The "collapse" postulate says that if part of the wave-function produces a click in a detector, the rest of the wave-function disappears. In the experiment described here, it is shown that no part of the wave-function disappears, namely, given a superposition of two wave-packets, while one wave-packet produces a click in a detector, the other wave-packet produces observable interference effects.
A quantum system is prepared in a state with maximum one particle, a photon, A;
(1) |ψ> = q{ |0>A + p( |1;a>A |0;b>A + eiθ |0;a>A |1;b>A ) },
see figure.
It is shown below that while the wave-packet |1;a>A
The wave-packet |1;b>A illuminates one side of the 50-50%beam-splitter BS, and on the other side lands a coherent beam
(2) |α> = N( |0>B + peiα|1>B + . . . ).
where N is the normalization factor. Thus, we have the total wave-function
(3) Φ = |α>|ψ> = Nq( |0>B + peiα|1>B + . . . ){ |0>A + p( |1;a>A |0;b>A + eiθ|0;a>A |1;b>A ) }.
At the beam-splitter the following transformations take place
(4) |1>B → (1/√2) ( |1;c> |0;d> + i|0;c> |1;d>);
(5) |1;b>A → (1/√2) (i|1;c> |0;d> + |0;c> |1;d>).
Introducing them in (3) one gets the following IMPLICATIONS:
(6) For θ = α - π/2, every click in the detector D is preceded by a the detection of the wave-packet |1>a in the detector U.
(7) For θ = α + π/2, every click in the detector C is preceded by a the detection of the wave-packet |1>a in the detector U.
Thus, one can see that by changing the phase θ, carried by the wave-packet |1;b>A , one can switch between a joint click in D and U, and a joint click in C and U.
CONTRADICTION: one can see in the figure that BS is more distant from the preparation region than the detector U. So, if the collapse hypothesis were correct, the tunning of θ would have no effect, since when the detector U clicks, the wave-packet |1;b>A would disappear instead of reaching the beam-splitter BS.
CONCLUSION: No part of the wave-function disappears - no collapse.
What does |1,b> mean in your notation? That there is the particle heading in b path? Then |0, a> is no particle in "a" path and U does not click.
@Ilian
The "collapse" postulate says that if part of the wave-function produces a click in a detector, the rest of the wave-function disappears. In the experiment described in the question, it is shown that no part of the wave-function disappears. Namely, given a superposition of two wave-packets, while one wave-packet produces a click in a detector, the other wave-packet produces observable interference effects.
If you want to comment my experiment, read it: experiment, implicatins, contradiction and conclusion.
If the criticism of the concept of collapse of the wave-function represents the first step of a more general criticism towards methods and contents of QM, that is based on the Indeterminacy Principle and on the probabilistic wave-function, then subsequent steps could represent a meatier basis for a productive Exchange of views.
P.s. I observe you make use of the two concepts of "wave-function" and "wave-packet". Are there differences between the two concepts in your interpretation?
@Daniele,
"If the criticism of the concept of collapse of the wave-function represents the first step of a more general criticism towards methods and contents of QM . . ."
I am on the side of standard QM, not against. But the collapse postulate is alien to QM.
"Are there differences between the two concepts in your interpretation?"
The wave-function is, in some cases, a quantum superpositio of a couple of wave-packets. Look at the formula (1). The wave-function is a superposition of a vacuum component, and two wave-packets with number of particles 1. I.e., in non-rigorous language, the particle is either in one or in the other of these two last wave-packets.
"the collapse postulate is alien to QM".
It depends on interpretations.
"I am on the side of standard QM"
I have instead a critical view of fundamentals of QM.
@Sofia
You wrote: 'The "collapse" postulate says that if part of the wave-function produces a click in a detector, the rest of the wave-function disappears.'
This is what standard QM says and you simply dont apply it. If you apply it your want have interference according to standard QM and would not show that 'In the experiment described in the question, it is shown that no part of the wave-function disappears.'
In the answer to Sasso you replied my question about what is |1,b> ' Two wave-packets with number of particles 1. I.e., in non-rigorous language, the particle is either in one or in the other of these two last wave-packets' - this what i wrote exactly. So it is all as I wrote in my first post.
So according QM there would be no interference (by the way this is Hong Ou Mandel interference you want to use with an empty wave). But if there is no collapse (e.g. if you adhere to Broglie Bohm interpretatiin) it would be possible to see both particles on the same side after beamsplitter2. I am not adicted to QM explanations at all. I think that there is a physical wave (or something) and it does not dissapear after the click. So try and do this exp. But it is not easy because you have to look for coincidences in time (look at HOM exp).
I have proposed a simpler exp. in a post earlier on RG. I will make efforts to fulfill and see if the collapse destroys totaly the WF. It would not be easy because the technical conditions by my side are not exellent and there would be too many people involved.
@Ilian, it's hard to follw what you say because the are a couple of errors with English. I repeat your statements here, while correcting the language
" You wrote: 'The "collapse" postulate says that if part of the wave-function produces a click in a detector, the rest of the wave-function disappears.' This is what standard QM says and you simply dont apply it. If you apply it your want have interference according to standard QM and would not show that 'In the experiment described in the question, it is shown that no part of the wave-function disappears.' "
Ilian, standard QM doesn't say that something disappears. (It is known that the collapse postulates is outside of the QM.) This is exactly what my calculus attacks, the disappearance of the wave-packet |1;b>A. Look at the picture! The detector U is closer to the preparation region that the detectors beam-splitter BS. So, if the wave-packet |1;b>A "disappears" as a result of a detection in U, the phase θ cannot reach the beam-splitter, because the wave-packet carrying this phase is |1;b>A.
Now, if the phase θ doesn't reach the beam-splitter, tunning θ to the values α ± π/2 won't have effect.
This effect appears exactly in the trials in which U clicks. It goes as follows: if we have a click in D and if θ was tuned to α - π/2, U is forced to click too. But if θ wasn't tuned to α - π/2, U is not forced to click.
Swithching θ from α - π/2 to α + π/2, we tell the dedtector U to tell in conjunction with C, i.e. if C clicks, U is forced to click too.
But, if you destroy the beam |1;b>A these implications disappear.
Besides, you read my article about the end of the wave-particle duality. You know that the wave-function may have effect in a couple of places. However, as I told you in a comment there, if the wave-function carries a single quantum of energy, it can be delivered only in one place. In my experiment, when the quantum is delivered to the detector U, the wave-packet |1;b>A is some sort of EMPTY WAVE. It does interference but delivers no quantum of energy, i.e. what triggers the detection in D or C is the photon from the coherent beam, not |1;b>A .
Ilian, leave Hong-Ou-Mandel, it's not the case here. I don't examine trials in which one gets a double detection in D or in C. I examine cases with ONE detection in C or D, and ONE detection in U.
Also, I don't discuss de Broglie-Bohm here, I discuss precisely the experiment described in the question. Though, I don't see a contradiction between de Broglie-Bohm and my conclusion. de Broglie Bohm didn't tell us that something disappears. I believe that the Bohmians can be happy with this experiment.
With kind regards and Happy New Year!
Sofia sory for the delay.
Answer: I can’t see what you have corrected, but there are really some errors due to changes made by the poor RG editor programme.
So I change them in your ‘changes’. "
You wrote: 'The "collapse" postulate says that if part of the wave-function produces a click in a detector, the rest of the wave-function disappears.'
Answer: TThis is what standard QM says and you simply don’t apply it. If you apply it you won’t have interference according to standard QM and would not show that 'In the experiment described in the question, it is shown that no part of the wave-function disappears.' "
If you believe QM is the Schrodinger equation only, then it is true that “standard QM doesn't say that something disappears”.
You wrote: ‘(It is known that the collapse postulates is outside of the QM.)’
Answer: Not in the books I read so far!!! Von Neumann is surely in QM!!!
You wrote: In my experiment, when the quantum is delivered to the detector U, the wave-packet |1;b>A is some sort of EMPTY WAVE.
Answer: |1;b>A can not be empty wave! |1; ..> here stands for the particle (carring the click via quantum of energy). The empty wave is |0; ..>.
You wrote: Ilian, leave Hong-Ou-Mandel, it's not the case here.
Answer: I don’t know what makes you believe you can have 1 photon type interference with two different photons. All I know is an experiment that uses different photons from one and the same laser. (but different lasers with different wavelenght?)
@Ilian: "This is what standard QM says and you simply don’t apply it. If you apply it you won’t have interference according to standard QM and would not show that 'In the experiment described in the question, it is shown that no part of the wave-function disappears.' "
Ilian, you cannot fight the quantum formalism. I apply nothing else than the QM standard formalism.
To your attention, the collapse postulate IS NOT part of the QM standard formalism, we apply it BY HAND. In my proof I applied nothing by hand. This experiment can be performed in practice, I am looking for a lab that possesses suitable sources of coherent beams.
Empty waves: you cannot change the definition used in literature. An empty wave is not defined as vacuum, but as a wave-packet which can do interference but cannot deliver a quantum of energy.
In general, if you want to argue, first of all you have to read attentively the proof. My proof is standard QM formalism, and if you don't believe me then read Hardy's article and the Tan-walls-Collett experiment WHICH WAS PERFORMED.
Well, I tried to find Tan et al. but I could not except for money. Would you be so kind to tell what exactly this equation:
(1) |ψ> = q{ |0>A + p( |1;a>A |0;b>A + eiθ |0;a>A |1;b>A ) } means?
Thank you in advance.
OK I found the formalism here: https://arxiv.org/pdf/1212.2019.pdf. Read it carefully. It is exactly what I told you.
"For instance, when sending a single photon on a balanced beam-splitter, one gets the output state ψ AB= (0А1B + 1A0B); (1) where the output modes of the beam-splitter are denoted A and B, and jA ; jB designates a state of j photons in mode A, B respectively."
I can not understand on what ground you are insisting I am defying Quantum formalism and changing definitions?
If these scientists from renown institutes of Spain, France and UK are changing the definitions and defying quantum formalism let me know.
@Ilian,
You answer at such long intervals of time that I forget what is the matter.
I suppose that those scientists don't change the QM. But what I am sure is that you didn't read my calculi in the question. Your comment does not refer to them. If I speak of my calculi and my experiment, and you speak of articles with other experiments and other calculi this is a discussion of deaf people. I understand that those people didn't prove that the collapse does not exist. I PROVED. So if you want to speak with me about articles that didn't prove what I proved, it's of no use.
Sofia, I read and understand very well your article. I am very glad that there are left people like you (very very few) interested in these subjects. Physicists today have thrown all things about collapse under the carpet and pretend as if Bohr and Born have solved everything. They clearly didnt solve anything, because they pretend to explain everything with nothing (namely the wavefunction - a truly fictious object).
You want to discuss your article and here is my comment and I suppose you to take it into consideration.
1.l0, b> is an empty wave (no particle in channel b) which I told at first but you deny and I send you this paper above to see you are wrong. (also mark they are talking about particles)
2. if you get a click at U you have the particle in a --- l1,a> and no particle in b channel l0,b>. You say it can not carry the phase tita to BS2 and then there nothing happens.
3. Where have you seen interference of two photons (Mandel made an experiment and many believe he has disproved Diracs opinion but its not true - I read Mandel article to the end and he has at the end that interference is seen only when it is not sure if the second photon is coming out of the first laser). I looked at an article recently with 2 photon interference but it was again with one laser. Two photons interract evry low (4 th order in QED) so I really doubt you can prove this.
@Ilian,
First of all, thank you for the good words!
Now, the definition of an empty wave is NOT VACUUM. An empty wave is a wave-packet |1>, not |0>, but which behaves exactly as a full wave, i.e. participates in interference, changes its linear momentum under the influence of fields, in short, all the behavior of the full wave, HOWEVER, has no quantum of energy to deliver. This is exactly how behaves the wave-packet |1,b> after the detector on the wave-packet |1,a> clicks. It means that |1,a> delivered the quantum of energy, and therefore |1,b> has no quantum to deliver, because the wave-function was what we call "a single-particle wave-function". However, while carying no quantum, |1,b> carries additional properties, e.g. linear momentum, so, it participates in interference with the wave-packet from the coherent beam.
If you'd ask me how it is possible for a wave-packet to possess linear momentum without possessing a quantum of energy, my answer would be: it's quantum mechanics here, not classical mechanics, s.t. what says the wave-function, THAT'S IT!
This is why I am telling people: READ THE EQUATIONS! The quantum objects behave as say the equations, we have no right to invent other things.
Ilian: "if you get a click at U you have the particle in a --- l1,a> and no particle in b channel l0,b>. You say it can not carry the phase tita to BS2 and then there nothing happens."
This is wrong: the concept of particle in QM is problematic, we can speak of quanta of energy, not of particle. A wave-packet delivers a quantum of energy, not a particle.
Next, there is no detector on the wave-packet |1,b> only on |1,a> is a detector, U. So, who told you that the wave-packet |1,b> transformed into |0,b>? SHOW ME THE EQUATION.
What we have on the upper side of the picture are detectors C and D after the beam-splitter BS, not on |1,b>. What you cn say, is that if the detector U clicks, (i.e. on |1,a> ) and also the detector D clicks, then, what produced the detection in D is a photon from the coherent beam, not the wave-packet |1,b> which carries no quantum to deliver. Moreover, as the equations show, |1,b> participates in destructive interference and is destroyed - by interference, not by the click in the detector U. LOOK AT THE EQUATIONS, YOU HAVE NO RIGHT TO SAY OTHER THINGS THAN THE EQUATIONS SAY.
If you read the equations, you see that WITHOUT the destructive interference between |1,b> and |1>B, the quantum predictions are not obeyed. READ THE EQUATIONS!
Mandel article is not relevant here - it's another experiment. I discuss my experiment not his experiment.
Sorry for great delay but i got other problems too.
"Now, the definition of an empty wave is NOT VACUUM."
I agree, though the Copenghagen interpretation would not confirm it.
"An empty wave is a wave-packet |1>, not |0>"
No. I send you the article -- lj> means j particles in the channel. l0> no paricles in the channel - e.g. empty wave. It looks like vacuum but is not as you say.
"So, who told you that the wave-packet |1,b> transformed into |0,b>? SHOW ME THE EQUATION."
You start with a BS1 and send a photon in port 1 -- l1> and vacuum in port2 --l0>. After the BS1 there is a linear superposition of l1>al0>b (e.g. the particle or click (quanta) in channel a toward the detector U and the empty wave in channel b) and vice versa l0>al1>b (your formula). As soon as U clicks the collapse kicks in and l0>al1>b disappears from the equation, because only l1>a can make U to click. l1>b doesn't turn into l0> but disapears. So when U clicks you are left with 0>b only!
"Mandel article is not relevant here - it's another experiment. I discuss my experiment not his experiment."
Mandel shows that you will not have interference with diffent lasers.
Dear Daniele Sasso
"I have instead a critical view of fundamentals of QM"
I am interested in your comment - can you share your view with us please. I am not a physicist but come from Consciousness studies but I am interested in QM -but I feel there are fundamental problems so I really would like to hear what you have to say.
KInd regards Tina
Dear Tina Lindhard,
my viewpoint on Quantum Mechanics is basically expressed in this work:
Article Basic Principles of Deterministic Quantum Physics
You are not a physicist but if you raise questions I will search for giving an answer.
Regards
Daniele Sasso
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