Saturday, March 30, 2013

Origin of mass energy equivalence

I reported before on someone who published the essence of E = mc2 before Einstein. Stephen Boughn just posted this paper:
In 1904, the year before Einstein’s seminal papers on special relativity, Austrian physicist Fritz Hasenöhrl examined the properties of blackbody radiation in a moving cavity. He calculated the work necessary to keep the cavity moving at a constant velocity as it fills with radiation and concluded that the radiation energy has associated with it an apparent mass such that E = mc2. In a subsequent paper, also in 1904, Hasenöhrl achieved the same result by computing the force necessary to accelerate a cavity already filled with radiation. In early 1905, he corrected the latter result to E = mc2.
These papers were published in the same journals that Einstein published in. Einstein went his entire life refusing to acknowledge or credit this work.

There was also earlier work by Poincare in 1900.

This is not an isolated example. Einstein's most famous papers refused to reference the earlier work, even when he obviously relied on that earlier work. Throughout his life, he always took credit for himself, at the expense of others, wheneven he could get away with it. And also when everyone knew he was dishonest, as in the above example.

I don't mind him taking legitimate credit for himself. But the way to do that is for him to explain how his contribution improves on earlier work. He was never able to do that with relativity theory.

Monday, March 25, 2013

Voigt pioneered Lorentz transformations

Wolfgang Engelhardt has a new paper on On the Origin of the Lorentz Transformation
The Lorentz Transformation, which is considered as constitutive for the Special Relativity Theory, was invented by Voigt in 1887, adopted by Lorentz in 1904, and baptized by Poincare in 1906. Einstein probably picked it up from Voigt directly.
It is true that Voigt had a scaled version of the Lorentz transformation before anyone else. See History of Lorentz transformations for details.
Einstein like Poincare was convinced of the validity of the generalized relativity princi-ple. In his famous paper of 1905 6 he raised this conjecture to a postulate and claimed that he could derive the Lorentz Transformation by using a second postulate, namely “that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body”. A careful analysis of §3 of his paper shows, however, that he worked on the same assumption as Voigt, namely that the velocity of light is constant for any moving observer. ...

It is likely that Einstein, who did not quote anybody in Ref. 5, found his trans-formation directly in Voigt’s paper of 1897. In the monograph of 1913 (Ref. 3) he assures us that he was not aware of Lorentz’s paper of 1904. This is credible, as he did not use Lorentz’s nomenclature (x, y, z, t) <-> (x', y', z', t'), but he adopted Voigt’s: (x, y, z, t) <-> (ξ, η, ζ, τ). ...

Einstein kept denying that the Michelson-Morley experiment had any influence on the development of his theory7. Probably he had read a paper with the title Theory of light for moving media by W. Voigt8 which appeared two months later than Ref. 1 in the same Journal. On page 233 Voigt analyzes the Michelson experiment and comes to the conclusion:

“It follows that the observed results in the experimental set-up that was chosen by Mr. Michelson are entirely independent of any translation. Hence, Mr. Michelson obtained the negative results which he factually obtained with necessity, regardless whether the ether moves with the earth or not.”
OIt seems much more likely to me that Einstein got the transformation from Lorentz, as Einstein follows the spirit of Lorentz's work rather closely.

The Michelson-Morley experiment was crucial for Lorentz, but not for Einstein. That is because they had different viewpoints. Lorentz was creating relativity theory out of the experimental evidence, and convincing the physics community that his outrageous conclusions were correct. Einstein's view was the reverse. His famous 1905 paper postulated the conclusions of Lorentz's theory, and gave an exposition of Lorentz's relativity. That is why Einstein ignored the physical evidence.

Wednesday, March 20, 2013

Math is reducible to logic

A math encyclopedia article on Logicism says:
One of the trends in the foundations of mathematics whose object is to justify mathematics by reducing its initial concepts to those of logic. The idea of reducing mathematics to logic was expressed by G. Leibniz (end of the 17th century). ...

On the whole the attempt to reduce mathematics to logic was not successful. As K. Gödel showed [3], no formalized system of logic can be an adequate basis for mathematics (cf. Gödel incompleteness theorem).
That last sentence would be a surprise to K. Gödel -- he did not prove that.

Yes, Mathematics was reduced to Logic, and Gödel helped with crucial work. Math knowledge is established with proofs, and proof are formalized with logic. A suitable logic system is Zermelo–Fraenkel set theory. If a math encyclopedia can misrepresent what math is all about, no wonder the public misunderstands it.

Alternative axiomatizations of Mathematics include Von Neumann–Bernays–Gödel set theory and Tarski–Grothendieck set theory. NGB has the advantage of allowing classes of objects that are too big to be sets, and of using only finitely many axioms. TG allows certain inaccessible cardinals that are popular in algebraic geometry, and allows types that are useful in computer theorem checking.

While these systems have some differences, all of the big theorems of modern mathematics can be formalized and proved in any of them.

Friday, March 15, 2013

Kuhn is fishy and unpersuasive

Vox Day writes:
Scoobius is dubious about Thomas Kuhn:
On a couple of different threads lately, knowing reference has been made to Thomas Kuhn and his book "The Structure of Scientific Revolutions". Like a lot of people I read it as a snotty college kid. But unlike a lot of people, I recall thinking at the time that there was something fishy about what he was saying, something perhaps even unpersuasive. To be honest it's so long ago since I read the book, I couldn't even tell you now with accuracy what his arguments were. I just recall thinking at the time, Hmm, I'd certainly like to at least hear the rebuttal and the counter-arguments, but universities being what they are, his book was assigned on the topic and no others; and it wasn't my key area of interest, so I just let the matter drop.
The main reason Kuhn remains popular is that his reasoning provides substance and cover for those who, for various reasons, doubt the legitimacy of the dictatorial scientific consensus. While one will not be taken seriously by claiming that the Bible contradicts global warming, the latest dating of homo sapiens sapiens, or the raspberry bush of life, one can cite Kuhn and it tends to take the wind out of the sails of even the most authoritative scientist.
Kuhn's book is the most influential anti-science book ever written. The heart of it is an argument that the big changes in science are Kuhnian paradigm shifts. Kuhn defined such a shift as an irrational change of viewpoint with no measurable evidence. (Kuhn preferred the terms arational and incommensurable.) Thus he denied that scientific theories were based on reason and evidence, and he also denied that science makes progress towards truth.

College kids are given Kuhn's thesis, without the rebuttal. All they get out of it is that science is just a bunch of popular fads, with no real validity. Yes, it is fishy and unpersuasive. And it is a gross devaluation of what science is all about.

Here is a quote from a book about creationists:
The third source of the idea that the scientific establishment is close-minded is a philosophical picture of the nature of science. Thomas Kuhn’s book The Structure of Scientific Revolutions has probably been more widely read — and more widely misinterpreted — than any other book in the recent philosophy of science. The broad circulation of his views has generated a popular caricature of Kuhn’s position. According to this popular caricature, scientists working in a field belong to a club. All club members are required to agree on main points of doctrine. Indeed, the price of admission is several years of graduate education, during which the chief dogmas are inculcated. The views of outsiders are ignored. Now I want to emphasize that this is a hopeless caricature, both of the practice of scientists and of Kuhn’s analysis of the practice. Nevertheless, the caricature has become commonly accepted as a faithful representation, thereby lending support to the Creationists’ claims that their views are arrogantly disregarded." [1]
Yes, that is an exaggeration of Kuhn's analysis, but the essence of Kuhn's argument is that science is unscientific.

Wednesday, March 13, 2013

Another Survey of Foundational Attitudes

I posted in January about a new poll on quantum mechanics. Now there is Another Survey of Foundational Attitudes Towards Quantum Mechanics.

The physicists were surprisingly uncommitted. They would not say that either Bohr or Einstein was correct, and many refused to back a particular interpretation. There was a lot sympathy for goofy views like Bohm's and nonlocality. All this tells me that the physics community is really confused.

Tuesday, March 12, 2013

Causal completeness of physics

Massimo Pigliucci writes about reductionism:
I had an interesting exchange with physicist Steven Weinberg, who played what he thought was a trump card in favor of reductionism “all the way down”: he mentioned the causal completeness of the laws of physics. I asked him to elaborate on the point, and he said that the laws of Newtonian mechanics, for instance, are causally complete in the sense that there is no room within the equations for any unaccounted parameters. It follows, according to Weinberg, that those equations are a complete description of the causality of the system, leaving no room for emergent properties. ...

To set the frame for the discussion I cannot do better than to quote Vicente’s abstract verbatim: “According to an increasing number of authors, the best, if not the only, argument in favor of physicalism is the so-called ‘overdetermination argument’. This argument, if sound, establishes that all the entities that enter into causal interactions with the physical world are physical. One key premise in the overdetermination argument is the principle of the causal closure of the physical world, said to be supported by contemporary physics.”
Are the laws of physics really causally complete? Is there a consensus with that opinion? News to me.

I thought that physicists were almost entirely of the opinion that the laws of physics were stochastic, and not deterministic. Therefore I don't see how Weinberg could say that the laws are causally complete. If the laws are stochastic, then a complete set of causes (or initial conditions) cannot predict the future. Events will happen by chance, and will not be completely explainable by causes.

There are a few physicists, like Einstein, who have a semi-religious belief in determinism. For them, I guess I can see how they can believe in causal completeness. But everyone else says that determinism has been disproved by quantum mechanics theory and experiment.

Am I wrong here? Please let me know if I am misunderstanding someone.

Meanwhile Lumo writes:
Much of the irrational disgust by string theory is caused by people's widespread mathphobia. People think that if the number of possibilities or solutions to certain conditions is large, the topic ceases to be a science and it can't be analyzed. But as this paper and others show, it may often be analyzed and the possibilities may be, in fact, fully listed and classified. In principle, one may also find the right vacuum that describes the Universe around us if it exists in a given set.
I would bet my last dollar that the universe vacuum state is not one of the 921,497 complete intersection Calabi-Yau four-folds. Maybe the irrational disgust of string theory is caused by mathphobia, but the rational disgust is based on the failure to find any relation between the real world and these mathematical models.

Tuesday, March 5, 2013

Chasing the Higgs boson

Today's NY Times Science Times is all about Chasing the Higgs. The articles are by Dennis Overbye, who also wrote an Einstein biography.

I do think that the discovery of the Higgs boson is the most remarkable confirmation of theory in the history of science. The particle was both essential to the established theory, and unlike anything that had ever been seen before. I cannot think of another discovery that was more spectacular on both counts.

Monday, March 4, 2013

Poincare disbelieved in the aether

Henri Poincaré's Wikipedia page says, "but contrary to Einstein he continued to use the ether-concept in his papers". This is backwards.

Here is an example of someone misreading Poincare to argue that he believed in the aether. A 2006 paper, Can science advance effectively through philosophical criticism and reflection?, by Roberto Torretti, says:

In the highly acclaimed electrodynamic theory — or ought we to say theories? — of Lorentz, the ether is completely motionless and its mechanical structure and behavior — if it has any — is of no concern at all. As Whittaker lucidly wrote: “Such an aether is simply space endowed with certain dynamical properties” (1951/53, 1:393).
That's right. Today people try to put down Lorentz's relativity by calling it Lorentz aether theory, instead of electron theory, as it used to be called. It did not depend on the aether, as noted here and here.
It is therefore no wonder that, despite Lorentz explicit warning to the contrary,50 the general public, including most philosophers and even some physicists, identified his ether with Newton’s absolute space, or at any rate assumed that it was at rest in it.51 Still, the idea that this elusive form of matter was part of the furniture of the universe had become deeply entrenched during the 19th century, and nobody seemed willing to dismiss it. Surely it is not easy for a highly respected profession to admit that one of its time-honored terms of art is a noun without a referent.52 Even Poincaré, who in 1889 had predicted that “the day will doubtless come when the ether will be rejected as useless”,53 at the Paris Congress of Physics of 1901 argued thus for believing in it:
We know where our belief in ether comes from. If we receive light from a distant star, for several years that light is no longer at the star and is not yet on the Earth. It must therefore be somewhere, sustained, so to speak, by some material support. The same idea can be expressed in a more mathematical and more abstract way. What we record are the changes suffered by material molecules; we see, for example, that our photographic film displays the consequences of phenomena staged many years earlier in the incandescent mass of the star. Now, in ordinary mechanics, the state of the system under study depends only on its state in an immediately preceding state; the system therefore satisfies differential equations. But if we did not believe in the ether, the state of the material universe would depend not only on the immediately preceding state (l’état immédiatement antérieur), but on much older states; the system would satisfy finite difference equations. To avoid this derogation of the general laws of mechanics we have invented the ether.54
[Footnote 54] Poincaré (1901b); translated by me from Poincaré (1968), pp. 180-181. I cannot repress the feeling that Poincaré the mathematician must have known (i) that if a given physical state depends on another in accordance with a system of differential equations, none of the two states can immediatelyprecede (or follow) the other one, and (ii) that time dependent vector fields can be defined on space without assuming a material support for them to sit on. I suppose (ii) is the reason why he talks of inventing the ether at the end of this tirade about believing in it.
Poincare did not argue for believing in the aether. He argued that it was a mathematical convenience. His philosophy is often called conventionalism because of opinions such as this.

This is a point that mathematicians grasp immediately, but physicists and philosophers have a lot of difficulty with. Poincare was a mathemetician. Mathematicians frequently define concepts for mathematical convenience, regardless of whether they are physically observable.

Anyone who says that Poincare believed in the aether fails to grasp that simple point.

Friday, March 1, 2013

Cause of the contraction

Rafael Ferraro just posted From aether theory to Special Relativity:
Michelson was convinced that the null result meant that the Earth carried a layer of ether stuck to its surface. If so, the experiment would have been performed at rest in the local ether, which would explain the null result. ...

Lorentz thought that Michelson-Morley’s null result could be understood in a very different way. He considered that a body moving in the ether suffered a length contraction due to its interaction with the ether. The interaction would contract the body along the direction of its absolute motion V, but the transversal dimensions would not undergo any change. ... This Lorentz’s proposal of 1892 had been independently advanced by FitzGerald three years before. This proposal did not mean the abandonment of the belief in the invariance of lengths. The contraction was a dynamical effect; it depended on an objective phenomena: the interaction between two material substances. The contraction should be observed in any frame, and all the frames should agree about the value of the contracted length. ...

Noticeably, the relativistic length contraction [of Einstein 1905] has the same form proposed by FitzGerald and Lorentz to explain the null result of Michelson-Morley experiment. However, its meaning is completely different. Lorentz considered that13 the contraction was a dynamical effect produced by the interaction between a body and the ether. For Lorentz, V in Eq. (26) was the velocity of the body with respect to the ether, and the contraction was measured in all the frames. In Relativity, instead, the length contraction is a kinematical effect.
No, FitzGerald and Lorentz never said that all the frames should agree about the value of the contracted length. Lorentz had his relativity theorem that observers in different frames could use the same equations.

There is no simple answer as to whether the contraction is caused by the motion, by the aether, by electromagnetism, or by what. The preferred explanation is that it is an illusion from the geometry of spacetime.

Sometimes people say that it is wrong to describe the contraction as being caused by motion thru the aether. To be wrong, you have to add hypotheses that make wrong observations possible. If you also assume that the aether defines one frame, that the contraction is based on the velocity thru the aether, and that a separately moving observer would see the same contraction, then you get a disagreement with experiment. But what FitzGerald and Lorentz said was consisent with experiment.

The above paper has some historical explanation of special relativity, but its attempts to credit Einstein are inaccurate.