Thursday, March 5, 2015

Poincare searched for symmetry-invariant laws

Here is a new paper on The Role of Symmetry in Mathematics
Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics.
Symmetry was crucial to XX century physics, but not exactly as described in this paper.
Einstein changed physics forever by taking these ideas in a novel direction. He showed that rather than looking for symmetries that given laws satisfy, physicists should use symmetries to construct the laws of nature. This makes symmetries the defining property of the laws instead of an accidental feature. These ideas were taken very seriously by particle physicists. Their search for forces and particles are essentially searches for various types of symmetries.
This is nonsense. Einstein did not do that. The particle physicists learned about symmetries from Noether and Weyl.
One of the most significant changes in the role of symmetry in physics was Einstein’s formulation of the Special Theory of Relativity (STR). When considering the Maxwell equations that describe electromagnetic waves Einstein realized that regardless of the velocity of the frame of reference, the speed of light will always appear to be traveling at the same rate. Einstein went further with this insight and devised the laws of STR by postulating an invariance: the laws are the same even when the frame of reference is moving close to the speed of light. He found the equations by first assuming the symmetry. Einstein’s radical insight was to use symmetry considerations to formulate laws of physics.
No, that is more or less what Lorentz did in his 1895 paper. Lorentz used the Michelson-Morley experiment to deduce that light had the same speed regardless of the frame, and then proved his theorem of the corresponding states to show that Maxwell's equations had the same form after suitable transformations. He extended the theorem to frames going close to the speed of light in 1904. Einstein's famous 1905 paper added nothing to this picture.
Einstein’s revolutionary step is worth dwelling upon. Before him, physicists took symmetry to be a property of the laws of physics: the laws happened to exhibit symmetries. It was only with Einstein and STR that symmetries were used to characterize relevant physical laws. The symmetries became a priori constraints on a physical theory. Symmetry in physics thereby went from being an a posteriori sufficient condition for being a law of nature to an a priori necessary condition. After Einstein, physicists made observations and picked out those phenomena that remained invariant when the frame of reference was moving close to the speed of light and subsumed them under a law of nature. In this sense, the physicist acts as a sieve, capturing the invariant phenomena, describing them under a law of physics, and letting the other phenomena go.
This sounds more like Poincare's 1905 relativity paper. It was the first to treat the Lorentz transformations as a symmetry group, and to look for laws of physics invariant under that group. He presented an invariant Lagrangian for electromagnetism, and a couple of new laws of gravity that obeyed the symmetry.

Einstein did not do any of this, and did not even understand what Poincare had done until several years later, at least.

The paper goes on to explain why symmetry is so important in mathematics.
A. Zee, completely independent of our concerns, has re-described the problem as the question of “the unreasonable effectiveness of symmetry considerations in understanding nature.” Though our notions of symmetry differ, he comes closest to articulating the way we approach Wigner’s problem when he writes that “Symmetry and mathematics are closely intertwined. Structures heavy with symmetries would also naturally be rich in mathematics” ([Zee90]:319).

Understanding the role of symmetry however makes the applicability of mathematics to physics not only unsurprising, but completely expected. Physics discovers some phenomenon and seeks to create a law of nature that subsumes the behavior of that phenomenon. The law must not only encompass the phenomenon but a wide range of phenomena. The range of phenomena that is encompassed defines a set and it is that set which symmetry of applicability operates on. ...

All these ideas can perhaps be traced back to Felix Klein’s Erlangen Program which determines properties of a geometric object by looking at the symmetries of that object. Klein was originally only interested in geometric objects, but mathematicians have taken his ideas in many directions.
The Erlangen program was published in 1872, and would have been well-known to mathematicians like Poincare and Minkowski.

The preferred mathematical view of special relativity is that of non-Euclidean geometry. It can be understood in terms of geometrical invariants, like metric distances (proper time) and world lines, or in terms of the symmetries of that geometry, the Lorentz group. This was all very clearly spelled out by Poincare and Minkowski.

Separately, I see that Einstein score No. 2 on The 40 smartest people of all time.


  1. They study symmetry because mathematics lacks expressive or comprehensible ways of dealing with complicated asymmetry. Quite circular.

  2. Pretty much everything physicists say about the history of their subject or science in general is wrong. No matter how simple or commonplace the claim is about the history of science, if a physicists makes it, it's almost certainly wrong.

    I remember being told repeatedly over the years by physicists the story about Maxwell's amazing discovery of electromagnetic waves. He boldly added the displacement current to his equations and out popped a wave equation whose speed was just that of light.

    The reality the basic idea dated back to Faraday at least, and the equation relating the speed of light to the electric and magnetic constants was discovered over a decade previously by Weber using a competing version of EM now considered defunct.

  3. Here is my on-topic comment: that useless paper is nothing more than a plug for a useless branch of math called category theory.

    The modern day intellectual "giants" that Roger so admires are directly responsible for this:

    Areva plans to cut costs by $1.1 billion by 2017


    Fire skilled labor and hire more "super geniuses" (read mathematicians who don't know shit about physics). Eventually the lights go off and France lives in the dark ages once again. This isn't unique to France, btw. The USA nuclear industry is already toast.

    All those idiots who are running to the universities to be "enlightened" (read get their union card) are finding out the hard way that those intellectual sewers are filled up with the likes of Coyne. Many of them don't even bother attending the lectures.

    Ahh, funny fiat money....the death of science.

  4. Einstein surely must be the #1 communist.

  5. "The preferred mathematical view of special relativity is that of non-Euclidean geometry."

    Non-Euclidean geometry does not replace Euclidean geometry at any time, Non-Euclidean geometry is in FACT utterly dependent upon Euclidean geometry. If Euclidean geometry were false, Non Euclidean geometry would be invalid, whereas if Non Euclidean geometry were proven false, it would have no bearing on the validity of Euclidean geometry.

    All dependencies aside, non-Euclidean geometry is used to cloak, not reveal the inner workings of special relativity, as it buries the mechanics and needlessly complicates the math for the purposes of misdirection and gatekeeping. I have no patience with hierophants who use complexity to hide from scrutiny and criticism. When your objective is to deceive and conceal, no wonder people do not understand what you say.

  6. Something that should be said there is NO NULL RESULT in the Michelson and Morley experiment. They didn't get a zero result. They didn't get what they expected but they didn't get zero as is FALSELY reported over and over and over. They expected to get 30 km/s and got I think 8 km/s. I've read the M and M report myself. This has been tested many, many times for years and there was some smaller number present. For some reason this is completely ignored. Look at the wikipedia page.

    Go down to "Subsequent experiments", They say,"... Morley was not convinced of his own results, and went on to conduct additional experiments with Dayton Miller from 1902 to 1904. Again, the result was negative within the margins of error...."

    This is a lie. Miller got 10 km/s where they expected 30 km/s. This is hardly a small error. Dayton Miller did years worth of testing and never got a zero/null result. Miller fended off the null result people while he was alive but for some reason they have taken over now and it's in all the text books. An interesting fact is the difference in speed was influenced by the planets position.

    Wiki says no one could replicate his results but that's not true. There was a naval laboratory scientist that replicated the results with microwaves. Notice also that they say no one can replicate the result of some frequency shift but Michelson-Morley themselves had a frequency shift. So they did replicate the result. The last test of this I heard of was done in a mineshaft and got a null result. This only means that ether (or whatever) can't effect light in a mine shaft. Meaningless. I read about this in an article by G. Harry Stine the former Science Fact editor of Analog SciFi and Sci Fact.