In classical physics there are no uncertainties - the properties of matter on an atomic level are deterministic, that is to say predetermined. The theories of quantum mechanics, however, only say something about how likely the properties are and the two interpretations of the laws of physics were a source of great controversy between Einstein and Niels Bohr. New research strengthens Bohr's quantum theories. The results have just been published in the academic journal, *Physical Review Letters*.

The new research, conducted in collaboration between the Department of Mathematical Analysis at the Complutense University of Madrid and Michael M. Wolf, professor of theoretical quantum physics at the Niels Bohr Institute at the University of Copenhagen, offers a reassessment of the historic dispute over the (in-)completeness of quantum mechanics.

The results strengthen Bohr’s position by showing that any hypothetical theory that would be ’more complete’ than quantum mechanics, is necessarily in opposition to Einstein’s principle that things can only function locally. So, for example, an event on Earth could not instantly affect what happens on the Moon. Ironically enough, Einstein’s wish for a more complete description of the physical reality fail because of his own principle.

**The beginning of history **

From the early days of quantum mechanics, Albert Einstein did not hide his dissatisfaction with the statistical nature of quantum mechanics and the fact that certain observations such as location and time cannot be simultaneously measured with any accuracy.

Einstein especially challenged the newly developed ’Copenhagen Interpretation’ of quantum mechanics at the fifth Solvay Conference in Brussels in 1927 by creating a series of hypothetical experiments. They were all concerned with a common measurement of observations that are irreconcilable (i.e. not measurable jointly) according to the new theory of quantum mechanics.

However, during the conference Niels Bohr was able to refute all of Einstein’s proposed examples by revealing gaps and inconsistencies in Einstein’s reasoning. The dispute between Einstein and Bohr continued and culminated in 1935 when Einstein, together with B. Podolsky and N. Rosen, used a characteristic - now called entanglement - to argue that it makes sense to ascribe values to irreconcilable observations. Moreover, since quantum mechanics does not predict these values, Einstein thought that it should be considered incomplete.

This time Einstein’s argument could not be refuted so easily. Even though Bohr answered quickly, it took several decades rather than a conference break before J.S. Bell showed how the matter could be settled by an experiment. Later people like A. Aspect actually performed the experiment and disproved Einstein’s claims.

**Future theories**

Today Bohr’s theories are generally accepted and we know that a complete theory in the sense that Einstein, Podolsky and Rosen argued for is in opposition with experiments or with Einstein’s principles.

However, one question remained, whether there could be a theory, which is more complete than quantum mechanics, but still incomplete enough to be in agreement with Einstein’s principle. The new results, which consist of a series of theoretical mathematical calculations all answer no to this question.

”Our findings not only close the past discussion. They also tell us something about theories of the future - how theories that go beyond quantum mechanics should be. It makes no sense to look for theories that are more deterministic, that is to say more certain than quantum mechanics. If we stick to Einstein’s principles, we have to accept a lot of fuzziness”, explains Michael M. Wolf, professor at the Niels Bohr Institute.

**Explore further:**
Jumping into the quantum whirlpool

**More information:**
Physical Review Letters -- prl.aps.org/abstract/PRL/v103/i23/e230402

arXiv -- arxiv.org/abs/0905.2998

## flaredone

Jan 18, 2010## flaredone

Even worse, his main ideas of general relativity are based on quantum mechanic phenomena, in fact. The effects like gravitational lensing or relativistic aberration are typical nonlocal phenomena, violating Lorentz symmetry, in fact. Just the fact, relativity can be used for their formal description doesn't mean, we could observe them in strictly local arrangement (the fact, you can observe lensing is the consequence of the fact, you're well outside of the source of gravitational field). In this sense, general relativity (like every generalization) is based on violation of special relativity.

Such faux pass is analogous to epicycle model, which describes the heliocentric system surprisingly well, albeit from reciprocal perspective

## RayCherry

One day modern science may be brave enough to admit that the Victorian visionaries where right to suggest that there exists a form of energy that permiates through all other forms of energy and matter, but that time is not now and it does not help to make false or weak arguments to force the point. Patience and helpful support to those studying similar phenomena will aid the aetherists more in the long term: interstellar medium; the fifth force; dark energy; "the eternal flame" and (ultimately) the energy within a sigularity when at complete rest. These all point in a similar, if vague, direction towards a single causal force/energy/carrier/medium upon which all else is dependent and related.

PS: MS Word with English spelling and grammer is the mysterious force behind many comments. It would help you to express your ideas.

Sincerely, Ray

## flaredone

Jan 18, 2010## cius

check your own spelling and 'grammer' Ray

## eachus

The Copenhagen interpretation says that the statistics are all that there is. You can't go beyond them. But lots of recent experiments have shown that you can, if you are careful determine a quantum mechanical property without "observing" in a QM sense. What do you see if a particle is here if spin up, and there if spin down? The particle is half here and half there--or whatever the right ratio is for that experiment.

It gets "worse." Send light through a beam splitter, but arrange it so that less than one photon goes through the left arm. You will get interference fringes if the left arm is not blocked. If you want you can even take a picture of this unilluminated object.

## eachus

It used to be a joke when I was young. QM, relativity, causality. Pick any two. Today it is far from a joke, and it is causality that is likely to go out with the bath water.

The holographic universe is coming up fast on the outside. This is the theory that says that everything inside a black hole can be determined by looking at the event horizon. Since the universe has an event horizon, everything inside it can be determined by looking at the (three dimensional including time) event horizon.

## Parsec

Einstein's Nobel prize for the photoelectric effect was for 2 things, using Plank's proposed incremental energy levels and establishing that light in this case can be considered purely as a particle. This has nothing to do with Quantum Indeterminacy or the locality principal. In addition, gravitational lensing is absolutely not a non-local phenomenon, and effects that happen at relativistic speeds are caused by nature adhering to the locality principle, not violating it.

I am nevertheless tickled by the intellectual density of the comments on this article.

## frajo

## frajo

## broglia

It seems, for certain people, the more confusing and obscure theory, the better - they tend to mysticism naturally and science replaced politically incorrect religion there. For such people science is obscured, because they just want so. We should say clearly, king is naked until we get some undertandable explanation.

## Mr_Man

About the "Event Horizon for the Universe" - Thought experiment here. Say you find a way to get further toward the edge of the Universe than any other piece of matter and you go even further out. You would essentially be extending the Universe. There isn't empty, unfulfilled space further out. "More space" only appears when more matter spreads out. Another way of looking at space is it actually "comes from" within existing space, as if dark matter is actually increasing and causing the universe to expand.

Ultimately this leads me to think that if you were to fly in a straight line thru space indefinitely, you would eventually end up where you started**. The expansion of the universe would simply make that "ring" larger as time passes (and the Universe increasingly expands), like a ring in a tree trunk only in 3D.

## Mr_Man

** Assume you were traveling faster than the speed of light so you could complete your journey and end up exactly where you started before entropy and the expansion of the universe would effect your trek. That said - traveling at near the speed of light your trek straight to the edge of the Universe would ultimately be a spiral expanding outward indefinitely.

I don't think you can compare the edge of the Universe to a black hole unless nothing spilled out from a black hole into the rest of the universe. But Hawking Radiation means the black hole isn't truly separated from the rest of the Universe. I know that wasn't your point, eachus.

## Mr_Man

My point is in my thought experiment I think many people see the Universe as flat - like an unfolded 2D model of Earth, but really it is a 3D globe. You can't travel to the "edge" of earth. The Universe is similar (obviously 3D) and not statically a sphere like the Earth, but the idea is the same. You go straight out but eventually you make a big loop. Now if the "Earth" in my example was to grow outward indefinitely, you may never actually get back to your starting point, you would have more area to cover the longer it takes to make your trek, like an outward spiral, so you'll never truly end up where you started. It may not exactly seem like you are making a loop, but you'll never get "outside" the Universe.

## Noumenon

Immanuel Kant believed that a-priori cognitive faculties determine the form of experience, and so understanding in general. Classical physics expected that theoretical models should be 'understandable' in addition to allowing for predictions. Therefore Classical physics presumed an artificial intellectual coherence to reality as a working premise, and so failure was eventually inevitable. There was no justification for presuming mental paradigms would be applicable beyond the macroscopic realm for which the mind evolved.

Bohr, perhaps not aware of Kant, realized that the role of the science was to make predictions, not to provide an understanding of the underlying reality. Einstein wanted it all.

## jsa09

Many people get them confused. The unknown is time line dependent and therefore is a temporary state. The unknowable is time line independent.

When dealing with our current understanding of measurement to the highest level of accuracy we can get it, turns out that as we get more accurate our results get more fuzzy.

And when our kids are doing geometry in school and are asked "How many points on the line AB?" the answer can not be infinite as it was when we went to school. Instead, the answer will have to be a mathematical formulae.

## frajo

Jan 20, 2010## johanfprins

The Copenhagen interpretation "explains" it by maintaining that we "cannot know how how this happens". Anybody who calls this explanation "physics" is in need of psychiatric treatment.

The simple fact is that within the essence of a Schroedinger wave, time does not exist: It is easy to prove that it does not "wave" within our three-dimensional space. It is thus a holistic entity which is in instantaneous contact with itself over the whole three-dimensional region that it occupies. This is also the case for an entangled wave. If you tickle it on one side the other side knows instantaneously. If your measurement disentangles it the disentangled parts are correlated at that instant: However they are now separate parts: Another measurement on one of these disentangled entities does not affect the other disentangled parts anymore.

## Noumenon

## Noumenon

## frajo

Yes.

Are you referring to mathematics or to physics?

No. Because in the mathematical discipline geometry line AB is defined to be the set of all real numbers between the real numbers at A and B. The cardinality of this set is aleph-one which means uncountable infinite.

You see: Two different things - mathematics and physics.

## Whatwhat

If I'm not mistaken the key word in that sentence is theoretical. If a theory rests on a false premise even a subtle one it can be used to prove anything. That is the reason experiments exist because without them the logical (at the time) theories of centuries past would still hold sway. Any scientist who believes one theory can, without any doubt, prove a "no go theorem" exists is deluding himself. It is impossible to prove a negative and fallacious to think it can be done based on a theory that is very obviously incomplete.Only experiments and open minded objectivity can prove a theory is likely and even they cannot prove a negative."No go theorems" are more akin to unprovable pseudoscience than they are to hard objective science. The reason they never seem to go away is that they aren't seriously accepted but mathematicians keep grasping at the straws of certainty.

## flaredone

http://en.wikiped...tization

## johanfprins

This is correct: Nature is modelled in terms of "state vectors" i.e. waves.

This is nonsense. It is the political stance by the Coettingen-Copenhagen group to distract attention from Schroedinger waves; and has led us into the quaqmire of quantum field theory; based on a quantum phase which cannot be the phase of a harmonic wave amplitude as required by Scgroedinger's equation.

Nonsense. Physics is the creation of models which allows us to "visualise" in terms of our known human experience how Nature functions: Obviously the visualisation must give correct predictions. Wthout visualisation we reduce physics to superstition

## johanfprins

Since the gobbledegook of the Copenhagen interpretation turned physicists into idiots, nobody noticed that matter waves (as can be derived from Schroedinger's equation) are already commensurate with Einsteins gravity. Like any wave the intensity must relate to the energy of the wave which is in this case its mass. The so-called "tunnelling tails" are the curvature of space around the mass. Using this interpretation it is easy to see that there are NO PARTICLES: In fact it is easy to derive Einstein's photoelectric equation solely in terms of wave-interactions.

## johanfprins

## Noumenon

My quote was badly worded; my point was that physics functions very well without the added burden of providing an intuitive comprehension which above I equated to classical physics to differentiate from the quantum revolution, which I believe was so do to epistemological reasons. If wave mechanics was shown to be equivalent to matrix mech then clearly an unvisualizable formulation could in principal serve the core purpose of physics, which I maintain to be of predictions only....

## Noumenon

It seems a weak argument that the Copenhagen interpretation was simply a "political stance" of distraction for two reasons; Schrödinger had shown his wave solution to be equivalent to matrix mechanics so no distraction was possible especially given the atmosphere of reluctance (Planck, Einstein, Bohr, etc, etc) of accepting the quantum theory; The motive for distractions are against Bohr interpretation, not the other way around, even today with the ultimate distraction of many-worlds interpretation. And secondly,..

## Noumenon

## Noumenon

Yes, time is an a-priori intuition of mind and a "classical" notion, so an observation necessarily adds this conceptual structure in the interface between minds and reality, yet the notion itself cannot be used for making sense of EPR. " Thus, Einstein was in essence correct",.. you have it quite backwards. It is neither a wave nor a particle.

## johanfprins

Matrix mechanics is just a second rate representation of wave mechanics within a coordinate system. The way you want to see physics is like visiting an oracle to obtain predictions without having a clue why they work. In my mind this is nothing else but superstition.

## johanfprins

Can you prove experimentally that "it is neither a wave nor a particle". I am so tired of people making claims they cannot substantiate. It clearly can never be a particle since particles can never diffract. It can though always be a wave since a localised wave with mass-energy (inertia) can move like a particle with a centre of mass. Thus an electron-wave is nothing else than a light wave with inertia. It is a light wave that has been stopped in its tracks so that it is stationary within an inertial reference frame. That one can stop a light wave like this is an experimental fact.

## johanfprins

For some reason my program does not respond when I want to quote your comment on the "political stance".

I am, however, afraid that you do not know your physics history well. When Bohr and Heisenberg subjected Schroedinger to third degree interrogation during 1926, Schroedinger had not yet proved the equivalence of matrix mechanics and wave mechanics. When he did later on the Copenhagen group would not reconsider their stance. I still maintain that it was political since the limelight would have shifted from Goettingen-Copenhagen to Zurich. This is typically how physicists respond, and the reason why physicists, like you, grab at superstition.

## Noumenon

-------

Heisenbergs formulation was done independently and in any case the Copenhagen interpretation continued unabated despite Scroedinger or even Einstein's best efforts, ... until relativily recently. The reason for this fact is more profound than I think you give it credit for.

## Noumenon

## Noumenon

It would not have shifted because no one was able to make sense of qm in that camp. You forget that the majority were reluctant in accepting Bohr/Heisenberg despite Einstein owning the limelight and shining it himself on Bohr by attempting to make 'sense' of it. The history your nit getting is that in order physics to move on, it had to stop trying to visualize things, and this is The reason Bohr's interpretation was accepted.

## Noumenon

## flaredone

I can admit, such approach may be useful for the rest of civilization - not saying for shamans itself - but why we should call it a science, after then?

## flaredone

Jan 23, 2010## flaredone

The particle character of light is not difficult to observe in spark chamber, where gamma ray photons are spreading. Or you can observe their path in scintillator. It's evident, the path of these thingies is pretty localized.

http://tinyurl.com/yg6lgs6

## Noumenon

@alexis? The shamans did not construct any models but just remembered that doing such and such results in such a colour. Science is about constructing models in order to make future predictions of observables. These models are not the reality itself, but are a means of relating observables only. Some terms that are used are treated like black boxes to define a thing, for example, no one knows what an electron IS, but it can be treated as an entity of itself.

## flaredone

Not saying, some formal models are unable to recognize their limits at all. As the result scientists are searching for gravitational waves, while filtering out CMB noise (which is formed by these waves), looking for extradimensions while having them all around and they're doing similar dumb or even dangerous research.

Which could be funny, if scientists would realise it for their own money at safe distance from Earth.

## PMende

You seem to be fairly adamant that you know for a fact that there are no particles. The only way that one can KNOW that there are no particles is to include in the definition of the word particle: "something that has the quality of not existing." Every single quantum mechanical process can be described through wave-like or particle-like behavior. EVERY SINGLE ONE.

The two interpretations are not mutually exclusive. In fact, they are EXACTLY IDENTICAL. This is most easily seen through the the equivalence of the path integral formulation and the wave equation formulation of quantum mechanics. There is no wave whose paths you're summing over. There is no particle whose amplitude oscillates through space. When we want to describe some process by saying it is a particle or a wave are merely using convenient theoretical constructs to describe the behavior of world as we see it. Nothing more, nothing less.

## johanfprins

It is a one-sided statement to say "there was simply no classical handle left". This excludes the possibility that there is such a classical handle, but it was missed at that time; and subsequently it became accepted dogma that "wave-particle duality" is self-explanatory. The fact is that physics is based on REsearch: All interpretations MUST always be questioned in perpetuity: If not we will miss paradigm shifts, which the main objective of physics.

The "classical" handle that has been missed is the foundation stone on which all physics is based: Galileo's inertia, which resulted in Einstein's equation E=mc^2. When you apply these classical concepts to a free electron wave, you will find that this wave MUST have a centre-of-mass. Unless such a wave diffracts, one will observe it as a moving particle.

## johanfprins

If you look closely at Schroedinger's equation, you will find that the harmonic motion does not Occur within our three-dimensional space but within two extra dimensions: one is the time dimension. The intensity within our three-dimensional space does not depend on time: Time does not exist within this region of space. It only appears when the boundary conditions change.

One then finds that the intensity of the wave relates to the mass of the electron and the curvature in space around this mass.

## johanfprins

## johanfprins

It is well known that when a light wave enters a material its speed becomes less than the light speed in vacuum; and that we must then use cochang

## johanfprins

So do you still think there is not a "classical handle"?

## johanfprins

Obviously it cannot be both: So there are three possibilties (i) It is something else which sometimes act like a particle and sometimes like a wave (This reeks to me of superstition) (ii) It is a particle that can act in a manner which we interpret as wave (We know that the definition of a particle excludes this possibility) (iii) It is a wave that acts under suitable circumstances in such a manner that we interpret its behaviour as being that of a particle: As outlined above I prefer the latter interpretation since a wave with a centre of mass will move through spcae like a particle even though it is a wave: When slowing down a light wave to move at a speed less than c, it gains inertia and a centre-of-mass. A free electron is a light wave which has stopped within an inertia reference frame owing to the curvature of space: I believe the latter is real physics.

## johanfprins

I know this history: But what you are not getting is that the decision to move on without visualising has been a convenient crutch and should not have bee elevated to become "holy dogma". This decision has served solid state physics well and led us "cookbook-style" to our age of digital electronics. Unfortunately in the case of quantum field theory it has led physics astray and we ended up in a quagmire of "renormalistion" and similar mathematical claptrap.

## johanfprins

I do not know WHY people state with such conviction that QED is a successfull model. Any model which allows fiddling factors, like subtracting infinity from infinity to get what you want will give you what you want. The fact is that the same concepts have been used by Leon Cooper to derive that electrons form pairs in superconductors, while the latter has nothing to do with superconduction. In fact Cooper pairs probabl;y cannot form at all.

I do not think we should bring in Kant at this point. Obviously for all physics we develop as human beings reality must conform to our a-priori cognitive faculties: So what!

## johanfprins

THe same waves which we can observe as light when they have no inertia (no mass energy) and that we can observe as matter when they have inertia.

So would be the path of any loclaised waves: Why call them "particles"? A wave morphs when its boundary conditions change: If the boundary conditions are such that it has to be a localised entity it does not mean that it has to be a particle!

## johanfprins

I am grateful that you brought up the path integral formulation since it is NOT equivalent to the wave equation formulation. The quantum phase angle used for the path integral formulation cannot form for a harmonic phase amplitude which is a solution of a harmonic wave equation. It is simple first year physics to prove this. A harmonic wave can only have a phase angle which is a continuous function of position when this angle is a linear function of position: i.e. equal to kx (k is the wave vector).

It is the use of this ephemereal "quantum phase angle field" which has been used to formulate impossible physics like Dirac's monopoles, and derivations for which a circular integral over a conservative vector field can supposedly be non-zero. claptrap!

## PMende

## Noumenon

Maxwell's theory failed as a 'classical handle' because the energy of a light wave depends NOT on it's intensity but rather on it's wavelength, and a photon imparts a momentum that depends on it's wavelength, and NOT it's intensity. The Maxwell form of EM with boundary condition of matter was attempted and didn't stand up.

## johanfprins

Schroedinger's equation cannot be used to model a free electron, since it incorporates its rest mass as an input; where-as the energy of a stationary free-particle IS its rest mass. Thus, the appropriate differential wave equation required to model a free electron relative to its inertial reference frame, must NOT have the rest mass as an input but as the solution.

Schroedinger's equation is an approximation which is ONLY valid when the mass energy of an electron wave is less than its rest mass energy. When it is more, the electron wave has momentum so that it moves relative to an observer and the path it follows can be accurately calculated using classical mechanics.

The Lorentz transformation allows such a classically moving "centre-of-mass" wave to have coherent wave fronts: For this reason it can diffract.

## johanfprins

## johanfprins

The Schroedinger equation is a harmonic equation: This limits the way in which its phase angle can change with position. The phase angles used for the path integrals cannot be be part of a harmonic wave. It is, of course, always possible to concoct a harmonic wave by adding components which are not harmonic waves in their own right: For eaxmple, one can generate violin music from digital code but this does not mean that when you play a violin you produce digital code. The digital code is "virtual reality": Also the path integral method.

This is why it is so important to "visualise" and not just to model and predict. Incredibly it is possible to use "virtual reality" and predict effects which are later measured. The prime examples are the Aharanov-Bohm prediction and Josephson's prediction of SC-tunnelling.

## johanfprins

It is undergraduate physics to prove that the total energy of any wave depends on both its frequency and intensity. Calculate, for example, the total energy in a violin string for different frequencies.

The quantum of energy discovered by Planck has NOTHING to do with a "particle": It is simply the lowest energy that a light wave with a certain frequency can have. A Maxwell macro light-wave with a definite frequency consists of an entanglement of quantum waves which coalesced to form a single wave with a single frequency. By entangling they do not exist separately "within" the macro-wave. The more quanta which entangle, the higher the intensity of the wave: i.e. the more energy it has. Thus the total energy of the wave is determined by its total intensity: If this were not the case radio antennas would not have functioned.

## johanfprins

It is for the latter reason that the photo-electric effect is observed: It is thus purely a wave-wave interaction.

A stationary electron within its inertial reference frame finds itself within a harmonic potential with a single degree of freedom. Thus the wave modelling this electron is a Gaussian wave with a zero-point energy: and this gives you the electron's rest mass energy. When you replace the rest mass in Schroedinger's equation with this expression you obtain Maxwell's equation for the electric potential subject to suitable boundary conditions.

## Noumenon

Given the context of my statement, when I said "energy of a light wave" I expected you to understand I was speaking of the quantum of the electromagnetic field, the photon, in which case explanation of the photo-electric effect could not be dependent upon intensity of light but rather wavelength, thus the Maxwell formulation could not be put to use by even the majority whom clung to it. But according to you Bohr brainwashed the entire physics community and the LHC uses massive amounts of liquid helium because of politics of superconductivity.

## johanfprins

I understood that very well, and explained to you how the photo-electric effect really works in terms of waves: Maxwell's equations also model a light wave even when it only has a single quantum of energy. Such a wave's intensity is equal to the quantum of energy. When such a wave enters a metal, the boundary conditions change and it thus collapses and entangles with an electron wave to add mass to this wave. When this mass is larger than the rest mass, an electron is ejected. Thus a macro-wave consisting of entangled quanta is NOT a quantum field as modelled in QED. QED is based on wave-particle duality: No wonder Bohr had a hoseshoe behind his office door!

## johanfprins

I just cannot imagine how you could logically connect Bohr's interpretation of quantum mechanics to the "large amounts of liquid helium" used at the LHC to cool the supermagnets. What "politics" of superconduction are you talking about in this case: Really, do you still have all your marbles?

## Noumenon

We are going to go around in circles I'm afraid. You can't save Maxwell EM and at the same time use the 'quantum of energy', to avoid qed.

## Noumenon

## Noumenon

As an independent analysis of knowledge his ideas suggest to me that 'visualization' or classical physics (intuitive), may not be a trust worthy guide to physics at the sub-micro realm. Indeed this is the history so far.

## johanfprins

Why do you not try and be a physicist for a change and read the publications about my discovery: and then critisize the actual physics, instead of mouthing off about "politics". It is people like YOU who placed Galileo under house arrest.

Not WE, YOU are going around in circles: Do you want to tell me a source cannot emit a light wave with energy equal to a quantum of energy, which will then spread out in space as determined by Maxwell's equations? Obviously, a light wave of ANY ENERGY will do exactly that. All experimental evidence confirm this. If not, Maxwell's equations should be wrong. So why do we have radios etc.? So please stop talking utter nonsense!

## johanfprins

Really: I have already demonstrated it 10 years ago for electrons extracted into a vacuum. At present I have prototype electronic substrates that can conduct laterally by superconsuction at room and higher temperatures: You arrange the laboratory and the tests, and I will provide these prototypes. Obviously the tests must be performed by people who are at least capable of understanding first year physics. This, unfortunately, excludes you personally.

## johanfprins

I always thought that classical physics, since Galileo, is supposedly based on experiment and logic: Where does "intuitive" suddenly come from?

AS pointed out above classical physics has to do with experimental results and then modelling these results in terms of processes we as humans can understand: i.e. in terms of processes we can visualise. If, as Kant says we cannot really visualise the actual reality, it is just too bad, since we only have the possibility try and understand physics within the constraints place on us. How do we know that these constraints are really such that we cannot visualise what happens in the "sub-micro realm"? It is only Kant's conjecture; not based on any experimental proof. It has no relevance to physics.

## Noumenon

## johanfprins

The Schroedinger equation is an approximation: It inputs the rest mass energy of a "free" electron whereas its solution must be the rest-mass of the wave. It does however prove that qm is complete: It is completely modelled in terms of waves having mass-energy. Wave-particle duality is thus superstitious voodoo.

A body with mass has a centre-of-mass which mandates that it MUST be stationary within an inertial reference-frame. When observed from another inertial reference-frame, this centre-of-mass moves as if it is a point particle. Thus an electron wave will move through space as if it is a point particle even though it is an extended object with a centre-of-mass. When, however, it reaches a diffraction grating it diffracts since it IS a wave all along. I see no "profound implications" here that are in opposition to classical physics; even though qm is complete!