Exploring Quantum Mechanics: A Visual Journey

[Aufbauwerk 2045]

This is an interesting QM video. It would be interesting to get opinions about it from the QM students and experts alike.

 

[ShayanJ]

Its accurate, except for the collapse part which may be controversial!(@vanhees71) But its good for someone who is just learning QM.

 

[MarcoJV]

I think the animation is very well done. I personally don't like this interpretation, and I believe it is much easier for students new to QM to be introduced to statistical interpretations. In fact, even in the video they recur to an statistical interpretation of the velocity of one particle (as they interpret the wave function) using a statistical approach. They know that it is much more close to the common sense, and I don't really see the point on reproducing old mystic interpretations instead of encouraging students to think in a deeper way.

Overall, it is very nice if you're into that interpretation...

 

[woody stanford]

I'm uncomfortable with the application here of a probability amplitude being applied to the relationship between the electrical and magnetic field in a beam of light. I'll be honest with you. I'm not saying it isn't so, I'm just saying I'm uncomfortable with the assumption that it applies here. Just because the probabalistic interpretation applies to much of QM I think doesn't necessarily mean its extensible to areas the discipline of physics is quiet on.

 

[Aufbauwerk 2045]

Thanks for your opinions so far. BTW I have no connection whatsoever with this video or whoever made it. I just found it on Youtube. I don't have my own opinion about it yet, except that it seems interesting. I haven't reviewed my QM in some time and I'm looking for presentations other than lectures, just out of curiosity.

I hope more people will see it and comment and/or suggest other videos.

:)

 

[ShayanJ]

I'm uncomfortable with the application here of a probability amplitude being applied to the relationship between the electrical and magnetic field in a beam of light. I'll be honest with you. I'm not saying it isn't so, I'm just saying I'm uncomfortable with the assumption that it applies here. Just because the probabalistic interpretation applies to much of QM I think doesn't necessarily mean its extensible to areas the discipline of physics is quiet on.

There was no mention of EM waves in the video as far as I can remember!

 

[mike1000]

This is an interesting QM video. It would be interesting to get opinions about it from the QM students and experts alike.

The description of wave collapse surprised me. It was not what I was expecting based on what I have read. However, to me, it makes perfect sense to zero out the part of the probability distribution where you know the particle is not located, so that only the non-zero part of the wave function remains. Something was learned from the measurement...where the particle was not located and the probability distribution is updated accordingly. But the measurement operator did not zero out the wave function, did it? The zeroing out the has to be something the experimenter does, mathematically, after the measurement, to create the final state, not something the actual measurement did?

 

[Jilang]

The description of wave collapse surprised me. It was not what I was expecting based on what I have read. However, to me, it makes perfect sense to zero out the part of the probability distribution where you know the particle is not located, so that only the non-zero part of the wave function remains. Something was learned from the measurement...where the particle was not located and the probability distribution is updated accordingly. But the measurement operator did not zero out the wave function, did it? The zeroing out the has to be something the experimenter does, mathematically, after the measurement, to create the final state, not something the actual measurement did?

Are you thinking that the wave function is a representation of the experimenter's knowledge, a relative type of thing?

 

[mike1000]

Are you thinking that the wave function is a representation of the experimenter's knowledge, a relative type of thing?

To be honest, I was not thinking that at all (I am not that sophisticated yet in QM).

I was merely repeating what the video tells us they did to the wave function after running their detector. That part of the video starts at 4 minutes and continues for about 60 seconds. If you get a chance please take a look at it and let me know what you think.

 

[Jilang]

Yes, I saw that bit. I believe there is a sense in which it is collapsed which is independent of whether anyone observes the interaction or not.

 

[mike1000]

Yes, I saw that bit. I believe there is a sense in which it is collapsed which is independent of whether anyone observes the interaction or not.

I guess the word "collapse" means "goes to zero". And how could it collapse the part outside the detector or inside the detector depending on whether it was detected or not? This seems really weird to me.

 

[Jilang]

Have you seen a bubble chamber?

 

[mike1000]

Have you seen a bubble chamber?

No. Only pictures of them.

Why do you ask? Is there something about them that can explain this "collapse"?

 

[Jilang]

It's a nice example of continuous collapses. The trail of bubbles localises the particle and It happens whether or not anyone is recording it. It would not be just a calculation so to speak, as the bubble chamber exists independently of the experimenters.

 

[mike1000]

It's a nice example of continuous collapses. The trail of bubbles localises the particle and It happens whether or not anyone is recording it. It would not be just a calculation so to speak, as the bubble chamber exists independently of the experimenters.

Are you saying this is analogous to what we see in the video? The wave function is not physical, is it? It is purely a mathematical description, isn't it? I am going to have a very hard time to try to understand how, if the particle is not detected, the part of the wave function corresponding to the detector collapses (ie goes to zero) leaving only the wings of the distribution.

Now, as I write this, I started thinking about "convolution". If some how the detection process convolves in some way with the particle, then this would change the wave function of the particle. Almost as if the detector was acting like a filter. In other words, where the particle's location (given by the wave function) and the detector overlap, there is some kind of convolution process occurring.

 

[Jilang]

Convolution, that is an interesting word, The particle becomes convoluted with the equipment and the equipment is already convoluted with the experimenters since it is macroscopic.

 

[mike1000]

Convolution, that is an interesting word, The particle becomes convoluted with the equipment and the equipment is already convoluted with the experimenters since it is macroscopic.

Convolution between two quantum mechanic states is physically impossible according to this paper. I am sure you already knew this, but I did not.

https://arxiv.org/pdf/quant-ph/0309070.pdf

It is becoming clear to me that entanglement is the quantum mechanical process that takes the place of convolution.

That paper has a lot descriptions that I am now able to understand. In particular, on page 3 it says "a state change of an isolated system must be reversible...which lead to Unitary operations on the state"

That implies, according to something else I read, that wave function collapse maybe implemented by applying a non-unitary operator to the wave function (ie not reversible)

I can definitely see an interaction between the particle and the measuring device, but it is pretty hard to swallow that the effect of that operation is to create a new state in which all the location eigenstates of the particle, where the measurement indicated the particle could not be, would be zeroed out by some natural phenomena.

 

[houlahound]

I am not good enough to critique if that paper is legit but I really enjoyed it . it speaks to the area of QM I find most interesting.

Printed & filed.

If any pro's here have a problem with the paper please inform on this thread.

 

[mike1000]

Convolution between two quantum mechanic states is physically impossible according to this paper. I am sure you already knew this, but I did not.

https://arxiv.org/pdf/quant-ph/0309070.pdf

It is becoming clear to me that entanglement is the quantum mechanical process that takes the place of convolution.

That paper has a lot descriptions that I am now able to understand. In particular, on page 3 it says "a state change of an isolated system must be reversible...which lead to Unitary operations on the state"

That implies, according to something else I read, that wave function collapse maybe implemented by applying a non-unitary operator to the wave function (ie not reversible)

I can definitely see an interaction between the particle and the measuring device, but it is pretty hard to swallow that the effect of that operation is to create a new state in which all the location eigenstates of the particle, where the measurement indicated the particle could not be, would be zeroed out by some natural phenomena.

I have found answers to some of my questions regarding "collapse".

The process of collapse is different for a discrete spectrum operator and a continuous spectrum operator. For a discrete spectrum operator, wave collapse means that all of the non-zero probability amplitudes in the state vector before measurement, collapse to zero after measurement, all except one that is, the coefficient of the eigenstate in which the particle is found. So collapse means all the ##C_{k \ne j}## go to zero while ##C_j## does not, i.e. state vector collapses to a single state.

For a continuous spectrum operator( such as the position operator) the wave function never collapses to a single eigenstate. In these cases the wave function partially collapses to a linear combination of "close" eigenstates that embodies the imprecision (whatever that means) of the measuring device. This explains what they show in the video for the particle moving at 4 meters per second.

https://en.wikipedia.org/wiki/Wave_function_collapse

The more I think about what the video shows, zeroing out the parts of the state vector where the particle was not detected has got to be done, after the fact by the experimenter or included somehow in the measuring process. It represents the new state. It is the state in which the particle was found. The detector determines which parts of the probability distribution must be zero. (ie need to be collapsed). If the particle was detected the probability distribution outside the detector is zeroed. If the particle was not detected, the probability distribution inside the detector is zeroed. That is the new state vector.

 

[BvU]

Could someone comment on the feasibility of the position detection process in the video ? Exact time interval and position interval ? Sounds like an awful lot of assumptions to me.

 

[ShayanJ]

Exact time interval and position interval ?

Weird thing to say. The very fact that there are time and position intervals means that the measurement is not exact and ideal!

 

[BvU]

Weird thing to say. The very fact that there are time and position intervals means that the measurement is not exact and ideal!

Why ? The bounds of those intervals are razor sharp and cause an unlikely sharp wave function at collapse.

 

[mike1000]

I have found answers to some of my questions regarding "collapse".

The process of collapse is different for a discrete spectrum operator and a continuous spectrum operator. For a discrete spectrum operator, wave collapse means that all of the non-zero probability amplitudes in the state vector before measurement, collapse to zero after measurement, all except one that is, the coefficient of the eigenstate in which the particle is found. So collapse means all the ##C_{k \ne j}## go to zero while ##C_j## does not, i.e. state vector collapses to a single state.

For a continuous spectrum operator( such as the position operator) the wave function never collapses to a single eigenstate. In these cases the wave function partially collapses to a linear combination of "close" eigenstates that embodies the imprecision (whatever that means) of the measuring device. This explains what they show in the video for the particle moving at 4 meters per second.

https://en.wikipedia.org/wiki/Wave_function_collapse

The more I think about what the video shows, zeroing out the parts of the state vector where the particle was not detected has got to be done, after the fact by the experimenter or included somehow in the measuring process. It represents the new state. It is the state in which the particle was found. The detector determines which parts of the probability distribution must be zero. (ie need to be collapsed). If the particle was detected the probability distribution outside the detector is zeroed. If the particle was not detected, the probability distribution inside the detector is zeroed. That is the new state vector.

I think that the detector can be in only one of two possible states, ##|D_1\rangle## and ##D_2\rangle##. The state ##|D_1\rangle## corresponds to the state where the particle's position was detected and the state ##D_2\rangle## corresponds to the state where the particles position was not detected. Figure 1 below shows these two states.

The inner product of the two states, ##\langle D_1|D_2\rangle## is zero indicating that the two states are orthogonal. This means that the detector can only be in one or the other of the two states after the measurement.

The state vector of the detector dominates the state vector of the particle and causes the collapse of the particles state vector in the manner shown in the video. Not sure where to go from here. Could use some help.

P.S. ##\|D_1\rangle and |D_2\rangle## the way I have illustrated them cannot be position state vectors because they are not normalized to one and there is no way, that I see, that they can be normalized to one and still give the result we see in the video.