Sofia, sorry but I don't understand this question. If B is an absorbing detector, there is no output from it, and additionally, you say you consider only where nothing goes to B. That does not make sense, so obviously I have not picked up on what you are saying. However, also a given photon will take a path - the superposition means it has a probability of taking each, but not that it does take each. If you did not mean that, once again I have misinterpreted, so the problem is not clear, at least to me.

Dear Ian,

Your question is good. So, here is my explanation:

If B is an absorbing detector, there are two possible outcomes from it: 1) NOTING i.e. 0; 2) VACUUM, i.e. |0>.

A) The first issue that my proposed experiment aims at answering is whether the initial state |B0> |1>s transforms unitarily even in presence of a macroscopic, absorbing detector.

If the answer is positive, from B exits VACUUM. The proper form to write that is the transformation (3) in the question

(3) |B0> |1>s → (1/q) ( t|B0> |1>a + ir|B*> |0>n ).

The alternative option, i.e. from the detector B exits NOTHING, is a non-unitary transformation,

(3') |B0> |1>s → (1/q) ( t|B0> |1>a + ir|B*> • 0 ) = (t/q) |B0> |1>a.

You can see that the norm is not preserves, on the LHS the norm is equal to 1, while on the rightmost wing the norm is t/q, where |t| < q, because q2 = t2 + r2.

B) I didn't say that nothing goes to B. I said that B does not report a detection. You see, the 2nd quantization form of writing the transformation (1) (through BS1) is

(1') |1>s → (1/q) ( t|1>a |0>b + ir|0>a ||1>b .

However, QM tells us only what we can get when we do the macroscopic measurement, not what we had before the macroscopic measurement. Therefore, from the equation (1') I can't infer what entered the detector B when it remained silent. Personally, I am SURE that something enters this detector, and I can explain you, but in another post, because it's long matter.

Anyway, I go in my treatment with the unitarity, with the transformation (3).

Now, since I would like to convince some experimenter to perform this experiment, comments are wellcome, s.t. please tell me if I explained myself clearly.

With best regards

The superposed quantum system S entangles with the measuring apparatus A . Assuming Q-bit (2-state) systems, this entangled state is the famous "Schrodinger's cat state" (|S1> |A1> + |S2> |A2> )/√2. It appears to be a paradoxical macro superposition but it is not: It is merely a superposition of correlations. That is, it does NOT say "S1/A1 are true, AND S2/A2 are true," i.e. it does NOT say the cat is both alive and dead. Instead, it says "S1 and A1 are correlated, AND S2 and A2 are also correlated." In other words, "S1 occurs if and only if A1 occurs, AND S2 occurs if and only if A2 occurs." This is not paradoxical. It is exactly what we want and expect. Locally, for an observer of S it says "either S1 or S2 occurs," and for an observer of A it says "either A1 or A2 occurs;" these are random 50-50 mixtures, but the two local outcomes are non locally correlated. This too is just what we want. All this is experimentally verified in such non-locality experiments as Aspect's famous 1982 experiment. The experiment that demonstrates all this most directly is the experiment of Rarity and Tapster in 1990 and the nearly identical experiment by Ou, Zou, Wang, and Mandel in 1900, in which the momenta (rather than polarization) of two photons were entangled. The measurement state (Schrodinger's cat state) cannot be understood without inquiring into the effect of phase changes, and the phase of a cat or other measuring apparatus is not experimentally accessible in this manner, so the non-locality experiments (such as Rarity et. al.) are essential if one is to understand measurement. This has not been done before, so Schrodinger's cat has been a paradox. See my paper "Review and suggested resolution of the problem of Schrodinger's cat," Contemporary Physics 59, 16-30 (2018), also available at my website. A proper understanding of entanglement shows that the entanglement process converts the superposition |S1> + |S2> of S into a mixture and also leaves A in a mixture. This is the collapse (once the result becomes macroscopic, i.e. single and irreversible). Meanwhile, the unitarity of quantum physics is preserved by transforming the superposition of S into a non-paradoxical superposition of correlations BETWEEN S and A. This is essentially how measurement works.

Dear Art,

I am aware that you sent me a couple of messages/comments. I will try to answer them. For the moment I try to reply to the above comment of yours.

You say

"The superposed quantum system S entangles with the measuring apparatus A ."

I AM NOT SURE. The collapse does not say that. Art, please read my last article,

Deleted research item The research item mentioned here has been deleted

It would be easier for us to talk. The article proposes an experiment which tests the collapse, beginning the mathematical analysis, exactly from such an entanglement as you say. It turns out that the collapse does not agree. So, I insist, please read the article.

I would like very much that this experiment be performed, we will learn things from it. Personally, I worry that the experiment would confirm the collapse.

Now, I have to leave the continuation for tomorrow, it's terribly late in my country.

Best regards!

Dear Sofia,

your question belongs to those ones that QM is not answering clearly. In particular, that includes interaction between macro-device and micro-particle. In QM such interactions in principle are described in semi-empirical terms. This also concerns so-called collapse of the wave function (there is no such thing, as can be shown rigorously using probability theory).

1. The best discussion of the subject and related problems of QM can be found in "Lectures on Quantum Theory. Mathematical and Structural Foundations" by Chris J. Isham, Chapter 8, "Some Conceptual Issues in Quantum Theory". I hope you decide to read the entire book. It's short and enlightening, written by a bright mathematician working on problems of math physics as related to quantum theory.

2. On account of the collapse, there are a number of papers by another bright mathematician, Igor Volovich, who proves that so-called wave function collapse, EPR paradox and related problems steam from poor understanding of probability theory as applied to QM. In particular, I recommend his paper "Bell’s Theorem and Locality in Space", arXiv:quant-ph/0012010v1, 1 December 2000.

Good luck!

Wavefunction collapse occurs when a superposed quantum system S entangles with a macroscopic detector (i.e. a system capable of distinguishing between the superposed states, e.g. between the two slits of a double-slit experiment). The "local" descriptions of S, and also of D, then instantly jump into mixtures, not superpositions, of both, while the full global wave function (i.e. the entangled "Schrodinger-cat state") continues evolving in a unitary fashion. These mixtures, predicted by quantum physics, are just what we want. They say that S is either in one or the other (not both) of the previously-superposed states, and D is in one or the other of the two "outcome states." Furthermore, the global state (the entangled cat state) is a superposition of correlations between S and D, not a paradoxical superposition of states of either S or D (which is what Schrodinger thought because he didn't understand non-locality in that early day). This global state is also just what we want: For a two-state system, state 1 of S is 100% positively correlated with state 1 of D, AND state 2 of S is 100% positively correlated with state 2 of D (the word "AND" indicates the superposition). This "superposition of correlations" is demonstrated experimentally by the non locality experiments in which the phases of S and D can be altered. For details, see A. Hobson, "Review and suggested resolution of the problem of Schrodinger's cat," Contemporary Physics 59, pp 16-30 (2018), also my preprint "Quantum realism is consistent with quantum facts" (arXiv). The first reference shows in detail how the "Schrodinger's cat paradox," i.e. the "problem of definite outcomes," is resolved. The second reference reviews this material and then proceeds to resolve the 2nd supposed-paradox of wave-function collapse, the problem of irreversibility.

Dear Liudmila Pozhar,

There is an endless number of articles about the collapse. I, personally, studied a very great number of them, and found NONE satisfactory. If you believe that the " "Some Conceptual Issues in Quantum Theory" ", and/or the material of Igor Volovich, bring a good explanation on the collapse, please be kind and tell us in a few lines the main idea. I appologize to say that I lost a lot of time reading material that people recommend, without finding anything new.

The articles discussing the collapse fall into two categories: those strictly mathematical, and those based on interpretations. I am not interested in more mathematics, but in phenomenology. Usually, the mathematics is not rigorous, introduces non-proved assumptions. The collapse is not part of the quantum theory, it is a postulate.

As to interpretations, there are many, but I'll refer to the most seriously ellaborated: Bohm's interpretation, and the GRW spontaneous localization of the wave-function. Bohm's interpretation introduces the idea of continuous trajectories for particles. I proved this idea false in my articleDeleted research item The research item mentioned here has been deleted

section 5. Please also see my explanation given to Ilja Schmelzer, beginning with the sentences "I owe you an answer for a couple of days already. I appologize!".

The GRW theory is attractive, but I still need some clarifications.

If you are interested, please continue to follow this thread, and the one named

https://www.researchgate.net/post/Could_this_be_a_NO-GO_of_the_quantum_mechanics

And please, it's not enough to mention articles. People are too busy. Tell us in a couple of lines what is the idea. If it is an interesting idea, people would read the article.

With kind regards,

Sofia

The problem with this question is it depends on what you think the wave function represents. Mathematics simply relates symbols, but in physics, strictly speaking the symbols have to represent something in the world. In quantum mechanics the issue depends on what you think ψ represents. If all you do is consider it a mathematical process, then you write your formalism, and in the case of Sofia's question, your answer depends on what your formalism gives you.

I am sorry, Sofia, that I have not tried to give an answer because when push comes to shove, this problem has some similarity to the delayed quantum eraser experiment, and I have argued that there is an alternative possibility, and if the experiment were done properly, you would be able to distinguish them. What should happen depends very much on exactly what the down converter does with a polarised photon, and exactly what happens in the beam splitter. This can be approached by assertion, or one could do the experiment I want done. Most will wave their arms and say there is no need because they "know" what will happen, but if they were that confident, they should simply do it. (In the first step it involves getting the experiment to work as published, then blocking one of the streams of idlers going to the mixer and seeing the effect on the signal photons. The concept is you have to change the nature of what you KNOW gives the effect before you make your choice.)

I agree with Ian Miller that, regarding many of the foundational quantum questions, "the problem with this question is it depends on what you think the wave function represents." Without some agreement on this question, it's hard to see how one can argue about the physical meaning of quantum physics. In my opinion, the wave function represents exactly what it appears to represent: A spatially extended field. For example, an electron exists wherever its wave function (i.e. its electron-positron field) is non-zero. It's squared amplitude, at any particular spatial point and time, is the probability density, given that the electron interacts with some other field at that time, that it will interact at the point in question. This view entails that each electron actually comes through both slits in the 2-slit experiment, and that photons are as big as their interference patterns, i.e. photons from distant stars can be huge. This view, which obviously raises some interesting questions, is defended in my paper "There are no particles, there are only fields," American Journal of Physics 81, 211-223 (2013).

My guidance wave interpretation is quite different. The square of the amplitude represents the energy the wave represents, which from the condition that the phase velocity has to equal the particle velocity, happens to equal the particle energy, and the wave front thus can only spread itself so far, which is not very far at all. The reason that probabilities come into it is the wave defines an energy field that guides the particle and in so doing the probability of the electron, say, being there, is (roughly?) proportional to the energy density. As you can see, this is a bit like Bohm's pilot wave, except I have a precise value for the quantum potential. Who knows who is right, however I dislike the wave front from spreading out like that for a travelling wave because you can propagate a laser beam for an extreme distance without its spreading.

Ian says,

"The problem with this question is it depends on what you think the wave function represents. Mathematics simply relates symbols, but in physics, strictly speaking the symbols have to represent something in the world."

I subscribe. We describe in formulas how becomes the wave-function when passing through devices, fields, etc. If the wave-function is only on the paper, and there is nothing real in the nature, how are felt the devices and fields?

Now, Ian, I understood nothing from the rest you said. Please see, I reformulated now my question after discussions with Art and with Juan. Do your comments with quantum eraser remain in place? If they do, then please explain more clearly because I do not see any issue of eraser here.

Now, you said in a next comment: "The square of the amplitude represents the energy the wave represents, "

That's totally wrong in QM. The energy is connected with the frequency of the wave, not with the amplitude of the wave. The absolute square of the amplitude represents the probability of detecting the particle. It's not classical physics here.

Then, you say "which from the condition that the phase velocity has to equal the particle velocity, happens to equal the particle energy, . . . ". There is no such thing "particle velocity". You either speak of phase velocity, or of group velocity. And in any case, velocity and energy are two different observables, connected with two different operators - phase velocity is connected with the linear momenyum and the energy with the Hamiltonian.

About Bohm's mechanics I claim that it is dead - if you can read the section 5 in my Deleted research item The research item mentioned here has been deleted

As I see you, the section 5 may be difficult for you. Then, I invite you to ask me questions.

With kind regards

Sofia, the issue of the quantum eraser experiment arises because polarised photons from a down converter go through beam splitters. My issue is exactly what to the splitters do, why, and what, if anything, will permit sorting?

You detect the photons as single hits, and by having a different distance between detectors and the down converter, you can work out when the photons were emitted from the down converter. They are emitted as pairs. You know when they were detected, one at a time. So the photons went from A to B as single entities. I call that a particle. I don't mean it his a little ball bearing, but I do mean it is a discrete entity of finite volume, and it travels with a velocity c.

If you have a wave and a particle, the argument is the wave has to have a phase velocity equal to the particle velocity, i.e. I have proposed that there are two entities. Do I know there are? No, no more than you know there are not, BUT if they are, then in my opinion, the rest follows. Unfortunately, the reasoning is too long for a post here - I wrote it up in my ebook "Guidance Waves". From the point of view of chemistry, you find the concept that the square of the amplitude reflects the energy greatly simplifies the calculation of covalent bond energies, which I show, WITHOUT any of the validation processes that can fix up to fifty constants in the standard procedure. My argument is that with fifty adjustable constants, if you can't get good agreement with observation, then there is something wrong with you, but the agreement does not mean you are correct. Finally, the argument that ψ.ψ* reflects probability is also an assumption - it is obviously roughly correct, but what determines it? Where is the physics that says that, not counting the interpretation. (There is nothing wrong with having an interpretation, but having one does not mean that something else is not in play.) (As an aside, in my opinion, if you accept the standard use of probability distributions to determine the so-called screening defect, then the equation Div D = ρ is violated. If anyone can show how it is not, I would be interested to hear it.

Ian,

who told you that polarized photons from down-conversion have to go through beam-splitters? In the experiment I describe I don't speak at all of polarization. The problem I pose whether there can be an entanglement between states of macroscopic bodies and states of microscopic bodies.

I don't care when were the photons emitted. When an idler photon is detected I know that I have in my apparatus a signal photon. Neither do I care of "particle velocity" - I repeat, in QM there is no such thing as particle velocity, we have either phase velocity or group velocity. Also, I am not in the Bohmian mechanics to speak of wave-guide, the value of ψ.ψ* is not an issue here. I am afraid that whatever you say is alien to my question

I examine the case in which the detector A does not give a response although a wave-packet |1>a passes through this detector - see the formula (1). It's a case that has to rise questions: how can a wave-packet pass through an ideal detector and not produce a detection?

Next, I pose the problem how does look the wave-function after the wave-packet |a> passes through the detector A which, though, remains silent. There are two possibilities: either we have collapse of the wave-function on the wave-packet |b>, or the wave-function becomes of the form (3).

I see no connection of what you say with my question. I suggest you to read again the question.

With kind regards

Sofia, the photons from a down converter are entangled and are polarised. Whether you make use of the polarisation is irrelevant, but it might affect your experiment. In answer to the question : how can a wave-packet pass through an ideal detector and not produce a detection? Strictly speaking, if you consider the photon as a particle it can't, unless the detector is not 100% efficient, in which case you can't know the photon went that route. However, it appears we are talking at cross-purposes, so there is no point in my continuing.

Dear Sofia,

1. I already offered you and advice to read 2 RIGOROUS publications on the subjects you seem to be interested in. They are the best, from my point of view. Moreover, I already mentioned that there was no such thing as the wave function collapse. Instead, there is RIGOROUS math behind that specific change in the wave function. Same concerns EPR pseudo-paradox. There is also a very interesting generalization of the Bell theorem due to Volovich. To understand this, one has to use proper probability theoretical methods. I suggest again, you read Volovich's paper first.

2. I do not have time to invest it into translating already publishes information for you in my own words. I am sorry, but you have to study those papers on your own. If you still have SPECIFIC questions, and I have time to help you, I will. However, your question must be specific, rather than of philosophical nature, or questions on some empirical approaches to already rigorously explained issues, because I am not interested in empiricism.

3. Indeed, there exists a lot of (primarily, semi-empirical) publications concerning issues of quantum measurements, macro-micro interactions (related to the phenomenon that empiricists call "collapse of the wave function"), entanglement, and such. Instead of playing empirical games, one has to use rigorous mathematical approaches to analyze and understand those issues. Many developments have already been done toward that goal. I know that many physicists find it difficult to do such meticulous math job, and prefer to tackle those issues emirically or semi-empirically. I do not support such approaches, and am not going to discuss them, as they are not really scientific. It's up to you, which way to follow.

Good luck!

@Liudmila Pozhar,

Dear lady,

You say that you do not have time. Please believe me that I also don't have. In general people are busy, s.t. nobody would read an article just because you recommend it, without saying what is the idea in it. If you realize, there are tens of people who recommend to read this and read that.

About the advices on using rigorous mathematics in QM, I am sorry for the time you wasted, I past a very long time ago the stage of needing such advices.

I modestly tell you that when I recommend a material, I describe in a few lines the idea, out of respect for the time of the people. I believe that I also deserve some respect. I lost a lot of time in the past with "excellent articles" recommended by specialists who had no time in giving a few lines about the main idea, and after reading those article I found that is either "more of the same" or the authors knew less than I, etc.

A person who recommends a material is supposed to know what is in it, and be able to describe the main idea in a few lines. I don't read a material because somebody thinks that it is good, but if I estimate that it contains an novel and worthy idea. So, I have to know what is the proposed idea.

All the best

As an aside, you cannot answer this question through mathematics. The "wave function collapse" is critically dependent on what you think ψ represents. Since there are different interpretations, it follows there will be different answers. However, if a detector does not register, you would normally assume that path was not used for that photon.

Sydney, in my opinion, there is a difference. In physics, in a mathematical expression, each symbol has to refer to something physical; in mathematics, it can be anything. In Physics, the expressions have to illustrate nature; in mathematics there is merely the need for everything to be logically self-consistent. Maybe I am not expressing this very well, but I see to recall there is a Youtube video from Feynman on this issue.

Sydney, Ian, and everybody,

It's no news that quantum theory is rigorous science and one has to know very well the formalism for discussing QM. (Of course, not everybody is a high specialist in QM, but everybody may ask questions for clarifying what he/she doesn't understand.)

But, there is a poin here. The danger in restricting oneself to the mathematics, is that one forgets that physics is a theory about the nature. In our days, in universities, people are so intoxicated with the formulas that they loose any contact with the phenomenology - the famous "shut up and calculate". Such an attitude is harm, since the quantum theory has many contradictions, at present there are many question with no answer. If one won't think about the phenomenology, one would stay with the illusion that everything is solved - and that is absolutely false.

Dear Sofia,

1. I recommended two best publication that would answer your questions. READ THEM first, and then ask questions later, not vice versa. A natural science student MUST INVEST TIME in his/her own thinking over his/her questions and answers, and do not expect someone else chewing those for him/her to swallow.

2. There is no point in wasting time to prove to you my credentials, as they have already been proved by my publications and experience. Type in Google Scholar my name, and you will find out. Or even this is too difficult for you?

Good luck!

Dear Liudmila,

I am not your student, neither do I work for you, and even more, without payment. I am ready to read your material even without you telling me the main idea, if you'd pay me 10,000$ per hour.

Did I make myself clear?

About who are you - credentials - I am not interested. I estimate people by what they know, and that goes by what they say. To the two questions I formulated, i.e. whether the detectors LIE to us, and whether there exist entanglements of microscopic bodies with states of macroscopic bodies, you could have answered by YES or NO, without so much negociations. If YES (or NO) you could have told me in a few lines what is the argument of your preferred author(s), and I would have decided if it is convincing. I have enormous doubt that somebody has an answer rigorously provable.

Most of the authors write discourses which are just brain-wash in favor of one idea, usually showing lack of knowledge of the last rigorous proofs, and also presenting no rigorous arguments for ruling out the opposite idea(s). There are mountains of such works in journals and I am sick with them. I can't afford to say more, although it's on the tip of my tongue.

I wounder; how can you do experiment with a "linear polariser" when it is known that the EM-field around a photon is rotating! How is such a photon interaction with a "linear" polariser? It's not possible to draw any definite conclusion on the data from an experiment using such a device, without giving a detail desciption of the interaction between the photon and the polariser.

@Stellan Gustafsson

The linear polarizer is standard material explained in text-books. Even in Wikipedia you can find the topic polarization of e.m. field.

Dear Sofia,

1. People, who do not need anyone's help, do not post questions on Research gate. If you were a self-sustained person scientifically, why did you ask me to explain major points of the publications I referred you to? You have to learn logic, and only after that quantum mechanics, not vice versa.

2. Also, learn to thank people for whatever help or response you received to your questions or statements. Further demands, especially on other people's time and in a rude form, are disrespectful and will not be honored.

2. Any scientist is a student of nature. Your statement suggests you are not a scientist, most likely, for the better. Also, I do not think anyone, including myself, would be pleased to have you as a student (even for your $10000 :):):).

3. I suggest you stop messaging me, as I do not find your communications informative, civilized or pleasant.

Good luck!

If "linear polarisers" are used as standard material, to examine a "rotating" photon then, this would put in question all results of such experiments! Entanglement might then just be a misinterpretation of experimental data!

@Stellan Gustafsson

There is no rotating photon. There may be circular polarization, |x> + i|y>.

Then, what's your problem with linear polarizer? It just cuts off, say, the polarization in some direction, say, u, and the photon is either absorbed, or transmitted with a polarization in the direction v, perpendicular to u.

What's the problem?

Dear Sofia,

Polarization is a phenomena of coherent phases of many photons or particles, a single photon is a rotating entity.

A linear polariser could for example force the photon to change its phase, modify its velocity of rotation and probably produce other problems also!

Yes, it obeys the collapse postulate (which thus does not need to be postulated because it is a logical consequence of the unitary evolution plus entanglement). Consider a two-state quantum system S in a superposition state |S1> + |S2> (I will omit normalization for simplicity). "Measurement" by a macroscopic detector D occurs when S entangles with D to form the "measurement state" or "Schrodinger's cat state" |S1> |D1> + |S2> |D2> where |D1> and |D2> are macroscopically distinguishable states of D. This state has often been interpreted as a macroscopic superposition in which D is in the two states D1 and D2 simultaneously. This, if it were true, would be a nonsensical paradox. But it's not true. Both quantum theory and experiment testify that the cat state is not a superposition of states of either S or of D, but rather a superposition only of correlations between the states of S and the states of D. For the relevant theory, and also one of the many experiments that show this, see M.A. Horne, A. Shimony, and A. Zeilinger, "Introduction to two-particle interferometry," in "Sixty-Two Years of Uncertainty," ed. by A.I. Miller (Plenum Press, New York, 1990). The cat state has precisely the non-local properties needed for a measurement: D and S are connected in such a way that each "knows" the phase setting of the other system no matter how widely separated they may be. Locally, S is in a mixture |S1>

Path integral is part of the formalism of QM. Entanglements are fully explained in base of the formalism. As to the future, it is not known!

If |S1> |cat alive> + |S2> |cat dead> can exist, then also |cat alive> + |cat dead> can exist. It is sufficient to bring |S1> and |S2> to a beam-splitter, and read the outcome, for forcing the states |cat alive> and |cat dead> to be in a superposition.

"Both quantum theory and experiment testify that the cat state is not a superposition of states of either S or of D, but rather a superposition only of correlations between the states of S and the states of D. For the relevant theory, and also one of the many experiments that show this, see M.A. Horne, A. Shimony, and A. Zeilinger, "Introduction to two-particle interferometry," "

A cat is not a "particle", it is a complex macroscopic object consisting in complex structures containing, each, a huge number of particles. I repeatedly reminded that Feynman showed in his book on path integral, that when ħ is by far smaller than the action function, the phase of the wave-function oscillates extremely rapidly, the values cancel one another, and only one path remains possible - i.e. we return to classical mechanics and to the principle of minimal action. It's not possible to make theories on the QM ignoring facts so widely confirmed.

"The cat state has precisely the non-local properties needed for a measurement: D and S are connected in such a way that each "knows" the phase setting of the other system no matter how widely separated they may be."

The cat is nonlocal? Bravo! Did somebody see a nonlocal cat?

As to the statement that each entangled particle "knows", that's lack of understanding of how the entanglements work. No particle "knows" anything! Moreover, the future is not known! No particle knows which choices will make the "other" experimenter in the future.

Entanglements are results of the interference of joint amplitudes (amplitudes preceding products of states of the two particles). The fact that from the preparation step, some of the combinations of results are eliminated, when the particles pass through devices, other combinations of results are destroyed. For instance, in the polarization singlet |x>A |x>B + |y>A |y>B, if Alice measures in a bases {|x'>, |y'>} and gets x', the wave-packet |y'>B is DESTROYED by two-particle interference of joint amplitudes. It's a simple exercise for a student to show this fact.

I am sorry, but I just cannot agree with your first sentence "If |S1> |cat alive> + |S2> |cat dead> can exist, then also |cat alive> + |cat dead> can exist." The entangled superposition and the direct superposition are two quite different situations. Your second sentence does not explain your first sentence. To put this another way: |cat alive> + |cat dead> has nothing to do with the micro system S, it is simply a superposition of a macroscopic system (and physically unrealistic of course). The entangled state of S and the cat is physically realistic, however, since it is merely a superposition of correlations between two systems rather than a superposition of states of either system.

Dear Art,

I don't know what is "superposition of correlations". I invite you to test this superposition of correlations with a beam-splitter. It is in absolutely agreement with the QM formalism to bring the two states, |S1> and |S2> of the microscpic system, to the two inputs of a 50-50% beam-splitter. For example, the state |S1> can be a downwards traveling wave-packet, and |S2> an upwards traveling wave-packet.

The beam-splitter indices the transformation

(1) |S1> --> (1/√2) ( |S'1> + i|S'2>); |S2> --> (1/√2) ( i|S'1> + |S'2>);

I advise to introduce on the input path of |S1> a phase-shifter by π/2. It is also in absolute agreement with the QM formalism. Then the "superposition of correlations"

(2) |ψ> = (1/√2) ( |S1>|cat alive> + |S2>|cat dead>)

transforms into

(3) |φ> = (1/√2) [i|S'1>( |cat alive> + |cat dead>)/√2 - |S'2>(|cat alive> - |cat dead>)/√2).

The entanglement (3) is as valid as the entanglement (2), because it was obtained by operations in absolute agreement with the QM formalism.

Next, we can read the outputs of the beam-splitter, nothing forbids us. If the entanglement (3) is correct, then, if we obtain the result S'1, the cat is left in the superposition (|cat alive> + |cat dead>). If we obtain the result S'2, the cat is left in the superposition (|cat alive> - |cat dead>).

I repeat the chain of steps, which are in absolute agreement with the QM formalism: we are permitted to bring |S1> and |S2> to a beam-splitter. Therefore, if the "superposition of correlations" (2) is correct, then the "superposition of correlations" (3) is also correct. We are permitted to read the outputs. Thus, if we obtain the result S'1 the cat remains in the superposition (|cat alive> + |cat dead>), but if we obtain the result S'2, the cat is left in the superposition (|cat alive> - |cat dead>).

Thus, the "superposition of correlations" leads to the generation of the absurd states (|cat alive> ± |cat dead>) by trivial procedures in quantum experiments. The conclusion can be only that, since the (|cat alive> ± |cat dead>) is impossible, the "superposition of correlations" (2) is impossible.

NOTE: I also remind Feynman's path integral, which was never contradicted. By the path integral theory, a macroscopic object has a precise trajectory, NO WAVE-FUNCTION. It is forbidden to confuse between a microscopic state - for which the ratio between the action function and ħ is small, and a macroscopic state - for which this ration is HUGE and in fact destroys the phase, leaving only one possible path - described by the Euler-Lagrange equations.

If somebody thinks that I did a mistake, I challenge him/her to show where is the mistake. Also, I challenge him/her to prove that the path integral theory is wrong.

I do not think that there are any problems with a priori superpositions, this is just a probabilistic question, not a mixture of two

incompatible things. Measurement resolves this as to one or the other, restoring reality.

Details of how measurement really works, ie. alternatives of collapse, entenglement and so on are very delicate questions,

which I do not bet on yet.

I think that the entanglement is a hoax!

Of coarse you can produce pairs (or more) of particles (or photons) with anti symmetric characteristics. This can be done in various ways. But, to prof entanglement, you should show that if you modify some characteristics of one, you should simultaneously obtain a corresponding change in the other.

According to my knowledge this has never been done!

The main problem could be a misunderstanding of polarization and characteristics of the individual particles (photons) characteristics (using linear polarizers to detect rotating particles).

Responding to Stellan Gustafsson: This is precisely what is done in all sorts of entanglement experiments, but it's a little more subtle than you indicate. You cannot expect photon 2 to itself show a corresponding change when photon 1 is altered, because such a change would be directly detectable at the position of photon 2 and could hence be used as a means for Alice (at photon 1) to send an instant signal to Bob (at photon 2), violating special relativity and violating causality because such a signal could, according to SR, allow a signal to be sent to the past ordering someone to murder Bob's or Alice's grandparents (a contradiction). Thus, the change in behavior must be accomplished with CORRELATIONS BETWEEN photon 1 and photon 2. Bell's theorem shows this is exactly what happens: When Alice alters photon 1's phase, the correlations between the two photons instantly change and Bell's theorem tells us that this change cannot have been due only to a change in the behavior of Alice's photon--the two photons must have cooperated to accomplish this change. Thus, non-locality happens in the real world, but since only correlations are involved and correlations cannot be used to send a signal, there is no violation of SR or of causality.

Dear Art Hobson You belive to much in theory. If you want to make a real discussion, let us take a given experiment and discuss the result. You seems to be more a specialist then me, so I give you the right to chose an experiment to your liking.

But maybe such a discussion is outside the purpose of this tread. So why not make a new tread to examine entanglement in general?

@ Stellan,

Would you kindly read the

https://en.wikipedia.org/wiki/No-communication_theorem

It proves rigorously that whatever change does one of the experimenters (Alice or Bob) in the particle landing in the lab of that experimenter, the other experimenter won't know that.

Now, I want to call your attention that my question is about macroscopic measurements on quantum systems and the so-called "collapse" of the wave-function. These are topics about which no current material is satisfactory - topics of research. My question is not about entanglements and not about polarization. Such simple material can be found in Wikipedia.

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

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

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

If you don't understand what's written there, you may ask a question of yourself. I appologize a lot, but I am not glad that my thread be modified, especially with standard material of text-books. Please understand me! Open questions of yours, and you'd get many answers.

With kind regards,

Sofia

Entanglement depends on how it is defined. The simplest explanation of entanglement is that two entities are created with correlated properties through the application of a conservation law. I devote a chapter to the Bell inequality issue in my ebook "Guidance Waves", and I show why the rotating polarizer experiment does NOT show violations of the inequalities, the reason being there are insufficient independent measurements made to generate the required number the inequalities require. This is simple logic, and I show what people assert to be independent measurements cannot be so because they violate the associative law of sets, upon which the inequalities require. (Actually, so does all mathematics.) Either prove the argument wrong, or accept it. As an aside the whole issue is dependent on the assertion that the variable is DETERMINED on measurement, as opposed to merely being measured. This is a simple example of how quantum formalism inserts quite unproven physics, which in the case of entanglement borders on magic, and it is all swallowed uncritically. You cannot prove a value of a variable was not determined physically prior to measurement, but the possibility is never considered by most. Just because Bohr thought so does not make it so, as for that matter, neither did Claudius Ptolemy thinking the Earth was the centre of the Universe make it so.

Hi all,

I think that basic laws of physics, like conservation of energy and signal speed (c) to be the local speed limit, are logical and proven laws.

The theory of entanglement is based on some experiment, with very doubtful experimental setup and analysis.

A detail discussion of entanglement can be done only by a detail analysis of a given experiment. If somebody can propose an (according to him or her) convincing experiment, i would be happy to participate.

Juan, my friend

I invested tens of years of my life on studying how measurement really works, the collapse, etc. I consider a SHAME for the human mind, the fact that we don't understand yet these processes.

The issue of collapse is partly outside of the quantum theory. The classical measurement on a quantum object is usually supposed to begin with an entanglement between the microscopic object we measure, S, and a microscopic part q of the measurement apparatus

|S1>|q1> + |S2>|q2>.

This is von Neumann's so-called "premeasurement". For instance, in an ionization chamber, S kicks out an electron from an atom ( |S1>|q1> ), or doesn't ( |S2>|q2>). But the entanglement extends: if the detector is placed in an electric field, the electron ( |q1> ) is accelerated and kicks out more and more electrons from their atoms. We get an avalanche, a current, which is already a macroscopically observable phenomenon. It's the classical electromagnetism that deals with it, not the quantum mechanics.

This conceptual model of measurement, quite typical, was proposed by Prof. Art Hobson.

I, personally, think that the "decision" whether a lot of electrons are kicked out, OR not, is taken in the interval of time BETWEEN the quantum and the macroscopic phase.

There is a theory that MAYBE can help: Feynman's theory of path integral, treated in a book of Feynman and Hibbs. But Feynman did not deal with the case when the wave-function is a superposition of wave-packets. Moreover, he dealt in detail with the extremal cases, i.e. the quantum case and the macroscopic case, not with the evolution in between.

@Stellan,

It's very unlikely that somebody would bother to open a thread for you. It's for YOU to open a thread if you have a question, and I'd be glad that elementary material be treated elsewhere than in my thread.

The issue of entanglements was theoretically and experimentally clarified slightely after the middle of the PAST century (1964). For the beginning, you can look in the arXiv:quant-ph for Bell's theorems (or inequalities), the CHSH inequalities, and Aspect's experiments, or the Rarity and Tapster experiment. There are many more experiments. Whatever you have to do is TO READ.

Ian, please!

My question is not about entanglements. It is about a much more difficult issue. Posting comments on other phenomena, it's non-desirable, all the more that entanglements were so widely studied.

Please be kind with me!

With thanks in advance

Sofia

Indeed, the Feyman theory only shows in what sense his trajectories have in number to do with the classical

resulting path, but is far from proposing what measurement might be like, except perhaps bundling everything within

Classically aceptable error of measurement.

Gustafson

Yes experients and their careful analysis have played a crucial part in the historical development. Now with picosecond

accesability there should start to be more progress.

My Dear Sofia,

You said:

"I consider a SHAME for the human mind, the fact that we don't understand yet these processes. "

Let me said: you are amazing!

And let me said too: "I consider a SHAME for the human mind-especially for those who surrendered- the fact that we don't understand yet these processes."

With best regards.

My dear Mazen,

You are lovely, as always. And I subscribe to the idea that we should not surrender, that we have to be stubborn and insist in research.

With kindest regards.

Dear Stam,

As I said in my message to you, I am not happy with your operator

M = sum_(a,b) m_(a,b)|b> + β|living cat>. See the proofs of the above physicists. Moreover, dead cat and living cat are not quantum states, but macroscopic states. I'll tell you more, privately.

With all the best wishes!

At any rate once the Quatum system is forced to jump to one of the possible eigenstates, the superposition is kaput,

the measurement is complete. It would take maybe a very short time analisis to see exactly how this develops.

Therefore I see it as more of an experimental question. Even very able people are not able to decide purely on theoretical

grounds. Experimentalists know that it is quite an art to set up their equipment and rule out spurious effects.

Juan,

How do you know the superposition is "kaput"? You can know nothing about a part of the wave-function that "said nothing".

Temporarily for that instance, that measurement. After a short time all is normal again, and there may be different measurements. For that initial measurement the state remains to where it jumped to for a short time, remember that a second measurement immediately following the first yields the same result.

Dear Juan,

I didn't finish yet reading what von Neumann said about measurement. It's a few tens of pages.

I am not sure that after a measurement the superposition is "kaput". It seems to me that it's us, who make it "kaput". We select only a subset of particles that gave a certain answer, and describe the subset by the eigenstate specific to that answer. I mean, we don't care what happens with the rest of the expression of the original wave-function.

You see, the wave-function is something we write on the paper. But the paper has no interaction with fields and devices through which our quantum system passes. How does the wave-function know of these fields? There is some "thing" that travels in the apparatus and feels all these fields.

When we perform a macroscopic measurement, in some trials it's a certain part of the "thing" that gives an answer, e.g. one of the wave-packets, say |a>. In other trials another part of the "thing" gives an answer, say, the part we describe by the wave-packet |b>. We may collect together all the particles that gave the answer b, and redefine their description asr the wave-packet |b>. But the part |a> of the "thing", what happened with it? Did it disappeared just so? It's an assumption that raises doubts.

The rest just, temporarily at least, dissapeared.

Juan,

"The rest just, temporarily at least, dissapeared."

How do we know this? Which experimental evidence we have of that?

Tell me, are you aware of Vaidman's "Noninteracting measurement"? Vaidman's experiment seems to tell us that the part of the wave-function that didn't click the detector was though absorbed by the detector (if the detector is absorbing), but the detector "shut up", didn't report.

I argue that when the quantum system jumps to a single state, and remains there a short finite time, this constitutes a measurement in some cases.

It is quite obvious that during this short time there is no superposition.

This is I think a minimum requirement to be able to talk about a measurement at all, and believe this coincides with experimental experience in some situations, as far as my knowledge extends.(ie. detection of a spin state)

Talking about atomic transitions, there are cases where multiple transitions are taking place at the same time, reflected in a spectrum with different lines, we could talk about multiple measurement.

In this cases it seems that there are simultaneous eigenstates with transitions.(an ongoing superposition?) It depends on the kind of experiment.

In other cases you can talk about transitions between spin states (epr), which depends on both states being relatively well defined together. So the standard story about measurement should be cualified in many cases.

That a state be well defined or not depends on the time it can subsist, according to the uncertainty principle.

Juan: "I argue that when the quantum system jumps to a single state, and remains there a short finite time, this constitutes a measurement in some cases."

No, it's not a measurement, but a measurement that by chance is done at that moment, would confirm that state.

Juan: "It is quite obvious that during this short time there is no superposition."

Aaaa! Now I understand where to you drive. You try to say that from a superposition of states the quantum system changes to a single state? I.e. the GRW (Ghirardi, Rimini, Weber) theory.There is no such thing. A state |a> + |b> doesn't jump ocasionally to |a> alone, or to |b> alone. If such a jump would happen, we would not get interference when we bring |a> and |b> to superpose. Superposition between |a> and nothing, or |b> and nothing, does not produce interference fringes.

Now, my example was with entangled particles. That was the proof against the idea of particle. You ignored my example.

I suggest you to leave atomic transitions, and multiple atomic transitions. You don't clarify a problem by complicating it. Entanglement of two particles is a trivial item that we produce in our labs, and it is enough for judging the issue. No need of complications.

So, it's the entanglements and the relativity of simultaneity, that advocate against the concept of particle.

No Sophia, this is not GRW alone, but standard orthodox quantum theory.

(Of couse you can choose not to believe it)

You can only have interference from some sort of superposition, usually spatial.

Of course you dont get superposition when it jumps. It means a click in your detector. or single spot.

Again my thesis is you cannot have both relativity (at least classical relativity) and a quantum particle at the same time.

You must choose theories. You cannot believe both (at the micro scale anyway).

The best, juan

Juan,

I don't understand what you say. You write tellegraphically, s.t. it is not understandable.

At another thread, "https://www.researchgate.net/post/Could_this_be_a_NO-GO_of_the_quantum_mechanics",

I explained what we mean by "particle" at low energies. It's Bohm's type of particle, i.e. something floating in the wave-function. Did you read that explanation? I am not sure whether we speak about the same thing. So, did you read?

"No Sophia, this is not GRW alone, but standard orthodox quantum theory."

No, WHAT?

Juan, you don't need to convince me that one has to choose between "particle" and relativity. The "particle" looses with or without the relativity. Imagine the wave-function of an electron in the form |a> + |b>, and both wave-packets pass through electric fields as in the picture. Imagine that for a short time as you say, the "particle" jumps from the wave-packet |a> to |b>. Then, for that short time, in |a> there is no charge s.t. it does not feel the influence of the field. QM does not permit such a thing, each wave-packets should feel the respective field all the time.

What I say is a weak point for the GRW too, with their spontaneous localization. If for some time the wave-function is no more |a> + |b>, but, say, just |b>, then |a> does no more feel the field for that time, because |a> does not exist for that time. QM does not permit.

You see, with or without relativity, with or without entanglements, the idea of "particle " in Bohm's style, is untenable. For the time the "particle" stays in one wave-packet and not in the other, the wave-packet without particle does not behave according with QM.

I also have a thesis - it's more an impression, because I didn't prove it rigorously. If something is not according to the way the Nature works, and we show that it goes wrong vis-a-vis the relativity, it should go wrong also without applying to the relativity.

Bottom line, we have to accept that we should speak of waves. The fields act on the wave-packets regarded as waves, not as possessing a particle floating inside one or another of the wave-packets. That means, both |a> and |b> carry the electron charge.