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An Intuitive model of Quantum Mechanics

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An Intuitive model of Quantum Mechanics

Post by Mgrinder » November 7th, 2019, 6:36 pm

Hello,

I recently came up with an intuitive model of Quantum Mechanics, mostly for the fun of it, it's quite the puzzle. Weird thing is, it seems to work. :) longer version is here. Seems to me it's philosophically interesting to have a intuitive, deterministic (but not determinable ) model of QM.

The goal is to articulate a few assumptions (or postulates) that, if entertained, would enable someone totally new to quantum phenomena (like a teenager) to deduce what will happen in a double slit experiment where you send a single electron through a double slit and then detect it at some distance away on a screen. Another way to put this project is to try to make up a "story" that can explain quantum phenomena ( randomness, uncertainty, wave particle duality, collapse, entanglement, etc.) in an intuitive manner. Of course, QM is not intuitive, at least how it is usually presented, so I thought, what set of assumptions would you have to make to try to present it in an intuitive manner? QM will still be weird, but the weirdness should be in the postulates, if you get my meaning.

Sorry for more preamble, but to explain the project more, one can compare QM to the Kinetic molecular theory (KMT) which states that everything is made of atoms that are in constant motion, the average speed of the atoms is proportional to temperature. Armed with this statement, one can then ask, what happens to a balloon if you heat it up? Well, you say, the temperature should go up, the atoms in the gas will move faster, hit the sides with more force, and the balloon should expand. Indeed it does. You can reasonably deduce what will happen in this instance and many others involving the KMT. In contrast, if you tell someone that electrons are waves and particles at the same time, and then ask what should happen if you send an electron through a double slit, there is no real way to reasonably deduce what will happen, or even understand it for that matter.

So, what did I come up with?

(1) Quantum Objects (photons, protons, electrons, quarks etc.) are instantly reformable wave packets.

The waves exist in a field (electron field for electrons, electromagnetic field for photons, quark field for protons, etc.) and each quantum object is a set of infinite waves that cancel each other out except for a region where they don't cancel themselves out. This wave packet can, under certain conditions, instantly reform itself. It can instantly shrink, or instantly expand, or instantly change itself so its angular momentum takes on a definite value (spin). Each quantum object exists everywhere, but it will only instantly reform to places where it is not cancelling itself out.

A wave packet is a set of infinite waves, each with different wavelengths, all adding together. A wave packet that is bigger than its average or characteristic wavelength has a well defined wavelength, and you can be fairly sure that when you measure it, you know what frequency (or wavelength) you will get. However, it does not have a well defined position, because, basically, it is all spread out. A wave packet that is smaller than its characteristic frequency has a well defined position (it is small) but not a very well defined frequency or wavelength.




I'm not certain how "real" these waves are, but they must have some reality to them. Previously I thought they had energy, now I'm not so sure. Now, as I say, these wave packets can instantly reform themselves. But why would they do that? That led me to come up with assumption (2)

(2) Quantum wave packets instantly reform themselves when they constructively interfere with other wave packets, and the combined amplitude in some region goes over some threshold.



So, what I am saying here is that, whenever wave packets collide and interfere with each other, they might instantly reform if the combined amplitude (amplitude is related to energy in a classical wave) of the interfering waves goes over some threshold. The better the phase match between the waves (the closer the timing of their crests and troughs are at the moment of passing) the larger the combined amplitude. Interference in the middle of the packet, where the intrinsic amplitude of the packet is largest, more readily causes collapse. So if there is more amplitude (which classically relates to energy density) you don't need as good of a phase match to get collapse at that region as you do on the outskirts.




The threshold (not at all sure what it is exactly, I don't have a simple way to define it) is defined by the entire packet. If only a portion is interfering and the other portion is not, then the threshold that is needed for collapse is increased, i.e. you need a better phase match to cause collapse than if all the packet is interfering. If all the packet is interfering with other ones, instant reformation will happen.


So if you split a photon in two, and try to detect it with only one detector (and leave the other half alone) you should detect it 50% of the time. That means that due to the reduced amplitude of a split photon, you need a better phase match to cause collapse (instantaneous reformation) than you do with a whole photon.



Another issue is that wave packets with intrinsic charge (electrons, protons and neutrons) instantly reform (collapse) and take on spin values (up or down) in magnetic fields. That is not interference of waves, but it seems like it might relate to some sort of "threshold." As a charged wave packet enters a magnetic field, you can imagine that if the wave is on the "upswing" and enough of it enters the magnetic field, then it can become "spin up", if it is on the downswing as it enters the field, it becomes spin down. This is just a guess, but it seems perhaps workable.

Another issue is that photons that pass through each other do not collapse, but photons hitting electrons can cause collapse. This is simply because bosons (photons) are the force carrying particles for fermions, and bosons hitting fermions (like electrons) can cause collapse.

So, now armed with these two assumptions, that all quantum objects are wave packets that can instantly reform due to their amplitude (which is something like energy density but I don't know exactly what it is) going over some threshold, let's look at the double slit experiment for a single photon.

So you shoot a photon at a double slit, what's going to happen? First of all, if the wave packet is smaller than the slits, you're not going to see any double slit pattern, so you have to ensure the wave packet is bigger than the slits. So, once that happens, what is going to happen at the slits? Well, with this model, you can reason that most of the time, the wave packet is going to get absorbed or reflected by the slit material. Most of the packet is interfering with the electron waves that are bound to the atoms of the slit material. The photon is interfering with the electron waves, and per assumption (2) might get instantly reformed by them. However, some the wave packet is not interfering, so if there is not a good enough phase match with the material, the wave packet might get through. Most of the time it does not (which is actually the case), but some of the time it will.

If it gets through, then it is much like a water wave passing through two slits, it should interfere with itself and approach the detector screen. In some regions it will be cancelling itself out, and in others the amplitude will be large. It then encounters the detector screen, which is simply a bunch of confined electron wave packets. The photon interferes with many electron waves, and if there is a good enough phase match, the photon will then instantly reform and deliver all its energy to that place of best phase match and big enough resulting amplitude. That electron will then be promoted to give enough energy to cause a signal on the detector.



Where will absorption happen? Only in the places where amplitude is not zero. Where is it most likely to happen? Where the amplitude is biggest.


Can we predict where this absorption will happen? Only if we can know the exact timing of all the waves. We'd have to know when all the wave packets were going to peak and trough. If we can't know the relative timing of the waves, we can't predict where and when instantaneous reform will occur. Notice this gives a reason for randomness.

This is the explanation for what happens to a photon, for an electron going through a double slit, it would be complicated by the fact that the interaction between electrons is mediated by the electromagnetic field. It should be essentially the same though.

So hopefully that is a clear enough explanation of what story this view of QM tells. A few issues:

(1) Wave/particle duality. In this interpretation, the only sense that quantum objects are particles is that the wave packets are all part of "one thing". They can instantly reform and put all their energy into one spot. Otherwise they are wave packets.

(2) Explanation for randomness. In this interpretation you actually get an explanation for randomness and unpredictability. If you cannot know the relative timing of the waves, you cannot predict when and where they will instantly reform.

(3) Explanation for measurement. Whenever measurement happens, you instantly reform a wave packet, and change it. Hence there is an observer effect. Instant reformation (collapse) happens all the time without measurement, however. So there is no Schrodinger's cat issue in this interpretation.

(4) Determinism. This interpretation of QM is deterministic, but not determinable. What happens is determined by the relative timing of waves, but you can't predict it. Thus it is a hidden variable theory. The variable is not hidden in that we know what it is (timing) but the value of timing is hidden from us.

So that's it. Much more to be said. For one thing, electrons around an atom are viewed as instantly reformable wave packets that are basically stuck to the nucleus. The pictures of s,p,d,f orbitals are the wave envelopes of the electron wave packets stuck to the nucleus. A nice explanation for entanglement. More things like that. But I wanted to keep this short (didn't work :D ). For more detail, please go here.

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Re: An Intuitive model of Quantum Mechanics

Post by Steve3007 » November 15th, 2019, 10:05 am

I had a look though this OP a couple of times but the length and depth of it meant that on both occasions I didn't really have time to properly take it in enough to comment on it and do it justice. It's certainly nicely illustrated. It seems to have quite a lot in common with standard models of Quantum Mechanics, such as the concept of wave packets and the idea that wave packets having finite length means that their wavelength is not precisely defined.

It might be helpful, if possible, if you could provide a shorter post just summarising the ways in which your theory differs from standard theories and the observational evidence that is consequently describes more accurately than those those theories do.

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Re: An Intuitive model of Quantum Mechanics

Post by Mgrinder » November 15th, 2019, 3:06 pm

Steve3007 wrote:
November 15th, 2019, 10:05 am

It might be helpful, if possible, if you could provide a shorter post just summarising the ways in which your theory differs from standard theories and the observational evidence that is consequently describes more accurately than those those theories do.
It's nice of you to try, sorry about the length. :)

It's not that it differs from standard theories, it shouldn't. It should not be more accurate either. It is basically a new interpretation, that is more intuitive and allows one to understand the quantum realm easier. it offers explanations of what is going on that no other interpretation offers. It is not mathematical, it's an intuitive set of ideas.

Basically there are two postulates:

(1) Quantum objects are instantly reformable wave packets.

(2) Quantum objects instantly reform due to the energy density (or similar concept to energy) of the wave packet going over some threshold in some region of the packet. This is often due to constructive interference of the wave packet interfering with another packet.



For instance, a photon wave packets hits an electron wave packet, the waves of each start to interfere, and then this might cause the photon to be absorbed, and the electron wave packet instantly reforms to a new size. How big? Depends upon the mutual wavelength of the photon and electron. Where does it instantly reform to? Where the threshold was breached. Where is it most likely to instantly reform to? Where the amplitude of the electron wave is highest. Why would it do that? Well, assuming all regions are equally likely to have a good phase match of the interfering waves, a region of high amplitude is more likely to go over threshold, as it doesn't need as good of a phase match as a lower amplitude region (which has less energy density) to go over threshold.

Can we predict where it will go over threshold? Not without knowing the timing of the various waves. If that's impossible, it's unpredictable, and we can only give probabilities. It's determined, but not determinable.

So how does this differ from the way QM is usually thought about? Usually you are told there are probability waves (imaginary waves), and the probability of where the wavefunction will collapse to upon measurement (where you will find the particle) is given by the squared amplitude of the wave packet. Why are they probability waves? no answer. How could something be a particle and a wave at the same time? no answer. Why would the squared amplitude of the wave packet have anything to do with the probability of finding the particle in that region? no answer.

In this interpretation, there are no "particles", there are instantly reformable wave packets. The only sense that they are "particles" is that the whole packet is part of "one thing". When it instantly reforms, all of it goes to one place.

So it seems that this interpretation (if it's close to reality, a big IF) provides far more answers to puzzling questions about quantum phenomena, and makes it more intuitive. You can explain randomness, you can explain the Born rule (probability is related to squared amplitude), and so on. Basically it's a collapse model, and thus explains a bunch.

Further, with this conceptual scheme, you can ask questions and the answers illuminate more issues. For instance:

(1) What if you took two electron wave packets and got all of their constituent waves to sync up? All the waves are in sync, but 180 degrees out of phase. So when one of the constituent waves of one electron was in a peak, the other wave in the other wave packet was in a trough at the exact same time. In this interpretation it seems reasonable (not necessary, but reasonable) that both electrons might now be part of "one thing". If so, then they are entangled. If you send one away and measure it, it seems reasonable in this interpretation that the other would be instantly affected.

(2) What is the effect of having an electron wave packet that is not spherically symmetrical? Since electron wave packets in s orbitals are spherically symmetric, and they produce no magnetic field, and electron wave packets in p orbitals are not symmetric, but do produce magnetic fields, then it seems like having a non spherically symmetric electron wave packet produces a magnetic field. This seems like it might explain spin. You put a free electron in a magnetic field, and it becomes spin up or down. In this interpretation, it seems reasonable that putting it in a magnetic field messes with the energy density, and it instantly reforms to a non symmetric packet. Thus becoming spin up or down.

Other conceptual schemes offer no explanation about entanglement or spin. With this, at least you get something that seems reasonable.

Hope that was not too long. :)

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Re: An Intuitive model of Quantum Mechanics

Post by Atla » November 15th, 2019, 5:44 pm

There are no known thresholds in QM? There is just a made-up micro vs macro threshold that works for most practical purposes most of the time.

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Re: An Intuitive model of Quantum Mechanics

Post by Mgrinder » November 15th, 2019, 5:52 pm

Atla wrote:
November 15th, 2019, 5:44 pm
There are no known thresholds in QM? There is just a made-up micro vs macro threshold that works for most practical purposes most of the time.
Sorry? I don't understand the question?

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Re: An Intuitive model of Quantum Mechanics

Post by Atla » November 15th, 2019, 6:05 pm

Mgrinder wrote:
November 15th, 2019, 5:52 pm
Atla wrote:
November 15th, 2019, 5:44 pm
There are no known thresholds in QM? There is just a made-up micro vs macro threshold that works for most practical purposes most of the time.
Sorry? I don't understand the question?
I mean, was there ever any hint that energy density reaching some threshold has something to do with collapses?

Or take the eraser experiments, where we have the same interactions (so same energy density I guess) but some cause collapses, some don't.

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Re: An Intuitive model of Quantum Mechanics

Post by Atla » November 16th, 2019, 3:57 am

Decoherence theory enjoys the same success as this equilibrium collapse model in that both seem to resolve the measurement problem: waves interfere whether we are looking at them or not, and this collapse occurs even if we are not measuring anything.
By now it's quite well known that decoherence doesn't solve the measurement problem, claiming so is just an evasion tactic.
And experiments seem to refute the idea that collapses happen 'on their own'.

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Re: An Intuitive model of Quantum Mechanics

Post by Mgrinder » Yesterday, 3:45 pm

Atla wrote:
November 15th, 2019, 6:05 pm
Mgrinder wrote:
November 15th, 2019, 5:52 pm


Sorry? I don't understand the question?
I mean, was there ever any hint that energy density reaching some threshold has something to do with collapses?

Or take the eraser experiments, where we have the same interactions (so same energy density I guess) but some cause collapses, some don't.
I don't know. I've read a quite a few books about interpretations of QM, and taken more than one class. I've never seen a suggestion that collapse might be due to energy density going over some threshold. Perhaps I'm the first to pose the question.

Which is weird, because it seems like an obvious question. I mean, classically, squared amplitude is proportional to the energy density of a wave. In QM, the squared amplitude is proportional to the probability of finding a particle in that region, or the probability that collapse will happen in that region. So an obvious question is: Is there a relation between energy density and probability of collapse? When ou ponder this question, it naturally leads to the idea of a threshold being breached causing collapse.

Since it's not known if these waves are real, I don't know if it's proper to call it "energy", but perhaps there is a similar, related concept more applicable. This interpretation needs to have these waves as "real" in some sense, but exactly how, I don't know.

In any event, it's puzzling that no writer of QM (who knows what they are talking about , not me) ever brings up this question of a threshold causing collapse. To me it's an obvious question. I would think that, even if this interpretation could be shown to be false, if you are writing a popular book about QM, it's still interesting to bring up this interpretation and show why it is false, to show the difficulty of understanding QM intuitively.

However, it looks like maybe nobody has ever thought of this before, and that's weird. I mean, I don't see why we have to accept there are particles at all? Why not just say instantly reformable wave packets? If correct, it leads to a much clearer understanding.
Last edited by Mgrinder on November 17th, 2019, 3:57 pm, edited 1 time in total.

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Re: An Intuitive model of Quantum Mechanics

Post by Mgrinder » Yesterday, 3:53 pm

Atla wrote:
November 16th, 2019, 3:57 am
Decoherence theory enjoys the same success as this equilibrium collapse model in that both seem to resolve the measurement problem: waves interfere whether we are looking at them or not, and this collapse occurs even if we are not measuring anything.
By now it's quite well known that decoherence doesn't solve the measurement problem, claiming so is just an evasion tactic.
And experiments seem to refute the idea that collapses happen 'on their own'.
I'm not a supporter of Decoherence theory. I was noting that it seems to claim that collapse happens with measurement and without (unless I am misunderstanding it). So does this interpretation. I agree that Decoherence does not solve much, I suppose I should write that section better.

I know of no experiments that refute the idea that collapses happen "on their own". The idea that collapse only happens upon measurement seems ridiculous, as Schrodinger pointed out in his thought experiment about the cat. The whole idea of "mesurement" is not well defined. It's a real problem this interpretation seems to resolve (if correct). :)

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Re: An Intuitive model of Quantum Mechanics

Post by Felix » Yesterday, 5:46 pm

Mgrinder: In QM, the squared amplitude is proportional to the probability of finding a particle in that region, or the probability that collapse will happen in that region. So an obvious question is: Is there a relation between energy density and probability of collapse?
You're barking up the wrong electron. Energy density is a Newtonian concept, which has no corollary in Quantum mechanics.
"We do not see things as they are; we see things as we are." - Anaïs Nin

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Re: An Intuitive model of Quantum Mechanics

Post by Mgrinder » Yesterday, 6:37 pm

Felix wrote:
Yesterday, 5:46 pm
Mgrinder: In QM, the squared amplitude is proportional to the probability of finding a particle in that region, or the probability that collapse will happen in that region. So an obvious question is: Is there a relation between energy density and probability of collapse?
You're barking up the wrong electron. Energy density is a Newtonian concept, which has no corollary in Quantum mechanics.
Not really. It's simply the amount of energy in a given volume. If quantum waves are "real" in the sense that they contain energy wherever they exist, then they have energy density. And, as I say, if energy denisty cannot be applied to quantum waves, then a related concept. Nobody knows how real these waves are. The question is whether or not a threshold model can be applied successfully to collapse. if so, then energy density or some similar concept would be the thing going over threshold.

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Re: An Intuitive model of Quantum Mechanics

Post by Felix » 35 minutes ago

Mgrinder: If quantum waves are "real" in the sense that they contain energy wherever they exist, then they have energy density.
They are not real in that sense, to measure the energy you would have to know it's location and trajectory, which can not be predicted.
Mgrinder: So, what I am saying here is that, whenever wave packets collide and interfere with each other, they might instantly reform if the combined amplitude (amplitude is related to energy in a classical wave) of the interfering waves goes over some threshold.
As I said, you are thinking in classical physics terms, quantum waves are theoretical phenomenon, not packets of physical energy that collide and interfere with one another.
"We do not see things as they are; we see things as we are." - Anaïs Nin

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