Are Schrodinger's cat and the double slit experiment the same idea?

[vadadagon]

Hello,

My highest level of physics is Physics 3 for engineers in college. So I don't have the math or physics background to know this hence the question.

I woke up thinking about the double slit experiment and how the simple act of observing somehow interacts or interferes with the experiment. The schorinder's cat theory is that a quantum particle has every possible quantum state until we open the box. Once we open the box we know the state of the particle (aka cat dead or alive).

It is the very act that shows us the state. Is it because the quantum state of the observer (sensor or eye) interacts with the quantum particle and provides us with a specific state?

An eye or sensor observing is made of quantum particles themselves. So would the act of observing force the particles to be in a specific state?

If this is a ridiculous question, I sincerely apologize. Just wondering if that's why the quantum wave collapses when observed.

 

[PeterDonis]

would the act of observing force the particles to be in a specific state?

"Observing" is the wrong word, because there is no requirement for a conscious observer like a human to be involved anywhere. The key thing that is involved is decoherence.

In the double slit experiment, putting a detector at each slit that registers whether the particle passes through that slit causes decoherence at the slits, which destroys the interference pattern; this happens even if no human ever looks at the results registered by the detectors.

In the Schrodinger's cat scenario, the cat itself is a macroscopic object, so it decoheres itself; in other words, the cat is either alive or dead long before anyone even opens the box (or whether the box is even opened at all).

 

[PeroK]

The simple answer is that the double-slit experiment and Schrodinger's cat are not the same. The former is an example of quantum interference. The second is a tricky thought experiment, which links a quantum mechanical phenomenon to the state of a macroscopic system (i.e. a cat). There are several open threads on this at the moment. For example:

https://www.physicsforums.com/threads/schroedingers-cat-is-it-just-mumbo-jumbo.1054279/

Note that observing a particle generally involves interacting with the particle in some way. For a macroscopic object (like a cat), we can observe it without significantly affecting its state. For an elementary QM system, a measurement generally results in the system's state changing to a so-called eigenstate of the measured observable. The simplest example is quantum spin of an electron. If we measure an electron's spin about a particular axis, then we have only two possible results $\pm \frac \hbar 2$. And, after the measurement, the electron will be in the appropriate eigenstate, corresponding to the measurement outcome. Also, this measurement corresponds to about one third of the electron's total spin.

This is very different from measuring the spin of the Earth or a basketball, where we can watch the object spin about a particular axis - with none of the elementary QM spin behaviour.

 

[PeterDonis]

The schorinder's cat theory is that a quantum particle has every possible quantum state until we open the box.

No, that's not the point of the Schrodinger's cat scenario, and it's wrong anyway.

If we consider a single quantum particle, it has a single quantum state; it never has "every possible quantum state". But if we consider a particular observable of the particle, say measuring its position, then before the measurement the particle's quantum state will in general not be a state of definite position; it will be a state that is a superposition of many different possible positions. After we measure its position, its state is in a state of definite position, the position we measured. So measurement does change the state in that sense.

Note, however, that exactly what "change the state" means is a matter of interpretation; different QM interpretations say different (and often incompatible) things about this. For our purposes here, ignoring any specific interpretation, the state just describes the probabilities of possible measurement results, and we make no assumptions about what the underlying "reality" is.

 

[Nugatory]

Schrodinger’s cat is routinely misrepresented in the popular press and you may have been misled by that misrepresentation.
He did not propose his thought experiment to explain how quantum mechanics says that the cat is neither alive nor dead until we open the box. He proposed it to show that there was something bad wrong with the then-current (almost a century ago now) understanding of quantum mechanics because the math, taken at face value, seemed to suggest that absurd outcome.

This problem was resolved a few decades later with the discovery of quantum decoherence; a good layman-friendly reference is David Lindley’s book, ”Where does the weirdness go”.
The basic idea is that the math says that the collective behavior of a very large ensemble of quantum particles, like say a cat, will be classical.

 

[vadadagon]

"Observing" is the wrong word, because there is no requirement for a conscious observer like a human to be involved anywhere. The key thing that is involved is decoherence.

In the double slit experiment, putting a detector at each slit that registers whether the particle passes through that slit causes decoherence at the slits, which destroys the interference pattern; this happens even if no human ever looks at the results registered by the detectors.

In the Schrodinger's cat scenario, the cat itself is a macroscopic object, so it decoheres itself; in other words, the cat is either alive or dead long before anyone even opens the box (or whether the box is even opened at all).

Thanks. I think. I don't know what decoherence is at all. I'll have to look that up.

 

[Nugatory]

I don't know what decoherence is at all. I'll have to look that up.

googling for “quantum decoherence” will bring up a bunch of good stuff, but you may find the math a bit daunting- hence my recommendation of the Lindley book.

 

[vadadagon]

The simple answer is that the double-slit experiment and Schrodinger's cat are not the same. The former is an example of quantum interference. The second is a tricky thought experiment, which links a quantum mechanical phenomenon to the state of a macroscopic system (i.e. a cat). There are several open threads on this at the moment. For example:

https://www.physicsforums.com/threads/schroedingers-cat-is-it-just-mumbo-jumbo.1054279/

Note that observing a particle generally involves interacting with the particle in some way. For a macroscopic object (like a cat), we can observe it without significantly affecting its state. For an elementary QM system, a measurement generally results in the system's state changing to a so-called eigenstate of the measured observable. The simplest example is quantum spin of an electron. If we measure an electron's spin about a particular axis, then we have only two possible results $\pm \frac \hbar 2$. And, after the measurement, the electron will be in the appropriate eigenstate, corresponding to the measurement outcome. Also, this measurement corresponds to about one third of the electron's total spin.

This is very different from measuring the spin of the Earth or a basketball, where we can watch the object spin about a particular axis - with none of the elementary QM spin behaviour.

PeroK

Thank you. I thought the cat thought experiment was simply using the cat as an example for a Quantum particle not as a macroscopic object (aka a cat). Where the cat is alive/dead simultaneously until you open the box. Meaning that once you look at a quantum particle (aka measure it or interact with it in any way) then it's quantum state become fixed.

I do understand that interacting with a cat won't affect the cat's quantum state or none that we are aware of, since I don't know of a way to measure the quantum state of a cat or even of it's quantum particles either (well not without destroying the cat first).

Also, thank you for the link to the other discussion.

 

[vadadagon]

No, that's not the point of the Schrodinger's cat scenario, and it's wrong anyway.

If we consider a single quantum particle, it has a single quantum state; it never has "every possible quantum state". But if we consider a particular observable of the particle, say measuring its position, then before the measurement the particle's quantum state will in general not be a state of definite position; it will be a state that is a superposition of many different possible positions. After we measure its position, its state is in a state of definite position, the position we measured. So measurement does change the state in that sense.

Note, however, that exactly what "change the state" means is a matter of interpretation; different QM interpretations say different (and often incompatible) things about this. For our purposes here, ignoring any specific interpretation, the state just describes the probabilities of possible measurement results, and we make no assumptions about what the underlying "reality" is.

Whoa! OK? So wait. I thought the whole reason for the wave interference of light (even when a single photon is fired one at a time) was because that photon could be at any place and hence the interference and the inference that light acts as a wave and that wave collapses when measured and that collapse causes light to act as a particle.

If a single particle has a single state wouldn't the double slit experiment only show two lines? I guess I better read some more, cause I'm no longer treading water here.

 

[vadadagon]

Schrodinger’s cat is routinely misrepresented in the popular press and you may have been misled by that misrepresentation.
He did not propose his thought experiment to explain how quantum mechanics says that the cat is neither alive nor dead until we open the box. He proposed it to show that there was something bad wrong with the then-current (almost a century ago now) understanding of quantum mechanics because the math, taken at face value, seemed to suggest that absurd outcome.

This problem was resolved a few decades later with the discovery of quantum decoherence; a good layman-friendly reference is David Lindley’s book, ”Where does the weirdness go”.
The basic idea is that the math says that the collective behavior of a very large ensemble of quantum particles, like say a cat, will be classical.

Thank you for the book reference. I'll into that.

Yes. I may have been mislead by the media on Schrodinger's cat. Although, I knew that Schrodinger proposed it to suggest the ridiculousness of the Quantum states, because he saw the Quantum "weirdness" (aka superposition) as a problem.

 

[PeroK]

Whoa! OK? So wait. I thought the whole reason for the wave interference of light (even when a single photon is fired one at a time) was because that photon could be at any place and hence the interference and the inference that light acts as a wave and that wave collapses when measured and that collapse causes light to act as a particle.

This is the popular science version! If you study QM as an academic subject, then the explanation is not valid. Not least because a photon is not a classical particle, but the quantum of the electromagnetic field. The photon, quite literally, does not have a position. Instead, you have an EM field that interacts with matter at a specific point with a specific quantum of energy (this is what a photon is).

I'm not sure why popular science authors don't tackle these issues head on. Instead, there appears to be a common script that they all adhere to. For example, the emphasis on "wave-particle" duality. QM itself contains no such thing. I have several textbooks on QM and wave-particle is not a thing. In Introduction to QM, by Griffiths it is mentioned only as a historical footnote.

If a single particle has a single state wouldn't the double slit experiment only show two lines? I guess I better read some more, cause I'm no longer treading water here.

A quantum state is a vector. All systems have a specific quantum state (which may or may not be known). But, for the double-slit, that state spatially encompasses both slits. Moreover, all quantum states can be expressed as a superposition of other states. In the double-slit, you can express the state of the EM field as a superposition of states corresponding to each slit.

It's actually easier to talk in terms of electrons, as they obey non-relativistic QM, and are conceptually clearer. In the double slit for a single electron:

1) Before the slits, the electron's state is a fairly compact wave packet. But, not as spatially compact as the slits (and the space between the slits).

2) There is a certain probability that the electron is absorbed by the first barrier. In fact, as you make the slits narrower, fewer electrons make it through. If you want a really spread out double-slit pattern and make the slits very narrow, then you will get quite a faint pattern, as so few electrons make it through. This is true for light as well.

3) After the slits, if the electron makes it through, it's state can be expressed as the superposition of two spatially separate states: one for each slit. Crucially, however, these states are no longer compact wave-packets. The interaction with the slits means that these states are spreading out laterally. Note that this only happens if the slits are narrow enough for the uncertainty principle to take effect. The narrower the slit, the more the wave-function spreads out afterwards.

4) When the electron interacts with the final screen, these two wave-functions have significant overlap and interfere with each other. To calculate the probability of impact at any point of the final screen, you treat the wavefunctions as probability amplitudes. These are complex numbers and may cancel each other out. This results in a double-slit pattern that is very similar to a classical wave interference pattern. It can, however, be calculated entirely using single-particle QM, with the electron described by its wave-function.

5) There is no point at which QM switches from "particle mode" to "wave mode", as most popular sources imply. Instead, it's a single-particle wave-function all down the line.

 

[PeterDonis]

So wait. I thought...

I would recommend that before thinking anything, you take the time to work through an actual textbook on QM. You can't get a good understanding of how QM actually works from pop science sources. I would recommend Ballentine for a start.

 

[vanhees71]

Another point is that you don't need decoherence to destroy the interference pattern in the double-slit experiment by gaining which-way information. It's sufficient to somehow mark each photon such that you can determine with certainty through which slit it came.

A very simple setup of this kind is to work with single polarized photons incident on the double slit. Say they are horizontally polarized (in $x$ direction). If you now just set up the double slit, you'll see a double-slit interference pattern after repeating a many times with such prepared photons.

Now to mark each photon going through the double slit, put two quarter-wave plates into the slits. Orient one at $45^\circ$ and one at $-45^\circ$ relative to the $x$ axis. A H-polarized photon going through a $45^\circ$ oriented quarter-wave plate will be left-circular polarized, and if it's going through a $-45^\circ$ oriented quarter-wave plate it will be right-circular polarized. That means that the photons behind the slit are marked such that you can with certainty say through which slit it came, i.e., if it's left-circular polarized it went through slit 1, if it's right-circular polarized it went through slit 2, i.e., it carries certain "which-way information", and then the quantum theory tells you that there'll be no double-slit interference pattern when repeating the experiment with many photons left anymore. It's just an incoherent superposition of the single-slit patterns.

It is sufficient that each photon's way is "marked" by its polarization. It's not necessary to really take note of which polarization it has, i.e., which way it took, to destroy the double-slit interference pattern. It's sufficient to somehow make it possible to do so.

 

[vadadagon]

This is the popular science version! If you study QM as an academic subject, then the explanation is not valid. Not least because a photon is not a classical particle, but the quantum of the electromagnetic field. The photon, quite literally, does not have a position. Instead, you have an EM field that interacts with matter at a specific point with a specific quantum of energy (this is what a photon is).

I'm not sure why popular science authors don't tackle these issues head on. Instead, there appears to be a common script that they all adhere to. For example, the emphasis on "wave-particle" duality. QM itself contains no such thing. I have several textbooks on QM and wave-particle is not a thing. In Introduction to QM, by Griffiths it is mentioned only as a historical footnote.A quantum state is a vector. All systems have a specific quantum state (which may or may not be known). But, for the double-slit, that state spatially encompasses both slits. Moreover, all quantum states can be expressed as a superposition of other states. In the double-slit, you can express the state of the EM field as a superposition of states corresponding to each slit.

It's actually easier to talk in terms of electrons, as they obey non-relativistic QM, and are conceptually clearer. In the double slit for a single electron:

1) Before the slits, the electron's state is a fairly compact wave packet. But, not as spatially compact as the slits (and the space between the slits).

2) There is a certain probability that the electron is absorbed by the first barrier. In fact, as you make the slits narrower, fewer electrons make it through. If you want a really spread out double-slit pattern and make the slits very narrow, then you will get quite a faint pattern, as so few electrons make it through. This is true for light as well.

3) After the slits, if the electron makes it through, it's state can be expressed as the superposition of two spatially separate states: one for each slit. Crucially, however, these states are no longer compact wave-packets. The interaction with the slits means that these states are spreading out laterally. Note that this only happens if the slits are narrow enough for the uncertainty principle to take effect. The narrower the slit, the more the wave-function spreads out afterwards.

4) When the electron interacts with the final screen, these two wave-functions have significant overlap and interfere with each other. To calculate the probability of impact at any point of the final screen, you treat the wavefunctions as probability amplitudes. These are complex numbers and may cancel each other out. This results in a double-slit pattern that is very similar to a classical wave interference pattern. It can, however, be calculated entirely using single-particle QM, with the electron described by its wave-function.

5) There is no point at which QM switches from "particle mode" to "wave mode", as most popular sources imply. Instead, it's a single-particle wave-function all down the line.

PeroK

I think I understand a little better now after reading some of David Lindley’s book, ”Where does the weirdness go”. Mind you, I still don't posses the education in physics or in mathematics to truly comprehend it intrinsically only theoretically and perhaps because of it, my logic may be entirely flawed.

Due to the uncertainty principle (and based on the Stern-Gerlach magnet experiments) we can only determine what we measure nothing else. So for the sake of argument (and for my own sanity) if we measure say 100 people of whether they are skinny or fat. That's all we know. We can't say anything else about them. If we want to know if they are short or tall we then have to measure for that as well and so on.

So in that sense Schrodinger's cat and the double slit experiment are the same. In the double slit experiment we are testing weather or not a photon or an electron went thru a specific slit. When we do, the results we obtain are based on what we are testing or measuring and why the wave form collapses (by collapsing I don't mean the wave ceases to exist, but simply that our measuring forces an answer). When we don't measure the results then the wave form remains. The cat is the same. While we don't open the box the possibility is that it is dead or alive or anywhere in between. Once we open the box it is the same as taking a measurement and we get the result of dead or alive. We can't know anything else because we are not testing for anything else.

As in the example of the rope & fence that David Lindley proposes. If you have a picket fence and rope, the only results you'll get from making a wave on the rope is up and down. Left or right or any other will be blocked.

In the double slit experiment. If we tested for something else instead of which slit a photon passed thru, then we would get a 50/50 answer as to the results. In the classical experiment we test how many photons go to the left or right slit and we get 50/50 split. However, I would venture to say (although I don't know of any experiments and/or even how to go about testing this) that if we tested how many photons were deflected at 45 degrees from the slit. I would imagine we would get a 50/50 answer again or if we could say take the electrons that passed thru one slit and then let them go thru another slit without measuring the 2nd result we would probably get the interference pattern again since the uncertainty principle is once again re-introduced.

I suspect if a magnet with 4 polarities could be devised and used in a Stern-Gerlach experiment (say a up/down and left/right magnet simultaneously) then I would suspect 25% of the electrons would be up/left, up/right, down/left & down/right. Because that's all we can test for or if you want are asking how many electrons are up/left, up/right, down/left, down/right. What I don't know is what we would get if we could test for every possible position. Also what we only know is the position of that particle as it passes thru the magnet, but that doesn't imply that's the actual position in reality these particles exhibit. Only what we can detect at that moment in time and space.

Just as with measuring whether someone is skinny or fat. It is only true when we measure them. If we go a year later to measure those same people, those measurements may be different and some of those that were fat could now in fact be skinny.

Is my logic sound and/or am I simply holding on to a cart careening down a hill?

 

[vadadagon]

I would recommend that before thinking anything, you take the time to work through an actual textbook on QM. You can't get a good understanding of how QM actually works from pop science sources. I would recommend Ballentine for a start.

Thank you for the recommendation.

Although with my level of education a QM book would probably be over my head. I will give it a try once I am finished with "Where does the Weirdness Go?" by David Lindley (currently reading) and "QED: The Strange Theory of Light and Matter" by Richard P. Feynman.

 

[vadadagon]

It's actually easier to talk in terms of electrons, as they obey non-relativistic QM, and are conceptually clearer. In the double slit for a single electron:

1) Before the slits, the electron's state is a fairly compact wave packet. But, not as spatially compact as the slits (and the space between the slits).

2) There is a certain probability that the electron is absorbed by the first barrier. In fact, as you make the slits narrower, fewer electrons make it through. If you want a really spread out double-slit pattern and make the slits very narrow, then you will get quite a faint pattern, as so few electrons make it through. This is true for light as well.

3) After the slits, if the electron makes it through, it's state can be expressed as the superposition of two spatially separate states: one for each slit. Crucially, however, these states are no longer compact wave-packets. The interaction with the slits means that these states are spreading out laterally. Note that this only happens if the slits are narrow enough for the uncertainty principle to take effect. The narrower the slit, the more the wave-function spreads out afterwards.

4) When the electron interacts with the final screen, these two wave-functions have significant overlap and interfere with each other. To calculate the probability of impact at any point of the final screen, you treat the wavefunctions as probability amplitudes. These are complex numbers and may cancel each other out. This results in a double-slit pattern that is very similar to a classical wave interference pattern. It can, however, be calculated entirely using single-particle QM, with the electron described by its wave-function.

5) There is no point at which QM switches from "particle mode" to "wave mode", as most popular sources imply. Instead, it's a single-particle wave-function all down the line.

"3) After the slits, if the electron makes it through, it's state can be expressed as the superposition of two spatially separate states: one for each slit. Crucially, however, these states are no longer compact wave-packets. The interaction with the slits means that these states are spreading out laterally. Note that this only happens if the slits are narrow enough for the uncertainty principle to take effect. The narrower the slit, the more the wave-function spreads out afterwards."

I have a further question - Has there been a double slit experiment where instead of letting the pattern emerge at one barrier, there are several smaller barriers at difference distances and what if any was the pattern which emerged? Is it still consistent with the wave interference pattern or not (as say something like the image attached)?

 

[PeroK]

Due to the uncertainty principle (and based on the Stern-Gerlach magnet experiments) we can only determine what we measure nothing else.

That's true at the fundamental QM level. That's true of the hydrogen atom, for example.

So for the sake of argument (and for my own sanity) if we measure say 100 people of whether they are skinny or fat. That's all we know. We can't say anything else about them. If we want to know if they are short or tall we then have to measure for that as well and so on.

It's not true that people can be modelled as fundamental QM systems. A person is a large macroscopic system, where the fundamental QM properties get washed out by a combination of the law of large numbers and the huge number of degrees of freedom. A person does not go from fat to skinny merely as the result of stepping on a set of bathroom scales.

So in that sense Schrodinger's cat and the double slit experiment are the same.

They are not, as already explained.

In the double slit experiment we are testing weather or not a photon or an electron went thru a specific slit.

That is not really true. In the double-slit experiment, it makes no sense to ask what slit the particle went through. This is another example of a non-classical aspect of QM.

When we do, the results we obtain are based on what we are testing or measuring and why the wave form collapses (by collapsing I don't mean the wave ceases to exist, but simply that our measuring forces an answer).

If we close one slit (which is the simplest way to measure that it went through the other slit), then we have a single-slit pattern.

When we don't measure the results then the wave form remains.

No. When we don't measure, we have a superposition of two single-slit wavefunctions - which subsequently interfere.

The cat is the same. While we don't open the box the possibility is that it is dead or alive or anywhere in between. Once we open the box it is the same as taking a measurement and we get the result of dead or alive. We can't know anything else because we are not testing for anything else.

No. That is essentially a classical situation. When we open the box, we are doing nothing specific that corresponds to a dead/alive measurement. I'm not sure exactly what a valid test would be - it depends on how dead the cat is. If it's nothing but a skeleton, then it's probably been dead for some time. Or, it may just have died. The state alive or dead is not quantized. I'm amazed at how many people get carried away wth QM and the quantization of electron spin or hydrogen energy levels and assume (against all the evidence) that alive/dead is a simple quantized property. There are a trillion ways a cat can be alive and a trillion ways it can be dead. And the process of dying may be a slow process that take place according to macroscopic biological processes.

In the double slit experiment. If we tested for something else instead of which slit a photon passed thru, then we would get a 50/50 answer as to the results. In the classical experiment we test how many photons go to the left or right slit and we get 50/50 split. However, I would venture to say (although I don't know of any experiments and/or even how to go about testing this) that if we tested how many photons were deflected at 45 degrees from the slit. I would imagine we would get a 50/50 answer again or if we could say take the electrons that passed thru one slit and then let them go thru another slit without measuring the 2nd result we would probably get the interference pattern again since the uncertainty principle is once again re-introduced.

I don't know that any of this is quite right. The behaviour of a photon is all about the wavefunction.

I suspect if a magnet with 4 polarities could be devised and used in a Stern-Gerlach experiment (say a up/down and left/right magnet simultaneously) then I would suspect 25% of the electrons would be up/left, up/right, down/left & down/right. Because that's all we can test for or if you want are asking how many electrons are up/left, up/right, down/left, down/right. What I don't know is what we would get if we could test for every possible position. Also what we only know is the position of that particle as it passes thru the magnet, but that doesn't imply that's the actual position in reality these particles exhibit. Only what we can detect at that moment in time and space.

Again, this sounds like you are making stuff up. I don't recognise this as QM.

Just as with measuring whether someone is skinny or fat. It is only true when we measure them.

It's absolutely not. Saying that someone is only skinny when we measure them is nonsensical. In what universe is that true? Skinny and fat are macroscopic states that take weeks, months and years to evolve. You don't collapse into an anorexic state because someone tests you for anorexia!

If we go a year later to measure those same people, those measurements may be different and some of those that were fat could now in fact be skinny.

That has nothing to do with QM. What if you measure someone to see how skinny they are and find that they are dead? Was it really a dead/alive measurement?

Is my logic sound and/or am I simply holding on to a cart careening down a hill?

You've completely missed the point. The whole point of Lindley's book, ultimately, is to explain why macroscopic objects are not fundamentally quantum mechanical. That the quantum "weirdness" has gone. And, to try to explain where it went!

 

[PeroK]

I have a further question - Has there been a double slit experiment where instead of letting the pattern emerge at one barrier, there are several smaller barriers at difference distances and what if any was the pattern which emerged? Is it still consistent with the wave interference pattern or not (as say something like the image attached)?

You could do your own research on that. Ultimately, however, there are only so many experiments you can do before something is accepted and it's time to move on to more enlightening experiments.

That said, Richard Feynman famously considered a large number of barriers with a large number of slits as a thought experiment, and so developed the path-integral formulation of QM. This also explains to some extent why Huygens principle applies in classical wave theory.

 

[vadadagon]

Another point is that you don't need decoherence to destroy the interference pattern in the double-slit experiment by gaining which-way information. It's sufficient to somehow mark each photon such that you can determine with certainty through which slit it came.

A very simple setup of this kind is to work with single polarized photons incident on the double slit. Say they are horizontally polarized (in $x$ direction). If you now just set up the double slit, you'll see a double-slit interference pattern after repeating a many times with such prepared photons.

Now to mark each photon going through the double slit, put two quarter-wave plates into the slits. Orient one at $45^\circ$ and one at $-45^\circ$ relative to the $x$ axis. A H-polarized photon going through a $45^\circ$ oriented quarter-wave plate will be left-circular polarized, and if it's going through a $-45^\circ$ oriented quarter-wave plate it will be right-circular polarized. That means that the photons behind the slit are marked such that you can with certainty say through which slit it came, i.e., if it's left-circular polarized it went through slit 1, if it's right-circular polarized it went through slit 2, i.e., it carries certain "which-way information", and then the quantum theory tells you that there'll be no double-slit interference pattern when repeating the experiment with many photons left anymore. It's just an incoherent superposition of the single-slit patterns.

It is sufficient that each photon's way is "marked" by its polarization. It's not necessary to really take note of which polarization it has, i.e., which way it took, to destroy the double-slit interference pattern. It's sufficient to somehow make it possible to do so.

Isn't passing a photon thru a polarized lens another form of measuring and therefore forcing an answer? Even if it is a "passive" type of measurement. A non-polarized lens allows all photons to pass thru. A Polarized only allows a specific(s) type to pass thru, which ultimately means you are interacting with the particle and therefore forcing an answer. It's essentially the same as testing which slit it goes thru or what spin a particle has.

Also, I may be wrong but it's like believing that because the photon passed thru a left or right (vertical or horizontal) polarized lens that it has always been either right or left when all we can really say is that it was that when it passed thru the lens. We don't know what happens afterwards. Sure we can deduce that they are all one by placing another lens right after at the angle of that photon and block 100% of the light. However, we are just forcing that answer, but what of the 3 Polarized lens paradox (link only to provide a reference of what I'm talking about). Doesn't that tell us that we get the results based on what we are testing and not necessarily a reality?



If we think of these lenses as forcing an answer or perhaps forcing an orientation then it makes perfect sense. Although, we assume it is the case but we don't actually know. All we really know is that a specific type of light is blocked and as demonstrated by the 3 Polarized lens paradox (which isn't a paradox in my book) because if we introduced another answer to be forced before we test if all are now perpendicular then light makes it thru the 3 lens when with two it doesn't.

However, if we used say the skinny fat as a model. We ask in the first group are you fat? If yes you can't move forward and in the second we ask are you skinny and if yes you can't move forward. Blocking all 100% of subjects. However, if you ask are you fat first and then ask are you medium girth second then those which answered yes to the 2nd answer will pass thru the 3rd questionnaire by saying they are not skinny. Please note that I am aware we are not physically asking anything of photons or electrons and this is just a logical exercise. But in that sense it makes perfect sense and it isn't a paradox at all, because you introduced a new measurement into the mix.

Or am I completely insane and way off the mark?

 

[PeterDonis]

I will give it a try once I am finished with "Where does the Weirdness Go?" by David Lindley (currently reading) and "QED: The Strange Theory of Light and Matter" by Richard P. Feynman.

That sounds like a reasonable plan. Those books are for laymen but their treatments are much more careful than most pop science books, and they should help give you useful background for starting with a textbook.

 

[PeterDonis]

Isn't passing a photon thru a polarized lens another form of measuring

No. By itself this does not cause decoherence. That's why @vanhees71 gave it as an example where decoherence is not required to destroy interference.

 

[Nugatory]

Has there been a double slit experiment where instead of letting the pattern emerge at one barrier, there are several smaller barriers at difference distances and what if any was the pattern which emerged? Is it still consistent with the wave interference pattern or not (as say something like the image attached)?

It’s been done. It’s part of almost every experiment, because setting up the experiment involves placing the detectors somewhere - and wherever we put them we have to calculate the expected results at that position.

 

[vadadagon]

That's true at the fundamental QM level. That's true of the hydrogen atom, for example.

It's not true that people can be modelled as fundamental QM systems. A person is a large macroscopic system, where the fundamental QM properties get washed out by a combination of the law of large numbers and the huge number of degrees of freedom. A person does not go from fat to skinny merely as the result of stepping on a set of bathroom scales.

They are not, as already explained.

That is not really true. In the double-slit experiment, it makes no sense to ask what slit the particle went through. This is another example of a non-classical aspect of QM.

If we close one slit (which is the simplest way to measure that it went through the other slit), then we have a single-slit pattern.

No. When we don't measure, we have a superposition of two single-slit wavefunctions - which subsequently interfere.

No. That is essentially a classical situation. When we open the box, we are doing nothing specific that corresponds to a dead/alive measurement. I'm not sure exactly what a valid test would be - it depends on how dead the cat is. If it's nothing but a skeleton, then it's probably been dead for some time. Or, it may just have died. The state alive or dead is not quantized. I'm amazed at how many people get carried away wth QM and the quantization of electron spin or hydrogen energy levels and assume (against all the evidence) that alive/dead is a simple quantized property. There are a trillion ways a cat can be alive and a trillion ways it can be dead. And the process of dying may be a slow process that take place according to macroscopic biological processes.I don't know that any of this is quite right. The behaviour of a photon is all about the wavefunction.

Again, this sounds like you are making stuff up. I don't recognise this as QM.

It's absolutely not. Saying that someone is only skinny when we measure them is nonsensical. In what universe is that true? Skinny and fat are macroscopic states that take weeks, months and years to evolve. You don't collapse into an anorexic state because someone tests you for anorexia!

That has nothing to do with QM. What if you measure someone to see how skinny they are and find that they are dead? Was it really a dead/alive measurement?

You've completely missed the point. The whole point of Lindley's book, ultimately, is to explain why macroscopic objects are not fundamentally quantum mechanical. That the quantum "weirdness" has gone. And, to try to explain where it went!

I'm using the people as an example. I get that people are macroscopic and it isn't about the people that I'm talking about. I think you get too literal when I'm simply using an example. If I were to use 100 people in a test subject and only measure for one thing. I can't deduce anything else in my lab report. I can't say all the fat people have high blood pressure or they eat too much or anything else. All I can say is I measured 100 people and x number of them are skinny and x number of them are fat. Yes I get that if I am standing in front of a actual human I can deduce gender, age, race, height simply by looking at them but intrinsically that's actually taking a measurement. If it were an actual lab test you wouldn't just measure one thing when you could measure 300 things. However, that's not the point of my example. In my report of measuring a person whether fat/skinny I have no way of knowing anything else and it's essentially the same thing as testing a particle as reading the report (because that's essentially what we are doing).

I think you missed the entire point of my post since you are talking about my examples as macroscopic objects when I am not using them that way at all but only as an example and I have never suggested people could be measured as a quantum particle or that it should.

I am not interested at arguing for the sake of arguing and/or talking in circles. I do appreciate your efforts at trying to explain.

 

[PeterDonis]

I'm using the people as an example.

Ok, then @PeroK is telling you that your example is a bad one and you would be better off just dropping it than continuing to try to defend it. Your example is irrelevant to QM and you should not be using it as a way to try to understand anything about QM.

 

[PeroK]

I'm using the people as an example.

It's not a valid example. QM requires a complete revision of how you think about nature and the laws of physics. Somehow you have to find a way to think differently.

I get that people are macroscopic and it isn't about the people that I'm talking about. I think you get too literal when I'm simply using an example.

Maybe, but there is no harm in being precise and literal if you want to learn and understand microscopic physics.

If I were to use 100 people in a test subject and only measure for one thing. I can't deduce anything else in my lab report. I can't say all the fat people have high blood pressure or they eat too much or anything else. All I can say is I measured 100 people and x number of them are skinny and x number of them are fat.

That has nothing to do with QM.

Yes I get that if I am standing in front of a actual human I can deduce gender, age, race, height simply by looking at them but intrinsically that's actually taking a measurement. If it were an actual lab test you wouldn't just measure one thing when you could measure 300 things. However, that's not the point of my example. In my report of measuring a person whether fat/skinny I have no way of knowing anything else and it's essentially the same thing as testing a particle as reading the report (because that's essentially what we are doing).

You are still analysing classical objects with classical properties using classical thinking. That's no good. Measurement in QM is subtle. You need to start thinking of precise processes. Not coarse-grained classical measurements.

I think you missed the entire point of my post since you are talking about my examples as macroscopic objects when I am not using them that way at all but only as an example and I have never suggested people could be measured as a quantum particle or that it should.

Then your arguments have no purpose that I can see.

I am not interested at arguing for the sake of arguing and/or talking in circles. I do appreciate your efforts at trying to explain.

Okay. I admit that I'm not the most conciliatory and tactful of people.

 

[vadadagon]

Ok, then @PeroK is telling you that your example is a bad one and you would be better off just dropping it than continuing to try to defend it. Your example is irrelevant to QM and you should not be using it as a way to try to understand anything about QM.

OK - Forget people, I'm not trying to defend anything and it seems using people is triggering something I'm not interested in explaining or discussing. I'm trying to understand and I am using people simply as an example (like Schrodinger used a cat).

Photons have many properties not just one property correct? However, we can only know one thing about them when we measure. Is that also correct or am I wrong? We can only get a yes or no answer or a binary result when we test is that also true? We can only know left/right, or top/bottom, or the location (here or not here). We can't ask of a photon where is the photon correct? We can only ask, is there a photon here and get an answer. We only get an answer because we ask the question and the answer is only true at the moment we ask. The answer isn't true 3 years from now or two days before only when we ask the question is the answer true or is that incorrect?

My argument is that the answers we get are there only because we asked the question and not because the question is always true. If we ask the spin of a specific particle we get the answer, if we ask the location we get the answer, if we ask the value we get the answer. However, we can't sit the particle in front of us and give it a questionnaire to fill out. In Quantum Physics we can't assume anything and we can only get one answer at a time. Before we ask anything can be possible or probable or uncertain if you will. Not until we test/measure/observe/ask are we going to get an answer.

However, our limitation is based on what we measure and/or how we measure and the answer is only valid for those particles at that time. Sure by making several experiments and asking many different questions at different times and sometimes the same question and getting the same answer we can make a deduction of the results and say something specific like light behaves like a wave until I measure it like a particle and it behaves like a particle. We can only test how the photon is behaving at that moment and based on what we test is the results we receive.

As far as I have read or understand (which isn't much), we can't simultaneously test for two things at once. Is that correct? We can't test a photon whether it is a wave or a particle simultaneously. We can't test if it has two different orientations at the same time (the polarized lens test). That's what I'm trying to understand.

 

[Nugatory]

We can't test a photon whether it is a wave or a particle simultaneously.

If you are going to unlearn just one thing…. Unlearn this notion of wave-particle duality.

 

[PeroK]

OK - Forget people, I'm not trying to defend anything and it seems using people is triggering something I'm not interested in explaining or discussing. I'm trying to understand and I am using people simply as an example (like Schrodinger used a cat).

Photons have many properties not just one property correct? However, we can only know one thing about them when we measure. Is that also correct or am I wrong? We can only get a yes or no answer or a binary result when we test is that also true? We can only know left/right, or top/bottom, or the location (here or not here). We can't ask of a photon where is the photon correct? We can only ask, is there a photon here and get an answer. We only get an answer because we ask the question and the answer is only true at the moment we ask. The answer isn't true 3 years from now or two days before only when we ask the question is the answer true or is that incorrect?

My argument is that the answers we get are there only because we asked the question and not because the question is always true. If we ask the spin of a specific particle we get the answer, if we ask the location we get the answer, if we ask the value we get the answer. However, we can't sit the particle in front of us and give it a questionnaire to fill out. In Quantum Physics we can't assume anything and we can only get one answer at a time. Before we ask anything can be possible or probable or uncertain if you will. Not until we test/measure/observe/ask are we going to get an answer.

However, our limitation is based on what we measure and/or how we measure and the answer is only valid for those particles at that time. Sure by making several experiments and asking many different questions at different times and sometimes the same question and getting the same answer we can make a deduction of the results and say something specific like light behaves like a wave until I measure it like a particle and it behaves like a particle. We can only test how the photon is behaving at that moment and based on what we test is the results we receive.

As far as I have read or understand (which isn't much), we can't simultaneously test for two things at once. Is that correct? We can't test a photon whether it is a wave or a particle simultaneously. We can't test if it has two different orientations at the same time (the polarized lens test). That's what I'm trying to understand.

There are some good points in there, but you need to develop more precision. Both Lindley's book and Feynman's strange theory are about quite specific topics. You have to decide which if either of those topics you want to learn. And then focus on them.

A more ambitious alternative is these notes, which are essentially at undergraduate level. If you do want to study these, then you must first forget everything you think you know about QM. I do mean that. You are already a little bogged down in imprecise generalities about QM. Anyway, you might want to take a look at this:

http://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

 

[vadadagon]

It's not a valid example. QM requires a complete revision of how you think about nature and the laws of physics. Somehow you have to find a way to think differently.

Maybe, but there is no harm in being precise and literal if you want to learn and understand microscopic physics.

That has nothing to do with QM.

You are still analysing classical objects with classical properties using classical thinking. That's no good. Measurement in QM is subtle. You need to start thinking of precise processes. Not coarse-grained classical measurements.

Then your arguments have no purpose that I can see.

Okay. I admit that I'm not the most conciliatory and tactful of people.

I'm trying to understand with my limited capacity of education. Yes, I get that people are people and it may not be a good example as quantum particles. My idea is that people have many different properties (age, height, girth, weight, gender, skin color, hair color, eye color, etc) just like quantum particles have many properties. If we measure one property we get one answer.

The reality is that particles have more than the single property we measure. What those properties are we don't know until we measure them, but as far as I am aware is that we can only measure one thing at a time. The uncertain principle says we can only know one thing, we can only get a binary answer to a question (yes/no) or is that not correct?

 

[PeterDonis]

The uncertain principle says we can only know one thing, we can only get a binary answer to a question (yes/no) or is that not correct?

That is not correct.

To say that particles have "more than one property" is technically true, but it doesn't mean what you appear to think it means. The same goes for "a measurement can only tell us about one property".

I'm trying to understand with my limited capacity of education.

The best way for you to understand is not to speculate based on what you currently think you know. As far as I can tell, pretty much everything you currently think you know about QM is wrong. You would be much better served by not trying to speculate or construct scenarios or analogies at all at this point, but to forget everything you think you know about QM and start from scratch: read the references you have been given and start building a new understanding from them.

 

[PeroK]

I'm trying to understand with my limited capacity of education. Yes, I get that people are people and it may not be a good example as quantum particles. My idea is that people have many different properties (age, height, girth, weight, gender, skin color, hair color, eye color, etc) just like quantum particles have many properties. If we measure one property we get one answer.

The reality is that particles have more than the single property we measure. What those properties are we don't know until we measure them, but as far as I am aware is that we can only measure one thing at a time. The uncertain principle says we can only know one thing, we can only get a binary answer to a question (yes/no) or is that not correct?

The UP (Uncertainty Principle) is subtler than that. The HUP (Heisenberg Uncertainty Principle) refers to preparation and measurement of the position and momentum of a single particle. If you have read popular sources on the HUP, they may have emphasised the "old" UP. In any case, here is a modern view. Note that the HUP is a statistical law. It puts no limitations on the accuracy with which we can measure either the position or the momentum of a particle! (I know that contradicts most popular science sources, but there you have it.)

Suppose we try to contain an electron. We have it confined to a small region - let's call it a box. We know that if we measure its position, we must get an answer that is in the box. If we repeat this many times, then we get a random spread of values - all in the box. There is a statistical measure called the variance of a set of data, denoted by $(\Delta x)^2$ in the case of position. In this case, the variance is on the scale of the width of the box.

Now, we measure the momentum of the electron in the box. What we find is a large variance in the measurements of momentum. This is denoted by $(\Delta p)^2$. Note that this excludes any experimental uncertainty in the measuring apparatus. We are assuming that we have a near perfect mechanism for measuring momentum. And, again, note that the HUP does not forbid these near perfect measurements.

What the HUP says is:$$\Delta x \Delta p \ge \frac \hbar 2$$Where $\hbar$ is the reduced Planck constant. It's about $1 \times 10^{-34}$ joule-seconds.

What does this mean? First, if the box is quite big, then the variance in position measurements will be quite large. And, that allows the measurements of momentum to have similar values. And, as the box is made progressively smaller, and the variance in position measurements gets smaller, then the variance in momentum measurements gets larger. In other words, we cannot both confine the electron to a very small space and control its momentum to a small range.

Note that we can apply this to the single-slit experiment. If we fire electrons through a wide slit at a detection screen, then we get a band related to the width of the slit. As we narrow the slit, the band narrows. All very classical. But, then, when the slit reaches a critical width where the value of $\hbar$ becomes relevant, the HUP kicks in. And by this I mean the HUP has a significant effect. At that point the the band on the detection screen begins to widen. And the narrower the slit becomes, the wider the band becomes. Moreover, the band begins to break up into sub-bands of light and dark.

Note that the HUP does not say you can only know position or momentum. You can simultaneously know both quite precisely - but only up to a point. You can't know both to arbitrary precision. And by "know" I mean predict the variance in measurements of position and momentum.

In this post I've tried to be as precise as possible. And have avoided woolly generalisations to try to explain precisely what the HUP says.

PS $\Delta x$, the square root of the variance, is also called the standard deviation.

 

[vadadagon]

If you are going to unlearn just one thing…. Unlearn this notion of wave-particle duality.

Uhmm.... OK. I thought that's the whole point of the double slit experiment. When we measure which slit it goes thru we see (or perhaps understand) light to behave as a particle and when not we see the wave pattern. Is this article then wrong and/or what should I think of light as if not a particle-wave duality?

"History of Wave-Particle Duality
Current scientific thinking, as advanced by Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, Erwin Schrödinger, and others, holds that all particles have both a wave and a particle nature. This behavior has been observed not just in elementary particles but also in complex ones, such as atoms and molecules."

"Wave-Particle Duality - Key takeaways
Wave-particle duality is a concept that explains how both light and matter can act like both waves and particles, even though we can't observe both at the same time. When we think of light, we usually think of it a wave, but it can also be made up of tiny energy packets called photons. The properties of wave motion, like amplitude, wavelength, and frequency, can be used to measure light. Light also shows other wave properties, like reflection, refraction, diffraction, and interference. The photoelectric effect is another important concept in this area. It describes how electrons can be released from a metal's surface when it's hit by light with a certain frequency. These electrons are called photoelectrons. Finally, there's the uncertainty principle, which states that we can't accurately measure both the position and velocity of something at the same time, even in theory."https://shiken.ai/physics/wave-part...at is the wave-particle,both at the same time.

 

[vanhees71]

If you are going to unlearn just one thing…. Unlearn this notion of wave-particle duality.

Also I strongly suggest to study non-relativistic quantum mechanics first, before you start with relativistic quantum field theory, which you need to understand what photons really are. A good starting point is wave mechanics as presented in the Feynmsn lectures vol. 3. The complete 3-vol. set is legally for free online:

https://www.feynmanlectures.caltech.edu/

 

[PeroK]

Uhmm.... OK. I thought that's the whole point of the double slit experiment. When we measure which slit it goes thru we see (or perhaps understand) light to behave as a particle and when not we see the wave pattern. Is this article then wrong and/or what should I think of light as if not a particle-wave duality?

"History of Wave-Particle Duality
Current scientific thinking, as advanced by Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, Erwin Schrödinger, and others, holds that all particles have both a wave and a particle nature. This behavior has been observed not just in elementary particles but also in complex ones, such as atoms and molecules."

"Wave-Particle Duality - Key takeaways
Wave-particle duality is a concept that explains how both light and matter can act like both waves and particles, even though we can't observe both at the same time. When we think of light, we usually think of it a wave, but it can also be made up of tiny energy packets called photons. The properties of wave motion, like amplitude, wavelength, and frequency, can be used to measure light. Light also shows other wave properties, like reflection, refraction, diffraction, and interference. The photoelectric effect is another important concept in this area. It describes how electrons can be released from a metal's surface when it's hit by light with a certain frequency. These electrons are called photoelectrons. Finally, there's the uncertainty principle, which states that we can't accurately measure both the position and velocity of something at the same time, even in theory."https://shiken.ai/physics/wave-particle-duality-of-light#:~:text=What is the wave-particle,both at the same time.

Now you have a conundrum! Who is right?

Shiken says: "The Wave Particle Duality of Light is a big deal in quantum theory".

I say: it was a big deal in the 1920's. In modern quantum theory, it's not.

Let's see what Feynman says (page 23 of QED):

You had to know which experiments you were analysing in order to tell if light was waves or particles. This state of confusion was called the "wave-particle duality". ... It is the purpose of these lectures to tell you how this puzzle was finally resolved.

I could go on. Suffice it to say, you have have to pick a reliable source and stick to it. There is nothing more to be learned from popular science sources that continue to emphaise the "state of confusion" of the 1920's as representing modern quantum theory.

My advice: ignore Shiken and all popular sources and YouTube videos, unless they have been specifically recommended. Read Cresser instead.

 

[Nugatory]

A more ambitious alternative is these notes, which are essentially at undergraduate level. If you do want to study these, then you must first forget everything you think you know about QM. I do mean that. You are already a little bogged down in imprecise generalities about QM. Anyway, you might want to take a look at this:

http://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

@vadadagon this is a good recommendation, any less mathematically demanding treatment of QM will be oversimplifying and cutting corners. It kind of has to be that way, because we’re dealing with things that are like nothing we’ve seen in our lifetime of experience with macroscopic objects. Without those comparisons, there’s nothing but the math on which to build our understanding.

But if you’re finding the math too much of a barrier to entry, Giancarlo Ghirardi’s book “Sneaking a look at god’s cards” is worth a try. It is no substitute for a real textbook, but it’s better than most of the pop-sci that’s out there.