1 Can We Believe in Modern Quantum Theories?

More than 30 years ago, I majored in physics. After a long interval, I recently studied it again, and got to have fundamental questions, one of which is shown below. If you give me a convincing answer, I really appreciate it.

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First of all, as an example, consider a photon traveling all the way from a far-away star. According to the traditional theory, the quantum cannot but diffuse, be diluted beyond measure and end up disappearing. [Suppose a photon is traveling in the z-direction. If x and y components of the momentum of the photon are both absolutely zero (xy-spectrum width = 0), the wave packet of the photon is already unlimitedly spread (plane wave). Otherwise (xy-spectrum width is not zero), the wave packet will spread even further.]

So, a kind of cohesive force like surface tension or the like is considered to be essential in each quantum field.

[According to the traditional interpretation of quantum physics, one may assume that, as soon as the photon is detected, the existence probability of the photon completely vanishes at all points including those millions or billions of light-years away. However, any theory has its own applicability limit. I cannot but judge the above assumption ignores the limit. The problem may be which is acceptable, the above mystical assumption or introduction of unknown cohesive force.]

A free and isolated elementary particle is considered to substantialize as a finite-sized wave packet (having finite length and width) and to have specific energy and momentum (if not, conservation laws cannot but be invalid). According to the traditional theory, however, finite-sized wave packet and specific energy-momentum are not compatible. Introduction of the cohesive force makes them compatible. [So, in my perspective, the Kennard (not Heisenberg) inequality fails.]

However weak the cohesive force is, Feynman diagrammatic calculation method is to be fundamentally changed and I wonder if renormalization is still needed.

These techniques are basis of modern quantum physics theories such as QED, QCD, and quantum gravitation theories including the superstring theory.

Then, can we believe in these theories?

Thank you.

SEKI Hajime

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2 Can We Believe in Modern Quantum Theories?

In my opinion, the tests of Bells Inequality imply that the universe is fundamentally non-local. This seems to be the issue you are questioning as well. It has been recognized for almost 100 years that the wave function is NOT the particle, that it is not in fact a real thing. Attempts to visualize a wave packet as being the physical particle will always be incompatible with the Bell's Inequality experiments, and no matter whether the results make sense to us or not, if we are being scientific we have to respect the experiments. The interpretation of those experiments is a matter of opinion however, and part of your comments concern interpretation.

A little more on locality: Based on our everyday experience we want to think of particles as originating at some point and ending up at some other point after following some specific (if unknown) path. I think this is a fundamental misconception at the quantum level. It appears that QM properly predicts where the particle can end up, and with what frequency (probability). If you look at how QM does this it is clear that there is no specific path, not at the quantum level. Bell's Inequality, as applied to QM, tacitly makes the assumption that once the particle has been emitted that its properties are fixed (e.g. polariztion angle) and independent of where it will eventually be detected. The fact that the inequality is violated by experiment shows, I think, that this tacit assumption is incorrect.

The resolution that I've come to is a slightly different interpretation of QM than the Copenhagen interpretation. I reject the Copenhagen interpretation because it is not compatible with Special Relativity. You can't have an event "causing" another event that is spatially separated from it because a different observer will say that the latter event "caused" the former event and that would violate the Relativity principle. Instead I accept non-locality.

Warning: the following may be a crackpot idea!!!

In my interpretation the source of the particle is in some kind of interaction with all the future potential destinations of the particle. The exact nature of this interaction is a bit mysterious but is described by the wave function. For electromagnetic interactions this appears to be the 4-potential. In any brief period of time the source can emit its particle to one and only one acceptable destination in the future, but only if it satisfies all required conserved quantities (energy, momentum, spin, polarization, charge, etc, etc.). In other words, the particle will not be emitted until a specific destination has already been selected. The probability of emission can be calculated by the wave function, but this calculation assumes that out there somewhere, in any direction, is a suitable destination.

This interpretation is inherently non-local in that the particle will not be emitted until the final destination has been chosen. This involves some kind of handshake forwards and backwards in time, but that is actually allowed by Special Relativity if inside the light cone. (This somewhat similar in concept to the Wheeler-Feynman emitter-absorber theory.) I understand this is distasteful to many, however, because it also implies that that the destination is already fixed. That is for example, a photon from the cosmic microwave background that was emitted about 13 billion years ago and is detected on earth today, this interpretation implies that even 13 billion years ago it was already determined that earth and our radio receiver would be here to receive it. That is such a crazy idea that I have trouble accepting it, frankly, yet it seems to be implied by experiment.

I share your suspicion that a proper theory of QM would avoid the infinities that require renormalization. The conventional opinion is that the need for renormalization is due to currently unknown physics at extremely high energies/short distances. When the physics at these scales are properly understood than the need for renormalization would go away. In this view current field theories are "effective" field theories. In my opinion this makes perfect sense, but sort of puts off the thinking to figure out the new physics (As a practical matter due to the lack of any experimental clues to how to formulate the new physics). I wonder if a field theory developed from scratch with non-locality in mind might lead to such a theory, but I have no clue how to do that myself (yet).

With regard to your final question, you have to accept that QED, QCD etc. give very accurate predictions, so there is clearly some "truth" to these theories. However, everyone recognizes that they are not yet complete. It is entirely possible that the next better theory will be very different in concept, but even then it will have to reproduce the current predictions that have been confirmed by experiment. Much as General Relativity is very different from Newtonian gravity, but reproduces the same experimental results that convinced people of the correctness of Newton's gravity. As a scientist you have to recognize that there is some "truth" in these theories. At the same time, there is clearly more to be figured out yet. Do you have to "believe" in these theories to say there is some "truth" to them? Does recognition that there is more to be figured out mean that you can't "believe" in them? Belief is an opinion, and it doesn't have to be black and white.

Rich L.

3 Can We Believe in Modern Quantum Theories?

My basic point is as follows: Without any cohesive force or some sort of cut-off mechanism, quantum wave of a free and isolated elementary particle cannot but diffuse, be diluted beyond measure and end up disappearing.

Your arguments do not seem to involve the above point. So, I cannot but say they are off-topic.

Thanks anyway.

SEKI

4 Can We Believe in Modern Quantum Theories?

>	In my opinion, the tests of Bells Inequality imply that the universe is fundamentally non-local.

Sorry Rich what do you mean by this.

The test of the Bell Inequality is in some sense only an experiment and based on the result of that specific experiment you declare that the Universe is not "local", not a combination of both "local and non-local", but: "non-local".

5 Can We Believe in Modern Quantum Theories?

I think your basic misconception is that the wave function IS the particle. It is not. That the wave function diffuses through space means that the PROBABILITY of where the particle can end up spreads out, but no particle, nothing real, is spread out this way. You need to separate the particle from the wave function, they are NOT the same thing.

As an example (that sort of implies hidden variables) consider a gun mounted on a spinning turntable with a random number generator determining when the trigger is pulled. Suppose the table is surrounded by a black cloth that prevents you from seeing the table, but does not imped the bullet in any way.

You can calculate the probability of finding the bullet at any time and place in the space outside the cloth screen. The probability will get smaller as you get further away from the table. The mathematics will imply diffusion, just like the wave function for a photon emitted by an atom. But this probability function is NOT the bullet just like the wave function is not the particle it describes.

There is no mechanism in QM that provides any "cohesive force" or "cut-off" to the wave function. This is not necessary because the wave function is not the particle, it is only a probability distribution describing the statistics of finding the particle someplace.

Rich L.

6 Can We Believe in Modern Quantum Theories?

Any distribution that is not sharp in momentum subspace, diffuses in postion subspace. This is not as mystery of physics but everyday experience.

What is the statistical distribution for one particle?

Its the distribution function one uses to model random choices of the starting conditions at time 0 for position amd momentum.

It is assumed that with fixed starting parameters the particle moves according to the classical canonical or Newtonian laws in its dynamical enviroment as a single event picked from a statistical ensemble of statistically independent experiments.

What is different in quantum mechanics?

Not so much. The algebra of observables spanned by position, momentum and spin is translated into the language of operators in a Hilbert space of function of position _OR_ momentum only, and the pure states - classical the trajectories with fixed starting position, momentum and spin - are replaced with pure states that are eigenstates of some observables, that can be given sharp values in an experiment dictating the starting distribution at time zero.

The apparent difference to canonical mechanics is now, that the pure quantum states evolving in a given dynmical environment display - as functions in Hilbert space - a statistical non-delta distribution over position and momentum variables and that these distributions still seem to act by conservation of momentum as if they were representing the position-momentum distribution of a classical swarm of particles.

This picture is naively wrong. The distribution again represents an ensemble of independent experiment recordings in identical environment with identical starting conditions at time zero.

Why is it wrong to think in pure state wave functions as particles?

Any measurement of any observable is an integral over the whole configuration space or momentum space. No local pointwise evaluable state properties can be measured locally only.

With the one exception: The set of commuting variables that are chosen to have a sharp set of common values remains so under the unitary time evolution in Hilbertspace of the set of pure states, wave functions, that are their common eigenbasis.

And this mathematical phenomenon is used widely in textbooks to circumvent the apparatus of probability theory in the 3rd theoretical course 'Quantum Mechanics', because with the introduction to quantum probability, that follows in course 4, most students drop out from reaching their personal limit point of aggregated mathematical inabilities.

Even if energy, angular momentum and spin components are constantly delta-sharp in atomic states, people reason much about momentum and position distributions. It reminds of being astonished as a human that bees cannot focuse on points in space because their eyes are built to control motion in 3-space and analyze colors of flowers in the environment.

The basic set of canonical observables does not expose itself in atomic states as an experimentally preparable entity.

On the other hand the set of q,p=-id/dq variables still constitute the mathematical basis in the construction of the relevant algebra of "good" quantum observables.

And this "goog" set, a set that is exactly or nearly constant in time with repect to atomic time scales i na given dynamical environment, is the only existing set of exactly measurable quantities in priciple.

Mathematically, all such quantities belong to category of the characteristics of symmetry groups and their representation by an operator algebra acting on Hilbert spaces or the like.

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Roland Franzius

7 Can We Believe in Modern Quantum Theories?

I consider that the assumption that there exist extremely small elementary particles (regardless of whether point-like or string) in reality is false and is the root of quantum paradoxes such as instantaneous wave function collapse, and single particle (quantum) interference in a double slit experiment, which your interpretation of quantum mechanics can never explain. And, quanta are basically considered to be only phenomena in the space-time with fields, which is con sidered to be the only substance existing in the most extreme sense.

I assume:
- Though a quantum behaves as a wave, it maintains its oneness while it exists.
- A free quantum carries its energy and momentum as a whole.
- A quantum can assume the character of a particle, which is extremely small, only momentarily.

(The following contains some parts of my first posting on this topic, of which I assume you do not take cognizance, and which are bracketed off.)
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In each quantum field, a kind of cohesive force like surface tension or some sort of cut-off mechanism is considered to be essential.

[As an example, consider a photon traveling all the way from a far-away star. Without any cohesive force or some sort of cut-off mechanism, the quantum cannot but diffuse, be diluted beyond measure and end up disappearing.] [Suppose a photon is traveling in the z-direction. If x and y components of the momentum of the photon are both absolutely zero (xy-spectrum width =3D 0), the wave packet of the photon is already unlimitedly spread (plane wave). Otherwise (xy-spectrum width is not zero), the wave packet will spread even further.]
[According to the traditional interpretation of quantum physics, one may assume that, as soon as the photon is detected, the existence probability of the photon completely vanishes at all points including those millions or billions of light-years away. However, any theory has its own applicability limit. I cannot but judge the above assumption ignores the limit. The problem may be which is acceptable, the above mystical assumption or introduction of unknown cohesive force.]

Unlike the four fundamental forces, this kind of cohesive force is to work only in each field.

On the above assumption, each quantum has only a finite size in the space even if it has specific energy and momentum. [So, in my perspective, the Kennard (not Heisenberg) inequality fails, and theories related to renormalization should be revised.]

Let's consider a process, a+b -> c(+d+=E2=80=A6), where each of a, b, c, ... stands for a quantum (elementary particle) which is real, not virtual. If a part of quantum a and that of b overlap one another in the space, both parts are assumed to reduce. Reductions of overlapped parts of quantum waves and above-mentioned cohesive force result in a kind of mutual attraction between the quanta. If the domains of quanta, a and b, both reduce to the same point or extremely small area, the above process can take place. As for quanta, among which no interaction is possible, no reduction of overlapped part of quantum wave is to occur.

Particle-antiparticle pair can be produced when high-energy photon collides with a nucleus or the like. It should be noted that no pair can be produced without a collision with a charged particle, which is to cause a reduction of quantum wave of photon.

The shape of a strongly accelerated quantum is to be distorted and intermittently reduce enough to emit a photon due to the cohesive force.

You may feel that the above arguments are quite odd, though I suppose that my interpretation of quantum mechanics is leastwise better than that of Copenhagen, many worlds theories and so forth.

Thank you.

SEKI Hajime

8 Can We Believe in Modern Quantum Theories?

>	As an example (that sort of implies hidden variables) consider a gun mounted on a spinning turntable with a random number generator determining when the trigger is pulled.

Such a comparison with a photon and a wave function is all very tricky

>	The mathematics will imply diffusion, just like the wave function for a photon emitted by an atom.

And what does tell you about the behaviour of photons in space?

The first thing you can do is to study the mathematics how water waves propagate through one or two holes. The same mathematics you can use to study the interference patern of (multiple) photons through one or two holes. This can even be used to study "individual" photons. The same mathematics you can also use (if I'am correct) to study the behaviour of electrons. With study I mean perform actual experiments not thought experiments as what you often see when I study (I mean read about) quantum mechanics.

But does that mean that an electron (photon) is a wave? Along that same line does it make sense to use a concept like the collapse of a wave function? IMO only when you can use in a mathematical way, with a model, to calculate the parameters of the debris of a reaction. Any way this collapse only says something about the position where this collapse took place and "nothing" about the past.

Nicolaas Vroom

9 Can We Believe in Modern Quantum Theories?

I agree, I made that argument only to get across the idea of the wave function as a probability distribution. The poster seems to be trying to think that the wave function is something real and represents the particle itself, which clearly doesn't work.

>

>>	The mathematics will imply diffusion, just like the wave function for a photon emitted by an atom.

>	And what does tell you about the behaviour of photons in space?

Only the probabilities of finding the photon in a particular location at a particular time. My point is that the wave function actually tells you nothing about how the particle gets there.

>	The first thing you can do is to study the mathematics how water waves propagate through one or two holes.

That can be misleading because the water waves ARE real and show locality. QM is inherently non-local, and that is one (of several) reasons why we consider the wave function to be a purely mathematical entity, and definitely not the particle itself.

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>	With study I mean perform actual experiments not thought experiments as what you often see when I study (I mean read about) quantum mechanics.

There are many real experiments to refer to about all this, the "thought experiments" are distillations of those experiments. Study the two slit experiment, Stern-Gerlach experiments, photon entanglement experiments (e.g. Aspects experiments) for the original experimental basis for the thought experiments.

>	But does that mean that an electron (photon) is a wave?

The photon is a QM particle embodying a real electromagnetic wave, that is represented by the wave function. However when you get into QED the photon becomes a very abstract concept. It is a handy concept for talking about how lumps of energy-momentum are transported through space-time, but I think it is a mistake to think of it as a spatially confined particle that somehow moves from point A to B. In this view (which may not be widely held) the classical EM wave is a fiction, like the wave function, that is useful mathematically for predicting the behavior of the quanta of energy-momentum.

>	Along that same line does it make sense to use a concept like the collapse of a wave function?

No, except as a mathematical concept, not a physical one.

Rich L.

10 Can We Believe in Modern Quantum Theories?

Again, you are equating the particle with the wave function. This doesn't work.

>	- A free quantum carries its energy and momentum as a whole.

I don't know what this means

>

- A quantum can assume the character of a particle, which is extremely small, only momentarily. (The following contains some parts of my first posting on this topic, of which I assume you do not take cognizance, and which are bracketed off.) ------------------------------------------------------------------ In each quantum field, a kind of cohesive force like surface tension or some sort of cut-off mechanism is considered to be essential. [As an example, consider a photon traveling all the way from a far-away star. Without any cohesive force or some sort of cut-off mechanism, the quantum cannot but diffuse, be diluted beyond measure and end up disappearing.]

Again, you are assuming that the wave function represents a particle spread ing out over all space. I know some people talk about the Copenhagen interpretation of QM like this, but I believe I'm correct in saying that most physicists dont think that way. The wave function is a probability distribution and it says nothing about what the particle is actually doing, or where it exists, between the emission event and detection.

>

[Suppose a photon is traveling in the z-direction. If x and y components of the momentum of the photon are both absolutely zero (xy-spectrum width =3D 0), the wave packet of the photon is already unlimitedly spread (plane wave). Otherwise (xy-spectrum width is not zero), the wave packet will spread even further.] [According to the traditional interpretation of quantum physics, one may assume that, as soon as the photon is detected, the existence probability of the photon completely vanishes at all points including those millions or billions of light-years away. However, any theory has its own applicability limit. I cannot but judge the above assumption ignores the limit. The problem may be which is acceptable, the above mystical assumption or introduction of unknown cohesive force.]

There is much talk about wave function collapse, instantaneous cause-effect relationships across space, that makes this seem more mysterious than it really is. I think the key to understanding this is non-locality (but others would disagree.)

>	Unlike the four fundamental forces, this kind of cohesive force is to work only in each field.

There is no need for any "cohesive force" because there is no real spreading out of the particle, only of the probability distribution.

I'm sorry, but I don't understand what you are getting at in the remainder of your post.

Rich L.

11 Can We Believe in Modern Quantum Theories?

That seems reasonable. After all, the mathematics of QM only describes the wavefunction, so why would we assume anything else exists? All else is mythology!

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>	I assume: - Though a quantum behaves as a wave, it maintains its oneness while it exists.

A wave remains a wave, you presumable mean.. But of course QM describes how single-particle wave functions sometimes evolve into two-particle and subsequently perhaps into multi-particle wave functions. So you have to describe reality at all times with the proper set of N-particle wave functions, one for each N, as QFT basically is doing in Fock space.

>	- A free quantum carries its energy and momentum as a whole.

Why focus on a "quantum"? The quantum is just the difference between two levels, or two states, in QM. The states are the real entities! A "quantum" could in classical physics be the difference in position between two point particles. That is *not* the building block of reality in that theory! The point particles themselves are.

>	- A quantum can assume the character of a particle, which is extremely small, only momentarily.

Why do you believe it can? The mathematical description of QM can of course describe a wave packet with a small size, but that is probably not what you mean here. If the wave is spread out, why do you believe it can suddenly be very small? That sounds like the wave function collapse so here you go back to the mythology!

..

>	In each quantum field, a kind of cohesive force like surface tension or some sort of cut-off mechanism is considered to be essential.

By whom is this considered to be essential? QM does not describe any such cohesion. QM very clearly *denies* that such a force exists. So this is considered essential only by those who reject QM!

>	[As an example, consider a photon traveling all the way from a far-away star. Without any cohesive force or some sort of cut-off mechanism, the quantum cannot but diffuse,

Exactly the description by QM. That is how reality is! If you believe QM. (I had hope that you did, when you wrote that you rejected small point particles!)

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>	[According to the traditional interpretation of quantum physics, one may assume that, as soon as the photon is detected, the existence probability of the photon completely vanishes at all points including those millions or billions of light-years away.

That's the mythology again. QM in its mathematical formulation never described such an effect.

...

>	You may feel that the above arguments are quite odd, though I suppose that my interpretation of quantum mechanics is leastwise better than that of Copenhagen, many worlds theories and so forth.

What you do is *not an interpretation, it is a rejection* of QM (at least of QM as it is formulated now) because you want to add a non-linear cohesive effect (which destroys the unitary time-evolution which is at the heart of QM!)

But my question is why you want any change. Why can't you accept that the wave function is reality? (Or at least the best approximation of reality that we currently know?)

-- Jos

12 Can We Believe in Modern Quantum Theories?

I would say at least these two things:
1. Those six variables cannot simultaneously be chosen independently at the start.
2. The evolution for the members of the distribution slightly differs from Newton's laws (or else the hydrogen atom would still have a radiation dipole in its ground state!)

To be honest, I think that full QFT needs a wave functional describing distributions over field shapes, not distributions over point particle in phase space, but your analogy at least suffices for simple Schrodinger-like wave functions in QM.

...

>	the pure states - classical the trajectories with fixed starting position, momentum and spin - are replaced with pure states that are eigenstates of some observables, that can be given sharp values in an experiment dictating the starting distribution at time zero.

But they cannot all be given arbitrary sharp values! You essentially only have to specify half of the starting values, compared to the classical case..

>	The apparent difference to canonical mechanics is now, that the pure quantum states evolving in a given dynmical environment display - as functions in Hilbert space - a statistical non-delta distribution over position and momentum variables

Of course Hilbert space is already described by *only* momentum variables or position variables (the difference is just the kind of basis vectors you construct.) So if you use both simultaneously, then your possible distributions over them are highly constrained. Of course that also applies to then classical case.

>	and that these distributions still seem to act by conservation of momentum as if they were representing the position-momentum distribution of a classical swarm of particles.

If they still do, why are you calling this an "apparent difference?"

>	This picture is naively wrong. The distribution again represents an ensemble of independent experiment recordings in identical environment with identical starting conditions at time zero.

Why do you believe that? Why can't the state in Hilbert space just represent reality, without your additional restrictions?

>	Why is it wrong to think in pure state wave functions as particles?

On the contrary: it is *exactly equivalent* to a distribution of particles! If you choose the density in your distribution proportional to the wave function squared and use the Schrodinger flux to pilot each of them, as in Bohm's theory (I never understood why he only talked about one particle at a time).

>	Any measurement of any observable is an integral over the whole configuration space or momentum space. No local pointwise evaluable state properties can be measured locally only.

"Measurement" has to be described in QM as an effect of interacting fields, so all you are allowed to use is the unitary time evolution. Unless you invoke the collapse of the wave function or "projection operators" like that. But those are not described by QFT, nor by the Schrodinger equation, so you could mean anything by that. You post becomes meaningless if that is the path you want to take (unless of course you give the altered time-evolution equations you want to use for your distribution, or your wave function, but you don't!)

>	With the one exception: The set of commuting variables that are chosen to have a sharp set of common values remains so under the unitary time evolution in Hilbertspace of the set of pure states, wave functions, that are their common eigenbasis.

That is also meaningless. It is just your choice of basis, so it will remain your choice. Just like someone else can keep another choice. The state evolution is described by any chosen basis in Hilbert space.

>

And this mathematical phenomenon is used widely in textbooks to circumvent the apparatus of probability theory in the 3rd theoretical course 'Quantum Mechanics', because with the introduction to quantum probability, that follows in course 4, most students drop out from reaching their personal limit point of aggregated mathematical inabilities.

This may of course happen, but why do you believe you can introduce "probability"? The unitary time evolution does not make choices (since there is no collapse). And if no-one plays dice, there is no concept of probability. So I think the students do at least have a second reason to reject your concept.

>	Even if energy, angular momentum and spin components are constantly delta-sharp in atomic states, people reason much about momentum and position distributions.

So what's wrong? Another basis where you need to use a sum over the basis vectors instead of using just one. No big deal, what is your point?

>	It reminds of being astonished as a human that bees cannot focuse on points in space because their eyes are built to control motion in 3-space and analyze colors of flowers in the environment.

OK, if the students are astonished that a different basis requires different coefficients then there are some inabilities...

>	The basic set of canonical observables does not expose itself in atomic states as an experimentally preparable entity.

Why not? An experimentalist can prepare atomic states, or plane waves, or Rydberg states with (somewhat) localized particles, so whatever more you want, with some ingenuity it might be prepared. (And if not, it is just an experimental difficulty, mathematically you can describe the state with any complete set of eigenstates or non-eigenstates that you prefer to use as a basis!)

>

On the other hand the set of q,p=-id/dq variables still constitute the mathematical basis in the construction of the relevant algebra of "good" quantum observables. And this "good" set, a set that is exactly or nearly constant in time with repect to atomic time scales in a given dynamical environment, is the only existing set of exactly measurable quantities in priciple.

Wrong. If you would say "in practice" you might be right, but *in principle* any Hermitian observable is exactly measurable. (Measurable of course meaning that you can 100% entangle it with the output state of some measurement device. You just construct a device having the right interaction with the state under test.)

>	Mathematically, all such quantities belong to category of the characteristics of symmetry groups and their representation by an operator algebra acting on Hilbert spaces or the like.

They may belong to such a group (they always do to a trivial choice of group of course) but it is not relevant. If you just choose any Hermitian operator (local or non-local, belonging to a well-known group or not) then in principle you can think of an interaction mechanism with an external measurement system that will entangle your operator's eigenvalues with the measured output. And that's all that QM will ever do for you in terms of measurements! The procedure is not in principle restricted to "good" observables. Also there is *no way* you can do anything more in QM than entangling aspects of the state under test with your measurement device. Not even for "good" observables.

(Of course if you go outside QM and add the usual mythology you can claim other things, but then I must admit that I feel some sympathy for the students that are not accepting it! If you cannot describe the mathematical time-evolution you stand empty-handed, in my view.)

-- Jos

13 Can We Believe in Modern Quantum Theories?

It# always a bit difficult, to explain, why a wrong perception of the scientific correct and accepted quantum theory fails at any point, if you dig just one Angstroem deep.

1. Momentum and position distributions can be chosen freely from the set of pure states that are in the common domain of p and x operators (x psi(x) and k F(psi)(k) both square ineetgrable).

The reason is that any Fourier composition can be placed anywhere in space just by a complex gauge transform fron the tranlsatin group repesentation. Any position space distribution can be boosted to a moving distribution by a boost from the unitary representation of the Galilei group. The last transform is a bit tricky for Schrödinger theory since it involves a transform of d/dt -> d/dt + v.grad as known from diffusion theory. So it disappeares from sight if on focuses on time independent theory.

The fundamental fact mostly overlooked in textbooks:

This complicated interplay of the six canonical variables, independent but dependent on each other in the set of soulutions by the equatons of motion, only is possible in a field theory with complex valued state functions in a unitary space. In this category the local degrees of freedom are doubled and this allows for two things: algebraical independence of position und momentum and coupling the momentum to the em-gauge field.

By the same trick its possible to get real spectra of selfadjoint observables, impossible

>	To be honest, I think that full QFT needs a wave functional describing distributions over field shapes, not distributions over point particle in phase space, but your analogy at least suffices for simple Schrodinger-like wave functions in QM.

Yes, that is selfexplaining. Eigenstate series of the interaction Hamiltonian as a basis are not available under any circumstances except the small oscillation models and the three exactly solvable models presented in the first course.

To calculate basis free one introduces the QFT field mechanism, that is trivially equavalent to a freely chosen tensor product of Hilbert spaces. There is never a chance that such two different theories have a common domain of definition for their constituting operators.

>

...

>>	the pure states - classical the trajectories with fixed starting position, momentum and spin - are replaced with pure states that are eigenstates of some observables, that can be given sharp values in an experiment dictating the starting distribution at time zero.

>	But they cannot all be given arbitrary sharp values! You essentially only have to specify half of the starting values, compared to the classical case..

No wave theory has pointlike concentrated states in their domain of the energetic form. The pointlike delta-distribution is not square integrable, neither in space nor in k-space.

By the very definition of

/ = < (grad f)^2 >

as the expected kinetic energy, the energy is infinite in both cases. In a certain way one may state, that sharp concentration is a matter of energy at hand as you can see in CERN eg.

>>	The apparent difference to canonical mechanics is now, that the pure quantum states evolving in a given dynmical environment display - as functions in Hilbert space - a statistical non-delta distribution over position and momentum variables

>

Of course Hilbert space is already described by *only* momentum variables or position variables (the difference is just the kind of basis vectors you construct.) So if you use both simultaneously, then your possible distributions over them are highly constrained. Of course that also applies to then classical case.

Inappropriate conclusions from a poorly understood theory.

>>	and that these distributions still seem to act by conservation of momentum as if they were representing the position-momentum distribution of a classical swarm of particles.

>	If they still do, why are you calling this an "apparent difference?"

>>	This picture is naively wrong. The distribution again represents an ensemble of independent experiment recordings in identical environment with identical starting conditions at time zero.

>	Why do you believe that? Why can't the state in Hilbert space just represent reality, without your additional restrictions?

The central point is not the replacement of a trajectory in space time ba a pure state wave function in space time. The real reason to reject the wave function as someting real: Its complex with its absolute square and the psi^* grad psi in position space representing a local electical current density. But with other n identical particles present any of these can represent the one-particle current-4-density when all the other coordinates are integrated over as a "neclect"-operation.

But many particle states are subject to the Pauli principle that renders useless the one-particle states as measurable entities to construct the many particle states.
The meaninglessness is a quality of a a discourse. From a life of teaching we lean at least, that not everybody is able to explain tjhe obvious to everybody. There remain always some 5% that even after the standard QM courses believe that all that is complitely misunderstood.

>>

And this mathematical phenomenon is used widely in textbooks to circumvent the apparatus of probability theory in the 3rd theoretical course 'Quantum Mechanics', because with the introduction to quantum probability, that follows in course 4, most students drop out from reaching their personal limit point of aggregated mathematical inabilities.

>

This may of course happen, but why do you believe you can introduce "probability"? The unitary time evolution does not make choices (since there is no collapse). And if no-one plays dice, there is no concept of probability. So I think the students do at least have a second reason to reject your concept.

>>	Even if energy, angular momentum and spin components are constantly delta-sharp in atomic states, people reason much about momentum and position distributions.

>	So what's wrong? Another basis where you need to use a sum over the basis vectors instead of using just one. No big deal, what is your point?

The point is that the observable algebra of movement on a 2-sphere with Hamiltonian L^2 of the angles theta, phi and the angular momentum d/dtheta, d/dphi allows sharp values of i d/dphi and L^2 at finite energy, but no delta in position space. Its nonsense to postulate any principles like "use any base" without specifying the context.

>>	It reminds of being astonished as a human that bees cannot focuse on points in space because their eyes are built to control motion in 3-space and analyze colors of flowers in the environment.

>	OK, if the students are astonished that a different basis requires different coefficients then there are some inabilities...

>>	The basic set of canonical observables does not expose itself in atomic states as an experimentally preparable entity.

>

Why not? An experimentalist can prepare atomic states, or plane waves, or Rydberg states with (somewhat) localized particles, so whatever more you want, with some ingenuity it might be prepared. (And if not, it is just an experimental difficulty, mathematically you can describe the state with any complete set of eigenstates or non-eigenstates that you prefer to use as a basis!)

No, experimentalist cannot do anything they want. Thats only the fantasy of interaction free "I can think of doing everything".

>>

On the other hand the set of q,p=-id/dq variables still constitute the mathematical basis in the construction of the relevant algebra of "good" quantum observables. And this "good" set, a set that is exactly or nearly constant in time with repect to atomic time scales in a given dynamical environment, is the only existing set of exactly measurable quantities in priciple.

>	Wrong. If you would say "in practice" you might be right, but *in principle* any Hermitian observable is exactly measurable.

Probably you have heard this sentence 100 times. Its nonsense nevertheless.

>	(Measurable of course meaning that you can 100% entangle it with the output state of some measurement device. You just construct a device having the right interaction with the state under test.)

>>	Mathematically, all such quantities belong to category of the characteristics of symmetry groups and their representation by an operator algebra acting on Hilbert spaces or the like.

>

They may belong to such a group (they always do to a trivial choice of group of course) but it is not relevant. If you just choose any Hermitian operator (local or non-local, belonging to a well-known group or not) then in principle you can think of an interaction mechanism with an external measurement system that will entangle your operator's eigenvalues with the measured output. And that's all that QM will ever do for you in terms of measurements! The procedure is not in principle restricted to "good" observables. Also there is *no way* you can do anything more in QM than entangling aspects of the state under test with your measurement device. Not even for "good" observables. (Of course if you go outside QM and add the usual mythology you can claim other things, but then I must admit that I feel some sympathy for the students that are not accepting it! If you cannot describe the mathematical time-evolution you stand empty-handed, in my view.)

I concede that it is indeed possible to think of any measurement.

In practice, there is a very limited set, best be described by the standard in-out experiments of scattering theory. One prepares a free particle, shots it into an interaction area much to small for inspection with waves much longer than its extension, and perform some meaningful measurements the free out scattering states.

On the other hand one can measure the fine structure of the Dirac hydrogen with radio waves. This is a measurement of a very slow changing state of a nearly constant observable, the spin or the magnetic moment of the nucleus in an external oscillation field.

You can measure the spectrum of the Quantum Hall resistivity niveau structure or the Josephson frequencies, which will possibly replace the current time and length normals.

And finally one measures the anomalous magnetic moment of the electron. Its comparison with theory shows that it cannot be explained by a single wave function. Its an effect of the fact that the interacting electron states need the full tensor product states of infinitely many identical electrons and positrons in order to describe a simple number measured in the spectrum of the bound states.

--

Roland Franzius

14 Can We Believe in Modern Quantum Theories?

A quantum is said to have wave-particle duality. Considering single particle (quantum) interference in a double slit experiment and other so-called quantum paradoxes, however, I cannot but assume quanta are definitely waves, which are countable and each can be localized.
Those who deny the possible existence of cohesive force seem to neglect the wave nature of a quantum.

Is it OK?

Thank you.

SEKI

15 Can We Believe in Modern Quantum Theories?

>	1. Momentum and position distributions can be chosen freely from the set of pure states that are in the common domain of p and x operators (x psi(x) and k F(psi)(k) both square integrable).

And that very much limits your choice, compared with the classical case! You can no longer get any arbitrary combined momentum-position distribution.

The clearest proof that your momentum-position distribution *cannot* be chosen freely is to attempt to make it a product of two Gaussian distributions, with the product of their widths less than 1/2 (or 1/2 \hbar if you prefer). This will not be possible by the uncertainty principle. So not every function is allowed, QED.

One can also say that there is much more information in a real function of six variables (the classical distribution) than in a complex function of 3 variables, Psi(x,y,z).

Explicitly, one can discretize space, e.g. on a 10x10x10 lattice. Then the QM wave function Psi(x,y,z) consists of 1000 complex numbers, i.e. 2000 real numbers, whereas an arbitrary position and momentum distribution (over the spectrum of the discretized operators) contains 1000000 real numbers! That simply is more information.

...

>

The reason is that any Fourier composition can be placed anywhere in space just by a complex gauge transform fron the tranlsatin group repesentation. Any position space distribution can be boosted to a moving distribution by a boost from the unitary representation of the Galilei group. The last transform is a bit tricky for Schrödinger theory since it involves a transform of d/dt -> d/dt + v.grad as known from diffusion theory. So it disappeares from sight if on focuses on time independent theory.

This will not help you. Your new situation will have a distribution in p with unchanged shape, only centered around another point in p-space. So you still can't make arbitrary shapes based on that approach.

...

>>	To be honest, I think that full QFT needs a wave functional describing distributions over field shapes, not distributions over point particle in phase space, but your analogy at least suffices for simple Schrodinger-like wave functions in QM.

>	Yes, that is selfexplaining. Eigenstate series of the interaction Hamiltonian as a basis are not available under any circumstances except the small oscillation models and the three exactly solvable models presented in the first course.

With discretized space (e.g. on a lattice) Hamiltonian eigenstates will also be available. (But one has the problems of the lattice, like broken Lorentz invariance..)

>>

...

>>>	the pure states - classical the trajectories with fixed starting position, momentum and spin - are replaced with pure states that are eigenstates of some observables, that can be given sharp values in an experiment dictating the starting distribution at time zero.

>>	But they cannot all be given arbitrary sharp values! You essentially only have to specify half of the starting values, compared to the classical case..

>	No wave theory has pointlike concentrated states in their domain of the energetic form. The pointlike delta-distribution is not square integrable, neither in space nor in k-space.

So again that is *different* from the classical ideal of point-particles! Of course point particles led to infinities in several ways in classical physics as well, so we do not have to mourn their absence in QM for too long..

...

>>>	The apparent difference to canonical mechanics is now, that the pure quantum states evolving in a given dynmical environment display - as functions in Hilbert space - a statistical non-delta distribution over position and momentum variables

>>

Of course Hilbert space is already described by *only* momentum variables or position variables (the difference is just the kind of basis vectors you construct.) So if you use both simultaneously, then your possible distributions over them are highly constrained. Of course that also applies to then classical case.

>	Inappropriate conclusions from a poorly understood theory.

So what exactly don't you understand about the claim? In QM the complex amplitude distribution over the spectrum of only one of the two (either momentum or position) suffices to completely describe the state. This differs from having an arbitrary real distribution function over the two spectra (which contains *much more information*, as explained above).

..

>>>	Even if energy, angular momentum and spin components are constantly delta-sharp in atomic states, people reason much about momentum and position distributions.

>>	So what's wrong? Another basis where you need to use a sum over the basis vectors instead of using just one. No big deal, what is your point?

>

The point is that the observable algebra of movement on a 2-sphere with Hamiltonian L^2 of the angles theta, phi and the angular momentum d/dtheta, d/dphi allows sharp values of i d/dphi and L^2 at finite energy, but no delta in position space. Its nonsense to postulate any principles like "use any base" without specifying the context.

The position space in this case is (phi,theta) and that is in fact the most widely used basis to set up the theory! I don't see why you suggest there is anything wrong with it: the Ylm's are in fact *defined* on that angle-basis, i.e. as functions Ylm(theta,phi) to begin with.

...

>>>	And this "good" set, a set that is exactly or nearly constant in time with repect to atomic time scales in a given dynamical environment, is the only existing set of exactly measurable quantities in priciple.

>>	Wrong. If you would say "in practice" you might be right, but *in principle* any Hermitian observable is exactly measurable.

>	Probably you have heard this sentence 100 times. Its nonsense nevertheless.

Remember that "measurable" only means "can get entangled with another system". Feel free to prove that it can't (or to give any other mathematically defined meaning to measurable). If you cannot do that then don't make claims about nonsense.

>>	(Measurable of course meaning that you can 100% entangle it with the output state of some measurement device. You just construct a device having the right interaction with the state under test.)

>>>	Mathematically, all such quantities belong to category of the characteristics of symmetry groups and their representation by an operator algebra acting on Hilbert spaces or the like.

>>

They may belong to such a group (they always do to a trivial choice of group of course) but it is not relevant. If you just choose any Hermitian operator (local or non-local, belonging to a well-known group or not) then in principle you can think of an interaction mechanism with an external measurement system that will entangle your operator's eigenvalues with the measured output. And that's all that QM will ever do for you in terms of measurements! The procedure is not in principle restricted to "good" observables. Also there is *no way* you can do anything more in QM than entangling aspects of the state under test with your measurement device. Not even for "good" observables. (Of course if you go outside QM and add the usual mythology you can claim other things, but then I must admit that I feel some sympathy for the students that are not accepting it! If you cannot describe the mathematical time-evolution you stand empty-handed, in my view.)

>	I concede that it is indeed possible to think of any measurement. In practice, there is a very limited set,

Yes, in practice, but I already conceded that! Your earlier use of "in principle" was the only thing I objected to.

>	best be described by the standard in-out experiments of scattering theory. One prepares a free particle, shots it into an interaction area much to small for inspection with waves much longer than its extension, and perform some meaningful measurements the free out scattering states.

It is likely that other descriptions might be more useful if the description is not that of a scattering experiment, but (for instance) of states in a quantum computer. The "very limited set" you mention may not forever remain as limited as it is now in our standard textbooks. In principle, nothing restricts us to that set.

...

>

And finally one measures the anomalous magnetic moment of the electron. Its comparison with theory shows that it cannot be explained by a single wave function. Its an effect of the fact that the interacting electron states need the full tensor product states of infinitely many identical electrons and positrons in order to describe a simple number measured in the spectrum of the bound states.

Already you see that the in-out states (the usual plane waves going in and out) are not useful here. As for the choice of a single wave function: you would of course have to combine different multi-particle sectors of the Hilbert space. But if you accept the "sum" of a wave function of one position, one of two positions, one of three positions, etc., as a generalized "wave function" then it still might be a description (in principle, not very practicle perhaps).

As a matter of fact, the same problems can occur for any description of a scattering process. Also without a magnetic moment you might need states containing up to an infinite number of soft photons to remove the IR divergence from the answer.

-- Jos

16 Can We Believe in Modern Quantum Theories?

I hope that more readers agree with us.

> >>	The mathematics will imply diffusion, just like the wave function for a photon emitted by an atom.

> >	And what does tell you about the behaviour of photons in space?

>	Only the probabilities of finding the photon in a particular location at a particular time. My point is that the wave function actually tells you nothing about how the particle gets there.

Again I agree with you

> >	The first thing you can do is to study the mathematics how water waves propagate through one or two holes.

>	That can be misleading because the water waves ARE real and show locality.

There is nothing misleading in studying experiments involving water waves.

>	QM is inherently non-local, and that is one (of several) reasons why we consider the wave function to be a purely mathematical entity, and definitely not the particle itself.

All physical reactions IMO are local. In fact each physical reaction is a result of an other physical reaction (or change).

> >	With study I mean perform actual experiments not thought experiments as what you often see when I study (I mean read about) quantum mechanics.

>

There are many real experiments to refer to about all this, the "thought experiments" are distillations of those experiments. Study the two slit experiment, Stern-Gerlach experiments, photon entanglement experiments (e.g. Aspects experiments) for the original experimental basis for the thought experiments.

Non of these experiments can be performed as a thought experiment. The only thing you can do is discuss different setups of each experiment and dependent about the possible results of the experiment which other setups (arrangements) to try next. At the same time, based on the results, you can devellop and refine the mathematics that describe the experiments.

For example as the results of experiments you can learn that there are correlations involved. Knowing that there are correlations you can refine the experiments to learn more about the boundaries of these correlations.

> >	Along that same line does it make sense to use a concept like the collapse of a wave function?

>	No, except as a mathematical concept, not a physical one.

When the 'collapse of the wave function' does not make sense physical, than the concept also not make sense mathematically.

I get the impression that for some people the action of performing a measurement involves the 'collapse of the wave function'. IMO if this is always the case then the concept does not make sense.

Nicolaas Vroom

17 Can We Believe in Modern Quantum Theories?

You then should tell us *why* it cannot work. Just saying "which clearly doesn't work" is not convincing. Why can't the QM state vector be something real? Why can't it be the complete description of reality?!

>>	... My point is that the wave function actually tells you nothing about how the particle gets there.

>	Again I agree with you

How can you be sure particles exist? If we accept that the QM state vector (generalized name for "wave function" in cases of ageneral superposition of multi-particle states) is all of reality, then there is no need to include any other concept. You first need to prove to us that it is necessary.

...

>>>	The first thing you can do is to study the mathematics how water waves propagate through one or two holes.

>>	That can be misleading because the water waves ARE real and show locality.

>	There is nothing misleading in studying experiments involving water waves.

Exactly! Just like there is nothing wrong in studying electron fields and photon fields. Your problem (and Rich L's) still is to first convince others that this would "clearly" not work to describe reality. Until then, I would say the case is solved by QM. We know what reality is: it is the state described by quantum field theory (QFT).

>>	QM is inherently non-local, and that is one (of several) reasons why we consider the wave function to be a purely mathematical entity, and definitely not the particle itself.

>	All physical reactions IMO are local.

"Local" has a meaning in QFT and our theories *are* local in that sense! If Rich (or you) use another meaning it just becomes a game of words.

>>	... Study the two slit experiment, Stern-Gerlach experiments, photon entanglement experiments (e.g. Aspects experiments) for the original experimental basis for the thought experiments.

>	Non of these experiments can be performed as a thought experiment.

Yes they can. If you use (e.g.) QFT as your theory, you can do Aspect's experiment as a thought experiment. It would require describing the photons by QFT, together with the measurement setup, and even aspects body and his brain as well. Very complicated of course, but in principle you could do it.

The system (including Aspect) would end up in a superposition of the different result (and Aspect himself in a superposition of different states of mind, i.e. having observed different results), all with the amplitude ratios that QM gives us for these interactions. In practice it's a lot of work to compute all of it, but doesn't that make it "par excellence" a good case of a thought experiment? (Of course this closely matches the already well-known "Wigners friend" thought experiment. We are too late to invent something new here..)

...

>>>	Along that same line does it make sense to use a concept like the collapse of a wave function?

>>	No, except as a mathematical concept, not a physical one.

>	When the 'collapse of the wave function' does not make sense physical, than the concept also not make sense mathematically.

Right! The mathematical description should preferably only describe things that are in principle falsifiable, so they should at least have some implications for the physical world. Which could be equated to calling them "physical".

...

>	I get the impression that for some people the action of performing a measurement involves the 'collapse of the wave function'. IMO if this is always the case then the concept does not make sense.

It doesn't and it never did, because no-one ever answered:
"When is an interaction *not* a measurement?"
Systems are interacting all the time in our universe and in some cases we call one of them "device under test" and another one "measurement setup". That is purely subjective, so giving any physical meaning to it is pseudo-science.

And if you try to be fair and say that everything is a measurement, then the wave function of the whole universe collapses at any point in time and it never acts as a wave so you have no QM left..

18 Can We Believe in Modern Quantum Theories?

>	Why can't the QM state vector be something real? Why can't it be the complete description of reality?!

A state vector is never something real. It is mathematics. A complete description of the reality does not exist. Laws are also a description of the reality. In fact each law of a small part of the reality.

> >>	... My point is that the wave function actually tells you nothing about how the particle gets there.

> >	Again I agree with you

>	How can you be sure particles exist? If we accept that the QM state vector (generalized name for "wave function" in cases of a general superposition of multi-particle states) is all of reality, then there is no need to include any other concept. You first need to prove to us that it is necessary.

We know that there are particles by performing experiments. Demonstrating superpositions also requires performing specific experiments. A "wave function" is a tool to describe the results of experiments but it does not help to understand the experiments.

> >	There is nothing misleading in studying experiments involving water waves.

>	Exactly! Just like there is nothing wrong in studying electron fields and photon fields.

I agree with you.

>	Your problem (and Rich L's) still is to first convince others that this would "clearly" not work to describe reality. Until then, I would say the case is solved by QM. We know what reality is: it is the state described by quantum field theory (QFT).

QFT is a description of the reality, like any law. It is not the reality. The reality are the elementary particles.

> >	All physical reactions IMO are local.

>	"Local" has a meaning in QFT and our theories *are* local in that sense! If Rich (or you) use another meaning it just becomes a game of words.

If you use the word local than you should describe what you mean. A disease starts local and become global (in time) Global also implies, in some theories, instantaneous actions i.e. faster than light communication.

> >>	... Study the two slit experiment, Stern-Gerlach experiments, photon entanglement experiments (e.g. Aspects experiments) for the original experimental basis for the thought experiments.

> >	Non of these experiments can be performed as a thought experiment.

>	Yes they can. If you use (e.g.) QFT as your theory, you can do Aspect's experiment as a thought experiment. It would require describing the photons by QFT, together with the measurement setup, and even aspects body and his brain as well. Very complicated of course, but in principle you could do it.

19 Can We Believe in Modern Quantum Theories?

What is meant by "particles by performing experiments"?

I consider each of them as a quantum localized in a small area (e.g. an electron captured in a molecule, a nucleon in a nucleus, a quark in a nucleon, ...). So, they can be identified as waves, not particles.

If this is not the case, please explain.

Thanks in advance.

SEKI

20 Can We Believe in Modern Quantum Theories?

But can it be the correct *description* of reality? That was the question! As always, you are evading it..

...

>>>>	... My point is that the wave function actually tells you nothing about how the particle gets there.

>>>	Again I agree with you

>>	How can you be sure particles exist? If we accept that the QM state vector (generalized name for "wave function" in cases of a general superposition of multi-particle states) is all of reality, then there is no need to include any other concept. You first need to prove to us that it is necessary.

>	We know that there are particles by performing experiments.

Certainly not! If another theory gives you a correct description of experiments, you have no proof that your particle-based theory is the right one. To make it worse: your particle-based theory apparently leads you into trouble (judging by the problems you raise) so it most likely is the wrong theory!

>	Demonstrating superpositions also requires performing specific experiments. A "wave function" is a tool to describe the results of experiments but it does not help to understand the experiments.

Again the hollow claim. You have to be more explicit: What are the explicit things that are lacking? What would you expect from the theory that is now absent?

I certainly don't claim that the theory is perfect (or even remotely correct). I don't know that. But you are not giving any clear explanation why it is wrong!

>	QFT is a description of the reality, like any law. It is not the reality. The reality are the elementary particles.

Why? I think the reality is most likely the fields. Particles in the old-fashioned sense do not exist (of course we do re-use the name 'particle' for states described by the QFT creation operators, but surely that's not what you mean. Your classical particles are obsolete!)

>>>	All physical reactions IMO are local.

>>	"Local" has a meaning in QFT and our theories *are* local in that sense! If Rich (or you) use another meaning it just becomes a game of words.

>	If you use the word local than you should describe what you mean.

21 Can We Believe in Modern Quantum Theories?

The GeDanken is evidently a class of thought experiment. Its form is proper relation. If you can state the experiment relation design it means the experiment is true. If the experiment is done to relate law to physics it simply affirms a correctly formed law.

Logical completeness becomes an inversion experiment completeness. ergo the name GeDanken. There is no technical need to experiment a physics, if GeDanken is the form.

This is exactly why dark matter needs no further confirmatory experiment.

22 Can We Believe in Modern Quantum Theories?

The particle nature of light and particles is that they depart and arrive in discrete lumps at discrete times. The wave nature is in how they propagate from the emission event to the absorption event. We have trouble separating these two aspects of their behavior because macroscopic particles propagate as particles, not waves and macroscopic waves are generated and destroyed as waves not particles. This is what causes so much conceptual difficulty.

Microscopic particles, such as a photon, are emitted at a discrete event that is localized (to varying degrees) in both time and space. How they propagate is a bit mysterious but shows more wavelike characteristics than particle characteristics. For example, a photon reflecting from a mirror does not reflect from a single electron or atom on the mirror, but is reflected from ALL the electrons or atoms on the surface of the mirror. If the photon is detected past an aperture with multiple holes, there is a wave of some kind that propagates through ALL of those holes to reach the detection event. This appears inconsistent with the particle nature of the photon, but that is only because we have been conditioned to think of particles like rocks or baseballs. Subatomic particles are different.

Rich L.

23 Can We Believe in Modern Quantum Theories?

I think that we can't deny the fact that a quantum is more of a wave than anything. In case where a quantum (wave) is localized in a small area, it can be seen as a particle. Don't you agree?

>

Microscopic particles, such as a photon, are emitted at a discrete event that is localized (to varying degrees) in both time and space. How they propagate is a bit mysterious but shows more wavelike characteristics than particle characteristics. For example, a photon reflecting from a mirror does not reflect from a single electron or atom on the mirror, but is reflected from ALL the electrons or atoms on the surface of the mirror. If the photon is detected past an aperture with multiple holes, there is a wave of some kind that propagates through ALL of those holes to reach the detection event. This appears inconsistent with the particle nature of the photon, but that is only because we have been conditioned to think of particles like rocks or baseballs. Subatomic particles are different.

How do you define what a particle is? To me, you seem to be obsessed by the particle model.

It should be noted that most of so-called quantum paradoxes can be resolved by abandoning the particle model. (Of course, the Bell's inequality is an exception, though can never be resolved with the particle model.)

Anyway, quantum theories are constructed as theories of waves, and particles appear only in interpretations.

Thank you.

SEKI