A PERSONAL JOURNEY THROUGH RELATIVITY

This is not an introductory text on the general theory of relativity.  I'm afraid some concepts won't be explained.  But most readers probably have some idea of the outlines of Einstein's famous theory.  I hope you will see in my journey that I had the same struggle you all have with the counter-intuitive nature of many of his ideas.

Jack was hesitant to publish this because there is no closure.  I'm afraid there is no final understanding.  In one of his famous books, professor of mathematical physics Paul Davis, multiple prizewinner, ends the book with a chapter titled "The Mystery at the End of the Universe."

In it he explains why, whether you believe in a personal God of the monotheistic religions, are a pure materialist, or believe in an infinite number of universes, in the end there remain unanswered questions.  You, as I, have to live with this.

There is an amusing story about Sir Arthur Eddington, who in the 1920s and 1930s was Britain's leading expert on Einstein's theory of relativity.  Eddington was once asked to comment on the rumor that only three people in the world, by implication including himself and Einstein, properly understood the theory.  There was a long pause before Eddington replied slowly,  "I wonder who the third person is."

The theory of relativity has a fearsome reputation, the widespread belief being that any theory formulated by a man of such legendary genius as Albert Einstein must be beyond the power of ordinary people to grasp.

Yet today, Einstein's theory is routinely taught in universities around the world, and libraries contain a range of student textbooks on the subject. Either the students of today are much brighter than they are sometimes given credit for, or the theory is not so fearsomely difficult to grasp after all.

Even so, it must be said that many people do have the greatest difficulty in understanding these ideas or in accepting that the world really does conform to some of the peculiar predictions of the theory.

My own struggle to master the theory of relativity began when I was 14.  A mathematician from UCLA was invited to give a special lecture to pupils and parents at my school in Los Angeles.  The subject was "The Theory of Relativity."

On the day of the lecture, the mathematician's eloquent exposition proved wonderfully inspiring.  Unfortunately, however, I became hopelessly lost in the technical details.  His diagrams of space and time, showing all sorts of light signals going back and forth, left me utterly mystified.

Soon afterward I found a book by Einstein himself, The Meaning of Relativity. Alas, for all his genius as a mathematician, Einstein was a poor writer, and I found the book curiously unrewarding.

The central idea did, however, sink in: The speed of light is the same regardless of who measures or how the source is moving.

Such an obviously paradoxical result defied imagination, but being young and enamored of unusual concepts, I accepted it uncritically.

Believing the Impossible

As my education continued, I came to learn about the various predications of the special theory of relativity – the time dilation and length contraction effects, the impossibility of exceeding the speed of light, the rise in mass when a body is accelerated, and the famous equation E = mc² expressing the equivalence of mass and energy.

All the results I believed to be true, but their actual meaning remained a puzzle to me.

At university I attended a proper course on the special theory. By that stage I couldn't avoid having to think through the time dilation effect in detail.

It didn't seem just odd that someone could go off on a space trip and return to find their twin ten years older than they were – it seemed downright absurd! How could the same things happen at different rates? I asked myself.

I formed the impression that speed somehow distorts clock rates, so the time dilation was some sort of illusion – an apparent rather than real effect.  I wanted to ask which twin experienced ‘real' time and which was deluded.

It was at this point that I discovered the main obstacle to my progress.  The trouble was that I kept trying to refer everything back to common sense and preconceived notions about reality, and this wouldn't work.

At first, this seemed a shocking failure.  I had to admit that I could not visualize time running at two different rates, and I took this to mean that I did not understand the theory.  To be sure, I learned how to manipulate the formulas and to calculate by how much differently moving clocks got out of step. I could work out what would actually happen, but I had no understanding of why this should be so.

It was then that I realized why I had been so confused.  So long as I could imagine the time dilation and other effects actually happening, and could work out the quantities involved, that was all that was needed. 

If I could always relate everything back to specific observers and ask what they would actually see and measure, then their observations would be the reality.

This pragmatic approach of merely inquiring about what is observed, not trying to formulate a mental model of what is in some absolute sense, is called positivism, and I have found it be of the greatest help in grappling with much of modern physics.