Philosophy is dead

A new paper on Science and Philosophy: A Love-Hate Relationship argues:

In this paper I will argue that: (i) The natural sciences need philosophy; and (ii) That scientists need philosophy. ...

Stephen Hawking has declared the official ‘death’ of philosophy in a way that seems to echo Nietzsche’s famous phrase ‘God is dead’. Commenting on questions such as the behavior of the universe and the nature of reality, Hawking writes: “Traditionally these are questions for philosophy, but philosophy is dead. Philosophy has not kept up with modern developments in science, particularly physics. Scientists have become the bearers of the torch of discovery in our quest for knowledge.” (Hawking 2010, p. 5). ...

In this section I give two examples where philosophical discussion has been genuinely contributory to science, along the line s discussed in 3a)ii. Before doing that, I will address the negative examples that were given in 2b) — examples where philosophy’s influence has been rather hampering for science: the iron clad of mechanistic philosophy and Plato’s dictum that celestial motions should be along circles. ...

In the past ten years we have seen the first commercialization of quantum randomness: the first bank transaction built on the basis of a code encrypted not by the usual algorithms of classical cryptography (which rely on unproven mathematical assumptions such as the difficulty in factorizing large prime numbers), but based on the new field of quantum cryptography: a technique for encoding messages based on the notion of entanglement between particles at long distances. Quantum cryptography has been successfully developed and commercialized by several groups over the past twenty years or so.

No, this is just not true. There are no successful commercial applications of quantum cryptography. Philosophy has contributed nothing.

You can tell that this guy doesn't know what he is writing about when he says "difficulty in factorizing large prime numbers". Prime numbers do not have (non-trivial) factors. Only the non-prime numbers can be difficult to factor.

He also recites the usual nonsense about Kuhnian revolutions. Hawking is right. Philosophy is dead.

The Oxford Questions

A new published paper on The Oxford Questions on the foundations of quantum physics, by G. A. D. Briggs, J. N. Butterfield, A. Zeilinger, starts:

1. The achievements of twentieth century physics

Much of the history of twentieth century physics is the story of the consolidation of the relativity and quantum revolutions, with their basic postulates being applied ever more widely. It is possible to forget how contingent, indeed surprising, it is that the basic postulates of relativity and quantum theory have proved to be so successful in domains of application far beyond their original ones. Why should the new chronogeometry, introduced by Einstein’s special relativity in 1905 [1] for electromagnetism, be extendible to mechanics, thermodynamics and other fields of physics?

References
1. Einstein A. 1905 On the electrodynamics of moving bodies.
Ann. Phys.17, 891–921.

No, Einstein did not introduce a new chronogeometry in 1905. He used the Lorentz transformations with the same geometry as previously by Lorentz and Poincare. The geometry of time was introduced by Poincare in 1905, and popularized by Minkowski in 1908.

The article moves on to these questions:

The Oxford Questions.
(1) Time, irreversibility, entropy and information
(a) Is irreversibility fundamental for describing the classical world?
(b) How is irreversibility involved in quantum measurement?
(c) What can we learn about quantum physics by using the notion of information?

(2) The quantum–classical relationships
(a) Does the classical world emerge from the quantum, and if so which concepts
are needed to describe this emergence?
(b) How should we understand the transition from observation to informed action?
(c) How can a single-world realistic interpretation of quantum theory be
compatible with non-locality and special relativity?

(3) Experiments to probe the foundations of quantum physics
(a) What experiments can probe macroscopic superpositions, including tests of
Leggett–Garg inequalities?
(b) What experiments are useful for large complex systems, including technological
and biological?
(c) How can the progressive collapse of the wave function be experimentally
monitored?

(4) Quantum physics in the landscape of theories
(a) What insights are to be gained from category-theoretic, informational,
geometric and operational approaches to formulating quantum theory?
(b) What are productive heuristics for revisions of quantum theory?
(c) How does quantum physics cohere with space–time and with mass–energy?

(5) Interaction with questions in philosophy
(a) How do different aspects of the notion of reality influence our assessment of the
different interpretations of quantum theory?
(b) How do different concepts of probability contribute to interpreting quantum
theory?

They claim that there has been progress in hidden-variables and many-worlds theories. I don't believe it.

Rovelli on free will

Physicist Carlo Rovelli writes:

Trying to force the meaning of "free will" beyond the simple meaning of freedom from "exterior" constraints, is an enterprise doomed to failure anyway. Is our "free" decision completely determined by internal factors? Let's assume for moment that it is not, and we see that we are in trouble. Suppose to be able to do an experiment where we can put a person in exactly the same mental situation (with the same memories, values, character, mood ...) and suppose we repeat the experiment many times, always with the same initial conditions. What would observe? There are two extreme possibilities: the first is that we see that the person will decide entirely at random. In this case the results will be just governed by chance. Half the time he will make a choice, the other half he will make the other choice. The second extreme possibility is that instead the person will always make the same choice.

In which of these two cases, is there free will?

Both answers are meaningles.

I mostly agree with this. Furthermore, those two cases are not the only ones. His thought experiment cannot be carried out, and we have good reasons to believe that it could never be carried out. It is a false dichotomy.

Any attempt to link this discussion to moral, ethical or legal issues, as is often been done, is pure nonsense. The fact that it is possible to say that a criminal has been driven to kill because of the ways in which Newton's laws have acted on the molecules of his body has nothing to do either with the opportunity of punishment, nor with the moral condemnation. ...

Free will has nothing to do with quantum mechanics. We are deeply unpredictable beings, like most macroscopic systems. There is no incompatibility between free will and microscopic determinism.

As I have noted before, quantum mechanics teaches that our naive preconceptions of microscopic determinism and randomness are both incorrect. To the extent that quantum mechanics is relevant, it rebuts the above dichotomy and also the one portrayed in this comic.

Relativity principle and covariance

Gomori and Szabo post a new paper on the meaning of the special principle of relativity (RP):

Let us illustrate this with only a few quotations:
“the laws of physical phenomena should be the same, whether for an observer fixed, or for an observer carried along in a uniform movement of translation” (Poincaré 1956, p. 167);
“If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K0 moving in uniform translation relatively to K.” (Einstein 1923. p. 111);
“it is impossible to measure or detect the unaccelerated translatory motion of a system through free space or through any ether-like medium” (Tolman 1949, p. 12);
“all physical phenomena should have the same course of development in all system of inertia, and observers installed in different systems of inertia should thus as a result of their experiments arrive at the establishment of the same laws of nature” (Møller 1955, p. 4);
“the laws of Physics take the same mathematical form in all inertial frames” (Sardesai 2004, p. 1);
“The same laws of nature are true for all inertial observers.” (Madarász 2002, p. 84)
“The uniform translatory motion of any system can not be detected by an observer traveling with the system and making observations on it alone.” (Comstock 1909, p. 767);
“The laws of nature and the results of all experiments performed in a given frame of reference are independent of the translational motion of the system as a whole. More precisely, there exists a [...] set of equivalent Euclidean reference frames [...] in which all physical phenomena occur in an identical manner. (Jackson 1999, p. 517);
“If we express some law of physics using the quantities of one inertial frame of reference, the resulting statement of the law will be exactly the same in any other inertial frame of reference. [...] we write down exactly the same sentence to express the law in each inertial frame.” (Norton 2013);
“all inertial frames are equivalent for the performance of all physical experiments” (Rindler 2006, p. 12);
“the laws of physics are invariant under a change of inertial coordinate system” (Ibid., p. 40);
“The outcome of any physical experiment is the same when performed with identical initial conditions relative to any inertial coordinate system.” (Ibid.);
“experience teaches us that [...] all laws of physical nature which have been formulated with reference to a definite coordinate system are valid, in precisely the same form, when referred to another co-ordinate system which is in uniform rectilinear motion with respect to the first. [...] All physical events take place in any system in just the same way, whether the system is at rest or whether it is moving uniformly and rectilinearly.” (Schlick 1920, p. 10);
“laws must be Lorentz covariant. Lorentz covariance became synonymous with satisfaction of the principle of relativity” (Norton 1993, p. 796);
“The laws of physics don’t change, even for objects moving in inertial (constant speed) frames of reference.” (Zimmerman Jones and Robbins 2009, p. 84);
“the basic physical laws are the invariant relationships, the same for all observers” (Bohm 1996, p. viii);
“laws of physics must satisfy the requirement of being relationships of the same form, in every frame of reference” (Ibid. p. 54).

They end up settling on the definition used by Lorentz in 1895, and copied by Einstein in 1905. But then they note that it does not match the modern definition:

RP and the covariance of equations E are not equivalent — in contrast to what is so often claimed in the literature. As Norton (1993, p. 796) writes:

The lesson of Einsteins’s 1905 paper was simple and clear. To construct a physical theory that satisfied the principle of relativity of inertial motion, it was sufficient to ensure that it had a particular formal property: its laws must be Lorentz covariant. Lorentz covariance became synonymous with satisfaction of the principle of relativity of inertial motion and the whole theory itself, as Einstein (1940, p. 329) later declared:

The content of the restricted relativity theory can accordingly be summarized in one sentence: all natural laws must be so conditioned that they are covariant with respect to Lorentz transformations.

The term "relativity principle" and its popularization is from Poincare and his 1902 book. So his definition ought to be the controlling one. He then proved Lorentz covariance in 1905, and Minkowski used that as the basis of his 1908 spacetime theory. After that, everyone used covariance, and not the weaker Lorentz-Einstein condition.

Norton is a little misleading, because Einstein's 1905 paper said nothing about covariance, and only about the weaker Lorentz 1895 notion. It is true that Lorentz covariance became synonymous with satisfaction of the principle of relativity, but that is because Poincare proved it in 1905 and Minkowski popularized it in 1908.

The Lorentz principle, used by Einstein, was that the equations have the same form in different frames. Covariance means that the equations have a unified geometric meaning that automatically subsumes the equations for the different frames.

Strictly speaking, covariance is a mathematical principle and RP is a physical principle. Poincare wrote about the relativity of space, meaning that you can just measure distances relative to other points, and you cannot deduce an absolute coordinate for position in space. Likewise, the relativity of velocity says you cannot measure your absolute velocity. Covariance becomes a physical principle after variable are identified with physically measurable entities.

Einstein's 1905 relativity paper is one of the most famous science papers every written, and yet people are still getting it wrong a century later. As quoted above, he said "the same laws hold good". That is, the law in one frame has the same mathematical form as the law in another frame. Poincare made the superior statement that the laws "should be the same". The laws do not just look the same, they are the same. Einstein did not appreciate how covariance makes this stronger statement possible.

This is all detailed in my book, How Einstein Ruined Physics.

Quantum mechanics leaves possibility of free will

I believe that free will is a metaphysical issue, not a scientific one. Denying free will is foolish.

Hard-core determinist Jerry Coyne writes on the free will theorem:

I haven’t seen his formal treatment of the Free Will Theorem, so I can’t say I can evaluate it — much less understand it. From the interview it sounds simply like a refutation of pure physical determinism, which most of us who accept quantum mechanics don’t see as problematic. The question is whether our behaviors and “choices” can be influenced by quantum dynamics, but even if that were true it wouldn’t prove “free will” exists in any meaningful sense. But the proof of “free will” is also connected with the bizarre phenomenon of quantum entanglement.

One of his readers comments:

I think that we agree that everything is determined from the Big Bang

Not that I like it ~ I want a loophole to exist, but I can’t imagine what a legitimate [non-woo] loophole looks like. I would like it to be true that brains can control events, but brains would seem to be just a higher order implementation of fields, forces & particles.

The problem is that they cannot imagine quantum mechanics.

Physicist Matthew Leifer comments on my essay:

The so called "free will theorem" does not establish that particles have free will or exhibit genuine stochasticity, whatever those terms may mean. It is just another proof of Bell's theorem, pure and simple. Of course, Kochen and Conway do not conclude this, stating instead that measurement outcomes must be undetermined prior to measurement. However, they fail to note that this is incompatible with the other assumptions they have made. In particular, TWIN implies that measurement outcomes on the two wings have to be perfectly correlated and the only way this can happen in a hidden variable theory is if it is deterministic. Therefore, undetermined measurement outcomes is not an option unless you give up at least one of their other assumptions, with locality and realism being the obvious choices.

Maybe Kochen and Conway overstate their results, and they are really restating Bell's theorem. Regardless, quantum mechanics leaves open the possibility of free will.

I do not think that free will can be scientifically proved or disproved. But for those like Coyne who say it can be disproved, they ought to reconcile their supposed scientific beliefs with quantum mechanics.

Essay on quantum information

The 2013 FQXi FORUM: FQXi Essay Contest - It from Bit or Bit from It? asks:

The past century in fundamental physics has shown a steady progression away from thinking about physics, at its deepest level, as a description of material objects and their interactions, and towards physics as a description of the evolution of information about and in the physical world. Moreover, recent years have shown an explosion of interest at the nexus of physics and information, driven by the "information age" in which we live, and more importantly by developments in quantum information theory and computer science.

We must ask the question, though, is information truly fundamental or not? Can we realize John Wheeler’s dream, or is it unattainable? We ask: ”It From Bit or Bit From It?”

I submitted my essay, and there is discussion on the FQXi site.

I submitted an essay to last year's contest, and got a lot of favorable comments, but the judges picked other essays. I would think that if they thought that I said something wrong, then they would say so in the comments. I think that they have reasons other than the essay quality.

Thurston's philosophy of proof

I have posted about Henri Poincaré being way ahead of Einstein on relativity. He was also a leader in other areas of mathematical physics. But he was known more as a mathematician, as this essay describes one of his more famous papers:

Algebraic and differential topology have had several episodes of excessively theoretical work. In his history [D], Dieudonné dates the beginning of the field to Poincaré’s Analysis Situs in 1895. This “fascinating and exasperating paper” was extremely intuitive. In spite of its obvious importance it took fifteen or twenty years for real development to begin. Dieudonné expresses surprise at this slow start [D, p.36], but it seems an almost inevitable corollary of how it began: Poincaré claimed too much, proved too little, and his “reckless” methods could not be imitated. The result was a dead area which had to be sorted out before it could take off.

That essay stirred up trouble with this dig at a famous mathematician:

William Thurston’s “geometrization theorem” concerning structures on Haken three-manifolds is another often-cited example. A grand insight delivered with beautiful but insufficient hints, the proof was never fully published. For many investigators this unredeemed claim became a roadblock rather than an inspiration.

Thurston was very annoyed at this, and published a 1994 rebuttal:

About two or three years later, I proved the geometrization theorem for Haken manifolds. It was a hard theorem, and I spent a tremendous amount of effort thinking about it. When I completed the proof, I spent a lot more effort checking the proof, searching for difficulties and testing it against independent information. I’d like to spell out more what I mean when I say I proved this theorem. It meant that I had a clear and complete flow of ideas, including details, that withstood a great deal of scrutiny by myself and by others. Mathematicians have many different styles of thought. My style is not one of making broad sweeping but careless generalities, which are merely hints or inspirations: I make clear mental models, and I think things through. My proofs have turned out to be quite reliable. I have not had trouble backing up claims or producing details for things I have proven. I am good in detecting flaws in my own reasoning as well as in the reasoning of others. However, there is sometimes a huge expansion factor in translating from the encoding in my own thinking to something that can be conveyed to someone else. ...

What mathematicians most wanted and needed from me was to learn my ways of thinking, and not in fact to learn my proof of the geometrization conjecture for Haken manifolds. It is unlikely that the proof of the general geometrization conjecture will consist of pushing the same proof further.

I am not really sure what he is rebutting here, as Thurston seems to concede that he never published the proof. Nevertheless, Thurston's paper is famous, and UCLA mathematician Terry Tao just wrote that he would tag it as a "must read" for all research mathematicians.

Go ahead and read it, but keep in mind that Thurston was on the fringe of mathematics by denying the importance of a written proof. He was cited in a notorious 1993 SciAm article on the Death of Proof, and the author says he relied heavily on Thurston. Thurston was probably embarrassed by this paragraph:

Thurston emphasizes that he believes mathematical truths are discovered and not invented. But on the subject of proofs, he sounds less like a disciple of Plato than of Thomas S. Kuhn, the philosopher who argued in his 1962 book, The Structure of Scientific Revolutions, that scientific theories are accepted for social reasons rather than because they are in any objective sense “true.” “That mathematics reduces in principle to formal proofs is a shaky idea” peculiar to this century, Thurston asserts. “In practice, mathematicians prove theorems in a social context,” he says. “It is a socially conditioned body of knowledge and techniques.”

No mathematician wants to be associated with a Kuhnian paradigm shifter, so this paragraph surely also prompted Thurston's essay. Meanwhile, Thurston's geometrization conjecture has been proved in connection with the solution to the Poincaré conjecture. Yes, Poincare's analysis situs led to a century of research by the smartest people to solve it. And of course the mathematical community has published the proof several times over, even if some of the original provers left some gaps.