The weird thing about QM is that no one really understands it. The quote popularly attributed to physicist Richard Feynman is still true: if you think you understand quantum mechanics, then you don’t. At a conference in Austria in 2011, 33 leading physicists, mathematicians and philosophers were given 16 multiple-choice questions about the meaning of the theory, and their answers displayed little consensus.

One of the most telling questions in the Austrian poll was whether there will still be conferences about the meaning of quantum theory in 50 years time. Forty-eight percent said “probably yes”, only 15% said “probably no”. Twelve percent said “I’ll organize one no matter what”.

However, QM, developed at the start of the twentieth century, has been used to calculate with incredible precision how light and matter behave – how electrical currents pass through silicon transistors in computer circuits, say, or the shapes of molecules and how they absorb light. Much of today’s information technology relies on quantum theory. A great deal of modern technological inventions operate at a scale where quantum effects are significant. Examples include the laser, the transistor (and thus the microchip), the electron microscope, and magnetic resonance imaging (MRI). The study of semiconductors led to the invention of the diode and the transistor, which are indispensable parts of modern electronics systems and devices.

I end with two great quotes:

"The atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts."

----Werner Heisenberg

"Anyone not shocked by quantum mechanics has not yet understood it."

---Niels Bohr

Although nobody understands it, quantum mechanics corresponds to reality. QM is by far the most exact physics theory. It accurately predicts phenomena of quantum nature. Thus, so far we have to belive is true.

It is a matter of perspective. I believe the mathematics behind QM is well defined, but the interpretation of this to suit a certain phenomenon may be baffling. Different researchers will have various point of views associated. However essentially these must coincide to obtain the same result and perhaps predict new behaviour. Regarding what is true, I'd like to mention Gandhi, "What may appear as Truth to one person, will often appear as untruth to another person. But that need not worry the seeker. When there is an honest effort it will be realised that what appears to be different truths are like apparently different countless leaves of the same tree."

Till this date QM has been able to explain and predict so many hitherto physically defying concepts, but essentially almost each of these have been experimentally verified or are on the process of verification.

So it is up to us to question the validity of QM or use it as a tool to understand reality to further depths.

First of all you should focus on the special value given by Feynman to the word "understand". He was not referring to the ability to make predictions or to provide an explanation for the behaviour of microscopic particles, but to the intellectual un-satisfaction of the explanation itself.

Just to name one of the oldest (and still unsolved) issue of the Copenhagen interpretation of QM, the problem of measurement: measurement is described as a fundamentally non-linear process, while all QM interactions are represented as linear processes. So one has to invoke a "decoherence" due to some coupling withe the macroscopic measurement apparatus. But no credible description of such "decoherence" has been given up to now.

However, this has nothing to do with the "scientific truth" of QM, in the sense that no experiment has been found up to now in contradiction with the QM results.

If we need to understand the way Feynman undertood the meaning of the word "understand," that poses the problem of undertanding the way we understand how Feynamn understood the meaning of the word "understand" and so forth, forever! Let's consider the analysis of the double slit experiment: Let A and B be the slits and C a spot on the screen. I am not going to be very rigorous in my approach, but I think it will be fairly clear.

According to the classical theory of probabilty: P(C)=P(C|A)P(A)+P(C|B)P(B). But what is P(C|A)? In the usual analysis of the double slit experiment, we act like if P(C|A) = P(A->C), but this is not an identity of mathematical statistics! P(C|A) = P(A and C)/P(A) and P(A -> C) = P(~A or C). (http://plato.stanford.edu/entries/conditionals/). It is my opinion that we need to stop for a while and examine the logical consistency of our theories. There is a logical principle of explosion: if there is a contradiction in a logical system any theorem can be proved true! If QM is inconsistent then it will explain everything and it will predict whatever we want it to predict. From this peril comes the need of understanding.

The question behind your question is 'how can we know that any physical theory is true', and the answer to this is very simple: If it can predict something that we can test, and these tests find the same answer as the theory, then this theory is true. If there is competing theory that explains the same thing with the same result, then the simpler of the two is to be preferred.

Quantum mechanics is extremely good at predicting the energy spectrum of hydrogen or the diffraction patter of photons scattered off a grating. Despite what most people think, quantum mechanics is also a very simple theory based on very few assumptions and equations. This makes it a very good theory.

Every theory has its limits though. Quantum mechanics and relativity don't go together. Quantum mechanics cannot deal with gravity in a coherent manner. In that respect quantum mechanics is false, but that has no impact on the part of physics where it works. On the other hand quantum mechanics is not a practical theory when it comes to describing large objects. It's construction requires that it be correct when describing say the trajectory of a cannon ball, but it is just not practical. Newtonian mechanics does a much better (i.e. simpler) job at doing so.

Well, regarding the prediction of the spectrum of Hydrogen let's remember that: a) "Although physicists were aware of atomic emissions before 1885, they lacked a tool to accurately predict where the spectral lines should appear. The Balmer equation predicts the four visible absorption/emission lines of hydrogen with high accuracy. Balmer's equation inspired the Rydberg equation as a generalization of it, and this in turn led physicists to find the Lyman, Paschen, and Brackett series which predicted other absorption/emission lines of hydrogen found outside the visible spectrum."(https://en.wikipedia.org/wiki/Balmer_series) b) Later, Bohr-Wilson-Somerfield "old quantum theory" was used to explain the spectrum of Hydrogen, applying Einstein's quantization rule $E = \hbar \omega$ to material particles which, in turn, inspired de Broglie's hypothesis, to explain electronic diffraction. An explanation after the facts is not such a powerful argument in favor of a theory as, for example, the successful prediction of the existence and discovery of Uranus and Pluto was for Classical Mechanics.

The new Quantum Mechanics, therefore, came after the facts and did not predict them. Quantum mechanics, on the other side is not such a good theory, the old problem of renormalization seems to be as good as new: http://inspirehep.net/record/29799/citations. Quantum mechanics is not even mathematically consistent. Let's take, as an example its "explanation" of electron difraction: considering that crystals are supposed to be made out of atoms and/or molecules, they would be made out of electrons, protons and empty space. Yet, for its "explanation" of electronic difraction quantum mechancis considers only the wave function of the incoming electrons, like if the elements in the crystal's lattice where some sort of hard inpenetrable objects, which is obviously absurd. I have performed some numerical computations in the classical limit where an electron was sent against a classical model of hydrogen with the result that the incoming electron was captured and the one that was originally turning around the proton was expelled. (The three body problem is not integrable, that's why I have used a numerical approach.) If I wanted to model the result of such an experiment as an electron being dispersed by an inpenetrable atom, I would have to accept that the electron's path was discontinuous. What means do we have to confirm the same is not happening in electronic difraction? (O. Chavoya; Influence of Internal Structure on Dynamics of Classical Particles; In Topics in Contemporary Physics; edited by J. A. Heras and R. V. Jimenez. IPN Press, Mexico (2000) pp. 127-142.)

But then, those considerations put aside: How do we avoid the circular argument? How can we know what is it that a theory predicts if we do not understand the theory. It appears to me that if we do not understand a theory we cannot understand its predictions and, if we do not undersand its predictions, how can we verify them?

Math is the answer. Physics is a precise science. Any theory that does not give precise predictions is not part of the realm of physics. Any theory worth its name has to make predictions that can at least in principle be tested experimentally. Whether one understands the motivation behind a theory or its very inner mechanics does not matter so much. It is the predictions and their testing that counts.

I recognize the need to use mathematics, as means to make statements as clear as possible. Nevertheless, in order for us to make a decision regarding a prediction by a physical theory, we need to understand the meaning of the numbers we are calculating, so we can match our necessarily incomplete mathematical description, to whatever it is that we are observing in the physical world.

A well known quantum theorist at Cornell Univeristy asked once: "Is the moon there when nobody looks?" Apparently he thought the question made sense. Let's now comfront that fact with this: http://www.astrobio.net/pressrelease/5679/water-hidden-in-the-moon-may-have-proto-earth-origin . How can we be sure that the Moon was formed 4.5 billion years ago if we are not sure if it exists and, therefore, it is there, when nobody looks at it? The Moon was formed 4.5 million years ago but it did not exist and it wasn't there because nobody was looking? This physicist is part of that elite in charge of protecting the legacy of the founding fathers of quantum mechanics; can you imagine the confusion in my mind, being a simple mortal?

I just don't think that the postdiction of the Hydrogen atom is in fact a thing to hold against the predictable qualities of QM. It seems merely a calibration of the theory. If I'm driving from town to town, I may hypothesize that my speed is more or less constant. I can then take measuremrents (distances and times) and cvalibrate my theory that in fact I was driving 80 kh/hr (and that the quadratic & higher order terms were close to 0).

@Robert Olling I agree wlith you, the postdiction of the Hydrogen spectrum is not a fact against QM, but it is not such a strong confirmation of it. That's my claim.

'One cannot disprove an axiom while remaining within a system that is based on that axiom.' (Godel's Theorem on Incompleteness)

When Feynman said that 'nobody' understands QM, this means that Feynman too did not understand it! In that case, how could he assert that nobody understands QM?

In his book "QED," Feynman says his theory is "crazy." I think he means the same thing in regard to "not understanding" QM. He demands an ontologically coherent account of nature in order to reach what he calls "understanding." A great divide separates the "realists" like Feynman from the "unrealists," who don't feel the same demand of realism as Feynman, and whom Feynman would dismiss as "crazy" themselves. Coming from the realistic "event ontology" of Russell and Whitehead, I've constructed the electron and its atomic cloud formations as causal set propagations, in line with the event ontology. The clouds produce Bohr's formula immediately, and further provide the FSC, plus the basis for the numerical calculations of QM. It seems that no one before has ever tried to construct physics from scratch using a temporal successor relation. It's all relativistic, since causal set theory is relativistic by default. That is why Russell and Whitehead adopted the event ontology. See the provided link for the causal set construction of physics.

http://vixra.org/pdf/1006.0070v1.pdf

Oscar

Where does it say a statement must be true. I like to refer to the current discussions in metaphysics. One can as well propose as long as it works a theory is OK.

I refer for instance to

http://plato.stanford.edu/entries/scientific-realism/

Harry

What is a theory, like quantum mechanics, if not a collection of statements about the physical world? The axioms of quantum mechanics are statements which we are supposed to admit as true, and all predictions of quantum mechanics are supposed to be logical consequences of those statements, even when we use approximations like in perturbation theory.

As Einstein puts it (in The Meaning of Relativity pp. 7-8):

"...In the present treatment, geometry is related to actual things (rigid bodies), and its theorems are statements concerning the behavior of these things, which may prove to be true or false.

One is ordinarily accustomed to study Geometry divorced from any relation between its concepts and experience. There are advantages in isolating that which is purely logical and independent of what is, in principle, incomplete empiricism. This is satisfactory to the pure mathematician. He is satisfied if he can deduce his theorems from axioms correctly, that is, without errors of logic. The questions as to whether Euclidean Geometry is true or not do not concern him. But for our purpose it is necessary to associate the fundamental concepts of geometry with natural objects; without such an association, geometry is worthless for the physicist. The physicist is concerned with the question as to whether the theorems of geometry are true or not."

Now, Harry, please, do not misunderstand me, I am not giving you an argument of authority with this quotation. Einstein might be wrong. Nevertheless, the way Einstein presents the relation between geometry and physics, both: explains what I am thinking and provides an answer to your question that's better than any answer I could give you. From your reference to the Stanford Encyclopedia of Philosophy:

“It is perhaps only a slight exaggeration to say that scientific realism is characterized differently by every author who discusses it, and this presents a challenge to anyone hoping to learn what it is....

...What all of these approaches have in common is a commitment to the idea that our best theories have a certain epistemic status: they yield knowledge of aspects of the world, including unobservable aspects.”

I am sorry to say that Einstein indeed is NOT the authority on Quantum Mechanics.

And as for scientific realism: there is also anti-realism as in the approach of empiricism or instrumentalism. In this approach a theory (QM) is just a handy tool to explain and predict observations and truth is not an item at all. This means that it is subjective whether one supports / accepts believes one of these concepts in metaphysics; but apparently it works and Bohr / Feynman could work with it while still not having a grip on why it is working

Oscar

I am not sarcastic at all. I just voice the latest in metaphysics. This is exactly the result of the embarrassment caused by Quantum Mechanics. It appears that philosophy of science (physics) just cannot cope with the principle non-determinicy of the theory/concept. The theory, as fullyestablished in the early 30's, has now been around for 80 years and nothing has yet replaced it showing its absolute strength. Also, it is now the foundation of theoretical chemistry.

Summarising, I am not a bit sarcastic, but voicing what I read with the modern philosophers of science. I particularly suggest Nancy Cartwright; most of her work also free on the web, such as "How the laws of physics lie"

I can only voice my support to the comment of Harry ten Brink. I am a researcher in the fundamentals of quantum mechanics (www.bec.gr). I truly believe that QM is one of the most beautiful and fascinating theories that mankind has come up with. However, I also believe that physical reality is a very difficult concept. We can only talk about what we can see (at least in principle) in our experiments. Any model of reality derives its meaning from its predictions. The physical reality that Oscar Chavoya-Aceves is missing in QM is very much there, it predicts and describes the world in a detail never possible before.

Let me give an example from my research. We can create matter-waves, where many atoms together behave just like a wave. If you send one matterwave and you take a picture of if, you will just see a fuzzy blob. If you send another one to the same region and you take a photograph of it you see interference stripes (just like you can see with water-waves when you throw /two/ stones into the water). Matter behaving like waves, what theory other than QM can predict something so simple and beautiful?

Of course I have not demonstrated it for the first time, but the Nobel laureate Ketterle

http://cua.mit.edu/ketterle_group/Projects_1997/Interference/Interference_BEC.htm

Nevertheless, any physical theory will always be limited to its own realm. It fails to explain social interactions or the precise shape of mountains...

http://cua.mit.edu/ketterle_group/Projects_1997/Interference/Interference_BEC.htm

Maybe we are just barking up the wrong tree in our search for understanding, be it QM or whatever else.

For decades, nobody has 'understood QM', but ultimately nobody understands a number of other phenomena.

A case in point is e=mc², a result that had already been derived several times before Einstein - but Einstein was the first to provide an insight that the formula had physical , real-world significance. Beside the fact that the math says so, it's hard to find any material reason why e=mc²

Another example is Bell's inequality - we're hitting a brick wall trying to tease out a physical significance behind the odd experimental results - results however borne out by math.

Yet another example is delayed choice experiments.

Another one is Big Bang(s) under a variety of possible scenarios (e.g. Tryon, etc.)

The list is well-nigh endless.

This has led many (the Tegmark's of the world, also Shing Tung Yau et al.) to posit that ultimate reality is ... math. If we adopt the view that the universe is a mathematical structure, and that physicality is a somewhat volatile and/or unstable epiphenomenon stemming from the underlying math structure, then everything falls into place: no other explanation is required than that of the math saying so.As Tegmark once put it: 'Nothing breathes fire into the equations (thereby answering a Stephen Hawking question): the equations themselves are the fire'

Math has, to date, never been falsified (to wit - real & predictive math, not arbitrary and non predictive systems of X equations fitting X variables aka experimental points, with any further experimental points being arbitrarily designated as further variables and leading to further equations to fit a model.)

It seems that our continuing bids to understand things 'physically' are never fully fruitful. Perhaps it's time we put aside a cognitive bias that leads us to seek 'material' explanations, and investigated thoroughly the possibility that our universe is ultimately nothing but a purely mathematical structure.

I would not quite go that far. We still have to sharpen our intuition using images, which are not fully grounded in Math. The test of these images, though, will always be in which way they guide us in the usage of this Math, and in how far they conform with the predicted by the theory (math) and with what we measure in our experiments.

Wolf

Please can you be more specific and give an example

Dear Harry, mathematic models are a bit too abstract at times. Of course, they are the ultimate tests. Nevertheless, I often use geometric representations in order to simulate experiments in my head.

For example, atoms tend to interact in the presence of near resonant light (e.g. in a magneto optical trap) this interaction causes a force in all directions. When thinking about the effect of this force, it makes sense to use as a model a compressible liquid. This is mainly in order to get an intuition and to do a quick check on what behaviour I expect, when I change some parameter in the experiment.

In the end, I still have to make a complete mathematical model some time later, in order to really understand what my experiment really does.

The weird thing about QM is that no one really understands it. The quote popularly attributed to physicist Richard Feynman is still true: if you think you understand quantum mechanics, then you don’t. At a conference in Austria in 2011, 33 leading physicists, mathematicians and philosophers were given 16 multiple-choice questions about the meaning of the theory, and their answers displayed little consensus.

One of the most telling questions in the Austrian poll was whether there will still be conferences about the meaning of quantum theory in 50 years time. Forty-eight percent said “probably yes”, only 15% said “probably no”. Twelve percent said “I’ll organize one no matter what”.

However, QM, developed at the start of the twentieth century, has been used to calculate with incredible precision how light and matter behave – how electrical currents pass through silicon transistors in computer circuits, say, or the shapes of molecules and how they absorb light. Much of today’s information technology relies on quantum theory. A great deal of modern technological inventions operate at a scale where quantum effects are significant. Examples include the laser, the transistor (and thus the microchip), the electron microscope, and magnetic resonance imaging (MRI). The study of semiconductors led to the invention of the diode and the transistor, which are indispensable parts of modern electronics systems and devices.

I end with two great quotes:

"The atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts."

----Werner Heisenberg

"Anyone not shocked by quantum mechanics has not yet understood it."

---Niels Bohr

Wolf

I see what you mean and actually, without being aware of it before, I have a similar approach nut then with respect to molecules their internal motion and interaction, or even the 2-slit experiment where I visualize a wave or rather a light-pulse or wave-packet.

Let's not forget that there was knoweldge of semicondutors and their properties before quantum mechanics (http://en.wikipedia.org/wiki/Greenleaf_Whittier_Pickard). Also, It was Einstein who predicted stimulated emission of radiation ( http://www.aps.org/publications/apsnews/200508/history.cfm ), he had his views, and perhaps his phobias regarding the theory he started in 1905, with his paper on the photoelectric effect; still we should give him some credit and have some respect. That, of course, doesn't mean we should take everything he wrote as true.

I posted this as a question somewhere else, but I think it goes well with the discussion here:

Is the equation E^2/c^2 - p^2 = m^2 c^2 true?

Why am I asking this question? Well, the logical principle of explossion states that if a contradiction is introduced in a logical system then any theorem can be proved true. (Ex contradictione sequitur quodlibet.)

In Einstein's "Meaning of relativity" pp. 43 and 44, Einstein wrote "...Let's imagine a body upon which the electromagnetic field acts for a time....We shall assume that the principles of conservation of energy and momentum are valid for the body. The change in momentum \Delta I_x, \Delta I_y, \Delta I_z, and the change in energy \Delta E, are then given by the expressions [some integrals] ...This four-vector can also be expressed in terms of the mass m, and the velocity of the body, considered as a material particle....which refers to an infinitely short portion of the four-dimensional line which represents the motion of the material particle....We see that this four-vector [the four-velocity] whose components in the ordinary notation are... is the only 4-vector that can be formed from the velocity components of the material particle... By equating the components we obtain in three dimensional notation: I_X = m q_x/\sqrt{1-q^2},..., E = m /\sqrt{1-q^2}. (in other words E^2/c^2 - p^2 = m^2 c^2)"

What is this four-dimensional line representing the motion of this body as a material particle? Is it the center of energy? It cannot be, because the path of the center of energy is not covariant. Actually, Years later a non-interaction theorem was proved for Special relativity! ( http://www.physicsforums.com/showthread.php?t=225026 ) The definition of a "center of mass" within the limits of special relativity, representing the motion of a system of particles as a whole, in the way of classical mechanics, is an open problem today. ( http://arxiv.org/pdf/0901.3349.pdf )

The equation E^2/c^2 - p^2 = m^2 c^2 was used by de Broglie in his Doctoral thesis; the belief that it is true is behind Klein-Gordon's equation, and the commutation and anti-commutation relations of the gamma matrices that appear in Dirac equation; and Dirac's electron theory is foundational for QED! (Michelle Maggiore; A Modern Introduction to Quantum Field Theory; (2005).)

If the equation E^2/c^2 - p^2 = m^2 c^2 is false then, I am sorry, but our beautiful quantum mechanics is just a mathematical game.

Oscar

There is an other question here in Research Gate "name the 2 greatest scientists of the 19th and 20th century". My vote went for 20th went to only ONE scientist: Einstein.

@Charles Francis

This is not the way I put it, it is the way it was put by Einstein, using the old Minkowski's formalism in his own papers; it is the way it appears (p^u=m dx^u/ds => p^up_u=m^2c^2 ) in the tensor calculus of his General Theory of Relativity, it is the equation he used to estimate the precession of Mercury's orbit; it is the equation he used to formulate his gravitational law ("Meaning of Relativity" p. 88 et seq.).

p^u appears as a four-vector, proportional to the four-velocity in C. W. Misner, K. S. Thorne, J. A. Wheeler, Gravitation (p. 54). Should I consider them ignorant also?

Of course, you can say E^2/c^2-p^2=m^2c^2 defines the set of states that are accessible to a particle with a mass m in the the four-momentum space, and that's the mass shell. Why is that the mass shell? Well because p^up_u=m^2c^2. But that begs the question, unless we drop Bohr's principle of correspondence or the General Correspondence Principle: P^a P_a = m^2 c^2, because P^a = m c u^a, where u^a is the four-velocity and, by definition of the four velocity, it is the derivative of space time coordinates with respect to the proper time, and u^a u_a=1. Some people will say: "Well, that's not a problem, electrons are point particles." What about protons and neutrons (Aren't they made out of quarks?) and alpha particles (Aren't they made of protons and neutrons?). What about Hydrogen: Isn't it true that relativistic corrections are required to account for the observed spectral lines.

The center of mass is well defined in classical physics, because there you consider the position of particles in a composite system, at the same time. There you have that if you divide a composite system S in two parts S_1 and S_2, and those parts have masses M_1 and M_2 , then the center of mass of the whole system is (M_1 R_1 + m_2 R_2)/(M_1 + M_2), where R_1 and R_2 are the centers of mass of the parts. This is a mathematical identity that can be proved without much effort. Thus the concept of particle is mathematically consistent in classical mechanics. Furthermore, if you start from the principle of inertia, the center of mass of a system made of two parts should move with constant velocity. In other words, the acceleration of the center of mass should be zero and the principle of equality of action-reaction follows immediately.

Unfortunately we cannot do the same for a system of particles in special relativity, much less if we consider that in this case we ought to consider the density of four-momentum of the electromagnetic field as well, because interactions are not instantaneous and the classical way of understanding simultaneity is disrupted.

Why is this important? Because if we cannot speak of the center of mass in a mathematically consistent fashion, then we cannot speak of internal, or intrinsic, energy and/or angular momentum of a system of particles, and we cannot therefore study, within the limits of special relativity, the motion of system of particles in an electromagnetic field. And what about the motion of a planet around the Sun? What is this mathematical point representing the path of Mercury in space-time?

The equation p^up_u=0, for mass-less particles, was used to put the four momentum of photons as \hbar k^u and formulate a relativistic theory of Doopler's effect, on which the theory of the expanding universe is based. Isn't that interesting? I mean, the classical electromagnetic field does not have a four-momentum, but a stress-energy tensor! You can define a total momentum by contraction with the elements of a three-dimensional simultaneity manifold and integration. If you pass to a different system of reference that simultaneity manifold will be different, the events won't be the same! (K. S. Thorne etal, pp. 89 & 142.) If we consider general relativity, is there a universal simultaneity manifold?

Yesterday, I posted this answer to a question by Dr. Issam Sinjab:

Suppose we have a formulation of a theory, let's say of heat, to be specific, written in a book, using mathematical equations and or inequalities. Both, mathematical equations and inequalities are relational statements about numbers, numerical functions, or any kind of mathematical objects (vectors, matrices, forms, functionals, you name it). Suppose our manuscript has no figures at all. We apply the following algorithm:

1) Do the sustitution of every mathematical expression with the corresponding expression in natural language.

2) Repeat until no sustitution is possible or the number of repetitions is greater than the number of words in the dictionary: Substitute every term that's specific to the theory with its corresponding definition.

3) If the number of repetitions was greater than the number of words in the dictionary Print: "The vocabulary has some circularities" else Print the text that resuls from all those substitutions.

If the cycle stops and prints the so obtained version of the theory then we can read it . No term that's specific to the theory will have a definition in the dictionary: we will be able to understand what we read (with a lot of effort) only if we have memories of stories told to us, actual things, and/or processes and asociations of those terms with those stories, memories, and/or processes. So I will say that the connection between Mathematics, Science and nature is this: Mathematics is a tool for science and the connection between science and nature is the meaning of those fundamental undefined terms that are used by science to describe it.

It is not the mathematical formalism that is important or the names we give to mathematical relations, but the connection between those undefined terms in our theories and our experiences that matters when we are doing science.

If you can, please, tell me how to define the center of mass, within the limits of special relativity. Do not introduce any quantum mechanical arguments, because that will begg the question. (petitio principii fallacy)

QM is so hard to understand because it is outside our everyday experience. it poses all sorts of strange questions that stretch the limits of our imagination- forcing us, for example, to conceive of objects like electrons that can, in different circumstances, be either waves or particles.

Depending on the experimental circumstances, EM radiation appears to have either a wave-like or a particle-like (photon) character. Louis de Broglie (1892-1987) who was working on his Ph.D. degree at the time, made a daring hypothesis:

if radiant energy could, under appropriate circumstances behave as though it were a stream of particles, then could matter, under appropriate circumstances, exhibit wave-like properties? For example, the electron in orbit around a nucleus. DeBroglie suggested that the electron could be thought of as a wave with a characteristic wavelength.

One of the most controversial issues concerns the role of measurements. In classical physics We’re used to thinking that the world exists in a definite state, and that we can discover what that state is by making measurements and observations. Quantum mechanics, however, on the scale of particles such as atoms and electrons, tell us that there may be no unique state before an observation is made: the object exists simultaneously in several states, called a superposition. Before measurement, all we can say is that there is a certain probability that the object is in state A, or B, or so on. Only during the measurement is a “choice” made about which of these possible states the object will possess. It’s not that, before measuring, we don’t know which of these options is true – the fact is that the choice has not yet been made.

This issue is probably the most controversial in QM. It disturbed Albert Einstein so much that he refused to accept it all his life. As the mathematical formulation(QM) of the quantum theory developed by pioneers, the like of Niels Bohr, Werner Heisenberg and Erwin Schrodinger, and certainties were replaced by probabilities, Einstein protested that the world could not really be so fuzzy. As he famously put it, “God does not play dice.” (Bohr’s response is less famous, but deserves to be better known: “Einstein, stop telling God what to do.”).

It is worth also remembering what happened at the famous Solvay's Conferences of 1930, when Einstein proposed a "Gedanken Experiment" in order to show that Heisenberg indeterminacy was problematic. Bohr was unable to give an immediate solution and could formulate a counter-argument only next day. The Bohr-Einstein debate continued however in 1935, when Einstein (with Podolsky and Rosen) proposed another gedanken experiment in order to show that QM was either a non-local theory or had hidden variables..

Bohr's answer, according to Bell, was completely unitelligible, but since Einstein views on QM after 1930 were not taken seriously anymore by the majority of scientists, Einstein objections were forgotten until the work of Bohm in the fifties, proposing a "hidden variable" version of QM (for a down and dirty source see: http://en.wikipedia.org/wiki/Bohr%E2%80%93Einstein_debates).

It was only with Bell that some light was shred on the apparent "non-local" nature of QM (Bell was able also to show that QM "non-locality" was not in contradiction with Special Relativity postulates).

The fact that even Bohr was unable to answer to the EPR argument is, in itself, a proof that "nobody really understand QM" as Feynman expressed.

All these 'famous' quotes the history of science has proved that were without meaning, just after obtaining a higher level of knowledge. There exists a multi-explanatory situation in many scientific disciplines: the same thing can be explained with two or sometimes three phenomenologically different theoretic views. I think time has not come yet for reaching the necessary 'next' level needed for solving QM understanding problems.

@Constantin Andronache

Perhaps you are right! The fundamental notions of quantum mechanics might appear to us more difficult to grasp than Euclid's "common notions" only because of the mathematical paraphernalia of Hilbertian Space. We, physicists, might have something to learn from Socrates!

Oscar

You mention Hilbert space, but Feynman made his remark when contemplating the simple double-slit experiment with single electrons (photons) for which the mathematics are very simple. It is the duality principle of wave-particle that he I think is alluding to and the Copenhagen interpretation. I am currently rereading his lectures in physics focusing on how he introduces QM as well as many other textbooks and I value him as the best teacher, apart from his. Because of that, even more than for his formulation of QED/QFT, I rank him second (rather far behind Einstein) in another question in ResearchGate: name the 2 most prominent scientists of the 19th and 20th century. I must add that this is for physics rather than science as a whole.

@Charles Francis

Hilbert's Space might be mathematically simple, not exactly very very simple, when we are speaking about a Hilbertian Space with a finite base.

Let's consider a Hilbert Space in a situation that should be very familiar to all of us. Consider a thermal classical electromagnetic field in a cavity; think of the distribution of the components of the electric field at a point inside, let's say at the center of a spherical cavity. This distribution should be isotropic and, therefore normal, as it can be proved in the same way as it can be established that the distribution of the components of the velocities of the molecules of and ideal gas must be normal (e.g. http://www.math.ufl.edu/~kees/MaxwellDistribution.pdf ). The average of this normal distribution must be zero, unless there is an external electrostatic field. Therefore, the average of the square of the field (which accounts for half the average density of electromagnetic energy) is 3*sigma^2. Should we get a different value for the average density of energy when we consider the Fourier components of the electromagnetic field? I don't think so, unless we introduce an unsound asssumption. Still, we have people talking about an ultraviolet catastrophe, as a consequence of the principle of equipartition of statistical mechanics applied to the normal modes of electromagnetic field in a cavity. The fact is this: the catastrophe was introduced in the theory from the very moment that the assumption was made that there was kT energy per "degree of freedom" when dealing with a system which, obviously, has an infinite number of degrees of freedom! (The only justification for this assumption was a mechanical analogy not a mathematical identity.) That deduction was unsound; still it was taken as evidence of a failure of classical physics by a lot of scientists who, I guess, did not realize that mathematics was very simple!

Oops! The same analogy has been used for the quantization of electromagnetic field and, now: we have a vacuum catastrophe and...an infrared catastrophe. Isn't it great?

Quantum Mechanics encompasses several, distinct, parts.

1. A limited number of "axioms", as citedin everywhere :

- the state of a system can be represented by a vector in a Hilbert space

- observables are represented by hermitian operators

- the only values that can be measured for an observable is one of its eigen values

- the probability to observe this eigen value is proprotional to the square of the product

- it two systems interact the hilbert space to consider is the tensorial product of the hilbert spaces

- the Wigner's theorem

- the Schödinger equation

All these "axioms" can actually be proven : they hold in very general conditions, for any model involving variables living in infinite dimensional vector spaces (see my paper).Indeed they are even valid for models out of physics. This is only a matter of mathematics.

2. Some additional assumptions about the implementation of these axioms, which are related to the representation of objects such as particles, and stem mainly from the "wavemechanics". They play a crucial part in the efficiency of the quantum theories , but are in a dire need of clarification.

I am always surprised to read, coming from physicists, the usual comments.

- QM is validated at an extreme precision. One the great tenets of QM is the impossibility to measure simultaneously position and speed. I hope that you do not take a plane. And if you are satisfied with the usual "decoherence" of the wave function to explain that this does not hold at our scale, I am not.

-Nobody can understand QM. OK : perhaps one day some tax payers will ask you why it is necessary to spend (not) so much money to repeat, word for word, the same statements about something that nobody can understand. The job of boffins is to find answers,and solutions.

- theoretical physics has stalled for 40 years. And perhaps the fact that almost everybody is convinced that one cannot understand QM is for something.

If we want to advance, we need to stop repeating the same, true of false, quotes by illistrious predecessors. It smells strongly of the arguments used against Galilée. After all the Ptolemean system, welll refurbished for a thousand years, was really efficient to forecast all the observable facts of the time. And the practicians could use it and state that "it was successfully verified with a great precision". WhatGalilée brought was not more precision in the computation, but a better understanding of the phenomena.

Jean Claude

An axiom can by definition not be proven; but I fully agree with you that up to now all experiments are in-line with the descriptions and predictions of QM.

However, one needs additional formulation for instance for the specific potentials and approximations in quantum chemistry.

.

Jean Claude

A small correction:

My last sentence should read:

"However, one needs additional formulation for instance for the specific potentials needed in specific situations and these are also axiomatic and stemming from classical mechanics / EM and also approximations are needed to apply QM in areas like quantum chemistry"

About axioms.in QM.

Axioms have a precise definition in mathematical logic (actually in one kind of mathematical logic). I used the word "axiom" because it seems usual to introduce these statements in most books about QM. What is stricking is that they do not seem to be related to physical objects (they do not use words such s time, energy, mass,...Compare the axioms with laws such as E = hv or E= mc² .), moreover,.besides the Schrödinger equation, they do not contain the Planck constant and should be valid whatever the scale. And indeed they are just mathematical, provable, consequences of the specification of most models in physics. They are "mathematical artefacts". Certainly useful, but in themselves they do not contain any physics. The true specificity of quantum physics is in "wave mechanics" which introduce new concepts to deal with physical objects at the atomic scale.

The idea or "axioms" in physics which could be provable only by experiments seems bizarre. Think at this statement : the ratio of the length of a circle to the length of its radius is a rational number. It can be experimentally proven with a great accuracy, but it is false.

Most physicists who have tried to understand QM have been focused on the relation between the observer and the measure. Which is useful at the atomicscale. But this is not all the story. Physics also use "models" to organize the data that they collect, and to make predictions. And the use of mathematical models, and stattical methods to estimate the variables, is not neutral. This fact is well understood by the workers in economics :they certainly do not imagine that people behave like their models tell. Only physicists seem to believe that "nature" must comply with their equations. If their models are stochastics, then nature shall be probabilist !

@Charles Francis

I have seen your papers Charles. As I told you they are not that easy to read as you say, but I am moving forward, on the second round.

In p. 11 of J. D. Bjorken & S. D. Drell; Relativistic quantum mechanics, we find this expression for the Lorentz force as predicted by Dirac's theory:

\frac{d \pi}{dt} = e [ \vec E + \frac{1}{c} {\vec v]}_{op} \times \vec{B} ], where {\vec v}_{op} is c \vec{\alpha} and, as a consequence does not include any derivatives. I have worked out the expression for the Lorentz force in Schroedinger theory in my paper http://arxiv.org/pdf/quant-ph/0305049v4.pdf eqs. 20, 21, and 22, and I got a different result: Dirac theory does not correspond to Schroedinger's in the non relativistic limit.

On the other side, those quadratic terms that are neglected in p. 12 and 13 of J. D. Bjorken & S. D. Drell are the ones that would save equation 1.35 of not being gauge invariant. Despite the attractiveness of equation 1.35, as you know, the kinetic momentum of a particle in a magnetic field is not -i\hbar\partial_i but -i\hbar\partial_i-\frac{e}{c} A_i and the vector potential appears also in the kinetic angular momentum which is the one we must use to compute the magnetic moment. It seems to me that Dirac's theory is not as good as the scientific elite pretends it is. If Dirac's theory is not true, what sense does it make to move forward to quantum electrodynamics and the like?

(Charles, if the lagrangian formulation is bad physics, or metaphysics, then the wave function is bad physics! As you know the phase of the wave function corresponds to the action and it has been used by Feynman again, to reformulate quantum mechanics with path integrals. What is \phi = p.r - Et if not the action of a free particle? Take the gradient you get p, take the partial derivative with respect to time you get -E. It's a solution to Hamilton-Jacobi!)

@Luca de Mate

I think the EPR argument was unfortunate as contribution of A. Einstein to a better understanding of QM. The Einstein-Podolsky-Rosen paper is an attempt to prove, by contradiction, that quantum mechanics is not a complete theory. The structure of such an argument goes like this: We have a set of statements (the axioms) mentioned by Dr. Jean Claude Dutailly {A_1,....,A_n} and we want to prove P true. We add ~P to the set of axioms and then we prove, using, only, sound rules of inference that {A_1,....,A_n,~P} entails a contradiction. This is the kind of argument Dr. Jean Claude Dutailly has used in "Think at this statement : the ratio of the length of a circle to the length of its radius is a rational number. It can be experimentally proven with a great accuracy, but it is false."

In their argument, Einstein-Podolsky-Rosen considered a particular state they supposed could appear as the result of time evolution via Schroedinger's dynamical law. They did not bother to prove that this state could actually appear and as it can be proved very easily it cannot, because a transformation to center of mass and relative position coordinates shows that their wave function is the product of two delta functions, and is not normalizable. Wave functions are known to spread not to collapse into delta functions when the system is not interacting with a measuring device. Furthermore, they introduced an assumption: "If we can determine with certainty the value of a physical magnitude then this physical magnitude corresponds to an element of reality." The only justification they gave for this was: "It appears to us that it is reasonable." With this assumption they invalidated their argument and generated a debate that is still going on. I have studied their work in http://physicsessays.org/doi/abs/10.4006/0836-1398-26.1.21.

However, I agree with you, Bohr response was clumsy, or politically correct, I don't know. This cult to personalities has created a situation where it is almost impossible to move forward, because the "academic establishment," those guys with power and influence to build those huge machines to test theories that nobody understands, will not allow it. My paper on the EPR argument was deleted from arxiv.org in 2004, on the grounds that it was "inappropriate." Since that time I was not allowed to publish in arxiv.org. My privileges were restored this year of 2013 with a restriction: I will need endorsement to publish any paper, and a warning: "Do not attempt to publish Logical Refutation of the EPR Argument here." Sounds Creepy, but it's the way it is. Arguments of authority are the most inappropriate in science, but here we are. Look at Charles Francis remark on his dissertation!

@Oscar, Francis

A look at how mathematicians proeed to check the consistency of a theory is useful.

A mathematical theory (say set theory) comprises statements. They can be studied from two different points of view :

1) with some basic rules one can build other statement from given statements, and the rules can tell when the rsult if true (or false) when we know the value (true or false) of the initial statements

2) using inference rules we can prove a statement from statements deemed true (the axioms)

To the great surprise of the mathematicians the two ways are not equivalent : in arithmetics there are statements which are true but not provable.

If we try to translate this scheme in physics, the first way consists in checking a statement by an experiment, the second way is to make a prediction, by computation from a given set of data. There are complications in physics : some experiments are impossible (for ever ?) and some predictions cannot be done with all necessary accuracy (think to thermodynamics). So my view is that it would be useful to establish some "logical physics" before affirming too strongly that such theory is true or false, and meanwhile to stay humble. Anyway the argument of authority are the weakest.

@Jean Claude

I could not agree with you more. We need a critical examination of our current knowledge. Regarding your example of the ratio of the circumference to the circle. The irrationals appeared in number theory because the diagonal of the square is not commensurable to the sides. This was a consequence of the Pythagorean theorem, and, therefore of the assumption of an Euclidean physical space. Einstein comes and challenges Euclides geometry, but he maintains the axiom of continuity when he reformulates the theory of gravity using the concepts and methods of Riemann's geometry.

@Charles

Can you clarify your first statement in your last posting?

Regarding your formulation of QED I ask you again why did you introduce complex and continuous amplitudes of probability, considering that all you can get from a experiment is a distribution of rational statistical probabilities. Same doubts about the introduction of continuous time.

The same thing I see in Bjorken et al I see also in M. Maggiore, A Modern Introduction to quantum field theory, p. 73 eq. 3.178. Does Dirac equation predict the correct Lorentz force. Yes, no, how? I really don't care that much about elegance in physics or mathematics . I am more concerned with correctness. Dismissing an argument because it is not elegant is a fallacious way of arguing.

And who is talking here about finite mathematical systems? Obviously the axioms of number theory are among the assumptions of physics, quantum mechanics in particular. Quantum physicist spend a good deal of their lives counting quanta, electrons, protons, and stuff.

Euclidean geometry is not challenged for the mathematician, in the sense that it is consistent, however it is challenged for the physicist, because it does not correspond to reality. The Pythagorean theorem is only an approximation and there is not a logical necessity for irrationals coming from geometry, but from mathematical analysis, on which both quantum mechanics and relativity rely.

Now, how can it be that we cannot speak of the path of an electron, because there is no physical manifold on which a path can be defined and, at the same time, we are free to speak of the expected value do the position of an electron? Is there a substantive manifold for expected values but not for instantaneous values? Those expected values are expected values of what then?

Well. This will take us nowhere.

Edit: a) The set of integers is countable and any statement about real numbers can be reduced to a statement about integer numbers, by continued substitution of terms by their definitions. b) I asked you on what grounds did you introduce complex amplitudes of probability, considering that all you can get is rational measures of statistical probability. You did not answer that question. What do I have in exchange? Ad hominem attacks about physicists that are in metaphysics. Remember that the set of complex numbers is not countable. Perhaps you are not that far from metaphysics as you think you are. A Hilbert space is not only euclidean but complete and the set of rays in a Hilbert space, even if the number of dimensions is finite, is not countable. On the other side, the set of propositions in subjunctive mode is numerable. That's why I keep asking you those questions. Perhaps you don't have answers. That's OK, there are many things I don't know either.

Edit: this gives me an idea on a new question.

@Charles

But there is an essential part missing in your answer, they do not correspond directly to reality, OK. Now: Why do their square modules correspond to probabilities? In a strict sense no number corresponds directly to reality, there is always an interpretation. If you give a number for the surface of Earth, let's say in square miles, that number does not correspond immediately to reality, there is an interpretation for that number, based on the definition of an area of a rectangle. You can very well represent the area of Earth by the length of the side of a square that has the same area and you can make this length complex if that amuses you and then say that, at the end you need to get the squared module of that number to get to an area. I will raise an objection if you start adding those complex numbers representing areas, or probabilities. I think it is fair, to ask that question, because the square of the sum is not the sum of the squares. If you tell me that's an assumption, it's OK, all our theories have plenty of assumptions.

Jean-Claude / Charles

Axioms are axioms and just starting points. One likes a theory with a minimum of these. In those physical axioms are the concepts of "reality": this has no mathematical counterpart because physics has to describe and predict macroscopically defined observables. By the way, these observables must be part of the basic axioms of QM even when it seems these are not explicitly stated in QM.

@Harry, Charles, Oscar

About infinte, uncountable and contable sets

Physics use mathematics to represent its objects and its laws. This is not the case for every science : Chemistry use a very efficient system based on the atomic theory, where letters represent atoms. Mathematics are very powerful, and they introduce very sophisticated objects, which are in some way "idealization" of reality (the issue of "are mathematics a language or a science" is still open). Bu it would be foolish for phsysicists to refuse the usage of objects which do not seem "real". They are too useful. But we have to keep in mind that they are not the "reality" (for whatever ths could mean). Take as example the trajectory of a body. We can easily represent it as a curve with some parametrization which gives a speed. A curve has uncountably many points, so it will for ever impossible to measure with a total accuracy the curve (and the speed). But fortunatly usually we do not bother with that ; we assume that the curve has some simple properties (it is a straight line, a parabole, a circle), the speed is constant, and then a finite number of measures allow us to find the data that we need in our computations. But the fact that we pick up certain curves among all the possible values entail an uncertainty. There is no trouble. But we cannot say that this uncertainty comes from the "reality" ! The point is that the trajectory is measured from a batch of data, after the experiment. has ended. The uncertainty lies on the choice of a curve amongst many others, and, as a consequence, there is an uncertainty about the position of the particle at a given time. But we cannot say that the particle has no precise position. Dirac notiiced that we cannot, at the atomic scale, measure simultaneoulsy some quantities. OK, but so what ? For centuries artillerymen did their job without the simulatneous knowledge of the position and the speed of their shells. And when a particle leaves an accelerator, collides with other particles, we assume that its position and its energy (that is its speed) are well known.

All the uncertainty laws, and discrete stories of QM come from this kind of discrepancy between what we put in our mathematical models (which are abstract and aknowledge infinity) and our measures, which are always in finite number. And the problem occurs whenever we have variables which belong to some infinite dimensional vector spaces (such as fields).

This is not to say that the "axioms" of QM are false (they can be proven) or useless, but that they are not some kind ogf new physics (as the "Copenhagen interpretation" says). And what matters, and what should be the core of the studies in atomic physics, is that some of the variables that we use at a macroscopic scale are not adequate at the atomic level. Example : think about rotation. This is a very difficult concept, notably in the relativist picture. And it is not easy to understand why the motion (meaning both the "translation" and the "rotation" ) of particle should be represented by a spinor. The "duality" field / particle seems similarly come from the fact that the mathematical object with which we can represent either particles or fields are similar.

Jean-Claude

Axioms can NOT be proven. The definition of an axiom is that it is a human CONCEPT that everyone who follows a model framework has to accept in order to use it.

Harry, I believe this is only a matter of semantics. The word axiom in mathematics conforms to your definition, however Jean Claude uses the word in the context of physics, where words like 'axiom' or 'principle' are sometimes used misleadingly, because they actually refer to proven theorems.

A telling instance of this is what is still called 'Heisenberg's principle' which is not a principle at all but a demonstrated theorem.

Chris

Thanks, but I would like to also hear it from JC.

You mention Heisenberg's principle: you say it can be proven; but that is inside the structure of QM and is basically an example of a mathematical relation. Then we can argue about if that is a proof

@Harry

I always use quotes when writing about "axioms" of QM. Axioms have a precise definition in mathematical logic, they are statements which are deemed true and from which other statements can be built. There is no such "physical logic", and it would be very useful to work on this subject (which broufght some surprises to mathematicians). In physics there are "laws", meaning relations between physical objects represented by some properties which can nation, and we find easily tha theychecked through experiments.What is striking about the "axioms" of QM is that they contain no physics. What is a "system", what is an "observable", what is a "state",, and why these axioms are obviously false when dealing with macroscopic objects ? The reason is that they are not physical laws, but mathematical relations, which exist for any model using certain classes of variables, and when we look at this kind of models, using purely mathematical concepts, they can be proven. So either you tll me exactly what you mean by "state", "observable", and so on, when related to physics, or we have to conclude that they are not specific to physics, we have to look foranother explanan,ation

@Jean Claude Dutailly

I agree, we must not confuse reality and our incomplete mathematical representation of it.

@Oscar

Actually there are "principles" in physics, which are closer to axioms (such as the axioms of the set theory in mathematics). The most important are :

- the principle of relativity : the laxs of physics shall not depend on the observer

- the least action principle :

- the second law of thermodynamics

These principles are general, intuitive, and not expressed in a precse way. This makes the "axioms" of QM all the more singular. We are fortunate that the Hilbert spaces have been imagined by mathematicians !

@ Mohammad

The Schrödinger equation can easily be proven as the consequence of the Wigner's theorem, in the framework of the "axioms'" of QM. This is not a physical law. Even if some people work on a "wave function" of the whole universe, my feeling is that is a pure b... Cosmology is ony an intellecual construction. Every decade the cosmologists loose 25 % of their objects. We have had the "dark matter", then the "dark energy". I am curious to learn the next one...

Jean-Claude

It is a pity that you did/do not refer to your essay that I now started to read. Now I know what you meant in your reply to me with respect to AXIOMS SYSTEM etc

For those interested:

https://www.researchgate.net/publication/234059918_Quantum_Mechanics_Revisited

Article Quantum Mechanics Revisited

@Charles

If Maxwell equations are absolutely precise in their description of electromagnetic field, why do we need quantum mechanics to explain the photoelectric effect? Why do we need it to explain atomic stability? Why do we need a QED? Where is this theorem that proves the second principle of thermodynamics: I do not find it in classical statistical mechanics I don't find it either in quantum statistical mechanics. Any logical consequence of the axioms of QM is an assumption. If the axioms of quantum mechanics are taken for granted any logical consequence of them is taken for granted, as it is. Those conclusion might be confirmed, I agree to that, but that's a different issue.

@Harry

Indeed, and there is a reference to almost 800 pages of mathematical physics there to read. I guess I have work for months. However, there is a possibility to understand and I think it will be rewarding. From an initial reading of the first pages of J, C. Dutailly, "Quantum Mechanics Revisited", two questions come to my mind (those won't be the only questions, obviously, the essay is difficult for me to read, being a physicist, not a mathematician and Dr, or Professor Dutailly has gone very deep into functional analysis, where I am not precisely strong.

To the questions:

@Jean-Claude

In your revision of QM you refer to a system that preserves its identity. This reminded me of a remark in Prandl, Tietjents; Fundamentals of Hydro and Hydromechanics p. 9: "We have not yet taken into account the fact that the molecules are in a state of perpetual movement. If this molecular motion be disregarded, then each volume element [in a moving fluid] will always contain the same molecules and will thus have a physical individuality; the effect of the molecular motion will be to destroy such physical individuality, since the molecules will be continuously changing positions." This remark (because Newton laws refer to particles that preserve their identity) prompted me to make a numerical experiment with a two-dimensional classical (planetary like) model of hydrogen and an electronic canyon shutting electrons with random velocities (normally distributed around a mean value, the mean value pointing in the direction of the center of mass of the atom). In most of the simulations I ran, and I ran hundreds, I observed the incoming electron being trapped by the hydrogen atom and the one that was initially orbiting the proton coming out of the region of interaction. This made me think this: if we consider a diffraction grid as an external, boundary condition, to study electron diffraction, we have a problem with the identity of particles emerging from the region of interaction. Something similar happens when we consider, for example, an electron that is trapped between two maxima of electric potential: from electrostatics we know that the Laplacian of the scalar potential is proportional to a density of charge. What is a density of charge made of? Charged particles! What guarantee do we have that the system, our electron, conserves its identity? I am not challenging your views, I have not had the time to read the whole paper, I am just asking questions.

Oscar

@QED versus Maxwell: there are phenomena that are NOT explained by Classical EM: photon correlation

As for QM: every theory has its axioms you must accept. If not, then you just cannot be a physicist in the atomic/molecular domain.

@Harry

That part was regarding Charles assertion "Similarly Maxwell's equations describe electrodynamics, and they are absolutely precise." Read his statements, they appear right before your reference to Jean's essay.

@Charles

That "proof" of the second principle is grounded on a definition of entropy. So, the second principle is true because we define it so. We do not have more reasons to believe a logical consequence is true than the reasons we have to believe our postulates are true if we stay within the limits of mathematical thinking only. If we introduce confirmation, then we can have more grounds to believe a logical consequence is true than the grounds we have to believe the postulates are true, but confirmation is not used in pure mathematics.

Edit: (from your own source) Due to Loschmidt's paradox, derivations the Second Law have to make an assumption regarding the past, namely that the system is uncorrelated at some time in the past; this allows for simple probabilistic treatment. This assumption is usually thought as a boundary condition, and thus the second Law is ultimately a consequence of the initial conditions somewhere in the past, probably at the beginning of the universe (the Big Bang), though other scenarios have also been suggested.[33][34][35]

Given these assumptions, in statistical mechanics, the Second Law is not a postulate, rather it is a consequence of the fundamental postulate, also known as the equal prior probability postulate, so long as one is clear that simple probability arguments are applied only to the future, while for the past there are auxiliary sources of information which tell us that it was low entropy[citation needed]. The first part of the second law, which states that the entropy of a thermally isolated system can only increase is a trivial consequence of the equal prior probability postulate, if we restrict the notion of the entropy to systems in thermal equilibrium. The entropy of an isolated system in thermal equilibrium containing an amount of energy of E is:

S = k \log\left[\Omega\left(E\right)\right]\,

where \Omega\left(E\right) is the number of quantum states in a small interval between E and E +\delta E. Here \delta E is a macroscopically small energy interval that is kept fixed. Strictly speaking this means that the entropy depends on the choice of \delta E. However, in the thermodynamic limit (i.e. in the limit of infinitely large system size), the specific entropy (entropy per unit volume or per unit mass) does not depend on \delta E.

@Charles

Yes we only have two alternatives: I am not using English or you are not reading it:

"We do not have more reasons to believe a logical consequence is true than the reasons we have to believe our postulates are true if we stay within the limits of mathematical thinking only." Actually, we have less reasons to believe on a logical consequence, because there is always the probability that a mathematical proof is unsound. (The longer the proof the higher the probability that the proof is unsound.) You think you have absolute proof of the second principle just because you have applied some rules of inference to move away from the equal prior probability postulate? Mathematical knowledge is conditional.

Well, I will follow your advice and try to get some more mathematical books. Thanks.

There are forgotten questions in physics. I have proposed a NATURAL solution to some of these questions. This is published in several peer-reviewed papers. In particular I have proven that quantum mechanics (e.g. the Feynman path integral) can be directly derived from relativistic dynamics by encoding the wave-particle duality in the space-time geometry. See attached paper. The typical reaction from academic people to this established and certified result was: "you are not even a professor. I have tried for 30 year to resolve this problem and it is impossible that you have solved it."

It seems that physicists have given up with understanding reality in a natural way. The philosophy "shout up and calculate" has prevailed. There is a proliferation of weird physics hypothesis and conjecture in phenomena that cannot be directly tested (dark staff, black object, extra dimension, hidden symmetries, and so on).

These subject are good to increase your number of publications as nobody can test the validity of your results, but they have poor scientific value.

It is worth to remember that Feynman and de Broglie presented their discovery in PhD theses. Today there is not space for fresh ideas that demand to reconsider fundamental aspects of physics. This probably the reason to the crisis modern physics.

Article Elementary spacetime cycles

Are you satisfied with 'biliard-like-Physics' which in a few words is just this: "I am a particle and in order to interact with you I have to send you a ball (a boson like W, Z, etc) and hit you".?

Nobody understands how reality could work in the way which QM says it works, but this does not prevent us from doing the physical modelling and the maths and computing the predictions of QM. When we say we "understand" some physical theory we mean we can reduce it in our minds to the simplistic mechanistic picture of the world which evolution had imprinted in our brains when we were born. Maybe that simplistic picture is inadequate. Why not? This would not stop QM from being (close to) true, and it doesn't prevent us from using it effectively.

I seem to be the "nobody" that understands quantum theory and QM. Feynman needed two graphic symbols for QED, since the electron and photon were mutually irreducible in his attempted reduction. Using the arrow diagrams of causal set theory, the single graphic symbol is sufficient to depict both the photon and the electron. See "Causal Set Theory and the Origin of Mass-ratio" for the quantum structure of the electron and its cloud formations, Bohr's formula, the FSC, and QM. The nuclear structure is also included. -- Carey

All professions are a conspiracy against the laity (G.B.Shaw)

One way conspiracy manifests itself is in the use of a jargon, so that outsiders cannot follow.

Take a simple problem, seed it with wave function, decoherence, (nobody knows what it means) and you are on the right path for a phD

You find divergent integrals ? Good, call renormalization. You have particles without mass ? Perfect, call for the Higgs boson. Your computations for the trajectories of star in a galaxy do not match what you observe? Excellent, call dark matter

Media love mysteries, tenure call for media, and Nobel Prizes even more !

Jean Claude, great post, although I hope you meant at least part of it in jest (I think everybody knows *exactly* what decoherence means ....)

Beyond that, the trick you describe has been rife for centuries.

It began when the clueless doctors of yore did not have the faintest inkling how to treat an ailing patient, so mumbling Latin with much nodding of heads looked good, prior to unleashing the leeches and then bewailing cosmic fate.

Today it is rampant in business, where basically no CEO nor Harvard MBA has any glimmer as to how not to run their companies into the ground (business being a chaotic environment.) So ignorance and panic are papered over with the latest meaningless faddish buzzwords and fanciful acronyms.

If quantum mechanics and art would work together  and organising an event instead of making underground tunnels some knowledge could see the light.

As observation is at the conscious level and consciousness is what the mind does.

Feynman was first of all an artist; he has put consciousness in the middle, which is the only way to come to the truth.

Quantum mechanics is about consciousness and in that domain art has more practise than science. Scientists are not used to follow consciousness, it's rather forbidden because here intuition is coming in and the causal principle is not solved yet.

Whas is not Feynman who spoke about the ‘one electron universe’, so that we always see the same electron. Is this not closer to the surrealism in art.

Steve Lacy has put the text  ‘Particles’ of Feynman on music. At the end of his life he was looking for musicians-scientists to perform it in Boston where he gave lessons at New England conservatory, but this never happened.

May be something for the future.

There is an asymmetric equilibrium between the views and the answers. Very strange.

Christian,

The issue is what you call "verify". There is no "scientific thruth". What we can expect from a scientific theory is that it is efficient : not too difficult to understand and use, and providing accurate predictions.

QM is not a Theory in Physics, it has no physical content : if you look at its axioms they do not involve any precise physical object. QM is a set of theorems (which can be proven) about the results of experiments and measures.

And as Niels Bohr said :

"There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature "

[Niels Bohr, Spoken at the Como conference, 1927].

So it is hopeless to try to find a physical explanation of QM (that is to relate the "axioms" of QM to some special properties of physical objects). None has ever been found and none will ever be found.

But one can also see that Feynman was wrong on both counts : his interpretation of QM could not be understood, so it could not be an efficient theory.

Charles,

Of course, we agree that we disagree about the meaning of a Theory in Physics... I put the concepts of space, time, particles, fields at first (that you consider metaphysical) and then QM appears as patterns caused by the measurements (that I prove from the hypotheses assumed in the model). You put measures first, and then, from the patterns of the measurement (that you explain from the processes of measurements iself), you deduce particles, interactions,...(what I consider empiricist...). I acknowledge that one can build a consistent axiomatic QM starting from measures, so, the difference is mainly about a philosophical point of view.

To stay in the scope of this thread, my point of view is easier to understand, because it does not assume any special property of the "quantum world". There is a unique physics with the same tools. The axiomatic QM (Jauch style), its relativist version (Haag style), and even the path integral, can be understood. But to say that there are easy would be a bit of a stretch, notably because the latter faces many mathematical inconsistencies. And the link with the "current physics" (at our scale) is awkward, as one can see with recurrent issues such as the collapse of the wave function (on this site). And the path integrals formalism is totally inefficient at our scale (the examples given in the litterature are a joke).