Cognitive Dissonance and Quantum Mechanics?

[mike1000]

For someone at my level, the following article is extremely informative. I would like to post a link to it. But first here are a few quotes from the article...

Here is his definition of wave-particle duality...

This view can be summarized by saying that in quantum-level experiments we always detect particles, but we predict or interpret the experimental outcome by assuming wavelike behavior prior to particle detection.

As Bragg once said, “Everything in the future is a wave, everything in the past is a particle.”

And here is his statement on Cognitive Dissonance...

This scientific dogma states, among other things, that there will be no future resolution of the cognitive dissonance that results from analyses that require, at root level, the use of irreconcilable concepts such as wave and particle.

"Quantum Mechanics and the Fourier Transform" by Frank Rioux
http://www.users.csbsju.edu/~frioux/q-intro/QM-FT.pdf

 

[phinds]

For someone at my level, the following article is extremely informative. I would like to post a link to it. But first here are a few quotes from the article...

Here is his definition of wave-particle duality...And here is his statement on Cognitive Dissonance..."Quantum Mechanics and the Fourier Transform" by Frank Rioux
http://www.users.csbsju.edu/~frioux/q-intro/QM-FT.pdf

"Wave Particle Duality" is no longer considered (for about the last 90 years) as a valid description. Quantum objects are not waves and they are not particles. They are quantum objects. If you measure them for particle-like behavior, that's what you will see and if you measure them for wave-like behavior, that's what you'll see. That does not make them waves and it does not make them particles. They are quantum objects. There IS no "cognitive dissonance".

 

[mike1000]

"Wave Particle Duality" is no longer considered (for about the last 90 years) as a valid description. Quantum objects are not waves and they are not particles. They are quantum objects. If you measure them for particle-like behavior, that's what you will see and if you measure them for wave-like behavior, that's what you'll see. That does not make them waves and it does not make them particles. They are quantum objects. There IS no "cognitive dissonance".

Maybe at your level there is no cognitive dissonance. It does not do any good to pretend it is not there.

You need to read the article. He is not saying that wave particle duality is a fact of nature. He says that experimenters always detect particles but they predict and interpret the outcome by assuming wave like behavior prior to particle detection.

 

[Nugatory]

You need to read the article. He is not saying that wave particle duality is a fact of nature. He says that experimenters always detect particles but they predict and interpret the outcome by assuming wave like behavior prior to particle detection.

You can spare yourself a ton of grief and almost limitless confusion by learning quantum mechanics from a real textbook instead of random stuff that you pick up off the internet and/or from pop-sci presentations. This is why Physics Forums has the rule requiring that all references be to standard textbooks or peer-reviewed papers in reputable and well-refereed journals, which this article is not.

It is true that in one class of problems we can get useful (often very useful, which is why the technique is used) results by assuming wave-like behavior prior to making a position measurement; and for historical reasons making a position measurement is often described as "detecting a particle". However, that's not how the modern (in this context, "modern" means "after about 1930") formulation of quantum mechanics works; no matter what Rioux says, you won't find wave-particle duality and the accompanying cognitive dissonance there. You will find many other strange and confusing things... but not that one.

 

[mike1000]

You can spare yourself a ton of grief and almost limitless confusion by learning quantum mechanics from a real textbook instead of random stuff that you pick up off the internet and/or from pop-sci presentations. This is why Physics Forums has the rule requiring that all references be to standard textbooks or peer-reviewed papers in reputable and well-refereed journals, which this article is not.

It is true that in one class of problems we can get useful (often very useful, which is why the technique is used) results by assuming wave-like behavior prior to making a position measurement; and for historical reasons making a position measurement is often described as "detecting a particle". However, that's not how the modern (in this context, "modern" means "after about 1930") formulation of quantum mechanics works; no matter what Rioux says, you won't find wave-particle duality and the accompanying cognitive dissonance there. You will find many other strange and confusing things... but not that one.

I have a degree in Physics. It is from some time ago, but I remember, vaguely, the elementary quantum mechanics principles. I have much more experience with Fourier Transforms. I know that momentum and position are Fourier transform pairs. I chose to link to that article because I believe it is a good article for someone who is trying to catch up. The way the author explains it helps to bridge some gaps between the way that most of the members here speak about it and what I was used to in the past. He makes some interesting comments that are easier for me to understand.

 

[bhobba]

The way the author explains it helps to bridge some gaps between the way that most of the members here speak about it and what I was used to in the past. He makes some interesting comments that are easier for me to understand.

You might benefit from seeing modern take on the formalism that dispels much of the mystery:
https://arxiv.org/abs/quant-ph/0101012

Now that's the formalism. There are issues remaining but I would rather discuss it once you have got the gist of the above. No need to delve into its mathematical detail - just an overview is fine for this purpose.

Thanks
Bill

 

[Demystifier]

I have a degree in Physics

Anything cognitive, including cognitive dissonance, exists only in ones head. Since you have a degree in physics, perhaps it would help you to see how something like "wave-particle duality" appears even in classical physics:
https://arxiv.org/abs/quant-ph/0505143
Since, I hope, you don't have cognitive dissonances about classical physics, it might help you to relief the dissonance in the quantum case too.

 

[PeroK]

Maybe at your level there is no cognitive dissonance. It does not do any good to pretend it is not there.
.

My definition of cognitive dissonance is what results from trying to learn QM from multiple sources at once, including popular science and philosophical approaches.

If you have a degree in physics and can handle the maths, there is no reason for you not to tackle the subject from a modern undergraduate text, such as Griffiths, which is available in a new edition from Cambridge University Press at a reasonable price.

This will give you a consistent and coherent basis for understanding the subject and for further study.

 

[mike1000]

I wish I did not use the term "cognitive dissonance" in the title to this thread because the articles that I linked to are not focused on that, quite the opposite.

Within the article there are links to several other articles, one of which is titled "Using Optical Transforms to Teach Quantum Mechanics Here is a link to the article

http://www.users.csbsju.edu/~frioux/diffraction/910012fr.pdf.

Here are a few quotes from that peer reviewed article...

In Marcellaís quantum mechanical analysis of the double slit experiment, what is subsequently measured at the detection screen is actually the particle's momentum. In other words, the well-known diffraction pattern created by the double-slit geometry is the particle's momentum distribution in the plane of the detection screen.

And one more ...

It should also be pointed out that the double-slit experiment has been carried out at low source intensity such that there is only one particle in the apparatus at a time [14]. The resulting diffraction pattern is the same as that observed with intense sources; it just takes longer to record to the same number of observations. This confirms the quantum mechanical view that wave functions 1 and 2 represent individual particles rather than an ensemble of particles. According to quantum mechanical principles the particles can be placed in a well defined state by the slit screen, but the outcome of a subsequent measurement, momentum in this case, is not uniquely determined. All we can do is calculate the probability that a particular momentum state will be observed. The mechanism, therefore, is single-particle, or self-interference; two particles do not interfere with each other [14, 15].

From the above statement, the mystery of the double slit experiment goes away...the electrons are placed in a well defined state by the slit and the corresponding momentum distribution is recorded on the detection screen.

That is a pretty simple and clear explanation.

Here are some images from the article showing the position and momentum distributions side by side.
The slit(s) in the screen IS/ARE the prior position distributions...i.e. positions where the electron is allowed to be. The momentum distributions are where the electron is likely to be found after. Figure 7 is amazing.

https://lh3.googleusercontent.com/mKCTRSPt9cgEnojXbzyDR320K99BckxSyEPqKyDWrd6ZKgyxvM0-HFSAQdcTRpBY-FNF7E2RqIupP2TQAve7PVNm9_-LaglYg7DtGVP5RyztCLp5oSUxsiPaY_i-A0SeeOAt1Xzm055Mun_BST9brfWhzfLgQ7ksOEMjvZN84amICtR0uUq6oSufFaAYJsOLfrw7EZuhypsLx6ggromK7J__wrNqhoXzagokyAs3YrBDIp3Xb_PtvgFnNzpzORAgZcqS-gpxfrW1vtFkRVEnGM_klZeFm6jaz0182xvX_P7UfZof7Lo63voANQQuDHYR-N-55dZtDZOI4iPRkbqKasYnbh3Jg2ebnYRN7qqcsoH1BBgRAFqwCvkeUsnNiESQtdKuoeqHoE0dHaeluEvaL918ZOSWN1GTJoey8lQXazhkptlChb90bS0MJrIJ_3sPZtItYPzfk9xd1SG2UjT8_S4-o8qZJZQnq7L8ocpfdsOaodo_NwAzuLxJLx5eFQoNgL-7uyNudkZ9ZWrtaTEKlQ2rwwYWolezqycQxG8PQFUy2DD-buMwHQLFoMppsGpQlN_rD5HSEaqMCY-kWTZloP8XOHsQ2t_Tgy1Euu0LDygyleZ0Th6u=w372-h667-no https://lh3.googleusercontent.com/d71Z0eonD9UhnoBJvjiKeV_COYAJ-H1wmg0YbYkY4T3xGOUqhMQvl7TIFkuUBvxsImESv5H9dYBtNiphVIiDBPWK_3jAwbMl70Dmikz096hNuSCWK4lCrY6AwZlQ0ceNxMVeLwGanfA_kOCVUjLyRPmV8skek3S2Uc1ITSaY_9HDBG4RVHa7XV86_1RWYgFLmc75LqcRQ7BOo4YXK5qjrWSYAQbP8UQx6tmFJ1uVNUKH_xMYbreTVcJsF6yG5oew1nouLesaUu0pq107jZpE6DWLRbqfzJklNbozdxuLqwLa3uhubfXQMMGRPRnX4ZCCRNBzNnBPvOv9rCq4REVc0dfXYua4s-2Y6ivN6uN99x-oz4j4r4qOdXYpGcgdBfdBIcTeaYJqcURxm68dJ2BAeeWr4Iz581g45fyccnknzt-oNiqWJn48fLFBMpPjWCX9vgYESpc4RjNP_Bo7QloBLzE8RAUn521x4JKfoyH-npvLGmGtfNPMg0xZtmvF_QbTMxCFKW7bzmaZiHKrY75P1fuKlu_pzE7RvQZBU1thUOFS9Y10DGU9KSMryv34SRWFmuRetx34t7VfhGGHU0IxkGsK7nwoA8z6thZdrGqW0yB79LQs=w354-h932-no

Do you think that this is not a good way to look at it?

 

[phinds]

I wish I did not use the term "cognitive dissonance" in the title to this thread ...

Well, your continued insistence on it (as in "Maybe at your level there is no cognitive dissonance. It does not do any good to pretend it is not there.") did support the original use

From the above statement, the mystery of the double slit experiment goes away...the electrons are placed in a well defined state by the slit and the corresponding momentum distribution is recorded on the detection screen.

That statement describes the spead in the single slit experiment, not the single-photon interference of the double slit experiment. If the two slits did in fact explain the mystery that way, it would not BE a mystery. The "mystery", to the extent that there is one, is why do the results of the double slit experiment depend on whether or not the "which path" information is detected. You are not addressing that.

Put another way, what you just said in this quote explains the vertical spread in Fig. 1 above but does nothing to explain the horizontal interference pattern.

 

[mike1000]

That statement describes the spead in the single slit experiment, not the single-photon interference of the double slit experiment. If the two slits did in fact explain the mystery that way, it would not BE a mystery. The "mystery", to the extent that there is one, is why do the results of the double slit experiment depend on whether or not the "which path" information is detected. You are not addressing that.

Put another way, what you just said in this quote explains the vertical spread in Fig. 1 above but does nothing to explain the horizontal interference pattern.

Please look at Figures 1 through 7. They show the momentum distribution for multiple slits, including the double slit. (These are 2-dimensional Fourier Transforms).

The mystery, and something that they do not address, is why don't we see a diffraction pattern if a detector is placed at the slit. Somehow, the detector at the slit, changes the position distribution. It must destroy superposition, in such a way, that the electron cannot take multiple paths through the slit, it always takes the exact same path through the slit.

 

[phinds]

Please look at Figures 1 through 7. They show the momentum distribution for multiple slits...

All of which support what I just said.

 

[mike1000]

All of which support what I just said.

Put another way, what you just said in this quote explains the vertical spread in Fig. 1 above but does nothing to explain the horizontal interference pattern.

How do they support your statement?

 

[phinds]

How do they support your statement?

They all show a spread which is equivalent to the single slit experiment which jibes with your statement about position localization by each single slit, resulting in a subsequent linerar spread due to the uncertainty in momentum exiting the slit. This does not say anything about the interference pattern, and I am trying to point out that the statement of yours which started the last couple of posts, does not address the interference. Clearly the figures SHOW the interference but what I'm saying is that your comment in post #9 does nothing to address that interference, it only addresses the spread caused by each single slit.

 

[mike1000]

They all show a spread which is equivalent to the single slit experiment which jibes with your statement about position localization by each single slit, resulting in a subsequent linerar spread due to the uncertainty in momentum exiting the slit. This does not say anything about the interference pattern, and I am trying to point out that the statement of yours which started the last couple of posts, does not address the interference. Clearly the figures SHOW the interference but what I'm saying is that your comment in post #9 does nothing to address that interference, it only addresses the spread caused by each single slit.

Unfortunately, they did not show the position and momentum distributions for a single slit. All of those figures are for multiple slit position distributions. The Fourier Transforms are 2-Dimensional transforms and the area of integration includes the area of all the slits. That is why the momentum distributions show interference.

We do not have to calculate the Fourier transform to see those distributions. All we have to do is conduct an experiment with the appropriate slit geometry and the recording screen will show the momentum distribution to us. Using his terminology, the screens with slits place the electrons in a well defined position state and the detection screen records the resulting momentum distribution, including interference effects.

The paper has been invaluable to me in many ways. In particular it has shown me what is meant by "state preparation" and the mathematical meaning of the quantum mechanical principle that the initial wave function is a superposition that places the wave function at all slits simultaneously.

https://lh3.googleusercontent.com/CT7nUd2WV-UreWAPpra1OqgjfEe4OtwgPDFggdpBhZbCHLnjhEHyz2IxC2cO4DNhgk9lxy8MQaqlOfrgM1DKnuBXmZWHttoYHYfX_BU_BnQ5kxXlxg6DokBkqVYZuz-f-mBCXUleLlGWSk0CnbFlxz68PxcRnd2QhnmdttM_yEdWjP57Bg05qp3METTT-JOBB5vEb5S7zkQ9tkx_xae2sYnB4o_71O8BhQfqfktF109hT8eP3rvLAVMMevV6Z2AbYYGR3uU_le5yTjd25vnvtkCWHZmuc96H3nr3XbTKt_2WEpEmFY2uTPvR8Wj5VQ5cSpqh7krAw_Z-5b_ZUxs3CVO89yLEYNpxEZITrXwGRS0GOm-u9cUxskLI_3JMv1zo8SMbel1ACMQumJoSN_FKfpjksYdjKsaKW5lTYG4vUlIhB0P2iH_iu09pxBljYDM9qXpaV14kh1yKrUO3IUTOAaMWPrqfCUVK2NRNUlt0iJxxWBKZL7uWN6COoITlz4XPHbL_7MiiQmiBmUBdSSKIHzQvSZXkHjBB_Xsl4b8OCdGgPOTYii4zTRGu_qEgt4ClIhCxSUyCzl5cq0wsoc8KAAdfGphzNpIj0PVbTngGEiiHpc5ef-AT=w522-h281-no

 

[phinds]

You are continuing to not address the issue of why there is interference if the "which path" information is not detected but no interference if the "which path" information IS detected. THAT is the "mystery" of the double slit experiment and it seems to me that you are not addressing it. You keep talking about "momentum distribution". OK, explain why the momentum distribution is different based on whether or not the "which path" information is known.

 

[mike1000]

You are continuing to not address the issue of why there is interference if the "which path" information is not detected but no interference if the "which path" information IS detected. THAT is the "mystery" of the double slit experiment and it seems to me that you are not addressing it. You keep talking about "momentum distribution". OK, explain why the momentum distribution is different based on whether or not the "which path" information is known.

I did address that in post #11. First, I really do not know the answer, but I can guess an answer now better than I could guess an answer before, because now I have a somewhat intuitive feel of what is going on. (Better than before and I am sure still not correct). Here is what I said about this in post #11

The mystery, and something that they do not address, is why don't we see a diffraction pattern if a detector is placed at the slit. Somehow, the detector at the slit, changes the position distribution. It must destroy superposition, in such a way, that the electron cannot take multiple paths through the slit, it always takes the exact same path through the slit.

 

[phinds]

I did address that in post #11. First, I really do not know the answer, but I can guess an answer now better than I could guess an answer before, because now I have a somewhat intuitive feel of what is going on. (Better than before and I am sure still not correct). Here is what I said about this in post #11

Ah. I missed that. So we are saying the same thing except that I got the mistaken impression that you thought you now completely understood the results of the two slit experiment. I based that inference on your statement "From the above statement, the mystery of the double slit experiment goes away." which you now are apparently admitting ("I really do not know the answer") is not what you meant.

@mike1000 on rereading the last few posts I notice that it appears that I was being argumentative just for the sake of being argumentative. I did not mean it that way. I was taken aback by my interpretation of your statements as meaning that your analysis of the momentum (which I believe does address the single-slit spread) explained the results of the 2-slit experiment being different based on whether or not the "which path" information is known.

 

[mike1000]

Ah. I missed that. So we are saying the same thing except that I got the mistaken impression that you thought you now completely understood the results of the two slit experiment. I based that inference on your statement "From the above statement, the mystery of the double slit experiment goes away." which you now are apparently admitting ("I really do not know the answer") is not what you meant.

@mike1000 on rereading the last few posts I notice that it appears that I was being argumentative just for the sake of being argumentative. I did not mean it that way. I was taken aback by my interpretation of your statements as meaning that your analysis of the momentum (which I believe does address the single-slit spread) explained the results of the 2-slit experiment being different based on whether or not the "which path" information is known.

I did not think you were being argumentative. I appreciate the fact that you read my posts. Thank you.