I do not believe so.

There was a twin slit experiment conducted using very large molecules. In one variation, the particles were passed through a heater before passing through the slits. It was calculated that there was a very great chance that the molecule would 'shed' a photon before passing through twin slits which, IN PRINCIPLE, could be measured and information regarding the particle's trajectory could be deduced. Although there was no means to detect the photon, nevertheless, the interference pattern disappeared.

What this experiment demonstrated is that quantum uncertainty is not a phenomena that requires an actual observer. What is critical is information!. With the situation that you have outlined, Dr Sitkar, transfer of information would be continuous and so quantum uncertainty effects would not play a role.

Generically such a situation does not represent a superposition of states. In principle, if you had all the information about the state of the coin you could have calculated its final state (unless there is some special conditions that would tie this state to a quantum superposition). The uncertainly here comes from a mechanical instability, or some sort of a mechanical chaos. The final state of the coin depends on the initial conditions - on the way you throw the coin, the flow of air around it, the surface it falls on etc... - but it is also very sensitive to these conditions. Therefore knowing the final state is not easy even if you know a lot about its initial state. This is not the same as quantum superposition, where the uncertainty is inherent,

No. Because superposition of states doesn't involve equal probability. It involves outcomes. When you can flip a coin and obtain both heads AND tails, then you will have something analogous to superposition states.

@ Eytan

Is there any study on what are all the initial parameters that can ultimately predict the final outcome of the result of a single case of coin toss? I think that for a classical problem, we think we can formulate the last result knowing all of its environmental conditions but it is not so. If that is so, we can do the same for quantum system too. We can discuss over this. Please comment...... ( And I think uncertainty is not responsible for superposition , they are two independent thing...)

@ Andrew

In superposition of states, we invoke no condition on the probability of obtaining a particular eigenstate. So, in that sense equal probability should not stop it from being superimposed. I might be wrong , please correct me for that. And , it is the measurement process which project the superposition to either one of the eigenstate ( in this case either head or tail). So, as a result of toss , you will either get head or tail. But, unless you have not measured it ,you have no prior idea, whether it is head or tail.

Besides the measurement problem, quantum mechanics differs from classical mechanics also in another important point: While classical mechanics is represented by discrete point-like particles, quantum system are described by a wave function which is a field.

This means in this case: the dynamical variable of the coin toss is a single value, e.g., the angle of a vector normal to the head-side of the coin, relative to the plane of the table the coin is falling onto.

In quantum mechanics you have a field which has more degrees of freedom, e.g., a phase. Without this phase, many important effects of quantum mechanics, such as quantum interference between superposed states cannot occur.

A classical theory of point-like, discrete variables such as your coin cannot simply be identified with a field theory like quantum mechanics.

@ Moritz

I totally agree with your answer. But, consider Stern Gerlach experiment, their the very interaction of up spin with magnetic field let it move up and the other way for down spin. In absence of magnetic field, they were in superposition ( we say). So, how the phase comes in picture to maintain their superposition? How this is different from a tossed coin before measurement?

let us take another example. You want to know the trajectory of a shell shot by a gune. This is some map X(t). The state of the system is the map X (from [0,T.] to R^3) and we can assume that it is square integrable, so it belongs to a separable Hilbert space. You have your famous vector. Now if you want to measure X, the problem is that X has an infinite number of coordinates and of course you have only a finite number of data. So what you do is to choose a specification for the map : it can be a parabola, or a more complicated map. Basically the specification can be represented as the choice of a basis of the Hilbert space, and keep only a finite number of vectors of the basis. Usually you do not do that explicitely (you do not screen all possible bases), so the choice of a specification (which is totally independant of the precision of the measures) can be represented as a random choice between all the possible bases. It is not too difficult to prove that the specification process is an operator, self adjoint, in the Hilbert space, that the result is necessarily an eigen vector, and the probability to find such result is proportional to the square of the norm of this value (indeed : the error is just the size of what you have drop). If you want you can buil a basis of orthogonal eigen vectors of this operator, and then say that the value which is measured is one of the possible vectors, with a probability law. Of course this does not imply any random trajectory for your shell. And you have rediscovered some fundations of QM.

This is not really different for particles. Because it is difficultor impossible to mesure the trajectory of a single particle, the choice of a specification is more crucial. If you involve the initial conditions, then you have a whole space of possible specifications (classic mathematicians would say a general solution of a differential equation) that you can call a wave function. If you include spin (rotation) general relativity and all the other things you have a section of a fiber bundle. That you can still call a wave function (it is defined in everypoint), but the logic is the same.

The trouble is that to explain some procedures that we use to solve practical problems, we look for bizarre behaviors of real objects and introduce mysteries where there are just our ones tricks.

It is important to remember that the dynamics of a quantum system (described by the Schrödinger equation) is only valid until a measurement .

After the measurement, you are dealing with classical values for, e.g., the particle spin in the Stern-Gerlach case.

So, the phase is lost at the moment of the measurement.

The situation at the moment of the measurement is the following:

Say, the probability of the particle having spin-up or spin-down is known (calculated by the Schrödinger equation), your result is just this probability P(up) and P(down).

For the result of the measurement, the same rules apply as for a classical statistical theory, where you have to draw from a given probability distribution.

So, yes, if you look at this the other way round, you can say that you can describe your classical probability problem (the coin toss) as one would describe the measurement of a quantum system, after someone calculated the probabilities for you, but this is a trivial statement.

Most of quantum mechanics is concerned with the question, what happens before the measurement and what are the actual probabilities. And this is something that you cannot map your classical coin toss onto. (i.e., you would need something like a Schrödinger equation for your coin toss, but there are some important constraints, like linearity and so on, which most probably will inhibit you from finding somthing like that)

@ Sikdar: Given a function, depending on whatever variables (here spatial and time variables), one can in principle expand this function in terms of other, ideally simpler, functions. Take for instance a periodic function (of x or t), which can be rigorously expanded in terms of sines and cosines of the integer multiples of the fundamental frequency (i.e. 2π over the fundamental period) of the periodic function as issue (for brevity, I do not go into the details of the class of periodic functions for which Fourier series expansion is possible). In general, given an operator equation, L x = α (where L is the operator at issue, α a known function and x the sought-after solution), one can rigorously expand x in terms of the eigenfunctions of L (I do not go into the mathematical details of the function space in which L operates, etc., and that in the spectral theory the notions of eigenfunctions and eigenvalues are somewhat restricted). The notion of superposition (or the 'superposition principle') as encountered in quantum mechanics falls into the category of eigenfunction expansion, which, as I indicated above, is not specific to quantum mechanics. For eigenfunction expansions, I refer you to the following excellent book (in two parts) by E.C. Titchmarsh: Eigenfunction Expansions (Clarendon Press, Oxford, 1958, 1962).

With regard to the coin you explicitly refer to, in mechanics it goes by the name of Euler Disk, for which classical dynamical equations (Euler's equations -- see for instance Mechanics, by Landau & Lifshitz) can be written down and in principle solved. Euler Disk received renewed attention by the following paper by Keith Moffatt:

http://www.nature.com/nature/journal/v404/n6780/full/404833a0.html

Amongst others, this work gave rise to the following very interesting experimental work:

http://journals.aps.org/pre/abstract/10.1103/PhysRevE.66.045102

Note added:

See also this paper by R.I. Leine (pdf): http://goo.gl/IBB4fI

I do not believe so.

There was a twin slit experiment conducted using very large molecules. In one variation, the particles were passed through a heater before passing through the slits. It was calculated that there was a very great chance that the molecule would 'shed' a photon before passing through twin slits which, IN PRINCIPLE, could be measured and information regarding the particle's trajectory could be deduced. Although there was no means to detect the photon, nevertheless, the interference pattern disappeared.

What this experiment demonstrated is that quantum uncertainty is not a phenomena that requires an actual observer. What is critical is information!. With the situation that you have outlined, Dr Sitkar, transfer of information would be continuous and so quantum uncertainty effects would not play a role.

@Christopher.

Nice example. Can you give a pointer to this specific experiment (e.g. names, so that I can google)?

@ Dr. Christopher

I think I got your point. If the information is available or can be fetched from the system, the coherence is no longer existing. But, in quantum mechanics, a superimposed state in no way provide any information about a particular state and hence they remain superimposed untill measurement is done.So, the coin case cannot be superposition as information can be made possible.

But, if we perform the act of coin toss in complete vaccum with no light , gravity or environment, would your answer will be same that it is not superposition.......

An answer to the quantum mechanical state problem in the case of the tossed coin can be found in http://arxiv.org/abs/1309.5002. Identical text is in attached file.

Wow... Nice one @ Alex.....Thanks. I will have a look and let you know....

@Behnam.

You stress the mathematical aspects of linear spaces and spectral representations. These are important but not at the heart of the coin problem. This is a problem of the quantum mechanics of macroscopic bodies, a field that is not covered in classical texts on quantum mechanics, not even in Landau/Lifschitz. The modern treatment of macroscopic systems is in terms of open quantum systems and stresses the notion of decoherence, pointer states, and environment-induced superselection (Zurek). On a non-technical level the basic facts are simple: the matrix elements of a state superposition of macroscopic bodies (due to the huge energies of the coins relative to hPlanck/(characteristic time)) do change their phase so fast and so sensitive to tiny external influences that only their time averages can have any empirically relevant effect. This lets the superposition of states turn into a statistical mixture which the has a direct meaning in terms of probabilities for the two possible tossing outcomes. BTW, you will not find any word about this essential aspect in Alex's exercise on ridgid body quantum mechanics.

Dear Ulrich; and others,

For a very elementary problem is it really necessary to involve such, non defined, mysterious, things such as field, decoherence, pointer state, superselection, ....

Excuse me, but I do not see any science at all in that.

The purpose of science is to provide answers, not enigma wrapped in riddles.

Or can you give a precise definition of what a state is, a wave function, ...other than : Feynaman said so, or the experiment proved that.

I believe that to try to make obscure phenomena is not good for science. After all you probably have students, and your job is to push them to understand, to see the why and the how, not to be buried in deep layers of undefined, not understood, rules and generally accepted processes (such as replacing some symbols by other in the name of first quantization).

@ Ulrich

For any given system, one could admittedly wonder as to the significance of quantum effects for a correct description of its behaviour. However, one could always describe any system at classical level; experiments will then establish whether the classical description has been justified. The problem of Euler Disk is a mathematically well-defined classical problem for which one can write down dynamical equations to be solved (numerically) for any given set of appropriate initial and boundary conditions. The suggestion has been invoked in the main problem posed on this page (by A.K. Sikdar) that somehow this problem had incontrovertible ties to quantum mechanics, a suggestion which you seem to subscribe to but which I do not.

My feeling has been, and remains, that Sikdar has been attempting to suggest that Euler Disk is necessarily a quantum object (by the specific way that he invokes the superposition principle -- probably he has the Schrödinger cat in mind). My earlier explanation on this page was aimed at clarifying that superposition is not specific to quantum mechanics, that the complex behaviour of any linear system can be expressed in terms of a linear superposition of the relevant eigenstates.

The Euler Disk problem is complicated essentially because of the Disk having to cope with a rigid body, the surface on which it is released, that constrains its motion in the vertical direction, and by the additional fact that there is friction (a dissipative process) in the problem; there is also the dissipative interaction with the surrounding air (which on its own has a complicated dynamics), but which experiments performed in vacuum (to which I have referred in my previous comment on this page) have shown not be relevant to the nature of the finite-time singularity in the motion of the Disk. The dissipation in the problem can be classically described in terms of a Langevin-type equation (which confers the underlying resonance frequencies imaginary parts), for which one does not need to invoke quantum mechanics.

Now my contention is that if Sikdar would watch the video of a numerical simulation of the motion of an Euler Disk (in such simulation, by construction all quantum effects have been discounted with), he would still be inclined incorrectly to tie the observed behaviour with quantum mechanics. No doubt, quantum mechanics is relevant at some level (notably, a correct description of friction involves quantum mechanics -- one could think of the process of the Disk hitting the surface exciting a plethora of phonon modes, not to say anything about the electronic excitation modes, that carry off energy from the Disk), but considering the problem fully classically will not change anything that we can see with our bare eyes when watching the motion of an Euler Disk.

There is actually a great deal of works dedicated to all sort of mechanical systems with outcomes that lead to randomness - namely dice, roulette, coin and others. A very good summary of those is given by the book:

Dynamics of Gambling: Origins of Randomness in Mechanical Systems

http://www.springer.com/materials/mechanics/book/978-3-642-03959-1

Regarding the paper on the quantum coin - I find it obscuring rather than clarifying the main point. It can be the case that a coin is governed by quantum mechanics but being a macroscopic object - most chances are that it is not coherent and therefore effectively ruled by classical mechanics. To produce a genuine quantum mechanical coin would be non-trivial in my opinion.

At any rate the question under discussion here is the difference between classically probabilistic problems and quantum superposition - and I come back and claim that generically (unless one produces a true quantum mechanical coherent coin) the are different.

Dr Dutailly,

Einstein tried to imagine what it would be like to ride a light wave and he saw a problem.... the rest is history.

Hypothetical thinking is a creative scientist's most valuable tool - especially when trying to decipher the mysteries of QM.

Dr Sitkar - interesting question - what temperature would the coin be? Would the coin exhibit coherence?

When you describe a coin toss language persuades us that there is a 'thing' that exists - a coin. Actually, it is only the mind that insists upon the unitary existence of the coin. What really exists is a fuzz of discontinuities - wave functions collapsing and re-configuring constantly. So, the coin (in a classical state) is many things. Each of these tiny individual coherent states can interact (and exchange information) with each other. Of course, a tiny momentary coherent state comprising a few molecules may exhibit a superimposition of possible states - but the whole coin? - It seems unlikely.

@ Eytan

Conform your statements, and I think mine, on page 145 of the book you have introduced, one reads:

"Currently, the vast majority of the scientists support the vision of a universe where random events of objective nature exist. Contradicting Albert Einstein’s famous statement it seems that God plays dice after all. But going back to mechanical randomizers where quantum phenomena have at most negligible effect we can say that God does not play dice in the casinos."

To Christopher

"Hypothetical thinking is a creative scientist's most valuable tool - especially when trying to decipher the mysteries of QM."

The job of scientists, for which they are paid, is to find answers...Sorry I do not see any answer in a "fuzz of discontinuities - wave functions collapsing and re-configuring constantly.", knowing that any book about QM says that nobody knows that what a wave function is.

For over 70 years we have had the same narrtives, with wave functions, decoherence, collapse,...and not the first bit of answer, only the same "nobody understand". So if after 70 years, tens of thousands of people working on the same subject, and nothing to show, perhaps it would be about time to look for something else.

In my example about the trajectory of a shell I gave precise, defined, and provable answers. And it can be extended to particles.

The short answer is no. The long answer is nope.

:-) I completely agree with @claude answer, except for very very light coins: electron spins, for example.

@Jean Claude

As I understood the (not completely clearly formulated) primary question it implied to look at the coin as a quantum system (probably in the mood of a Gedankenexperiment). I tried to scetch the ideas that allows such a view and nevertheless say that a hypothetically assumed superposition of states would not have empirical consequences (such as observable interference effects). That such a 'quantum view' on macroscopic systems is not of any direct practical value is sufficiently evident that I did not state it. There is, however, a indirect practical value of clarifying the quantum view on the coin. The scientist who convinced himself that the quantum view allows to understand the classical view as an approximation has a more harmonic world-view as the quantum-classical-dualist and, as a consequence, may be more productive as a physicist.

The problem is that the Schrödinger equation is deterministic, not probabilistic. Relatedly, the states of quantum systems are not equivalent with the apparatus (QM) used to predict the outcomes of measurements. A flipped coin is typically described as having a probability of yielding either heads or tails. This probability describes two mutually exclusive states, and at no time do we describe the coin as existing in some H/T (head/tail) "superposition"-like state. We do this in QM (and in quantum physics in general). Regardless of whether we obtain one and only one outcome for a given experiment in QM (and recent empirical studies have shown ways in which this fails to hold true, as what were formerly only thought experiments, from Wheeler's delayed choice to Schrödinger's cat, have seen multiple and varying experimental realizations), the theory describes the system as existing in multiple, classically incompatible states at the same time. There is a natural analogue between QM and statistical mechanics, and thus by extension to probabilistic systems in general. However, the difference is that the standard interpretation of QM entails an IRREDUCIBLY statistical mechanics. It is not a probabilistic formulation of outcomes given insufficient knowledge any more than the probability of getting heads or tails for some fair coin toss describes a coin in the air that is both heads and tails.

@Charles

The question probably refers to the process of throwing the coin. Classically there are initial states which lead to final position 'number up' and other (nearby) initialstates which lead to final position 'number down'. 'By unity of physics' there is a quantum version of the classical description and one may wonder what the properties of a quantum trajectory are which results from a pure state made as a superposition of a 'number up' initial state and a 'number down' initial state. The interesting thing is: as long as the trajectory is determined by a linear evolution operator, the state of the coin remains a pure state and not a statistical mixture. As I pointed out (and probably Jauch points out --- unfortunately I no longer have the book) by replacing the very fast varying matrix elements of the density matrix by low-pass filtered versions it will end up as a statistical mixture of up and down.

@Ulrich you can get an electronic version of Jauch's book:

http://libgen.org/book/index.php?md5=459BFA6DB4234FC0EDD2B6DA8ADB34A0

Dear Charles Francis:

A few points:

1) The Schrödinger equation wasn't "proven" but derived.

2) Eigenvectors are neither unique to quantum physics nor defined by possible outcomes, but by a basic linear transformation which ensures the transformation matrix maps a vector to a multiple of a constant (the multiple being the eigenvalue). It's ridiculous to describe coin flips using the formalism of linear algebra whether or not it is the linear algebra of quantum mechanics in Hilbert space or the far more ubiquitous linear algebra of Euclidean space. When you can describe the "phase space" of a coin flip in terms of Hilbert space and linear operators, then we might get somewhere.

3) The "Hamiltonian" is a classical description which is incompatible with the equations of motions in QM. This is because classical systems necessarily have single values for observables, while QM has operators that map would-be observables in classical physics to measurements using a formulation of probability used nowhere else.

4) Equating measurements with the states of quantum systems is a serious error. The reason for QM wasn't due so much to measurable values but to measurable values that yielded incompatible results thus requiring ridding physics of classical theories. There was no way to explain photons and other "quanta" within the framework of classical physics. We kept getting measurements that depended upon the nature of our observations. This doesn't happen in classical physics, and no matter how you look at a coin toss you will never change the outcome because (and only because) you looked at it in a particular way.

Dear Charles Francis:

1) The postulates of QM are just that: postulates. Their formulation into a quantum theory is based upon empirical results, and the mathematical apparati that follow from early formulations of QM are a consequence of mathematics, true, but are meaningless without the context of quantum theory. Quantum theories of motion depend upon a fundamentally different use (and, most would argue, interpretation) of probability and statistical structure than is found in classical physics. The "meaning of quantum formalism" is currently one of the most debated aspects of modern physics, and answers range from the classic so-called "Copenhagen interpretation" to multiverse theories. Relating epistemic indeterminacy to ontological doesn't provide "insight", it just clouds the issue.

2) QM doesn't deliver conditional probabilities. Probability theory describes conditional probability rather precisely (as is expected of formal systems). Quantum probability differs from mathematical probability or probability theory in a qualitative way. Nobody calculates probabilities using the mod square of an amplitude, whether they are working within some science or are mathematicians. The exception is those who deal with probabilities in QM. These differ radically in numerous ways from classical probabilities. They are calculated differently and correspond to events in ways that no classical formulation does.

QM encompasses several aspects. One of them is expressed in 3 or 4 axioms, related to representation of states of a system on Hilbert spces, observables, interacting systems. It is possoble to prove these axioms for any systems meeting some general conditions (usually agreeed upon). The probabilist interpretation is then just an efficient way to represent the values which are measured. All these results are purely mathematical, and have no physical content. They hold at any scale. So one can have a clear, rigorously proven, interpretation and use of these axioms. In this context the Schrödinger equation can be proven, in some conditions, and is no longer an axiom.

Other aspects of QM (mainly the motion of particles) require physical assumptions. But the spinors (as representing the motion of a material body) have a clear explanation,, even in the GR context.

To Charles,

Sorry, but in all thebooks about QM you have assertions such as : nobody knwos what is a wave funtion, nobody understand the spin, nobody understand spinors,....There are many citations of scientits on the subject.

Moreover the issues of axioms (or postulates) stay : you have to add many hypotheses as fundations of the usual interpretation of QM. They can be right but one of the criteria for a scientific theory is simplicity : it should involve as few postulates as possible.

To Charles,

"How can anyone sensibly declare the ignorance of others? " What do you mean??

This is a fact that almost all texts on QM say that there are some things that one does not understand And we have the celebrated :

”I think I can safely say that nobody understands quantum mechanics.” Richard Feynman, in The Character of Physical Law (1965)

"The fundamental axioms of QM merely say that as systems is set up in an initial configuration, and then a measurement will be performed. One can hardly get more innocent in terms of postulates than that." ...You forget Hilbert spaces, observables, eigen values, minimum substitution rules, ...And even just the previous statement would require some precisions, such as : what a system ? is there a scale involved ?

I do not say that QM is wrong, just that the what is usually called QM is full of postulates, axioms, generally accepted practices that are, at best just that : hypotheses that you have to accept. If you are comfortable with that, OK, but I am not. After 70 years we should demand more.

I have tried to bring my humble contribution. The basic axioms of QM can be explained, and proven, in a rigorous framework. This leads to simpler explanations and safer use. And perhaps further on the path new discoveries. I do not claim any prize, tenure, or anything like that. I just think that it is a bit sad that the scientific community is so full of bigotry.

To Charles,

I have read your lattest paper and I better understand your point of view. Indeed you propose an explanation (formal) of the axioms of QM, what I think is necessary. For this I thank you. But two remarks :

- your explanation is actually based on the measure of variables belonging to Hilbert spaces, which can be estimated from a finite number of data. Actually one can go further : the issue occurs in most models where the variables are vectors of infinite dimensional vector spaces. It can be proven that then the variables belong to Hilbert spaces and observables are self adjoint operators. So this property has no physical content, but from there one can deduce most of the usual postulates of QM (in particular for intercting systems). The probabilist interpretation is then clear.

- I disagree with the relationist interpretation. Actually the usual cartesian model is almost never used for practical purpose. If you wand to locate somebody you give its address, and for star its coordinates. So the genuine model for the localisation of any material body is a manifold, where coordinates are given in charts and the structure of manifold is given by the equivalence of charts. The cartesian frames actually appear for the vector space,,they are used for the definition of motion (meaning to introducerotation). But the concept of motion(translation and rotation) is more complicated than its common definition in galilean geometry. The spin is a relativist feature, and the spinors can be introduced with some sense as a representation of the full motion, and this holds in GR.

To Charles,

1. A sound explnation of QM is still useful, at least, as you say, so that more people can understnd

2. The same axioms can be used in new domains . I have been an economist for years and I see clrealy where they can be fruitful (for instance in phase transitions, .).

3. The usual interpretation of QM has hampered a deeper understanding of some basic phenomena. Notably motion : a local frame is necessary not for the location of a material body, but for its mtion, and the usual representation in galilean geometry (by the diisplacement group) cannot be transposed in relativity. The use of spinor is fully justified, but should be grounded more clearly in Clifford algebras. Then the extension to GR is easy. In some way physicists have been fooled by mathematicians with cartesian representation.

Dear Charles Francis:

"All you are saying is that loads of people don't understand qm"

I wasn't aware I was saying anything of the sort. I agree with Mark Silverman: Feynman's quip may be clever, but it isn't accurate.

" You should try Jauch's book to get a better insight."

I've read it. The disadvantage of having to learn QM, QFT, etc., in order to work on a dissertation in a field that isn't quantum, theoretical, or particle physics is that one has to read a lot more textbooks and unofficially audit courses (sometimes with undergrads) in order to gain the requisite background knowledge to a graduate physicist requires. I can give you dozens of QM textbooks aimed at the graduate level that aren't from the 60s and inferior even then (for goodness sake, Dirac's Principles of Quantum Mechanics (4th Ed.), Feynman's classic path integral text, even Bohm's Causality and Chance in Modern Physics were all published before or around the same time). You want insight? Short of actually working in a lab (and trust me, even doing so in a lab that requires the use of principles of quantum mechanics doesn't necessarily mean applying QM), this comes with doing problems and the best text for that is A. A. Kamal's 1000 Solved Problems in Modern Physics. There are plenty of excellent metaphysical, mathematical, theoretic, and philosophy of science treatments in series like The Frontiers Collection, Cambridge Monographs in Mathematical Physics, Lecture Notes in Physics, Fundamental Theories of Physics, Graduate Texts in Contemporary Physics, even Springer Briefs in Physics. Why "Jauch's book to get a better insight" compared to hundreds of better treatments? Because it's made such an impression that unlike texts written a decade earlier it hasn't been republished and emended? Because the author's treatment was criticized thoroughly by reviewers such that it made virtually no impact? Or is there some special nature of this text that you have identified which you do not find in the hundreds of superior texts published in the last several decades (not to mention previously)? Shankar I'd expect (even though I don't like it as much as others). Same with Griffiths. Personally, coming from a background in mathematics I found Quantum Mechanics and Quantum Field Theory: A Mathematical Primer by Dimock and Quantum Theory for Mathematicians (Graduate Texts in Mathematics) by Hall better than most textbooks, but that's a consequence of my background more than it is a commentary on standard QM textbooks. But what, exactly, should I have gotten from Jauch's text that I (apparently) didn't?

To Andrew,

I have read Dirac's and Feynman's book (bought at the Coop in Cambridge by the way)..

Your are convinced, I am not. And I feel that I am not alone.

We have the standard model, it is still true and strong, 40 years later, good.

We have not seen any progress in understnding gravity, no problem.

Theoretical Physics has completely stalled since 70 years, and it shows.

The issue is not to know how to implement some tricks, it is to understand what they mean. That is science.

Dear Jean Claue Dutailly:

What is it I am convinced of, exactly? Other than that Jauch's text isn't much good compared to others, that is?

I do disagree that theoretical physics has stalled for 70 years. This is because thought experiments from Schrödinger's cat to Wheeler's delayed-choice have now been empirically realized. Thus certain aspects of quantum physics which were mostly relegated to the domain of the philosophy of science have, in recent decades, required physicists to stop the "shut up and calculate" approach (a quip from Mermin that was wrongly attributed to Feynman). Recent progress has forced a re-evaluation of what Bohr tried to bury. Apart from that, what am I convinced of?

Dear Charles Francis:

Precisely what is your objection? That I have experience in labs or that I have read too many texts on quantum physics? I've read the text you recommended and hundreds of others, and spent years keeping up with physics literature. I'll ask again: 'Why 'Jauch's book to get a better insight' compared to hundreds of better treatments?" You have mentioned von Neumann. His contribution was invaluable and I thoroughly agree that it is fundamental. However, you haven't referenced his work in your responses to mine.

You haven't read the textbooks or monographs I have and thus can't possibly say whether they are "on a different topic" (even if you had, as I haven't named them you couldn't know this). Basically, having recommended I read a text I did years ago, you are now making claims about the experiences I have had you can't speak to and the texts I've read you know nothing of. This isn't exactly an argument. Again, what it is about what I said and the text we've both read that makes what you have claimed correct relative to what I've said?

To Andrew,

You have read many books on QM

You practise QM in a lab

Everything is clear, all answers given, Physics go forward,

Thee is no contradiction, no need for an explanation,

This is no longer Shut up and compute, this is Shut up and read

As I see in this Forum not everybody is convinved, but, whatever...

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

As far as the laymen pay the tuition fees and the grants, ...

Dear Jean Claude Dutailly:

Interestingly enough, the "shut up and calculate" apothegm was made by Mermin and misattributed to Feynman. Mermin, when he realized that he was the origin, thoroughly criticized this approach. I do to. I have repeatedly argued that QM presents serious challenges in multiple ways primarily because of the lack of any one-to-one correspondence between the physical and the formalism. Our inability to understand just what, exactly, QM describes or what physical systems in quantum physics are does not mean that incredibly simple probability is somehow equivalent to the statistical structural of QM. Representing a coin toss as a system in Hilbert space is just idiotic and pointless. There is probability, and then there is calculating probability using amplitude (unique to quantum physics).

Also, I prefer Oscar Wilde.

Dear Andrew,

Point taken.

I agree with you that the example of coin toss is indeed bad publicity for QM.

3 years ago F.Laloë published a book (in French) prefaced by C.C.Tannouudji "Do we really understand QM ?" and the latter said "Whom of us has ever felt at least once some trouble about the fundations of QM ? the feeling that a convincing and satisfying formulation of QM is still missing ?"(translation is mine).

So, I donot, in any way, pretend that QM is wrong, just that I feel myself that there is still something which is missing. As Charles Francis (excuse me Charles if I extrapolate on your thoughts) I would feel better if we had this deep understanding. One reason being that we could be more comfortable about our use of QM. The other being that it could open new horizons.

Myself I have found some results. Actually there are pure mathematics, without any physical content, but they give back most of the usual axioms of QM, and moreover they have a simple interpretation. They are mathematically proven, so there is no qualms about exotic assumptions. What is fascinating is that they can be extended to other fields than physics (I have a background in Economics and the theorems provide some guidelines to find phases transitions). QM encompasses more than these axioms, and of course this is where, from my point of view, the real physics stands. One point which is troubling is the concept of motion, which is misrepresented in the common mathematics (location is actually easy and done in manifold, speed and rotation are more complicated and need the spinor in a relativist context). But this is another story.

@Andrew

If this representation would be done in the hope to learn something about how coin tossing works, this assessment would be correct. If it is done as a thought experiment in the hope to learn something about how QM works it is as idiodic and pointless as Schroedingers cat.

BTW, to whom do you prefer Oscar Wilde, and why do you mention him?

I would like to consider a slight variation on your thought experiment Dr Sikdar.

Let us suppose we have a coin - at room temperature. The coin is spinning in a vacuum.

At some point we are able to completely surround the coin with a spherical Bose-Einstein condensate layer. However, this does not alter the classical state of the coin inside the coherent sphere.

In this case - what state is the coin in when considered from a point OUTSIDE of the sphere and before the BEC collapses?

Probability theory is applicable to problems where there is a degree of uncertainty in the outcome of a process. There are two kinds of uncertainty that need to be conceptually distinguished. There can be uncertainty in our knowledge of a state of affairs, and there can be uncertainty inherent in the actual state of affairs. In classical physics there was only the former kind of uncertainty. In classical physics initial conditions determine, in principle, the future evolution of a system: "If it were possible to know the position and velocity of every particle in the universe, then we could predict with utter precision the future of those particles and, therefore, the future of the universe." - Isaac Newton. The toss of a coin is a deterministic process in this sense. The uncertainty is uncertainty in available knowledge. Quantum mechanics introduced uncertainty of the second kind - uncertainty inherent in the very fabric of reality. That is the difference between tossing a coin (or casting dice, etc), and the Schrödinger's cat kind of scenario.

See my paper "Are all probabilities fundamentally quantum mechanical?" where this issue is discussed.

regards,

Rajat

A short remark on what I believe to be a useful test to distinguish between incoherent superposition (where we do not know in which state a system is, so we assign different probabilities to the, say, two possible states) and coherent superposition, in which the state is the sum of two states. In the latter case, if psi1 and psi2 are the two (orthogonal) states, there is a very real physical difference between psi1+psi2 and psi1-psi2. In fact, the entire interpolating set

psi1 + exp(i phi)*psi2

can be distinguished and the value of phi is measurable, even though all these states correspond to being in psi1 and psi2 both with probability 1/2. If you can devise a physical procedure, in a coin in flight, to work out whether it is head + tails or head - tails, then it is indeed a coherent superposition. If not, which is certainly what is generally accepted, then we only deal with a density matrix and the probabilities involved are purely classical.

Indeed, the probability that a coin lands on heads is only 1/2 to someone who has not looked at the coin in any detail: a precise camera could in fact predict it it, or at least give much better odds than 1/2 on its falling heads or tails (people have in fact used such an approach to make money at roulette, so it is a practical truth, not just a theorist's fantasy). This in fact strongly hints that we are dealing with probabilitites involving lack of knowledge, not fundamental quantum mechanics issues.

Dear Leyvraj,

Is it not lack of knowledge always that leads us to the use the notion of probabilities?  Please see the detailed arguments given in my paper as to why the classical coin-toss can be taken up as a quantum mechanical case. 

Dear Sanjay,

There is no system in the universe including the universe itself that is not quantum mechanical. The kind of argument that you make is invalid since any system can be treated quantum mechanically and they reduce to classical i appropriate limits. And no system is fundamentally classical. Thus it is perfectly legitimate to treat the "classical" coin toss quantum mechanically. You can treat any problem quantum mechanically.

Regards,

Rajat

Dear Charles,

Could you please elaborate a little more on the fundamental difference between classical and quantum probabilities?

The outcome, as long as it has not come out and has not become a definite knowledge, is definitely indeterminate both in Classical mech. as well as QM.  The probability reduces to definiteness upon observation both classically as well as in QM. 

Regards

Rajat