Philadelphia, PA

Dear Janjic, 

The determinism of Laplace is akin to the determinism of Einstein--in his opposition to QM indeterminacy. "God does not play dice with the universe," Einstein famously said. He thought that QM was correct, as far as it went, but that it must be incomplete. 

Why would it be incomplete? Well, basically, because it doesn't predict specific outcomes of the sort Einstein expected. Instead, it predicts statistical generalizations about outcomes. It tells you how the statistics change. But it leaves out predictions of individual runs of the statistical generalization. The determinism of QM is a unitary evolution of the probabilities of particular measured outcomes. This is not determinism in the sense of Laplace and Einstein. 

There have been many RG discussions of related points, over the past few years. One theoretical option is simply to take QM at face value. That's the one I'm most inclined toward.

You may find the following paper of interest:

https://www.researchgate.net/publication/296327588_Fundamental_Physics_Partial_Models_and_Time%27s_Arrow

H.G. Callaway 

Chapter Fundamental Physics, Partial Models and Time's Arrow

Painlevé pointed out that, if you wanted to predict the evolution of a dilute gas over a second, deterministically, getting the position of a kilogram of mass wrong by a meter at the distance of Sirius would, via the tidal forces involved in that error, entirely spoil your prediction.

So questions as to whether the universe is deterministic or not are in a sense unanswerable, as they cannot possibly be addressed by experiment. The universe, from a practical viewpoint, is undoubtedly stochastic, and this has nothing to do with quantum mechanics.

Whether small, simple quantum systems, such as a hydrogen atom in an excited state, behave deterministically or not is a somewhat more subtle question. However, we can only really get a handle on it when we actually measure something, in which case we lose the simplicity of the system.

Philadelphia, PA

Dear Leyvraz, 

A further argument along the same lines: All measurement involves some margin of error. But if our measurements all involve some margin of error, however small, then how can we conclude to absolutely determinant values of the things measured on the basis of such evidence? Whatever our hypothesis predicts, we can only check it to some finite degree of accuracy. 

H.G. Callaway

Philadelphia, PA

Dear Cornwall,

Prey tell, What's not the issue? 

I see nothing much you say, just above, with which I would be inclined to disagree. You simply take a different approach. Moreover, you do not actually argue against anything I said (as contrasted with differing). You wouldn't be just a little disputatious, now, would you? 

If you have any margin of error in measurement, then the hypothesis from which the measurement is predicted could be changed slightly, in various different ways, with the relevant prediction still falling within the margin of error of the measurement. In consequence, given that there is always a margin of error in our measurements, we will have to allow for variations in the predicting hypothesis as well. It is difficult to see how, on the basis inexact measurement we can justify perfectly determinate hypotheses about things measured. 

I think you have merely a wrinkle on the same argument. 

H.G. Callaway

Philadelphia, PA

Dear Kralj, 

You present a pretty conventional view of the alternatives in debates concerning QM indeterminacy. So far, so good. No doubt there are the various intense debates, but I tend to think that the "hidden variables" approach is pretty much a lost cause. Physics has simply failed to develop in that direction in recent decades. 

One significant problem concerns QM entanglement at great distances. While physics is generally content with recognizing the correlations, on the hidden variables approach, there must be a causal influence involved--which becomes increasingly implausible as the distances increase. The flat-footed approach is simply to accept the correlations--much in the spirit of accepting QM indeterminacy itself. (Subject to merely possible correction, but this goes without saying.) 

As you suggest, the debate has shifted, away from hidden variables, toward close evaluation of the experimental tests of the Bell inequalities. There is a good deal of that. But on the larger scale, physics simply goes on with the usual indeterminacy. The philosophers will be wary of departure when the physicists chiefly agree in practice.

H.G. Callaway 

Dear F. Leyvraz:

   Don't you think Painlevé was exaggerating?

Dear Raul: no. In fact, I guess, from a modern viewpoint in which we would take greater account of the kind of issues Remi was mentioning, it might well get worse.

On the other hand, it is not conceptually impossible for a deterministic universe to exist: were the universe a perfectly regular piece of *regular* clockwork, then indeed we might predict everything knowing the initial conditions and, additionally, predict everything to an excellent approximation if you but know the initial conditions to an excellent approximation: this would, indeed, be a truly deterministic universe, in practice as well as in theory. Due to the instabilities mentioned by Remi, things are not that way in the real world.

So indeterminacy is not a real problem: it was always with us, even in a fully classical world.

The difficulties of QM, as pointed out in this thread, have essentially nothing to do with indeterminism, and everything to do with nonlocality. The latter is, indeed, a truly quantum feature of reality, with no classical counterpart.

"On the other hand, it is not conceptually impossible for a deterministic universe to exist: were the universe a perfectly regular piece of *regular* clockwork, then indeed we might predict everything knowing the initial conditions and, additionally, predict everything to an excellent approximation if you but know the initial conditions to an excellent approximation"

Thank you for the comments F. Leyvraz. Still i don't think it answers my actual question. The question is not if we could ever be able to determinate universe, but: Why do we say that universe is not deterministic because we are not able to determine position and impulse of particles exactly? Why does our ability to measure has something to do with the reality of particles itself? I don't get the link between measurement and reality. If we can't measure the position and impulse at the same time perfectly, the particle itself could still have an perfect own impulse and position in spacetime. Let's say thats the assumption which is not accepted in todays quantum mechanics interpretations. But I don't see an answer which negates this assumption so far in the comments and I haven't seen a concrete negation in a book or something else either. 

Philadelphia, PA

Dear Janjic, 

I think you have to turn your question around and ask about the possible evidence for the existence of perfectly determinate objects of measurement, given the absence of perfectly determinate measurements. It is not that the hypothesis of determinism is somehow senseless, it is more that it does not find sufficient support. 

Compare Leyvraz:

On the other hand, it is not conceptually impossible for a deterministic universe to exist:

--That is, the hypothesis is not senseless. 

He continues:

were the universe a perfectly regular piece of *regular* clockwork, then indeed we might predict everything knowing the initial conditions and, additionally, predict everything to an excellent approximation if you but know the initial conditions to an excellent approximation:

--Well, of course, this is a merely hypothetical claim drawing out the implications of the antecedent statement : "Were the universe a regular piece of clockwork, " 

--One might also add (if I may) "And if pigs had wings, then they could fly." After  all, this is certainly true.

--In addition, however precise the measurements become, in our deterministic universe, there is always still a margin of error. Accordingly, our particular "clockwork" laws could be changed slightly in one way or another, without  effecting anything within the margin of error of the measurements of initial conditions and of the predicted results.  (So, how to argue for determinism?)

Finally he says:

this would, indeed, be a truly deterministic universe, in practice as well as in theory.

---End quotation

This is only to say that in a deterministic universe, things would be deterministic. Although the supposition is made, as in my paper above, that great difficulties in calculation arise even for the Newtonian three-body problem, it is important to notice that QM indeterminacy is something additional. Few are the theorists who would think to try to extract Heisenberg's uncertainty principle from quantum physics. We have to recall, perhaps, the fundamental role of the Planck constant. 

H.G. Callaway

el indeterminismo asociado a parejas de variables no conmutables , de la teoría  cuántica es  fundamental ,es decir no es el resultado de nuestra incapacidad tecnológica para medir las variables en cuestión

@ H.G. Callaway: I certainly did not mean to state that ``a perfectly deterministic world would be deterministic''. My point is that, for determinism to be at all observable, and distinguishable from randomness, we need predictability. That is, precisely we need to exclude the sort of behaviour that arises, say, in the 3-body problem.

When we have such behaviour, then saying that the universe is ``deterministic'' is idle, as there is no way whatever to imagine a setup which would confirm or invalidate that remark. To be able to speak meaningfully about determinism, we need  not only a universe that is formally deterministic (in the sense that initial position and velocities determine the entire future) but one that is effectively predictable.

Now while that hypothesis is not logically inconceivable, it is also clearly false. So our universe is, as a matter of experimental fact, not predictable at all. It is thus not a matter of ``difficulties of calculation'': there is simply no way you can know the initial conditions in any way well enough to predict large systems over any time scale. See Painlevé's remark above.

So we must, as physicists, live with indeterminism, even classically. Once we have understood that fact, I believe living with the mild, additional quantum indeterminism, may not be so hard.

Finally I stated that, in quantum mechanics as in classical mechanics, simple systems are previsible and deterministic, due to the deterministic nature of the Schroedinger equation (see Remi's remarks). In QM, this is related to the fact that any measured system requires a measurement apparatus, and is thus not simple. It has been argued that the whole indeterminism of QM is in fact the same as the indeterminism of complicated classical systems. The randomness only appears when you measure, and then only because the measuring apparatus is complex.

Philadelphia, PA

Dear Leyvraz, 

I do not think that the criticism I offered to your note above would extend to what you say here. I am going to be somewhat skeptical, though, of the idea that the indeterminacy of QM "is in fact the same as the indeterminism of complicated classical systems." It is an interesting idea.

But your use of the words simple bothers me somewhat. I recall that it is often said, on the contrary, that specifically quantum mechanical phenomena only appear in simple systems--as with the double slit experiment. A supporting concept is the claim, widely held among theoretical physicists, that specifically quantum mechanical phenomena do not appear on larger scales, because of environmental decoherence. This is an appealing explanation of the paradox of Schödinger's cat and similar puzzles, and it rest upon decoherence in complex system. 

You seem to take comfort in the idea that the randomness only appears when one takes measurements. But I find this somewhat curious, because the measurements taken, showing randomness, are the only evidence we have for the unitary character of the Schrödinger wave function--which is never itself observed.  That the Schrödinger equation is "deterministic" only means, after all, that  given appropriate information we one can calculate the probabilities involved in future observations. Its is only the propagation of probabilities which is determinate (it is not even clear that these probabilities are fully physical), and in the end one has to bring in the Born rule to get specific predictions. Quantum mechanical randomness just strikes me as basic and irreducible. But, if so, it is not produced by complexities. 

Regarding the Newtonian three-body problem, what seems distinctive is that the laws involved work so well in simpler cases--as in calculating the orbits of moons and planets. There is plenty of evidence, for the validity of Newton's laws --at low energy. The known problems with the Newtonian system seem to have little or nothing to do with complexities. That is reason to attribute the character of the three-body problem to the intractable character of the calculations. It is not that alternative explanations are impossible. But what has to be shown is that they are preferable --that there is some special merit or theoretical advantage in adopting an alternative to difficulties in the calculations. 

You go too far is saying that "our universe is, as a matter of experimental fact, not predictable at all." 

H.G. Callaway

``specifically quantum phenomena appear only in simple systems'': correct, to be sure. But these phenomena are usually well in line with unitary evolution, so that they are not really indeterminate. They do become indeterminate when you look, but then looking destroys the simplicity. What is typically quantum involves complementarity and entanglement, but the purest manifestations of these (Aspect's experiment, for example, or delayed choice) only involve indeterminism in a very peripheral way.

As to the 3-body problem, it is a mathematical theorem that any kind of error committed, either in the initial conditions or in the control of external influences, will grow exponentially, hence uncontrollably. For a system such as the planetary system, doubtlessly you can ``tame'' this growth. The impredictability then only arises on long time scales. But for faster processes involving more particles, this effect is catastrophic. A thermodynamic system can never be viewed as deterministic, even in principle. There is thus plenty of irreducible randomness in classical mechanics, in particular there is no problem whatever with free will: biological systems are quite unpredictable at the mechanical level, and again it is no issue of calculational ability, but of the indomitable growth of error.

Philadelphia, PA

Dear Leyvrav, 

Thanks for your further reply, which unfortunately, does not seem to meet my doubts as expressed above. 

You seem to be going back and forth about what is "simple" and what is not. Do you believe the exchanges are worth carrying forward? It strikes me that the probabilistic scattering observed in the two-slit experiments, when efforts are made to determine paths, fully belongs to the category of quantum mechanical phenomena. In fact, it is crucial evidence. 

I've not really seen much evidence of deeper interest in critical perspectives on what you have contributed. BTW: I don't see indeterminacy as crucial to all interesting approaches to the theme of "freedom of the will."

H.G. Callaway

``But I find this somewhat curious, because the measurements taken, showing randomness, are the only evidence we have for the unitary character of the Schrödinger wave function--which is never itself observed. That the Schrödinger equation is "deterministic" only means, after all, that given appropriate information we one can calculate the probabilities involved in future observations.''

Actually, not quite. In QM, if we prepare a state and then let it evolve, and if we then have a prediction for the evolved state, it is possible to design a measurement which will answer 1 with certainty if, and only if, the system is in the predicted state. On the other hand, such a measurement will not always give zero if the state is different from the predicted state, so we do need to repeat the measurement several times to confirm our prediction. But such a measurement, in principle always possible, is in a sense not really probabilistic.

Further, the last sentence is a bit ambiguous. The fact is that the Schrodinger equation changes a state of which we have full knowledge into another such state. Such a state cannot be said to be fully characterised by ``the probabilities'' unless we specify that we mean the probabilistic outcome for any observable we choose. Since there are incompatible observables, the full information is much more than what could be  given by any one set of probabilities. Thus, given the state, I know both the probability of finding the system in  a given position, and that of finding it at a given momentum.

Of course, QM as referred to observable quantities is probabilistic. But the underlying theory which tells us how the ``true'' system evolves, even when not looked at, is deterministic. Whether it makes sense to consider such entities in science is clearly a matter of opinion, but as far as I know several physicists, myself included, think it does.

Philadelphia, PA

Dear Leyvraz, 

Though you seem to want to dispute my way of putting the matter, I don't really see much to disagree with in what you say in reply. 

I would have preferred some attention to the following passage from my prior note:

You seem to be going back and forth about what is "simple" and what is not. Do you believe the exchanges are worth carrying forward? It strikes me that the probabilistic scattering observed in the two-slit experiments, when efforts are made to determine paths, fully belongs to the category of quantum mechanical phenomena. In fact, it is crucial evidence. 

If there is any significant difference regarding QM in this set of exchanges, then I believe it has to do with the comparative emphasis which theoretical physicists may give to the "deterministic" evolution of the Schrödinger wave-function vs. the randomness of state reduction --as appears in measurement. However, you do not really focus on that issue. Instead you seem to focus on a special case, at one point and some complexities at another. 

I would suggest that an "underlying theory which tells us how the `true' system evolves, even when not looked at" is of less interest than you seem to think. This is particularly so, when one considers the theoretical equivalence of measurement/ observation with environmental decoherence. Undue emphasis on the formalism of QM tends to discount the actual evidence we have for making use of the formalism--usually or typically in the service of emulating the determinism found in physical theories of old --as in Newton, Laplace or Einstein. 

No one doubts the usefulness of the Schrödinger formalism. It is just that it is not the whole story; and we have to look at state reduction as well, since this is central in the evidence available. It is not a "matter of opinion" whether one must include the Schrödinger equation in understanding QM --or matrix mechanics as an equivalent alternative. So, it is somewhat misleading, as it seems to me, that you should make such a suggestion at the end of your note. 

H.G. Callaway

So we mainly agree, with a difference in emphasis. To clarify: what I said to be ``a matter of opinion'' was the relevance and importance of considering real systems when not observed.

My point so far is that (so-called?) quantum non-determinism arises when we couple a quantum system to a large system, thus leading to decoherence, measurement and the like. However, when such complex systems are considered, the appearance of indeterminism is wholly to be expected, be the system classical or quantum.

@ Remi: if you assume the universe is in a fully quantum pure state,you are in the framework of Everett-like, relative state (or more luridly, many-worlds) interpretations. There is a large literature on how to understand the universe's classical features in this framework. It mainly rests, as far as I can see, on the fact that we cannot measure everything. "Consistent histories" may be a good place to start from.

Philadelphia, PA

Dear Cornwall, 

I think there is more than a little room for skepticism regarding "the universe as a whole," since we cannot treat of the universe as a whole without suggesting an outside observer--who would then not be clearly part of or outside of "the universe as a whole." Many a logical paradox arises in that territory. 

You may want to take a look in on the Russel paradox:

https://plato.stanford.edu/entries/russell-paradox/

You wrote:

There is one problem with decoherence theory. As a whole the universe evolves deterministically by the Schrödinger equation, yet we find it classical. So how does it do einselection on itself? What is measuring the universe?

---End quotation

I would not be inclined to count any theoretical considerations regarding the wave-function of the "universe as a whole" as strongly counting against decoherence theory --or much else for that matter. 

H.G. Callaway

Philadelphia, PA

Dear Leyvraz, 

Thanks for your short reply. I remain skeptical.

You wrote:

My point so far is that (so-called?) quantum non-determinism arises when we couple a quantum system to a large system, thus leading to decoherence, measurement and the like. However, when such complex systems are considered, the appearance of indeterminism is wholly to be expected, be the system classical or quantum.

---End quotation

I am not convinced that we can accept the assimilation of QM indeterminacy to the difficulties encountered in relation to calculations of complex classical systems. But as I say, it strikes me as an interesting idea. The problem seems to be that it runs against the typical and pervasive distinction between classical and QM systems: the idea that QM uncertainty is unique and additional. 

Very briefly, consider, as an example the classical theory of black holes as distinguished from the QM approach to the same phenomenon. The one approach gives us singularities, points of infinite density, the other not; classically, nothing ever comes out of black holes, but on the QM approach we get the Hawking radiation. It does seem that something additional has been added on the QM approach. It provides a distinctive theoretical image of the world. 

H.G. Callaway

Philadelphia, PA

Dear Cornwall & readers, 

I notice some reflections on the role of philosophy. 

You wrote:

Callaway, once again thank you, philosophy is important and has helped physicists and scientists in general but without that final attunement to "natural philosophy", experimental experience and having the mathematical tools to work arguments, I tend to find philosophers miss and then dwell on things they've incorrectly understood.

---End quotation

I think this kind of issue depends a great deal of what one may think philosophers are doing. The idea that philosophers must be doing physics, or capable of doing physics, in order to productively engage with what is taking place in physics is a deeply flawed idea. It misapprehends what philosophy of science may aim to do. 

That some philosophers may "dwell on things they've incorrectly understood" basically seems neither here nor there. I'm sure the same could be said about physicists. We may doubt that the physicists working in one corner of the field always properly understand what is going on in other far corners. More to the point, of course would be criticism of some specific misunderstanding --particularly one of relevance in this discussion. Failing that, I think your pronouncement is no news. No remark without remarkability. 

One role of philosophy of science which I have often emphasized is to help make developments in contemporary physics available to the more general educated public. For example, I think we better appreciate the speculative character of developments in quantum gravity, given a comparison to the accomplishments of the standard model. Philosophy does specialize in estimate of epistemic standing; and, of course, those sorts of questions also interest physicists, 

H.G. Callaway

@ Callaway: Important differences between QM and classical surely exist! I would merely like to state that, in my own view, indeterminism, however much it has been quoted in this regard, is not such a primary difference.

Such things as Hawking radiation, or in a simpler instance, the tunnel effect, are indeed truly nonclassical. Another instance is the fact that, in classical mechanics, whenever I have uncertainty about position and momentum, I can always define a joint probability distribution function for p and q, that is, a function which allows me to predict the expectation value of any function of p and q. In QM, this is provably impossible in general.

Issues of joint measurement, nonlocality and the possibility fully to distinguish distinct states by measurement (possible in CM, generally not so in QM) are doubtless profound differences. They just do not fit simply into a scheme: predictable---unpredictable, deterministic---probabilistic.

Dear Alexander your question is very important in order to clarify several points concerning the issue about probabilities in QM. First of all I would like to underline that a probabilistic theory may well have deterministic equations, there are several examples in chaos theory and non-linear systems. As a consequence, the notions of determinism and predictability are logically distinct. To this regard there is an important paper of P. Suppes on the subject which is called "The transcendental character of determinism".

Secondly, I would highlight that there is a deterministic formulation of quantum theory due to David Bohm in which quantum particles have always definite positions. This theory works well in the non-relativistic level, but according to this framework it is possible for the particles to have well defined position and momentum at every time (particles follow trajectories in physical space). J. S Bell in "Speakable and Unspeakable in quantum mechanics" wrote many important essays on this issue. 

In the third place, without mentioning a different formulation of quantum mechanics, if we consider the statistical interpretation suggested by Ballantine (The statistical interpretation of QM) and, more recently, by D. Bowman (Essential quantum mechanics), the Heisenberg's uncertainty relations are explained in purely statistical terms: these uncertainties are technical notions (statistical notions) and have nothing to do with the real properties possessed by the quantum objects.

I hope to help with these few suggestions!