We frequently ask what is the wave-function. Some people are satisfied with the answer that the wave-function is the solution of the Schrodinger equation, but this answer just transfers the question mark further, i.e. what is the Schrodinger equation and what is the physical meaning of its solution?
The solution of the Schrodinger equation is a wave, but on a photographic plate we record a point, as if a particle hit the plate, not a wave.
Does this contradictory situation point to a limitation of the human logic?
Some people explain that we are used to classical concepts and this is why we seem to find a contradiction here. But the wave-packet occupies a volume in space, while the point in the photographic plate has practically zero-volume.
So, is there something wrong with our logic, is the human logic insufficient for understanding the quantum world?
Dear George,
It doesn't go like that. If you admit that some facts have no logical explanation, you admit that those facts contradict some physical laws.
This is the problem with the wave-packet: it occupies some volume, but on the photographic plate it seems to shrink suddenly to just one point, of volume incomparably smaller than the wave-packet volume.
One can assume alternatively that only one point from the wave-packet impresses the plate. But in this case, it is not clear what happens with the rest of the wave-packet in continuation. Where does it go. Or, does it disappear?
To admit that it disappears is not a pleasant idea, because the wave-packet should be some sort of matter. Indeed, when passing through fields it modifies its path accordingly. So, does a whole volume of matter disappear?
Dear Prof. El Naschie,
The problem is deeper. It's not matter of physical limitations, neither the difference between zero and almost zero. The wave-packet occupies a volume, while the spot on the photographic plate has by far a smaller volume. Our apparatuses don't lie to us.
Next, all the energy of the quantum system (electron, atom, whatever it is), is delivered to that single spot on the plate. So, what shall we say, that the wave-packet was mostly empty and all the energy was concentrated into a tiny volume, as big as the spot produced on the plate? Experiments seem to show that we can't say this.
I got into more elaborations in my answer to George - maybe you'll read them.
My kindest regards,
Sofia
Dear George,
I saw indeed in the list of your skills that you are a mathematician, not quantum-physicist. So, maybe you are not involved in the "fever" of the quantum community. You say, "one does not have a physical law at hand to explain everything". As far as I know, it's not the situation in quantum mechanics. What is the wave-function is a problem so intriguing, so much investigated and debated, that I hardly can imagine a physicist in QM field that didn't give a deep thought on that. Bottom line, each grain of sand is/was turned in trying to understand the wave-function.
About cosmology, the situation in QM is different than in cosmology. We produce wave-functions whenever we want in our labs, we did thousands of experiments with it, we measure it, we don't need to guess what was an enormous time ago.
(The aging process is mainly governed by the 2nd law of thermodynamics - there are all sort of irreversible processes in our body that gradually worsen its functioning.)
Dear Prof. El Naschie,
The basics of physics is EXPERIMENT. The experiment may confirm a mathematical model, or rule it out. Moreover, we have to continuously test the predictions of the model with the experiment.
Now, you say "ORTHODOX QUANTUM MECHANICS ASSERTS THAT QUANTUM WAVES HAVE NO MATTER NOR ENERGY IN IT"
Where you saw such an assertion? (By the way, now I see why you speak of empty sets.)
How can the wave-function carry no energy? A beam of photons carries no energy? Send a laser beam of appropriate energy onto a metal and the beam will cut the metal.
Let me remind you that standard quantum mechanics admits no dichotomy into wave, and particle. There is a wave-function and nothing else.
The wave-function is supposed to display at each point where its intensity is non-zero, all the properties of the type of particle: mass, charge, spin, number of particles (in 2nd quantization), etc. When a single-particle wave-function hits a photographic plate, some molecule on the plate is broken, because it gets the energy needed to dissociate the molecule. Where from gets the molecule this energy if the wave-function doesn't carry it?
But, let me give another example: imagine the wave-function emitted by an electron source, and let this wave-function pass through an electric field. The wave will bend, i.e. the linear momentum will change. How can something non-material carry a linear momentum? How can a field act on something non-material?
So, in standard QM the wave-function is not an empty set, devoid of mass and energy, it carries the mass and energy because standard QM admits no other carrier of these (and the other) properties.
(I am sure that you take this talk between us as a talk between friends. It is just an examination of how can we regard the wave-function.)
My kindest regards,
Sofia
Dear Prof. El Naschie,
There is an international saying that "about color and taste one doesn't argue". So, we probably came to the essence of our difference of opinions: you say "it is a PROBABILITY WAVE", while I say "it's some form of MATTER because it INTERACTS WITH MATTER and is INFLUENCED BY MATTER."
About experiment vs. theory I won't argue with you because it reminds me the un-answerable question "what was first, the egg, or the chicken?" More exactly, the answer is that they evolved together.
Bottom line, let's not argue.
I wonder whether you met sometime Prof. Abner Shimony (one of the fathers of the CHSH inequality). He was a good friend of Asher Peres, he visited Technion a couple of times and also gave lectures. He had in mind something quite nebulous, he spoke of the wave function in terms of a dichotomy: "potentialities" and "realities". In those times we didn't understand him, and now, that I would be curious to understand that idea of him, I don't even know whether he is anymore among us, if he is in good health, etc.
Well, my kindest regards,
Sofia
Dear Prof. El Naschie,
(and friend), first of all there was a fish. As the surface of the Earth began to dry into continents, additional forms appeared. But, all these things I learnt decades ago, in the school, I don't remember precise details.
About probability waves, I suggested not to argue. For a rigorous talk we should take an specific example, and analyze it by asking all the necessary questions, a talk in generalities leads nowhere. Unfortunately, I won't be present in the ResearchGate for a while, I have an urgent article to finish.
As to Bohm, I take him very seriously. I hold that his interpretation has to be experimentally tested. This wasn't done sufficiently until now. It's not enough to say that Bohm's interpretation leads to the same distribution of measurement results as the QM predicts. Bohm's interpretation is based on additional assumptions besides those of QM, and those additional assumptions have to be tested.
Warmest and kindest regards, as always,
Your Sofia
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