# Possible explanation for the wave-particle duality ?

Gold Member
Why - its not inconsistent with anything I said.
Maybe you are right, I'm sorry in that case, it’s just that it feels maybe a little bit 'awkward' to put empirically verified theories in the "dustbin of history"... and as you see the "abandoned matter waves" are still in use in today...

#### bhobba

Mentor
Question: What would happen if the world only was made of only "Ballentineists"? Would we have the electron microscope and neutron diffraction then? And would that be a better world??
It would make no difference.

It makes exactly the same predictions.

Thanks
Bill

#### probert84

So many things have been said here, unfortunately I still have not had time to read them completely, but I think some of you have not completely understood what my original assumption was. I cant really explain it better, I'd rather show something similar to it:

so I supposed that the mater (or rather energy) may look like this swarm, and the 'shape' of it is determined by a field of probability. The different behavior we experience may come from the different properties of the structure of the examined object, I mean that there are areas where the energy is more dense (like the birds or thee quanta) and this makes energy appear as a particle, but how these 'densities' move together and their path is determined by a constraint on a larger scale (swarm) which results in wave phenomena. You cant look at them at the same time and 'merge' your viewpoints, because these are two different pieces of the puzzle and put one over another because then one will overlie the other, but you have to put them next to each other along the line where they fit.

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#### atyy

So many things have been said here, unfortunately I still have not had time to read them completely, but I think some of you have not completely understood what my original assumption was. I cant really explain it better, I'd rather show something similar to it:

so I supposed that the mater (or rather energy) may look like this swarm, and the 'shape' of it is determined by a field of probability. The different behavior we experience may come from the different properties of the structure of the examined object, I mean that there are areas where the energy is more dense (like the birds or thee quanta) and this makes energy appear as a particle, but how these 'densities' move together and their path is determined by a constraint on a larger scale (swarm) which results in wave phenomena. You cant look at them at the same time and 'merge' your viewpoints, because these are two different pieces of the puzzle and put one over another because then one will overlie the other, but you have to put them next to each other along the line where they fit.
Yes, there is an interpretation of non-relativistic quantum mechanics called de Broglie-Bohm theory in which each individual particle has a definite trajectory, but the trajectory is guided by a nonlocal wave. In addition to the dynamics of the wave, and how the wave guides a particle, an important point for reproducing quantum mechanics is a postulate about the initial density or distribution of particles. However, the analogy to the swarm is only partial, so take a look at de Broglie-Bohm theory itself.

Although not exactly the same as de Broglie-Bohm theory, this video of droplets guided by a wave is similar in many respects, and can give some intuition for de Broglie-Bohm theory (I learnt about this from Bohm2 who posted it on another thread here). http://web.mit.edu/newsoffice/2013/when-fluid-dynamics-mimic-quantum-mechanics-0729.html

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#### Zag

Well, the Schroedinger equation is precisely a Diffusion equation with a imaginary/complex diffusion constant. Having said thay, try not to push the analogy too far because, after all, analogies always fail at some point.

#### Jilang

Well, the Schroedinger equation is precisely a Diffusion equation with a imaginary/complex diffusion constant. Having said thay, try not to push the analogy too far because, after all, analogies always fail at some point.
Yes Zag, it's intriguing! It's also a diffusion equation with real time replaced with imaginary time depending on how you look at it!

#### probert84

@atyy :

Yeah this is exactly what I thought. Nevertheless I claimed that this is the consequence of HUP. Because when you launch a 'particle' (a pack of energy), you know (more precisely) where it is, so it must be uncertain that which one of the slits it goes through, because you must know its momentum to be able to predict that. And the same applies to the particles past, not only to its the future, when the particle has already hit the detector screen, we know its place, therefore we shouldnt be able to know where it came from, and the consequence of this: it must have passed both slits by some chance.

Gold Member
It would make no difference.
I don't agree bhobba, and the paper l quoted in #42 is just one example of experiments that most probably would not have been made if everybody, in their bones, believed that the ensemble interpretation is the "final truth".

Gold Member
[...] but how these 'densities' move together and their path is determined by a constraint on a larger scale (swarm) which results in wave phenomena. You cant look at them at the same time and 'merge' your viewpoints,
I'm afraid the "scale factor" has nothing to do with QM, neither has any clustering of particles. To understand how far your swarms of birds are from QM, consider this:

You could send one electron for, let's say, every decade, and continue this experiment for ten thousand years, and then gather all the data, and you will still get the interference pattern. Or, you could set up the double-slit experiment in a thousand different laboratories around the globe, to fire one single electron, and then gather all the data = same interference pattern.

Or if we had the technology – we could perform "The One Single Electron Double-Slit Experiment" in different galaxies, and then gather all the data in one place = same interference pattern!

This has nothing to do with 'swarms' or 'scale' (except it's extremely hard to do with bigger objects).

Your birds would be completely lost if they where to perform those beautiful patterns, one by one (in different galaxies! ).

P.S: Entanglement has absolutely nothing to do with.

#### bhobba

Mentor
I don't agree bhobba, and the paper l quoted in #42 is just one example of experiments that most probably would not have been made if everybody, in their bones, believed that the ensemble interpretation is the "final truth".
The reason its called an interpretation is because there is no way to tell the difference from any other interpretation.

I think questions like you pose are best taken up with historians of science - its really got nothing to do with the actual science - merely how it actually came about. That's an interesting thing in its own right, but not really germane to the question asked by the OP.

Thanks
Bill

#### probert84

You still dont understand it. You think that I say that the other electrons affect the trajectory but I don't. The electron has nothing to do with the interference, therefore it doesn't matter how much time or space is between each launch of the particles, and this is why you get the same interference pattern each time.
The swarm means all the paths what a single electron can take. The swarm is not the electron itself, its just the part of it. Just like when it appears as a particle. It is not a particle, but a particle is a manifestation, a realization of that energy, and basically when you are detecting it as a particle you are realizing that manifestation by localizing it. I would say if you localize any kind of energy, it should appear similar to a particle. Otherwise how could it be localized ? The reason why it appears to be a 'solid' object is because you narrowed its possibilities down, while when you do the opposite it looks more like a wave. So its appearance is rather the end result of your process of examination than the real (or so thought) properties of the energy.

And I meant 'scale' in this interpretation, by larger scale (like local vs global scale) I mean more possibility, more options, more values for the same variable, and I was not referring to it in a meaning of a difference in the size of objects.

I think that energy has no form or 'shape' by itself, it is not determined, until you determine it by your own choice.

Think on it as kinetic energy vs potential energy, for ex imagine a spring dropped down and hitting the ground and squeezing together, now would you say that the energy that the spring carries consists of two different energies (the moving and squeezed one), or its the same energy with two appearances ?

The same is true for the electron or whatever particle. When you are localizing the particle you are narrowing your viewpoint from the energy distribution that is behind the object to a particle, and in the moment when you detect it with a detector it turns into a particle. Its like when the spring hits the ground and gets into a squeezed state. So both the particle and the wave are a form of the same energy, an image, and not the object itself.

#### bohm2

You could send one electron for, let's say, every decade, and continue this experiment for ten thousand years, and then gather all the data, and you will still get the interference pattern. Or, you could set up the double-slit experiment in a thousand different laboratories around the globe, to fire one single electron, and then gather all the data = same interference pattern.
I haven't looked at the paper referenced in this paper but how would one interpret these results:
In one experiment, Kim et al. controlled the exact interval between independent signal photons emitted in pairs [12]. As the time delay between photons was increased, first-order interference gradually vanished.
Interpreting Negative Probabilities in the Context of Double-Slit Interferometry
http://arxiv.org/pdf/physics/0611043v1.pdf

#### atyy

@atyy :

Yeah this is exactly what I thought. Nevertheless I claimed that this is the consequence of HUP. Because when you launch a 'particle' (a pack of energy), you know (more precisely) where it is, so it must be uncertain that which one of the slits it goes through, because you must know its momentum to be able to predict that. And the same applies to the particles past, not only to its the future, when the particle has already hit the detector screen, we know its place, therefore we shouldnt be able to know where it came from, and the consequence of this: it must have passed both slits by some chance.

You still dont understand it. You think that I say that the other electrons affect the trajectory but I don't. The electron has nothing to do with the interference, therefore it doesn't matter how much time or space is between each launch of the particles, and this is why you get the same interference pattern each time.
The swarm means all the paths what a single electron can take. The swarm is not the electron itself, its just the part of it. Just like when it appears as a particle. It is not a particle, but a particle is a manifestation, a realization of that energy, and basically when you are detecting it as a particle you are realizing that manifestation by localizing it. I would say if you localize any kind of energy, it should appear similar to a particle. Otherwise how could it be localized ? The reason why it appears to be a 'solid' object is because you narrowed its possibilities down, while when you do the opposite it looks more like a wave. So its appearance is rather the end result of your process of examination than the real (or so thought) properties of the energy.

And I meant 'scale' in this interpretation, by larger scale (like local vs global scale) I mean more possibility, more options, more values for the same variable, and I was not referring to it in a meaning of a difference in the size of objects.

I think that energy has no form or 'shape' by itself, it is not determined, until you determine it by your own choice.

Think on it as kinetic energy vs potential energy, for ex imagine a spring dropped down and hitting the ground and squeezing together, now would you say that the energy that the spring carries consists of two different energies (the moving and squeezed one), or its the same energy with two appearances ?

The same is true for the electron or whatever particle. When you are localizing the particle you are narrowing your viewpoint from the energy distribution that is behind the object to a particle, and in the moment when you detect it with a detector it turns into a particle. Its like when the spring hits the ground and gets into a squeezed state. So both the particle and the wave are a form of the same energy, an image, and not the object itself.
Actually, the picture you paint here is not so much like that of de Broglie-Bohm theory. It is more like the standard textbook picture. Both de Broglie-Bohm theory and the standard textbook picture give the same predictions for non-relativistic quantum mechanics, so they are essentially different methods of calculating the same predictions of non-relativistic quantum mechanics.

In the standard textbook picture, the electron is a wave or a field. Since a wave or field is in general spread out over all space, it does not have a definite trajectory. However, if it happens to be very localized, then we say that it has a definite position in space. In contrast, in quantum mechanics, to have a definite momentum means having a well defined sinusoidal wavelength. A wave which has a well defined sinusoidal wavelength is by definition spread out over all space, and so does not have a definite position. This is the essence of the uncertainty principle. And yes, it is correct that when you measure the position of an electron, you force it to become a well-localized field, which indeed does not have a well defined sinusoidal wavelength, and therefore does not have a well defined momentum.

So the uncertainty principle basically comes about because
(1) the electron is a wave
(2) position is position
(3) momentum is related to wavelength

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#### probert84

Well I think I paint the same picture because in the de Broglie-Bohm theory there is a carrying wave which defines the possible trajectories of the particle and I found this similar to the swarm which defines the trajectory of a bird in it. I think on this as sort of a random path dispatching algorithm.

Let the slits be dices. Each throw of the dice represents a chosen direction from 1-6 for a signal we want to send. If we throw two dices(two open slits = two possibilities) at the same time, we have 21 options, and these are:

11 22 33 44 55 66
12 23 34 45 56
13 24 35 46
14 25 36
15 26
16

Say we throw '25' then x % of the signal will go towards direction #2 and 100-x % towards #5. When we throw the same direction with both dices (for ex '11'), we must throw again, because otherwise 100% of the signal would go in the same direction and this means 100% accuracy, which we assume to be impossible (and this is where HUP comes in). Hence 11,22,33,44,55,66 fall out. Let this signal be light and what do you see in these directions ? Black lines, and the overall picture is an interference.

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Gold Member
The reason its called an interpretation is because there is no way to tell the difference from any other interpretation.
It's good that we agree on the "interpretational status", since earlier in this thread there were a lot of talk about "formalism" and "bog standard", which of course the ensemble interpretation is nothing like.

I think questions like you pose are best taken up with historians of science - its really got nothing to do with the actual science - merely how it actually came about. That's an interesting thing in its own right, but not really germane to the question asked by the OP.
That would make the "Shut up and calculate!" physicist David Mermin a "historian", which we both know is not true.

"[...] the notion that probabilistic theories must be about ensembles implicitly assumes that probability is about ignorance. (The 'hidden variables' are whatever it is that we are ignorant of.) But in a non-deterministic world probability has nothing to do with incomplete knowledge, and ought not to require an ensemble of systems for its interpretation" -- David Mermin

I don't think we will get any further on this issue, except to agree on disagreement – you did/do claim the statistical ensemble interpretation to represent the bog standard of QM, fait accompli.

I, in company with prominent physicists, do not agree. Let's move on.

#### Jilang

It seems to me that we have the maths to describe the physical process, but no real idea do that that physical process is. Any questions raised about what might be the physical process are classed as "interpretation". This appears to be regarded as a type of mysticism or witchcraft. So it's off to the ducking stool, the thread is closed, deleted if you are less lucky. Either way we die.

Gold Member
The same is true for the electron or whatever particle. When you are localizing the particle you are narrowing your viewpoint from the energy distribution that is behind the object to a particle, and in the moment when you detect it with a detector it turns into a particle. Its like when the spring hits the ground and gets into a squeezed state. So both the particle and the wave are a form of the same energy, an image, and not the object itself.
It's good that you try to visualize and make pictures of the problem (it's basically what I do all the time... ), but you have to realize that QM is nothing like our classical "everyday experience", and sometimes (mostly) – pictures don't make it all the way.

How come??

Well, to begin with, you must have some basic understanding about the mathematics, which is the only foundation of QM. It requires an understanding of complex numbers (and partial differential equations). In our everyday life we use real numbers:

Adding the imaginary unit to a real number forms a complex number:

To make it even 'weirder', the wavefunction does not give any information about the QM particle per se, but only provide the probability of finding the QM particle at a given position:

Left: The real part (blue) and imaginary part (red) of the wavefunction.
Right: The probability distribution of finding the particle with this wavefunction at a given position.
The top two rows are examples of stationary states, which correspond to standing waves.
The bottom row an example of a state which is not a stationary state.

As you see, there are 'imaginary processes' in the calculation of the wavefunction, to make it possible to get the probabilities of a 'real output' in the other end. That is weird!

Therefore, to translate your picture of "energy distribution", we must be able to calculate the energy with complex numbers (i.e. $\sqrt{-1}$), which don't make a happy end for the resolution of the "energy distribution", i.e. it don't work.

To give you some comfort, Erwin Schrödinger – the genius who formulated the Schrödinger wave equation – did not know what it represented at first. He tried to interpret his wavefunction as "the density" of the stuff of which the world is made. He tried to think of an electron as represented by a wavepacket. But wavepackets diffuse, and become indefinitely extended, but how ever far the wavefunction extends; the detection of an electron remains 'spotty', i.e. localized. Hence Schrödinger's 'realistic' interpretation of his wavefunction did not survive.

Then Born came and said that the wavefunction does not represent "the density of stuff", but gives the density of probability (modulus squared).

And this is the theory we have today.

Gold Member
I haven't looked at the paper referenced in this paper but how would one interpret these results:

In one experiment, Kim et al. controlled the exact interval between independent signal photons emitted in pairs [12]. As the time delay between photons was increased, first-order interference gradually vanished.
Woowa!! :surprised

If this is true... that would mean that bhobba is right after all!? ()

Must check it out...

#### bhobba

Mentor
you did/do claim the statistical ensemble interpretation to represent the bog standard of QM, fait accompli.
I never claimed that, and its obviously not true.

I claim the ensemble interpretation was related to the frequentest interpretation of probability, Copenhagen the Baysian view.

QM formalism simply speaks of probability without interpretation, as do most areas of applied math. To be specific probabilities enters into it via Born Rule which says the expected value of an observation O of a system in state P is Trace(OP). Nothing about ensembles there. That comes when you try and give meaning to expected value. Most applied mathematicians do that via Kolmogorov's axioms and a reasonable mapping without actually worrying about specifics. But some want to go further and say it applies to statistical ensembles, while others say it applies to a level of belief which is Copenhagen. But really it doesn't make much difference.

Thanks
Bill

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#### atyy

Well I think I paint the same picture because in the de Broglie-Bohm theory there is a carrying wave which defines the possible trajectories of the particle and I found this similar to the swarm which defines the trajectory of a bird in it. I think on this as sort of a random path dispatching algorithm.

Let the slits be dices. Each throw of the dice represents a chosen direction from 1-6 for a signal we want to send. If we throw two dices(two open slits = two possibilities) at the same time, we have 21 options, and these are:

11 22 33 44 55 66
12 23 34 45 56
13 24 35 46
14 25 36
15 26
16

Say we throw '25' then x % of the signal will go towards direction #2 and 100-x % towards #5. When we throw the same direction with both dices (for ex '11'), we must throw again, because otherwise 100% of the signal would go in the same direction and this means 100% accuracy, which we assume to be impossible (and this is where HUP comes in). Hence 11,22,33,44,55,66 fall out. Let this signal be light and what do you see in these directions ? Black lines, and the overall picture is an interference.
Here you are controlling the distribution of the initial positions of the particles. de Broglie-Bohm theory has something like that also. However, it does allow all possible initial positions, although they may not all occur with the same probability. To reproduce the interference pattern, the trajectory in space of a particle is nonlinearly guided by the wave function, so that particles do not go straight after passing through a slit. Here is a picture of trajectories in de Broglie-Bohm theory http://scienceblogs.com/principles/2011/06/03/watching-photons-interfere-obs/.

Gold Member
I never claimed that, and its obviously not true.
I very sorry bhobba, my fault, and I do apologize for my misinterpretation.

Hope it's accepted.

#### bhobba

Mentor
I very sorry bhobba, my fault, and I do apologize for my misinterpretation. Hope it's accepted.
Of course it is, and no apology necessary.

We all glean others views from what they write and its simple human nature that sometimes its not conveyed properly or we interpret it incorrectly. It happens all the time.

Thanks
Bill

Gold Member
Thanks bhobba! As always, you're a wise and reasonable man!

Gold Member
I haven't looked at the paper referenced in this paper but how would one interpret these results:
It looks 'strange'... why only photons? When electrons easily could be more controlled? For example afaik, Tonomura could easily have experimented with longer time delay between every single electron, right?

And this looks troublesome:

[PLAIN said:
http://arxiv.org/abs/physics/0611043v1]This[/PLAIN] [Broken] evidence is sufficient for us to conclude that self-interference did not happen in a context, in which its preconditions were met. Whatever the nature of matter waves, they do not seem to produce quantum interference via self-interaction.
In comparison to this:

Paul Dirac said:
Some time before the discovery of quantum mechanics people realized that the connection between light waves and photons must be of a statistical character. What they did not clearly realize, however, was that the "wave function" gives information about the probability of one photon being in a particular place and not the probable number of photons in that place. The importance of the distinction can be made clear in the following way. Suppose we have a beam of light consisting of a large number of photons split up into two components of equal intensity. On the assumption that the beam is connected with the probable number of photons in it, we should have half the total number going into each component. If the two components are now made to interfere, we should require a photon in one component to be able to interfere with one in the other. Sometimes these two photons would have to annihilate one another and other times they would have to produce four photons. This would contradict the conservation of energy. The new theory, which connects the wave function with probabilities for one photon gets over the difficulty by making each photon go partly into each of the two components. Each photon then interferes only with itself. Interference between two different photons never occurs.
Conservation of energy is not easy to ignore...

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