The map is not the territory

I got some good comments on my FQXi essay. Jonathan Burdick reduced me to 6 words:

Our friend Rog needs 10 pages to opine that "the map is not the territory"? :-)

That's right, the mathematics is the map that describes how to observe the physics, but it is not identical to the physics. His slogan would have made a great title.

Another said:

I enjoyed reading your essay. It is really clearly written and thoroughly accessible, even to someone without a maths or physics background. You have set out your arguments very clearly and I might have been convinced had I not previously given this subject quite a bit of thought.

In other words: Good argument, but my mind was already made up!

I'm somewhat in sympathy with Jonathan Burdick's pithy response, but of course in ten pages you do more that say that the map is not the territory. I take you also to say that the territory (reality) is not mathematical. ...

What is left to do is very hard, in the usual story of all the low-hanging fruit having been picked, but we have made better tools than our forebears. It is also possible that there is some part of the territory that only ever happens once, so that it cannot be subject of Physics taken to be a repeatable experimental subject. ...

In any case, there has been a constant interplay between Mathematics and Physics, ...

I like his phrase "construction of a new systematization of experimental data." Yes, that is a laudable goal and mathematics is a terrific tool. I also "accept that Physics is the systematic description of reproducible experimental results."

My purpose is to better understand the limits to mathematical reasoning in physics. For example, consider the No-cloning theorem. If a physical state is perfectly representable by some numbers or other mathematical objects, then it is very hard to understand why a perfect copy cannot be made. Perfect cloning of mathematical objects is axiomatic. I say that the quantum state is great for systematizing experimental data, but when you take it too literally as being reality then paradoxes result. It is better to step back, and admit that our mathematical models may be necessarily imperfect.

My essay's public rating is currently a meager 4.4 out of 10. My essay goes against conventional wisdom, but I don't expect a high rating, but I hope that it is good enough to qualify for judging this fall. At least my essay answers the contest question:

Questioning the Foundations: Which of Our Basic Physical assumptions are Wrong?

What assumptions are ripe for rethinking? ...

What are the implicit assumptions we tend to forget we have postulated, or that have become so ingrained that they have become unquestioned dogma? ...

Note: Successful and interesting essays will not use this topic as an opportunity to trot out their pet theories simply because those theories reject assumptions of some other or established theory. Rather, the challenge here is to create new and insightful questions or analysis about basic, often tacit, assumptions that can be questioned but often are not.

Grossmann's help on general relativity

Galina Weinstein posted Genesis of general relativity - Discovery of general relativity

The intermediate stage of the development of general relativity is inseparable of Marcel Grossmann's mathematical assistance. Einstein acknowledges Grossmann's help during 1912-1914 to the development of general relativity. ...

Einstein and Grossmann's first joint paper entitled, "Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation" ("Outline of a Generalized Theory of Relativity and of a Theory of Gravitation") is called by scholars the "Entwurf" paper. ... Grossmann wrote the mathematical part of this paper and Einstein wrote the physical part. ...

The "Entwurf" theory was already very close to Einstein's general theory of relativity that he published in November 1915. The gravitational field is represented by a metric tensor, the mathematical apparatus of the theory is based on the work of Riemann, Christoffel, Ricci and Levi-Civita on differential covariants, and the action of gravity on other physical processes is represented by generally covariant equations (that is, in a form which remained unchanged under all coordinate transformations). ...

Scholars asked: Why did Einstein discard in winter 1912-1913 what appears in hindsight to be essentially the correct gravitational field equation, and what made his field equation acceptable in late 1915? Why did he reject equations of much broader covariance in 1912-1913? ... His rejection of the Ricci tensor need not be explained in terms of simple error. He was rather not prepared to accept generally covariant equations as a result of a number of misconceptions. ...

He introduced an ingenious argument – the Hole Argument – to demonstrate that generally covariant field equations were not permissible. The Hole Argument seemed to cause Einstein great satisfaction, or else he persuaded himself that he was satisfied. Having found the Hole argument, Einstein spent two years after 1913 looking for a non-generally covariant formulation of gravitational field equations.

The Einstein-Grossmann collaboration was one where Einstein wrote the wrong stuff and Grossmann wrote the correct stuff. Einstein argued for two years that Grossmann was wrong to require generally covariant field equations, even tho Levi-Civita explained the advantages of covariant equations, until David Hilbert eventually convinced Einstein of those equations.

Einstein's famous 1916 general relativity paper starts:

The theory which is sketched in the following pages forms the most wide-going generalization conceivable of what is at present known as "the theory of Relativity;" this latter theory I differentiate from the former "Special Relativity theory," and suppose it to be known. The generalization of the Relativity theory has been made much easier through the form given to the special Relativity theory by Minkowski, which mathematician was the first to recognize clearly the formal equivalence of the space like and time-like co-ordinates, and who made use of it in the building up of the theory. The mathematical apparatus useful for the general relativity theory, lay already complete in the "Absolute Differential Calculus", which were based on the researches of Gauss, Riemann and Christoffel on the non-Euclidean manifold, and which have been shaped into a system by Ricci and Levi-Civita, and already applied to the problems of theoretical physics. I have in part B of this communication developed in the simplest and clearest manner, all the supposed mathematical auxiliaries, not known to Physicists, which will be useful for our purpose, so that, a study of the mathematical literature is not necessary for an understanding of this paper. Finally in this place I thank my friend Grossmann, by whose help I was not only spared the study of the mathematical literature pertinent to this subject, but who also aided me in the researches on the field equations of gravitation. [1920 translation]

About half the paper is an explanation of tensor analysis. There is no reference to the Entwurf theory or Hilbert. The only papers cited were those by Einstein and K. Schwarzschild showing how Grossmann's covariant equations affect the precession of Mercury's orbit. The assistance from Levi-Civita and Grossmann is understated.

The Wikipedia article on general relativity mentions Einstein about 50 times, and says nothing about Grossmann or Hilbert. There is a lot more historical info at Relativity priority dispute.

Positivist interpretation

There are many interpretations of quantum mechanics, and no experiment to prove that any one is better than any other. So choosing one is a matter of convention. You might even prefer one interpretation for some problem, and another interpretation for others. Medieval astronomers sometimes used a geocentric model for some planets, and a heliocentric model for others, even tho the models conflict.

The founders of quantum mechanics were believers in positivism, a philosophy that has since gone out of favor. Positivists believe in what is observable, and avoid giving opinions on what is not. I believe that the more the interpretations stray from positivism, the harder it is to make sense out of them. Therefore I propose what I call the positivist interpretation as the core minimalist way to understand the theory.

The positivist interpretation is instrumentalist. However the terms are confusing because a lot of physicists talk as if they are instrumentalists, but they are not positivists. For example, Max Tegmark (MIT) writes:

I advocate an extreme "shut-up-and-calculate" approach to physics, where our external physical reality is assumed to be purely mathematical.

But that assumption is extremely dubious, and not substantiated by any observation. I cannot prove him wrong, but a positivist would reject it just because there is no observational support for it, and because it is not even particularly useful in modern physics. I have written a FQXi essay against it.

The original Copenhagen interpretation was positivist, but it is widely misunderstood. The Ensemble interpretation is supposed to be minimalist, but it is not truly positivist because it does not predict single experiments. Other interpretations assume all sorts of things that can never be observed.

English science writer Philip Ball writes:

Most physicists accept something like Bohr and Heisenberg’s Copenhagen interpretation. This holds that there is no essential reality beyond the quantum description, nothing more fundamental and definite than probabilities.

This is close to being positivist, but a true positivist would not say that there is no essential reality. He would accept the observable realities, and dismiss talk of other realities as being meaningless until someone relates them to observables. He also would not say that probabilities are fundamental, as they are interpretational and not observable.

Here are characteristics of the positivist interpretation.

It is local. No action-at-a-distance has ever been observed, nor is it possible in a relativistic theory. Lumo gives recent explanation of why nonlocality research is pseudoscience.

It rejects hidden variables, as they are not observed and all evidence is to the contrary. Even the wave function is not real, as it is not directly observable.

Positivism also rejects Counterfactual definiteness. As A. Peres said, Unperformed Experiments Have no Results.

I am neutral on Determinism. I am convinced that no quantum probabilities are needed. If the theory does not need them, and they are not observable, then they are not part of the positivist interpretation.

I am also neutral on what I call the weak mathematical universe hypothesis. When a positivist says he is neutral, that means that he rejects it as extraneous. I have never seen anyone explicitly reject it, but I believe that it will eventually be seen to be false.

Explanations of quantum mechanics often get hung up on trying to attach some meaning to reality that is independent of what is observed. Physicists will even say that quantum mechanics proves that there is no such thing as reality. What they are really saying is that non-positivist interpretations are hard to understand. Adopt a positivist philosophy, and the problems disappear.

A good explanation of positivist quantum mechanics is this essay on Quantum Reality. The author favors a positivist variant of the Copenhagen interpretation that he calls the London (Ticker-Tape) Interpretation. He says "Bohr got it pretty much right" and positivism has the virtue of "no deeper meaning than that obtained through measurement".

Positivists are sometimes criticized for saying that there is no deeper meaning, when they cannot prove that there is no deeper meaning. But that criticism misunderstands positivism. The more correct statement is that positivists admit that there might be a deeper meaning involving determinism or probability, mathematical or physical universe, waves or particles, etc. But quantum mechanics experiments are unable to resolve these issues, so they are not worthy of scientific discussion.

Adding to the confusion, modern philosophers not only reject positivism, they also deny that Bohr was a positivist.

Yes, Bohr did get it right with his positivism, and he was considered the winner of the Bohr–Einstein debates. But as positivism has gone out of fashion, so has Bohr's view. Probably a lot of physicists and philosophers today would say they prefer Einstein's view because it is more realist. They cause a lot of confusion. It would be better if quantum mechanics were taught with the positivist interpretation.

The main virtue of the positivist interpretation is that it only requires you to believe in the core physics, and does not require you to take a position on determinism, many-worlds, consciousness, or anything like that.

Lumo writes today:

In the last 85+ years since the discovery of quantum mechanics, all people opposing quantum mechanics have lost, all of their predictions differing from the predictions of quantum mechanics have been proved wrong, and the whole philosophy of trying to find and promote "problems" with the proper Copenhagen quantum mechanics – and all these efforts are always driven by the desire to undo the quantum revolution and return physics to the age when the classical framework was dominant – has been an utter failure, an embarrassing pseudointellectual catastrophe, a huge pile of stinky junk that no sensible scientist would associate herself with.

I am amazed that even this modest and balanced summary of the situation may be considered controversial by some physicists in 2012. I am amazed that Brian Greene may be on the evil side, too.

Niels Bohr treated the theories about many worlds as garbage bringing nothing new and correct to physics for a simple reason: they were garbage that was bringing nothing that was both new and correct.

I agree with this. I believe that the richer interpretations of quantum mechanics are wrong for reasons explained in my FQXi essay. I differ from him in that I subscribe to an even more minimalist interpretation, as I say that no quantum probabilities are needed, not even for the double slit.

Contrarian books

A reader tells me that she found my book, How Einstein Ruined Physics, in a bookstore next to the new book, How The Beatles Destroyed Rock 'n' Roll: An Alternative History of American Popular Music. That's funny. I am going to contact the publisher and suggest a series of books. I will propose How Babe Ruth Ruined Baseball, How Mark Twain Ruined Literature, How Pablo Picasso Ruined Art, How Margaret Mead Ruined Anthropology, and How Steve Jobs Ruined Computers.

The Higgs aether

With all the publicity about the discovery of the Higgs boson, hardly anyone is explaining that it is a confirmation of modern Aether theories. Usually any mention of the aether is followed by saying that it was a quaint 19th century concept that was disproved by Einstein's relativity. But that is not true, and was not even Einstein's view.

The concept of the luminiferous aether dates back to ancient times, and refers to whatever fills outer space that allows us to see the light of the stars. It is sometimes said that the vacuum is empty space, and that no such aether is needed to explain the propagation of light. But that is not true either, as modern theories of light require a nonempty vacuum. Quantum electrodynamics is a perturbation theory of the aether.

The authoritative description of the 19th century aether is J.C. Maxwell's 1878 encyclopedia article. That concluded:

No theory of the constitution of the aether has yet been invented which will account for such a system of molecular vortices being maintained for an indefinite time without their energy being gradually dissipated into that irregular agitation of the medium which, in ordinary media, is called heat.

Whatever difficulties we may have in forming a consistent idea of the constitution of the aether, there can be no doubt that the interplanetary and interstellar spaces are not empty, but are occupied by a material substance or body, which is certainly the largest, and probably the most uniform body of which we have any knowledge.

Whether this vast homogeneous expanse of isotropic matter is fitted not only to be a medium of physical interaction between distant bodies, and to fulfil other physical functions of which, perhaps, we have as yet no conception, but also, as the authors of the Unseen Universe seem to suggest, to constitute the material organism of beings exercising functions of life and mind as high or higher than ours are at present, is a question far transcending the limits of physical speculation.

Maxwell's view was that the aether was pervasive, uniform, invisible, frictionless, and permeating matter. It is sometimes said that the aether presupposed some sort of fixed coordinate system, but Maxwell does not say that.

What I say here is the consensus view, except that not everyone uses the word "aether". Frank Wilczek, the 2004 Nobel Prize winner in physics, wrote the book, The Lightness of Being: Mass, Ether, and the Unification of Forces:

In the first part of the twentieth century, the upheavals of relativity and (especially) quantum theory shattered the foundations beneath classical physics. Existing theories of matter and light were reduced to rubble. That process of creative destruction made it possible to construct, over the second part of the twentieth century, a new and deeper theory of matter/light that removed the ancient separation. The new theory sees a world based on a multiplicity of space-filling ethers, a totality I call the Grid. The new world-model is extremely strange, but also extremely successful and accurate.

He details:

What is Space? Is it an empty stage, where the physical world of matter acts out its drama -- an equal participant, like the classical Ether, that both provides background and has a life of its own -- or the primary reality, of which matter is a secondary manifestation? Today, the third view is triumphant. Where our eyes see nothing our brains, pondering the revelations of sharply tuned experiments, discover the Grid that powers physical reality.

The Higgs boson is not just some isolated particle. It is the quantization of an aether that is pervasive, uniform, invisible, frictionless, and permeating matter. And that aether is completely essential to modern physics.

The Higgs aether gives mass to the electrons and quarks, the basic constituents of matter. All electrons are identical, and have the same mass. So the Higgs is the same everywhere. The aether is the largest and most uniform body, just as Maxwell said.

You could also say that there is an electron field in a vacuum, with fluctuations making virtual electrons. But there is no net number of electrons. The Higgs aether is different in that the Higgs field is nonzero in the vacuum.

Higgs boson discovered

The Higgs boson discovery is being announced:

On Wednesday (July 4), scientists heading two major experiments at the LHC plan to announce their most recent findings ...

The Higgs boson is the last piece of the physics Standard Model, a collection of theories that underpin all modern physics. The Higgs particle is theorized to mediate mass -- like a photon (also a boson) mediates the electromagnetic force, i.e., light -- and creates the "Higgs field" that must pervade the entire Universe, endowing matter with mass.

Dennis Overbye writes:

Known as the Higgs boson, it explains why things in the universe have mass, and is a cornerstone of modern physics despite never being seen.

Here is why we believe in the Higgs, and why it was really discovered decades ago.

Geometry symmetry is the most important concept in 20th century physics. Poincare introduced it with his 1905 geometric version of special relativity, and his search for physical laws that obey symmetries. Its crucial importance to classical mechanics was shown by Noether, and the importance to quantum mechanics by Hermann Weyl. The concept can be used to generalize electromagnetism to other fields (like strong and weak forces), as shown by Weyl, Higgs, 'tHooft, and others.

The Standard Model is based on geometric symmetries, but if there are too many of them, then all particles are massless like photons and nothing interesting happens. So there has to be a field that breaks the symmetry. All fields are quantized, so there has to be a particle also. That is what is being found at 125 GeV.

In a sense, the Higgs is like an aether that is uniform, everywhere, and invisible. You could say that mass is just a measure of resistance to passing thru the Higgs aether. This description is a little misleading because most of the proton mass comes from the binding energy of the quarks, but the quark mass is believed to be derived from the Higgs breaking the symmetry. This is all explained in my book. For a recent survey by an expert, see Wilczek, Origins of Mass.

If you have been watching PBS TV science shows, you might have been expecting LHC announcements on string theory, supersymmetry, and the multiverse. However, all of the evidence has been against those misguided concepts.

Update: Overbye adds in the July 4 NY Times:

Physicists working at CERN’s Large Hadron Collider said Wednesday that they had discovered a new subatomic particle that looks for all the world like the Higgs boson, a potential key to understanding why elementary particles have mass and indeed to the existence of diversity and life in the universe. ...

Confirmation of the Higgs boson or something very like it would constitute a rendezvous with destiny for a generation of physicists who have believed in the boson for half a century without ever seeing it. And it reaffirms a grand view of a universe ruled by simple and elegant and symmetrical laws, but in which everything interesting in it, such as ourselves, is due to flaws or breaks in that symmetry.

According to the Standard Model, which has ruled physics for 40 years now, the Higgs boson is the only visible and particular manifestation of an invisible force field, a cosmic molasses that permeates space and imbues elementary particles that would otherwise be massless with mass. Particles wading through it would gain heft.

Without this Higgs field, as it is known, or something like it, physicists say all the elementary forms of matter would zoom around at the speed of light, flowing through our hands like moonlight. There would be neither atoms nor life. ...

Although they have never been seen, Higgs-like fields play an important role in theories of the universe and in string theory. Under certain conditions, according to the strange accounting of Einsteinian physics, they can become suffused with energy that exerts an anti-gravitational force. Such fields have been proposed as the source of an enormous burst of expansion, known as inflation, early in the universe, and, possibly, as the secret of the dark energy that now seems to be speeding up the expansion of the universe.

The Higgs boson is the most unusual known particles, being spin 0 and playing a unique symmetry-breaking role. Its discovery is the most dramatic achievement of theoretical physics in history. It is part of the aether that is completely essential to modern physics. The aether is everywhere, uniform, and invisible.

The aether probably explains dark energy, but none of this has anything to do with string theory. String theory does not predict an aether, Higgs boson, or dark energy. After 30 years of work by the world's smartest physicists, it has never had a success like the Higgs. The Higgs is a confirmation of the theory that string theory was supposed to replace.

SciAm blogger John Horgan writes:

Hearing all the hoopla about the Higgs, the public might understandably assume that it represents a crucial step toward a unified theory–and perhaps at least tentative confirmation of the existence of strings, branes, hyperspaces, multiverses and all the other fantastical eidolons that Kaku, Stephen Hawking, Brian Greene and other unification enthusiasts tout in their bestsellers.

But the Higgs doesn’t take us any closer to a unified theory than climbing a tree would take me to the Moon.

That's right. The LHC spent $10B to confirm the high-energy physics of the 1970s, but all hopes for a grander theory have been a total failure.

Horgan also says:

Physicists have already produced theories –- Newtonian mechanics, quantum mechanics, general relativity, nonlinear dynamics –- that work extraordinarily well in certain domains, and there is no reason why there should be a single theory that accounts for all the forces of nature. The quest for a unified theory will come to be seen not as a branch of science, which tells us about the real world, but as a kind of mathematical theology.

I agree with that, and I go further in my FQXi essay. I say that there is no reason that this mathematical theology should even be valid for those domains like quantum mechanics. Theoretical physicists are chasing the impossible.

Copernicus cartoon

This is from The Argyle Sweater by Scott Hilburn. Sometimes people assume that Copernicus was particularly novel or courageous by saying that the Sun does not revolve around the Earth. Maybe not.