quotidian answer. — Wayfarer

You are absolutely on track. Bohm's book I mentioned is a good read and will confirm. His theories were rejected because of the nature of the quantum field but action at a distance is more experimentalky verified, the Chinese have demonstrated that at a minimum it acts 10,000x the speed of light. Space-time (which doesn't exist) had nothing to do with anything, not even gravity. The Relativity equations have no ontological merit.

Do what I do, ignore the common physicist and search for the exceptional like Erik Verlinde. They are rare (as Bohm was rare) but it is worth the hunt, since you'll actually get some usable insights.

Rich

But memory comes from a stable structure of neurons in your brain now. — WISDOMfromPO-MO

And you know this how? Had anyone ever seen your memory?

WISDOMfromPO-MO

And you know this how? Had anyone ever seen your memory? — Rich

They are not my words.

Rich

↪WISDOMfromPO-MO

A rather startling assumption in the author's part.

As for the actual flow of time, real time, the duration of life, everyone who is alive has experienced it every day of their life.

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