Friday, April 19, 2013

History of Science -- Part Eight: Relativity

I introduced Lord Kelvin in the last chapter of this series so that I could use a quotation attributed to him. There probably was no scientists since Newton who was held is such regard, had such a scientific reputation, or was held in such high esteem by the general public and the government than Lord Kelvin at the end of the nineteenth century.

At that point it seemed that science had completely wrapped up the issue of describing Nature and discovering all her secrets. With a complete set of the rules of motion based on Newton’s discoveries and improved and expanded upon, with a complete understanding of heat and energy, and with Maxwell’s equations describing the electromagnetic wave and the application via telegraph and wireless radio, the dawn of the twentieth century was to be a bright dawn indeed.

Although there is some conflict among historians on whether Lord Kelvin said this or not, this quotation is often used in popular books on science to make the point of just how wrong he could be. Put this quote along side Bill Gate’s, “No one will need more than 640 K of memory” that he stated at the advent of the IBM PC in 1982.

To be historically accurate, it appears it was the Albert Michelson, the Nobel Prize winning physicists of the Michelson-Morley experiments described below who is the source of the quotation. He quoted Lord Kelvin, perhaps inaccurately. But this statement certainly indicates the mood of the Victorian era in the late 1800's.

Michelson said that, in physics, there were no more fundamental discoveries to be made. Quoting Lord Kelvin, he continued, “An eminent physicist remarked that the future truths of physical science are to be looked for in the sixth place of decimals.” In other words, all the major discoveries had been done, and now it was just the work of science to add a few more decimal points to what was already known.

Some scientists expressed sadness for the next generation of physists because they thought all the fundamental work had been done and there were no more great discoveries to be made.

Yes, that is a statement worth posting in the “could not be more wrong — ever!” Hall of Shame. Odd that one of the scientists so intimately involved with the very experiment that would be a trigger to the thoughts of another young scientist just starting his career would make such a claim. But then it did fit well with the Victorian era of science with all its formality of class and thought. But there were several warning signs in the body of knowledge at the start of the next century that should have cautioned these learned men to not be so cocksure of what was coming.

When light became accepted as being a wave, it was assumed that something had to be waving. Electric and magnetic fields would be distortions in this waving medium. Since material bodies moved through it without resistance, it was ethereal and was called the “luminiferous aether” or just “ether.” It presumably pervaded the universe since we receive light from the starts. Motion with respect to this ether would define an absolute velocity, something not meaningful without ether as a stationary “reference point” for the universe.

In the 1890’s Albert Michelson and Edward Morley set out to determine how fast our planet was moving through the universal ether. A boat moving in the same directions as the waves sees the waves pass more slowly than when the boat moves in the direction opposite the waves. From the difference in these two wave speeds, one can determine how fast the boat is moving in the water. This is essentially the experiment Michelson and Morley did with light waves.

They measured the speed of light, very accurately, from a distant star at two times of the year six months apart. Therefore one measurement was at a point where the Earth in its orbit was speeding toward the star at a rate of nearly 30 km per second or about 19 miles per second or 68,000 mph, and the second measurement was when the Earth was speeding away at the same velocity.

To their surprise, the Earth seemed not to be moving at all. They measured the speed of light to be the same in all directions. Ingenious attempts to untangle this result with electromagnetic theory failed.

Enter Albert Einstein. He postulated the observed fact that the speed of light is the same no matter how fast the observer moves. He took it as a new law of Nature. Two observers, though moving at different speeds, would each measure the same light beam to be passing them at the same speed. The speed of light in a vacuum is therefore a universal constant and it is called “c.”

In that case, an absolute velocity could not be measured. Any observers, whatever their constant velocity, could consider themselves at rest. There is no absolute velocity; only relative velocities are meaningful. This became the theory of “Relativity.”

His initial theory is now called the “Special Theory of Relativity,” because ten years later Einstein expanded this theory into the “General Theory of Relativity,” which included gravity and space.

Relativity is a theory of the structure of space-time. It was introduced in Einstein's 1905 paper "On the Electrodynamics of Moving Bodies." Special relativity is based on two postulates that are contradictory in Classical Physics:

  1. The laws of physics are the same for all observers in uniform motion relative to one another (principle of relativity).
  2. The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light.

The resultant theory copes with experiment better than classical mechanics, e.g. in the Michelson–Morley experiment that supports postulate 2, but also has many surprising consequences. Some of these are:

  • Relativity of simultaneity: Two events, simultaneous for one observer, may not be simultaneous for another observer if the observers are in relative motion.
  • Time dilation: Moving clocks are measured to tick more slowly than an observer's "stationary" clock.
  • Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to the observer.
  • Mass–energy equivalence: E = mc2, energy and mass are equivalent and transmutable.
  • Maximum speed is finite: No physical object, message or field line can travel faster than the speed of light in a vacuum.

The defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations. Basically, Einstein proved that Newton’s equations were wrong. Or, at least, they required a correction. We now recognize Newton’s laws as approximations. They work well under normal circumstances, but must be adjusted for situations that involve high velocity or high mass. (The latter a result of the General Theory of Relativity.)

In physics, the Lorentz transformation (or transformations) is named after the Dutch physicist Hendrik Lorentz. It was the result of attempts by Lorentz and others to explain how the speed of light was observed to be independent of the reference frame, and to understand the symmetries of the laws of electromagnetism. The Lorentz transformation is part of special relativity, but was derived well before the theory was published by Einstein.

The Lorentz transformation is given mathematically by this formula:

Where v is the velocity of the object and c is the speed of light. As long as v is very small relative to c, this reduces to very nearly one and can be ignored. But, at high velocities, it must be taken into account.

It was already known that Mercury didn’t exactly match in its orbit the mechanics of Newton. It was close, but precise measurement showed disagreement with theory. Some supposed it was due to another planet closer to the Sun than Mercury. That supposed planet even got a name: Vulcan. It was searched for, but in vain. Upon applying Einstein’s corrections to Newton’s laws, scientists found a match. As the innermost planet, Mercury traveled the fastest in its orbit, and, therefore, needed the correction more than the other planets. We now adjust all our measurements of planets and stars using the special and general theories of Relativity.

With just simple algebra, Einstein deduced further testable predictions from his postulate. The prediction most important is that no signal, no information, can travel faster than the speed of light. Another prediction is that mass is a form of energy and can be converted into other forms of energy. It’s summarized as E = mc2. Both of these predictions have been confirmed, sometimes very dramatically.

The prediction that is hardest to believe is that the passage of time is relative: Time passes more slowly for a fast-moving object than it does for something at rest. This too has been proven multiple times with experiments involving the life of particles created when cosmic rays strike the upper atmosphere to very accurate clocks flown around the world. This isn’t fiction. It is fact.

Although the seeds of the special theory were widely planted and growing in many gardens, Einstein's follow up, the General Theory of Relativity, was a complete surprise to everyone. This greater, in-depth theory by a man who was likely the greatest thinker of the twentieth century caught all of physics off guard.

The special theory only worked with constant velocity. Einstein began to ponder acceleration, a changing velocity, Newton's second law, and the cause of gravity, Newton's other famous discovery.

He developed what is called "General Relativity." General relativity is a geometric theory of gravitation published by Albert Einstein in 1916 and the current description of gravitation in modern physics. General Relativity generalizes Special Relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or space-time. In particular, the curvature of space-time is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.

Some predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Examples of such differences include gravitational time dilation, gravitational lensing, the gravitational redshift of light, and the gravitational time delay. This theory solves an age old question about the difference between the acceleration of gravity and the force of acceleration on a body. The issue was how one could tell the difference between being accelerated in an elevator in free space, causing "weight" vs. a stable box on the surface of the Earth where the notion of "weight" comes from gravity. Einstein's simple answer is that there is no measurable difference. Again a result he developed from his Gedankenexperiment or "though experiment." However, Einstein's conclusions have been proven over and over again by experiment.

The predictions of general relativity have been confirmed in all observations and experiments to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory that is consistent with experimental data. However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity. This attempt, sometimes called "GUT" or Great Unified Theory was a focus of Einstein's for the rest of his life, but he did not accomplish it. It is still a search going on in modern physics and the solution has yet to be discovered.

Unlike Lord Kelvin at the dawn of the twentieth century, scientists today have many challenging problems to work on. We know we're not done yet.

The general theory is the most important tool used today in Cosmology, the study of the origin and eventual fate of the universe. Out of this theory comes predictions of black holes and other astrological objects which have since been discovered and studied.

Yet this wonderful, and powerful, and thought provoking, and somewhat unbelievable new discovery and way of looking at physics was proven by every experiment devised to test its authenticity. Einstein's contemporaries did not all accept his new theories at once. However, the theory of relativity is now considered as a cornerstone of modern physics.

Although it was brilliant thinking by Einstein that established these principles, the special theory of relativity had many other contributors and discoverers. The history of special relativity consists of many theoretical results and empirical findings obtained by Albert Michelson, Hendrik Lorentz, Henri Poincaré and others. It culminated in the theory of special relativity proposed by Albert Einstein, and subsequent work of Max Planck, Hermann Minkowski and others. Minkowski, particularly, improved on the simple math of Einstein and put the space-time continuum on solid mathematical and geometrical grounds. Einstein later adopted the principles of Minkowski in his work on the general theory.

Einstein arrived at his conclusions through logical reasoning and “thought experiments” that would have made Aristotle proud. However, it was the experimental evidence that eventually convinced the scientific community of the theories relevance. In 1905 Einstein had no reputation with which to make an appeal as an authority. His brilliant work was accepted because, as contrary to most views of the universe, his view matched the experimental data and every prediction of his theory proved true.

But relativity wasn’t the only unimaginable idea of science to find root at the turn of the Twentieth Century. Basically unrelated was another new concept now called Quantum Physics. Einstein had a big hand in that too, but it is really separate from Relativity and much of Quantum Mechanics was also an approximation in need of correction for Relativity. That is our next chapter.

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