Pi Day 2015

Pi Day and Einstein's birthday. This year you can celebrate 3-14-15 at 9:26 am if you like, and get 8 digits.

Voigt stumbled upon relativistic time

I have credited FitzGerald and Lorentz for early work on relativity, but some earlier work was done by Voigt, as I have noted here and here.

A new paper explains Voigt's transformations and the beginning of the relativistic revolution:

In 1887 W. Voigt published a paper on the Doppler effect, which marked the birth of the relativistic revolution. In his paper Voigt derived a set of spacetime transformations by demanding covariance to the homogeneous wave equation in inertial frames, and this was an application of the first postulate of special relativity. Voigt assumed in his derivation the invariance of the speed of light in inertial frames, and this is the second postulate of special relativity. He then applied the postulates of special relativity to the wave equation 18 years before Einstein explicitly enunciated these postulates. Voigt’s transformations questioned the Newtonian notion of absolute time for the first time in physics by suggesting that the absolute time should be replaced by the non-absolute time t' = t - vx/c². Unfortunately, Voigt’s 1887 paper was not appreciated by most physicists of that time.

I am not sure that anyone saw the significance of Voigt's paper. A paper last year argued:

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 Poincaré in 1906. Einstein probably picked it up from Voigt directly.

Einstein did not cite Voigt, but did not cite anyone else either.

Voigt corresponded with Lorentz, but did not send the 1887 paper until 1908, with Lorentz agreeing to credit him after that. From this I deduce that Voigt himself did not realize how his paper related to relativity, and it had no influence on Lorentz or Poincare.

Wikipedia has a good broad overview of the History of Lorentz transformations.

Voigt should certainly be credited for early publication of some crucial ideas about Lorentz transformations. I tend to credit Lorentz and Poincare because they had all the relativity formulas but also because they had a big-picture theory. They clearly understood and explained how relativity followed from Maxwell's equations and the Michelson-Morley and other experiments, and they had the really big ideas -- FitzGerald contraction, local time, covariance, non-Euclidean geometry, etc.

Tests for psychological determinism

I have posted about the scientific merits of free will and determinism, but there are psychologists who look at the matter completely differently. They see these as just mental beliefs, and study people with these beliefs without regard to whether anyone is right or wrong. Here is a sample of views from a psychological test:

Free will

People have complete control over the decisions they make.
People must take full responsibility for any bad choices they make.

Scientific Determinism

People’s biological makeup determines their talents and personality.
Psychologists and psychiatrists will eventually figure out all human behavior.
Your genes determine your future.

Fatalistic Determinism

I believe that the future has already been determined by fate.
No matter how hard you try, you can’t change your destiny.

Unpredictability

Chance events seem to be the major cause of human history.
No one can predict what will happen in this world.

It does seem that people have different views that have little to do with hard scientific evidence.

We know that genes do not completely determine your future, because identical twins often develop significant differences. (Actually identical twins do usually have slightly different DNA, and we now have the technology to distinguish them, but the differences are not thought to be significant.) But for the most part, these questions are largely psychological. We have no scientific definition of a "chance event". Was the election of Barack Obama a chance event, or the product of some long-term trends?

To have a scientific worldview, you have to have beliefs that some things are scientifically determined. But you also have to have some belief in free will if you are going to make your own decisions.

Some people have a fatalistic view of life, and believe that bad things are always happening randomly and out of control. Or bad things that are predetermined to be bad. It appears to me that these are superstitious people who will be hampered in life because they will not take necessary action to avoid trouble.

What is odd is to find smart science professors who do not believe in free will.

Update: A reader asks about DNA tests to distinguish identical twins. See Twin DNA test: Why identical criminals may no longer be safe or Genetic Sleuthing, Or How To Catch The Right Identical Twin Criminal.

One Hundred Years of General Relativity

NPR Radio Science Friday celebrates One Hundred Years of General Relativity and 30 years of string theory. The analogy is that both with constructed about of pure theory, with no good experimental tests for decades.

This argument is sometimes used to justify string theory. But development and acceptance of general relativity was driven by experiment, and string theory has failed to even reproduce previous theories.

A couple of new papers discuss the history of general relativity: Outline of a dynamical inferential conception of the application of mathematics and Gone Till November: A disagreement in Einstein scholarship.

These explain debates about how to credit Einstein, because his notebooks are filled confusing errors, and no one can figure out how he got to his conclusions.

Peter Woit quotes a review:

Einstein employed two strategies in this search [for the GR field equations]: either starting from a mathematically attractive candidate and then checking the physics or starting from a physically sensible candidate and then checking the mathematics. Although Einstein scholars disagree about which of these two strategies brought the decisive breakthrough of November 1915, they all acknowledge that both played an essential role in the work leading up to it. In hindsight, however, Einstein maintained that his success with general relativity had been due solely to the mathematical strategy. It is no coincidence that this is the approach he adopted in his search for a unified field theory.

Einstein's decisive breakthru of 1915 was discovering that Ricci = 0 could explain the unexplained portion of the precession of the perihelion of Mercury. He had rejected the Ricci tensor when Grossmann based his 1913 theory on it, but Levi-Civita and Hilbert convinced him that it was the crucial tensor.

So yes, experimental evidence was necessary for Einstein. The pure theorizing of his later unified field theory went nowhere.

Google claims qubit error correction

I am skeptical about whether quantum computers will ever be built, even tho Google, Microsoft, and Amazon are all spending millions of dollars on research. So I expect that the typical reader will assume that these companies employ 1000s of very smart people, and they do not waste their money on foolish dead-ends.

Here is the hype:

When scientists develop a full quantum computer, the world of computing will undergo a revolution of sophistication, speed and energy efficiency that will make even our beefiest conventional machines seem like Stone Age clunkers by comparison.

But, before that happens, quantum physicists like the ones in UC Santa Barbara’s physics professor John Martinis’ lab will have to create circuitry that takes advantage of the marvelous computing prowess promised by the quantum bit (“qubit”), while compensating for its high vulnerability to environmentally-induced error.

In what they are calling a major milestone, the researchers in the Martinis Lab have developed quantum circuitry that self-checks for errors and suppresses them, preserving the qubits’ state(s) and imbuing the system with the highly sought-after reliability that will prove foundational for the building of large-scale superconducting quantum computers.

It turns out keeping qubits error-free, or stable enough to reproduce the same result time and time again, is one of the major hurdles scientists on the forefront of quantum computing face.

Instead of "When scientists develop", it should say "In the unlikely event that scientists develop".

MIT Tech. Review reports:

A solution to one of the key problems holding back the development of quantum computers has been demonstrated by researchers at Google and the University of California, Santa Barbara. Many more problems remain to be solved, but experts in the field say it is an important step toward a fully functional quantum computer. Such a machine could perform calculations that would take a conventional computer millions of years to complete.

The Google and UCSB researchers showed they could program groups of qubits — devices that represent information using fragile quantum physics — to detect certain kinds of error, and to prevent those errors from ruining a calculation. The new advance comes from researchers led by John Martinis, a professor at the University of California, Santa Barbara, who last year joined Google to set up a quantum computing research lab ...

To make a quantum computer requires wiring together many qubits to work on information together. But the devices are error-prone because they represent bits of data—0s and 1s — using delicate quantum mechanical effects that are only detectable at super-cold temperatures and tiny scales. This allows qubits to achieve “superposition states” that are effectively both 1 and 0 at the same time, allowing quantum computers to take shortcuts through complex calculations. It also makes them vulnerable to heat and other disturbances that distort or destroy the quantum states used to encode information and perform calculations.

Much quantum computing research focuses on trying to get systems of qubits to detect and fix errors. Martinis’s group has demonstrated a piece of one of the most promising schemes for doing this, an approach known as surface codes. The researchers programmed a chip with nine qubits so that they monitored one another for errors called “bit flips,” where environmental noise causes a 1 to flip to a 0 or vice versa. The qubits could not correct bit flips, but they could take action to ensure that they did not contaminate later steps of an operation.

My prediction is that these companies will never see a dime of business value from this research.

Implementing the quantum error correction may well be a legitimate technical advance, but I suspect that this is just a disguised quantum experiment and does not give any scalable computing power.

Google is promising self-driving cars with 5 years or so. No promises are being made for quantum computers, as far as I know. If they were honest with their investors, what would they say? Those investors consider the self-driving cars a long-term project.

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.

Holographic principle is poorly understood

Peter Woit quotes:

Perhaps there is no greater illustration of Nature’s subtlety than what we call the holographic principle. This principle says that, in a sense, all the information that is stored in this room, or any room, is really encoded entirely and with perfect accuracy on the boundary of the room, on its walls, ceiling and floor. Things just don’t seem that way, and if we underestimate the subtlety of Nature we’ll conclude that it can’t possibly be true. But unless our current ideas about the quantum theory of gravity are on the wrong track, it really is true. It’s just that the holographic encoding of information on the boundary of the room is extremely complex and we don’t really understand in detail how to decode it. At least not yet.

This holographic principle, arguably the deepest idea about physics to emerge in my lifetime, is still mysterious. How can we make progress toward understanding it well enough to explain it to freshmen?

And then comments:

From what I can tell, the problem is not that it can’t be explained to freshmen, but that it can’t be explained precisely to anyone, since it is very poorly understood.

I left this comment:

What is so profound about saying that things may be determined by boundary data? My textbooks are filled with boundary value and initial value problems. Some are centuries old. The boundary of a black hole mixes space and time, so the distinction between the 2 kinds of problems may not be so clear. But either way, a lot of physical theories say that things are determined by data on one lower dimension.

He deleted my comment, so I am posting it here. After that, someone posted a similar comment:

On the topic of the holographic principle being held in such high regard, I have a naive question. What is the difference between the holographic principle and specifying the physics via boundary conditions? “all information in the room is in the walls” seems like an obvious quote given that the fundamental field equations are second order and hence are uniquely specified by giving the values of the fields on the boundary of the region?

I do not think that his answer is very satisfactory, but you are welcome to read it.