It might be useful to study quantum mechanics firzt, before writing up lists of elements, that, only, show ignorance.’

One postulate of quantum mechanics is the Schrödinger equation, that describes the evolution of the wavefunction, ψ. Another postulate is ``Born’s rule", that |ψ|^2 is the probability density for finding the system in the state of position between x and x+dx ar time t.

From these postulates, in fact, evrrything else follows, as described in any textbook on quantum mechanics.

Stam Nicolis

Stam, my friend, I studied in depth the quantum mechanics (QM). I am not an ignorant. The uncertainty principle does not follow from the Schrödinger equation. I wonder whether the Born rule and the fact that the QM uses the Hilbert spaces algebra, are independent. What you say? Are they independent?

With best regards

Sofia D. Wechsler Hi Sofia. Well done for pressing on with the quest to make sense of quantum theory.

As I mentioned, the list I gave you was from memory and not comprehensive.

I think a useful reference is the Wikipedia page titled interpretations of quantum mechanics:

https://en.m.wikipedia.org/wiki/Interpretations_of_quantum_mechanics

The comparison table is quite revealing as it shows that there is no consensus on the interpretation of QM.

As you know I don’t agree with any of the interpretations listed and assert that the correct physical interpretation is the Spacetime Wave theory.

So wave/particle duality does not apply because we are dealing with pure waves.

The Heisenberg uncertainty principle which talks about the uncertain position of particles is not needed because we are dealing with waves.

The Pauli exclusion principle for electrons is replaced with a model in which electrons are found to occupy a surface area.

An idea of how this interpretation can be applied in practice is to be found in the description of the hydrogen bond.

Preprint The Hydrogen Bond (June 2022)

Richard

Richard Lewis

Dear Richard, what kind of wave do you propose as the ontic counterpart of the wave-function? Do you think that the wave-function is a reality? I showed in my article that the wave-function has an ambiguous expression.

Sofia D. Wechsler As I see it the wave function describes the “trajectory “ of the object. Previously it was thought that the object was a particle so that the wave function could tell you the probability of finding the particle at any point in space.

Now when we think of the object as a wave it is a real physical wave spread out in space. The wave function is then telling us the outcome of measurement when we detect the wave.

The detector plays an active role in absorbing the entire wave which has the effect of localising the wave at the detecting atom.

Richard

Richard Lewis

Richard, you did not answer my question. The wave you speak of and the wave function are the same thing? It seems to me that you don't think so, but I prefer that you say it.

I remember that I asked you how it comes that the wave is absorbed by a single atom and you said something like this: the wave disappears in all the places and accumulates at the position of the absorbing atom. And I told you that if so were the case, we would record a current from different parts of the space to the absorbing atom. But no such current was ever detected.

What if t=0.

Examples:

A) The "Twin-Paradoxon' ...is no MORE a paradox.

B) THE INFINITE MONKEY- PROBLEME .....IS NO more A "PROBLEM"

C) The 3rd Claim of "Termodynamik". If you set (with NEW MATHEMATIKS)...infinity no "PROBLEME" because t=0

BEST from Hamburg (Germany).

I am happy to get in Touch with YOU ALL.

CHRIS 😃 👍🙏

Sofia D. Wechsler Both very good points.

Firstly about the wave. I do think that the wave function is not describing the real physical wave. The wave function is describing the probability of where the wave will be detected when you have an array of detectors such as the atoms on a photographic plate. The wave itself is a real physical wave in Spacetime. The wave function is a first order differential equation using complex numbers whereas the wave itself is a real physical entity.

As regards your second point again a very good question. Think about the light interference experiment which can be run successfully emitting one wave quantum (photon) at a time. If you put any kind of detector near the slits to see which slit the photon went through, the interference pattern disappears. Similarly if you were to put any detection device into the experiment to try to observe the collapse of the photon onto the photographic plate then this detector if detecting would prevent the photon from reaching the photographic plate and absorb all the wave energy itself.

So the collapse of the wave onto an atom cannot be detected except by the atom itself which changes state and produces a dot on the photographic plate.

Richard

In my mind there are still troubles with a definite list of axioms.

For example if a wave function has to obey the Schrodinger eqn. (instead say of Dirac)

Then that the state of a system is unknown until measurement, sometimes a whole lot of states sometimes emerge together (ie the hydrogen spectrum)

The wording sometimes does not convince me. Some general ideas are clear enough.

The wave function does not identify a trajectory, only a limitaation on possible trajectories. Actual trajectories have been banned from QM.

Juan Weisz I understand your point about trajectories in the interpretation of QM. My analogy is to liken the wave equation to the equation describing the path of a projectile fired from a gun. It is clear that the equation of the motion of the projectile ceases to apply when the projectile lands. Just in this way the wave function ceases to apply when the wave quantum reached the detector screen. There is no mysterious collapse of the wave function, just an interaction between the incoming wave and the detector. This interpretation does not have a measurement problem.

As you say in the standard QM interpretations the state of a system is unknown until a measurement is made. I take the view that it is a real physical wave passing through both slits of the interference experiment and this wave has a definite energy and position during its trajectory.

This interpretation is the Spacetime Wave theory interpretation.

Sofia D. Wechsler I know that you have difficulty with the idea of the detector causing the collapse of the wave but this is a conclusion arising from the idea that it is a real physical wave passing through the apparatus. The only other possible explanation is that the wave spontaneously collapses to a particle and then hits the detector screen and then we are back to the measurement problem of QM.

Richard

Regarding the uncertainty principle, it results from the property of the state space of quantum mechanics to be a Hilbert space.

In particular, a generalized uncertainty principle can be shown for any two non-commuting observables, as a result of the well-known Cauchy – Schwarz inequality. Particularly, it can be shown that the product of the uncertainties of the two observables in a given normalized state is bounded below by the absolute value of the expectation value of their commutator in the given state over 2.

The proof is not trivial, but it is not too difficult either. Standard textbooks or couse notes on quantum mechanics provide the details of the proof.

As a corollary of the generalized uncertainty principle, if the commutator of two observables is a constant, then it gets out of the expectation value, and since the examined state is assumed normalized, we derive that the uncertainty in this case is bounded below by the absolute value of the commutator of the two observables over 2. As an example, using that the commutator of the position and momentum operators is equal to ih(bar), we derive the well-known relation that the uncertainty in position and momentum is bounded below by h(bar) over 2.

It is useful to note that the Cauchy – Schwarz inequality holds in any vector space equipped with an inner product (inner-product vector space). The state space of quantum mechanics is a Hilbert space. A Hilbert space is an inner-product vector space with the additional property of completeness; i.e. with the property that every Cauchy sequence of vectors belonging to the space converges to a vector of the space. Since a Hilbert space is also an inner-product vector space, the Cauchy – Schwarz inequality holds for the elements of a Hilbert space.

Sofia D. Wechsler,

Can the uncertainty principle be derived mathematically?

Issam Mohanna

Yes, but only for two cases: 1) time and energy, 2) position and linear momentum. In both cases the derivation is done using the sinc function.

Sofia D. Wechsler,

The uncertainty principle can never be a basic postulate in quantum mechanics because it can be derived mathematically.The postulates of quantum mechanics can be found in a huge number of textbooks,lecture notes,and websites.

Regarding the false statement in the one before the previous post, that the uncertainty relation can be proved only for position and momentum, and in a special state described by a trigonometric wave function, here is a link https://physikmethoden.weebly.com/uploads/1/1/0/9/11093021/qmech_plenio.pdf

(page 71, theorem 37) for the readers who want to read a proof of the uncertainty relation – the uncertainty principle – for any two observables. These are lecture notes on quantum mechanics by Martin Plenio, from Imperial College.

The proof can also be found in standard textbooks; see, for instance, David J. Griffiths, Introduction to Quantum Mechanics, 2nd Edition, page 110.

As I explained in my previous post, the uncertainty relation results from the Cauchy – Schwarz inequality, which is an elementary inequality holding in any inner-product vector space; thus also in any Hilbert space.

Issam Mohanna

Dear Issam, the uncertainty principle with energy vs. time is proved. So, it's not a principle, it is rather a theorem. So is the principle with position vs. linear momentum. The extension to any two noncommuting observables is a postulate, I know no proof.

About the principles of the quantum mechanics (QM), I know no book or article that displays a list of the principles of the QM, e.g. principle 1, principle 2, principle 3, etc. For collecting the principles one has to browse through the book and pick what seems to be a principle. For instance, the quantization of the angular momentum and the allowed projections given a total angular momentum, are principles, or theorems?

Sofia D. Wechsler,

The uncertainty principle is both a principle and a theorem but not a postulate.

Issam Mohanna

What you think there is a difference between a principle and a postulate?

Sofia D. Wechsler,

To know the difference between a principle and a theorem is kept to you as homework.

I think the most important statement in the Wikipedia page about the uncertainty principle is: "It has since become clearer, however, that the uncertainty principle is inherent in the properties of all wave-like systems, and that it arises in quantum mechanics simply due to the matter wave nature of all quantum objects."

This reinforces the ideas of the Spacetime Wave theory that protons, neutrons and electrons are pure waves:

Conference Paper THE UNIFICATION OF PHYSICS (Conference Paper)

Richard

Issam Mohanna

I did not ask you what is the difference between a principle and a theorem, but what you think that is the difference between a principle and a postulate. I know the answer, but I asked what you think.

Sofia D. Wechsler,

A postulate was defined in one of previous comments;so to know the difference between a principle and a postulate,try to understand the difference between a principle and a theorem,taking into account that the uncertainty principle is both a theorem and a principle,both mathematically and empirically.

This Einsteinian YouTube video is helpful to understand the uncertainty principle as a principle:https://www.youtube.com/watch?v=OiHjzY6-088

Issam Mohanna

Principle = a statement widely accepted. For instance the fact that the state of a quantum system belongs to a Hilbert space.

Postulate = axiom = a statement which is adopted in a given theory, and is not widely accepted. For instance, in the Bohmian mechanics, it is postulated that particles follow continuous trajectory.

Theorem = a statement proved in base of principles and axioms.

Olivier Denis

Yes, but one should add the principle that the quantum states belong to a Hilbert space endowed with all the properties of Hilbert spaces.

Olivier Denis

The postulates of the QM cannot be circulary. "states are defined by postulate" is circulary.

Sofia

Just some comments, not full story.

I note you side step one difficulty altogether without mention of Schrodinger equation. Maybe you say only an H exists so that H psi(total) =i hbar d/dt psi(total)

The born rule is associated with "probability density"

Certainly quantum superposition

Psi (total) = sum over i of (a(i)) i> together with measurement or reduction rule

a(i) may be time dependent

Olivier: bats