Is Max Born's probabilistic proposal artificial?

[slow]

I want to start by explaining my concern in detail.

Engineers often use predefined algorithms to perform physical calculations on the systems they manage. In research, engineering algorithms are not the first thing that appears. The principles and laws of physics appear before, which then allow algorithms to be established for one case or another.

Now comes what causes me consternation. It can only be a subjective feeling and, in that case, your help to understand the matter objectively will be useful. The quantum theory and its derivations give me the same impression as a set of algorithms, found before investigating and understanding the principles and laws that support all that. As if the engineers had developed algorithms to design radiating systems centuries before being investigated the electromagnetic field, including the principles and formulated the corresponding laws.

Suppose someone proposes a mathematically coherent definition of something called the Sanskrit wave. He then postulates that the probability of finding in a region the presence of a Hindu priest is proportional to the square of the amplitude of the Sanskrit wave in that region. Surely that postulate will be verified without counterexamples. But he can not pretend that the Sanskrit wave is included in the same category as the detectable waves, in which a physically detectable magnitude ripples. He may argue that the presence of a Hindu priest is precisely the detail that confers physical significance to that probability, proportional to the square of the amplitude of the Sanskrit wave. And he can argue that, consequently, the Sanskrit wave is a physically adequate term. But on what physical principles is the definition of the Sanskrit wave based? Different would be the case of a research in neurobiology, which finds a pattern of brain waves characteristic and exclusive of the Hindu priests, in such a way that the electrical potentials of the brain radiate electromagnetic waves with that pattern and, then, where the amplitude of those electromagnetic waves has a local relative maximum, you will find a Hindu priest. The latter would have a legitimate place within physical science.

Here the point that most puzzles me. The probabilistic interpretation that Max Born introduced into quantum theory. The probability wave seems artificial to me. The example of the Sanskrit wave tries to show why it seems artificial to me. Is Max Born's proposal artificial or is it based clearly on principles and laws of physics?

 

[vanhees71]

The proabilistic interpretation is the only one which is consistent with all observations, and there's no contradiction to the probabilistic interpretation. As any theory in physics QT has been developed based on empirical facts.

 

[slow]

The proabilistic interpretation is the only one which is consistent with all observations, and there's no contradiction to the probabilistic interpretation. As any theory in physics QT has been developed based on empirical facts.

That shows that the interpretation is successful. Success and artificiality are two different issues. I'm worried about the second issue, artificiality.

 

[vanhees71]

Well, QT deals with a realm of reality we don't have much intuition about, because we are used to the behavior of macroscopic objects which behave according to classical physics. That they do so is, however, an apparent phenomenon and only due to the fact that we don't need and cannot resolve all the microcscopic details of macroscopic objects. On the microscopic level, as far as we know, everything is described by quantum theory. The one exeption is gravity, which we don't know, how to describe on the quantum level yet. It's the unsolved puzzle of contemporary fundamental physics!

 

[Nugatory]

Success and artificiality are two different issues. I'm worried about the second issue, artificiality.

That objection applies to all forms of experimental science. For example, the claim that there is a gravitational force between objects, proportional to their masses and inversely proportional to the square of the distance between them, is successful and supported by many experiments. But it is no less artificial - if you look for the physical principles upon which it is based, you will eventually end up with "because that's the way the universe we live in works", or to use your terminology, "that's the successful algorithm". The difference here is just that Newton's law of gravitational is less offensive to our classical intuition so we feel better about accepting it.

 

[slow]

Thank you vanhees71 for expanding the exhibition, and Nugatory for be present. I am in complete agreement with what you say. I will also try to expand a bit.

After the diffraction and interference experiments designed for particles, it would be foolish to believe that there are no wave properties in what we call particles. And it would be an antimethodic attitude to attempt to study the phenomenon without including a wave function. All this is well understood before the Solvay Congress of 1927. It happened that the main physicists did not want to operate with a wave function without attributing some kind of explicit concept to it. If the only quantum were light, it would have been possible to express the wave function in electromagnetic terms. In reality, light is not the only thing. And neither in 1927 nor today is an electromagnetic theory of particles available. Neither another theory based on something deeper, that in the light produces electromagnetic effects and in the matter the other known effects. Max Born proposed the probabilistic interpretation to fill the conceptual void, which is also a methodical vacuum. And as in the case of the Sanskrit wave, the priest almost always appears where the square of the amplitude maximizes the integral. The mathematical proposal is successful in both cases, quantum and Sanskrit, because it is defined mathematically in such a way that its non-compliance is impossible. But between the definition of the wave of Sanskrit and the properties of the body of a Hindu priest there is a difference that makes them incomparable. As a description of a Hindu priest, the proposal of the Sanskrit wave is completely artificial. We can not believe that by calculating well where we will find a priest the wave of Sanskrit describes what a priest is. I hope I have expanded with clarity.
P.D. : For a few hours I will be attending a course. Sorry for the delay I will cause.

 

[bhobba]

Max Born proposed the probabilistic interpretation to fill the conceptual void, which is also a methodical vacuum.

Well there is this theorem cooked up by a not that well known, but actually one of the 20th centurys best mathematicians, called Andrew Gleason:
http://kiko.fysik.su.se/en/thesis/helena-master.pdf

After reading it you might like to rephrase your question - I won't say the obvious question - I think you can nut it out.

Dr Gleason had an interesting history well worth a minute or two reading:
https://www.ams.org/notices/200910/rtx091001236p.pdf

Thanks
Bill

 

[slow]

Hello everyone. For Bill, thanks for the link to the theorem although I am unable to understand the development and the implications regarding Max Born's proposal. The good thing is that I do not need to worry about an obvious issue, as you said. Best regards to all.

 

[slow]

Well, I searched Wikipedia and it seems that Andrew Mattei Gleason has saved the cat that Erwin Scrödinger had left in risky situation.

 

[bhobba]

Hello everyone. For Bill, thanks for the link to the theorem although I am unable to understand the development and the implications regarding Max Born's proposal.

Well as a theorem you don't worry about it - its just an inevitable consequence of the operator formalism of QM.

But it does raise an important issue. Why? The Kochen-Specker theorem is a simple corollary - and that is both interesting, important and, while I wouldn't call it a worry its something to cognate on. You can prove it without Gleason, and Bell took it as a personal challenge that if he could not do it he would give it away. He did not fail

Thanks
Bill

 

[Michael Price]

Is Max Born's proposal artificial or is it based clearly on principles and laws of physics?

It is one of lesser-known ironies in the history of quantum mechanics that the Born Rule was a defective guess, based on optical principles. We know it was defective reasoning /inuition because Born guessed wrong the first time and only corrected his result in proof, as the article was in the publication pipeline. If you read his original article an incorrect rule appears in the main text, and the correct rule appears as a sheepish addendum in a footnote!
My guess is Max Born corrected his guess when he realized that total probability would not be conserved with the probability density being the modulus of the wavefunction. So he squared it, and viola, everything worked!