It was discovered that even in magneto-hydrodynamics, there are certain cases where the topology induces an effect Similar to the Boehm-Ahronov effect, even though magneto-hydrodynamics is a classical theory.
By Prof. Asher Yaholum
The Aharonov-Bohm effect was discovered by Prof. Yakir Aharonov (now Professor Emeritus at Tel Aviv University) and Prof. David Bohm (deceased) while working at the University of Bristol in England in 1959. In their work, the two showed that an electron passing near an area where there is a magnetic field is affected by the field Although the magnet does not feel the magnetic field directly, this result is obtained only if the effect of the electron is calculated with the help of quantum mechanics and is not obtained if the electron is described as a moving particle under the laws of classical mechanics.
The effect has been tested countless times experimentally and found to be true, and it is considered one of the victories of quantum mechanics over classical mechanics. Last year, a conference was held to commemorate the 50th anniversary of the discovery of the effect at Tel Aviv University, and Prof. Aharonov, who is one of the discoverers of the effect, was nominated for the Nobel Prize.
A mathematical examination of the effect reveals that the magnetic field divides the types of loops that exist in space into two: loops that do not surround the magnetic field and therefore can be shrunk to a point without crossing the magnetic field, compared to loops that are bound around the magnetic field and cannot be shrunk without crossing the magnetic field. In mathematics, this situation is called "non-trivial topology" (in trivial topology you can shrink any loop to a point).
The Aaronov-Bohm effect is therefore a topological effect since it is caused by electrons passing through both sides of the magnetic field and forming a loop that cannot be reduced to a point. Even in magneto-hydrodynamics, which deals with the movement of currents under the influence of magnetic fields, there are cases where a loop cannot be contracted to a point, such as in the case of magnetic field lines or lines of flow and magnetic field that are connected within each other described in the figure below (each loop prevents the other loop from contracting to a point).
In a study carried out at the University of Cambridge and the Ariel University Center in Samaria by Prof. Asher Yaholum, it was discovered that even in these cases the topology induces an effect similar to the Boehm-Ahronov effect, even though magnetohydrodynamics is a classical theory. First results were published in the scientific literature:
Asher Yahalom and Donald Lynden-Bell "Simplified Variational Principles for Barotropic Magnetohydrodynamics" [Los-Alamos Archives - physics/0603128] Journal of Fluid Mechanics Volume 607 pages 235-265 (2008) (Cambridge University Press).
Asher Yahalom “A Four Function Variational Principle for Barotropic Magnetohydrodynamics” European Physics Letters 89 (2010) 34005, doi: 10.1209/0295-5075/89/34005 [Los-Alamos Archives – arXiv:0811.2309]
The results were also presented at the 50th anniversary of the Bohm-Ahronov effect conference and the annual conference of the Israel Physics Society.
40 תגובות
Peace and blessings to Professor Asher Yhalum,
I have an idea, but I can detail it by attaching a drawing.
I can attach the drawing to the email.
I would appreciate it if you would send me your email so that I can send you the drawing with the explanation.
To Prof. Yaholom
Thanks for the link I hope to check it out tomorrow.
I will return again to the subject of the point of the electron. In my opinion, if the electron is described by the Schrödinger equation, it cannot be point-like and must comply with the uncertainty principle when the momentum can be replaced by the wave number (up to hbar) and thus a wavelength is obtained for the electron.
The fact that an electron has a wavelength can be learned, for example, from the wave function of an electron in a lattice, which is a Bloch function that is not localized, on the contrary, it extends over the entire lattice.
An electron is an elementary particle, that is, as far as we know, it is not composed of smaller particles, this fact does not make it pointy.
Regarding interference, I have no problem with connecting two solutions of a linear equation and getting a solution that is a superposition, as you wrote, such a solution exists for the wave equation, but for the wave equation, the object that performs interference is a wave described by amplitude and phase (a real wave - in the sense of a physical reality, not mathematically). On the other hand, if I understood you correctly, you believe that the wave function describes the probability of finding the electron and not the electron itself. How do you explain that probability has a complex value? Probability is a continuous variable between 0 and 1, not a complex number.
Indeed the square of the absolute value of the wave function gives a probability, but the wave function has more information. If we use the analogy to the AM field, the name of the field is described by a complex number, but the square of the absolute value gives the strength of the field at any point in space. On the other hand, regarding the wave function, you claimed that it does not represent the electron itself, but only a probability. I asked if the electron is a point particle and the wave function is only related to the probability of finding it, how can the wave function be a function that accepts complex values?
In my opinion, a basic understanding of the meaning of quantum theory can be obtained from Masdia de Bergoli who attributed a wavelength to the electron and also Bohr who used this wavelength to explain why there are stable electron orbits in atoms. Although Bohr's model is incorrect, his semi-classical quantization rule is still valid and this rule is based on the wavelength of the particle, in particular the electron moving around the nucleus in the atom. Therefore, in my opinion, the founders of quantum theory did not see the electron as a point particle.
to Elad 36
Not every problem in quantum mechanics is related to topology, the problem addressed by Aaronov and Boehm is.
The connections between hydrodynamics and quantum theory are known and are mainly related to Boehm's formulation of quantum mechanics.
For a longer discussion on the subject, see for example:
R. Englman and A. Yahalom "Complex States of Simple Molecular Systems" a chapter of the volume "The Role of Degenerate States in Chemistry" edited by M. Baer and G. Billing in Adv. Chem. Phys. Vol. 124 (John Wiley & Sons 2002). [Los-Alamos Archives physics/0406149]
There may be deeper connections between quantum mechanics and magnetohydrodynamics, this is a topic worth exploring.
Lahud 34
First, the presentation can be downloaded from the link
http://rcpt.yousendit.com/
856959525/abbe556ae73defbeb19e1bc78e771cd1
Hopefully there will be answers to some of the questions here.
The fact that the electron is a point particle is not my opinion, this is what elementary particle experts claim.
If the electron was a "smeared" particle like a wave function, the particle scientists would insist on this in the high energy scattering experiment they conduct.
The photon is actually what is obtained from the quantization of electromagnetic fields and the discussion of it deviates from the discussion of the Aharonov-Bohm effect, since here we are dealing with quantum field theory and not purely quantum mechanics. By the way, a photon with a precise wavelength is not a point particle and in fact it occupies a very large space.
The "interference" is a connection of two possible solutions of the Schrödinger equation to produce a third solution, I don't understand why you think this is impossible. This phenomenon is typical for all linear equations, when all the wave equations you mentioned belong to this family, I don't understand what the problem is here. If you admit that the Schrödinger equation is correct, the interference phenomenon inevitably follows.
De Broglie belongs to another period in the history of science before the development of the Schrödinger equation, in that period they did grapple with the question of why wave phenomena exist in electron experiments. De Broglie proposed that the electron has a wavelength that is inversely proportional to its momentum. But he did not explain what this wave is and why in other phenomena the electron appears as a point particle. Only later did Schrödinger propose his equation whose solutions are waves. Regarding the meaning of the solutions even today there is a dispute, the Copenhagen school sees the solutions as probabilities of the electron being in a certain place and at a certain speed. According to this approach, the electron does not have a "track" and the term track is only correct in the classical approximation. The Boehm school maintains the concept of the orbit and explains the wave action on the electron through the concept of the "quantum potential".
Ehud, Prof. Asher Yaholom,
The equivalence of the quantum wave function to magnetohydrodynamics is non-micrian.
It is very possible that the topology is an essential matter for what the wave function is supposed to describe.
The particle-wave quanatic duality that the function is supposed to represent is not the whole story.
In my opinion the function should represent more complex dynamics than a particle wave.
Additional potentials and dimensions or topologies.
Elad
The wave function has all the information needed to describe processes. The problem with the essence of quantum processes does not arise if it is not raised. It can always be argued that quantum mechanics is the recipe that gives the probabilities of experimental results given initial conditions. If we try to reproduce only experiments and not objective reality, there is no problem in quantum theory.
Beyond that, I am not aware of any corrections the wave function has undergone since Schrödinger or Dirk.
There is no problem at all regarding conflict processes. Regarding measurement, there is ambiguity or even complete lack of clarity.
The equations of quantum theory are the most accurate equations we have, there is no point in expanding them to more solutions. What is probably lacking is our understanding of what they represent.
Prof. Diamond
First of all, thank you for your answer and for your willingness to give additional material on the subject, I assume that the question regarding the analogy to the Aaronov-Bohm effect is too complex for a simplistic discussion and can be understood better from the slides.
Nevertheless, I would like to understand why you believe that the electron is a point particle? And do you think that the photon is like that too? Regarding the wave function, if it only contains information about the position of the electron and its momentum, how can it get confused? Wave phenomena have been known to us for hundreds of years and can be described using a complex function that describes the phase and amplitude of the wave, what is information interference? I would also be happy if you refer to de Bergoli wavelength and why, even though the electron has a wavelength, you call it a point particle? Could it be that our definition of spotty is different?
"By Ehud:
16-04-2010 בשעה 15:32
Prof. Diamond
Allow me to be more detailed. You claim that the particle in quantum mechanics is point-like and that what undergoes entanglement is the wave function. I would appreciate it if you could explain to me what the wave function is in your opinion. As far as I know
Wrestling only material! Waves: light, water or sound. It is not clear to me how a function that, according to you, is mathematical and represents probability performs a struggle? Maybe I missed something?
Michael
Thanks, but I didn't find any mention of the Aharonov-Boehm effect in the article."
Ehud, I agree with you that this is not a physical quantity that interferes, as for example with sound waves or light, but a wave function that represents information is what exists in quantum mechanics according to the interpretations of Copenhagen and Boehm. I know of only one attempt to explain the origin of the wave function and that is Nelson's attempt. Nelson tried to explain the function as a result of the action of stochastic forces created in Brownian collisions between the electron and its environment.
There is no mention of the Aaronov-Bohm effect in the articles I mentioned, there is only a mention of the "multivalued" functions that create the analog effect and are marked with the Greek letters Nu and Zeta. To see the connections between these functions and the Boehm Aharonov effect I uploaded the slides of my lecture on the subject to LOS ALAMOS ARCHIVES. When the link is available I will send it to you.
Prof. Asher Yehalom:
The wave function has undergone revisions since Schrödinger first introduced it and also after Dirk.
However, it is still not enough to explain the essence of quantum processes.
There is still a great deal of ambiguity regarding entanglement processes and the connection between a particle and a wave.
It is very possible that these analog quantities in a non-quantum field indicate that the wave equation is still far from perfect.
It's time to expand the wave equation so that it has fewer non-trivial solutions.
Today it describes some parts very well on the one hand and on the other hand it fails to generalize other parts.
Prof. Diamond
As far as I know in physics only matter waves perform entanglement and not information waves.
Is the photon also a point particle according to your perception? Or is there a separation between light and matter. De Bergoli showed us that even massive particles behave like waves and can be assigned a wavelength. If the electron has a wavelength, is it a point particle?
to love
You claim that "most accepted interpretations do not separate the wave function from the electron" but this is conceptually impossible. After all, the electron is a physical entity and the wave function only contains information about the probability
for the presence of the particle in a certain place and is not a physical entity in itself.
In Bohm's interpretation (which you mentioned), the wave function not only describes a probability but also creates a "quantum potential" which in Bohm's opinion (who holds the classical interpretation that the electron has a "track") causes changes in the electron's track so that an entanglement image is created.
The quantity that creates the interference in the wave function is the phase of the wave function, this phase can have special values in case the topology is not tribal and hence the Aaronov-Bohm effect. There are quantities analogous to the phase in the weighted field theory of magnetohydrodynamics which was discovered by Prof. Donald Linden-Bell together with the author of this article.
Elad in response to your question:
1. The condition for the appearance of the phenomenon we discovered is that the magnetic field lines be connected within each other, the phenomenon does not exist when the magnetic field lines are not connected within each other. As I explained, this is a topological phenomenon
When the topology is trivial the phenomenon disappears.
2. Regarding your claim that the phenomenon is not a result of quantum properties and of the wave function but a result of the assembly of the topological pattern, I would say that it is impossible to be more precise. Hooray for wording.
questionnaire
The loops are not magnetic loops but possible paths of the electrons around an area where there is a magnetic field.
For example, the movement of electrons can be limited to certain areas by creating loops of conductive material around a magnetic field. For the sake of demonstration, imagine that the magnetic field is confined to the face of a long, narrow cylinder, current loops that surround this cylinder cannot be shrunk without breaking the cylinder, while ram loops that do not surround the cylinder can be shrunk to a point. How a narrow and long magnetic field is created is beyond our attention, but it can be done using a coil solenoid that has many current rings in the center of which the magnetic field it produces is located.
point
In your opinion, what is the point of a point particle? And interesting because you claim that it is not described by the Schrödinger equation. By the way, did you read about de Broglie? I would also like to hear what your claims are based on. Also, you didn't explain to me how a mathematical object (the wave function) can perform interference, a phenomenon reserved for material waves? And is the photon, which is also an elementary particle, a point particle?
sympathetic. You just write a lot. You just repeated the same things you said. You didn't add anything.
The elementary particles are point-like. And they are not described by the wave equation but by fundamental quantities (such as mass, charge, spin).
I especially liked your "correction" that it is the square of the absolute value and not the absolute value, you are simply ridiculous.
I did not understand this sentence in the article:
"Mathematical examination of the effect reveals that the magnetic field divides the types of loops that exist in space into two: loops that do not surround the magnetic field and therefore can be shrunk to a point without crossing the magnetic field, compared to loops that are bound around the magnetic field and cannot be shrunk without crossing the magnetic field. In mathematics, this situation is called "non-trivial topology" (in trivial topology you can shrink any loop to a point).
Aren't magnetic loops supposed to form between two poles? If I understood correctly
So this is the feature of the second type. But in the first type did the poet mean champagne
There are no poles, so the loops can be shrunk?
If someone can explain please?
Thanks
I apologize the last comment was written by me and not by dot.
point
First of all, you write precisely in the details: "The absolute value of the wave function is the wave function of the probability of finding an electron (wave). The electron is a point (particle).” As every undergraduate physics student knows, the absolute squared value of the wave function is the probability of finding the particle at a certain point.
Second, the electron is indeed an elementary particle, but it is certainly not pointy, with all the sadness in the matter especially for you (pointy, point ha ha ha). The square of the absolute value of the wave function gives the probability of finding the particle (in this case the electron) since this value is different from Dirac's delta distribution in most cases it cannot be claimed that the electron is a point particle. When the position of the electron is measured like any particle by its position
course to a point (theoretically at least).
Indeed, the wave function of the electron is a complex mathematical quantity, but the square of its absolute value is not, and it represents the probability of finding the electron. When the wave function performs interference, it is an electron performing interference with itself.
The difference between classical mechanics and quantum mechanics is that in classical mechanics the particles are point-like and their motion is described by Newton's equations and in quantum mechanics particles are described by the Schrödinger equation which is a kind of wave equation. The measurement problem is indeed a problem that produces different interpretations of quantum mechanics, but the revolution of quantum theory is in the understanding that both particles: electrons and waves: photons are described by the same equation, ie the Schrödinger equation. If the electron is point-like, should I understand that a photon is also point-like? I would recommend that you take advantage of the Sabbath to read a little about de Broglie.
The revolution of quantum mechanics is not in any artelite knowledge but in the type of equations we use to describe the particles and waves. Just for your information, today there is no physical mechanism for the collapse of the wave function, this is a postulate of quantum theory
The wave function is a complex mathematical quantity. An electron is something real.
The absolute value of the wave function is the wave function of the probability of finding an electron(wave). The electron is a point (particle).
The revolution of quantum mechanics is knowing that there is a gap between what we perceive (the real world measured experimentally by real sizes). and what the universe itself (the real world described mathematically by composite sizes).
The mechanism of collapsing a composite function into something real is steeped in mystery.
Elad
I actually mean quantum entanglement of the electron with itself. As I tried to argue in the Aharonov-Bohm effect the electron struggles with itself. This effect manifests itself in the interference of the wave function describing the electron and nothing else.
Contrary to what is said:
1. In quantum mechanics, the electron is not a point particle. This is the fundamental revolution in the transition from classical physics to quantum physics.
2. The wave function describes the electron only and nothing else. A mathematical object that represents a probability cannot perform entanglement.
Therefore the comparison of the article's results for magnetohydrodynamics seems irrelevant to me. It is possible that in this field we get non-trivial topologies, but in my opinion this is not enough to make an analogy to the Aharonov-Bohm effect.
sympathetic:
In this topology the effect is not the result of classical interference
Yeh*el
In my opinion, the Aharonov-Bohm effect is basically a quantum effect resulting from interference, when the author of the article claims that something similar can be obtained classically, I think the burden of proof is on him.
sympathetic:
The quantum wave equation differs from a classical wave equation in that it has different non-trivial solutions when the topology of the field is as described. The connection to the Bohm-Arhonov effect is for topologies of the type in the article.
sympathetic:
Right. There is no mention of the Aharonov Boehm effect but that is the description of the study.
Whether or not there is a similarity is a matter for the beholder (the current article only claims a similarity. It does not claim that the Aaronov-Boehm effect exists there).
Prof. Diamond
Allow me to be more detailed. You claim that the particle in quantum mechanics is point-like and that what undergoes entanglement is the wave function. I would appreciate it if you could explain to me what the wave function is in your opinion. As far as I know
Wrestling only material! Waves: light, water or sound. It is not clear to me how a function that, according to you, is mathematical and represents probability performs a struggle? Maybe I missed something?
Michael
Thanks, but I didn't find any mention of the Aaronov-Boehm effect in the article.
http://arxiv.org/pdf/0811.2309v1
Prof. Diamond
Most of the accepted interpretations do not separate the wave function from the electron except perhaps Bohm's interpretation. Do not make a separation between the wave function and the electron, the material itself is described by the wave function.
The change between classical mechanics and quantum mechanics is in the transition between the perception of the particle as a point particle and its description using a wave function. The particle in quantum mechanics becomes a point when its position is measured.
The Schrödinger equation is a type of wave equation, so it is still not clear to me what in magnetohydrodynamics causes the interference, so I am not clear what the source of the Aaronov-Bohm comparison is. I would appreciate it if you could elaborate.
Prof. Asher Yehalom:
It is possible that the phenomenon is not a result of quantum properties and of the wave function but a result of the assembly of the topological pattern.
Prof. Asher Yehalom:
In the phenomenon you discovered (in magnetohydrodynamics) are there transition conditions between the state in which the result appears and the state in which it ceases to exist and vice versa. What needs to be added or subtracted from the system to make it move from state to state.
And is it a single condition or different conditions each time. Please specify if possible.
sympathetic. You're an idiot.
sympathetic
What you quoted in English except for the use of the archaic term WAVE-PARTICLE DUALITY is completely accurate. And as is clear to any physicist, what undergoes interference is the wave function itself and not the electron, which is, as mentioned, a point particle.
A solution of the Schrödinger equation for the wave function in the presence of a magnetic field is what leads to Aharonov-Bohm's result and is closely related to the topology of the physical state. A similar topology in magnetohydrodynamics results in similar results.
Prof. Diamond
The interpretation we give to the wave function has no significance in the experiment. The results of the experiment are independent of interpretation. Beyond that, the wave function is a probability amplitude and not a probability, so it can perform interference and cause the Aaronov-Bohm effect, which is a wave effect. The wave function is the one that is sensitive to the magnetic field in the Aaronov-Bohm experiment, so I again ask how a similar effect can be obtained classically?
Regarding your claim that I wasn't accurate when I wrote that the electron is both a wave and a particle: "As of today, at the energies we reach in the largest accelerators, we find that the electron has no structure at all, that is, it is a point particle."
There is no connection between the fact that a particle is an elementary particle and does not consist of additional particles, for example nucleons and particles, to the fact that the particle can behave as a wave or as a point particle.
For example, you can read about the duality between a wave and a particle in:
http://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality
When the subsection entitled: Treatment in modern quantum mechanics is particularly relevant
I am qouting
"Wave-particle duality is deeply embedded into the foundations of quantum mechanics, so well that modern practitioners rarely discuss it as such. In the formalism of the theory, all the information about a particle is encoded in its wave function, a complex valued function roughly analogous to the amplitude of a wave at each point in space. This function evolves according to a differential equation (generically called the Schrödinger equation), and this equation gives rise to wave-like phenomena such as interference and diffraction
to love
According to the accepted interpretation of quantum mechanics (Copenhagen school) the electron is a point particle whose probability of finding it in a certain place and at a certain speed is determined by its wave function.
That's why you weren't accurate when you wrote that the electron is both a wave and a particle, as of today at the energies we reach in the largest accelerators we find that the electron has no structure at all, that is, it is a point particle.
What gets complicated in the famous crack experiment and also in the experiment proposed by Aaronov and Boehm is the wave function of the particle.
Eddie send me an email address and I will send you more material.
Prof. Diamond,
I'm having trouble understanding the distinction you make between the particle and its wave function.
To the best of my understanding, an electron is a wave or a particle depending on the experiment performed on it
Whereas the Aaronov-Bohm experiment tests the wave nature of the electrons - therefore the electron undergoes a struggle with itself. A similar thing happens in the two-crack experiment. I am therefore having trouble understanding how it is possible to get a similar effect in a classical system. I would appreciate it if you could elaborate.
Prof. Asher Yaholom,
For 3:
please send
I thank you in advance.
I wonder if it is possible to build listening devices based on the Aharonov-Bohm effect.
Eddie I would be happy to send you more material.
The electrons do not undergo a struggle with themselves since they are point particles. What goes through a struggle with itself is the wave function of the electrons. The Schrödinger equation describing the evolution of the wave function has special solutions when the topology is non-trivial, hence the Aaronov-Bohm effect.
Eddie
I agree with you that it is a shame that the article is not more detailed. In my opinion, a discovery in classical physics of systems with a non-trivial topology is not enough to accept Aharonov-Bohm physics. Aharonov-Bohm physics is obtained from a particle performing a struggle with itself (it is convenient to describe this in the language of Feynman's trajectory integrals). In classical physics, particles don't fight with themselves, so I don't see how a classical Aaronov-Bohm effect can exist.
What's more, the claim quoted in the article seems to me to be wrong: "The Aharonov-Bohm effect is therefore a topological effect since it is caused by electrons passing on both sides of the magnetic field and forming a loop that cannot be reduced to a point". The magnetic field is the reason why it is not possible to shrink the loop to a point and the flowing electrons are simply sensitive to this, but in particular it is not about many electrons but the fact that each of the electrons on its own is fighting with itself.
The discovery seems to be important for understanding the Aharonov-Bohm effect in a classical perspective, and perhaps it has fundamental implications regarding the essential connection that exists in the XNUMXth century between the two mechanics. It is possible that he alludes to more generalized mechanics.
It is a shame that the article is not more detailed and does not allow even a general understanding.