Today, simple but brilliant. The University of Houston’s College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.
I came across an old journal article the other day — a very famous one. I wasnít sure what to expect. After all, it was written by a physicist. It couldíve been filled with complicated mathematics. But it wasnít. The ideas were explained in clear, simple terms, comprehensible to a first year college student. Thatís rare for an original paper. The best explanations of an idea usually come years after itís first conceived. The paper? ďOn the Electrodynamics of Moving Bodies,Ē where Albert Einstein introduced the theory of special relativity.
As a child I was fascinated by special relativity. It seemed so mysterious. Time travel became real. Not any type of time travel. Most science fiction gets it wrong. The Terminator canít go back and kill John Connorís mother to prevent his birth. But in theory we can send spaceships out at near light speed, and when they return a thousand years later those on board may have aged only a few days.
I must have read a half-dozen popular books on special relativity when I was younger. They were amazing. Here were unimaginable paradoxes accepted by the scientific community. These popular books were teasers; filled with explanations that seemed too simple. I knew that someday Iíd have to learn what relativity was really all about.
That time came during my first college physics course. And I was shocked at its simplicity. To this day I remember thinking ďThatís it? Thatís all there is to it?Ē
But thatís the beauty of special relativity. Itís not complicated. What makes Einsteinís contribution so phenomenal is that he started with two basic premises and followed them to their logical conclusion. Other physicists had been playing with similar ideas for decades. But they never made the leap of imagination Einstein did. They couldnít imagine that time and distance could change with the relative speed of an observer. The idea was too outlandish. Einstein made that leap. And it forever changed how we look at our world.
Since Einstein, physicists havenít been afraid to propose the seemingly preposterous. Our world may have more than three physical dimensions. There may be infinite universes, with infinitely more created every instant. Respectable conferences are held; distinguished papers are published. If a theory explains the world we see, weíll accept it, no matter what strange consequences it entails.
Unfortunately, many of these new ideas are complicated. Popular accounts just donít do them justice. Years of mathematics and physics are required to truly comprehend them. Which makes Einsteinís original paper on special relativity all that much more wonderful. Itís a unique opportunity to understand our mind-boggling universe in the words of one of its most inventive minds.
Iím Andy Boyd at the University of Houston, where weíre interested in the way inventive minds work.
Albert Einstein. On the Electrodynamics of Moving Bodies. English translation of the original 1905 German publication. The translation is taken from the book The Principle of Relativity, first published by Methuen and Company, Ltd., London, 1923. It was accessed on December 15, 2008, on the public domain web site http://www.fourmilab.ch/etexts/einstein/specrel/www/.
The picture of Einstein, taken when he won the Nobel Prize in 1921, is taken from Wikimedia Commons.
An excerpt from the translation of Einsteinís journal article appears below. It is taken from Part 1 of the paper, ďKinematical Part,Ē which covers special relativity.
If we wish to describe the motion of a material point, we give the values of its co-ordinates as functions of the time. Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by ``time.'' We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say, ``That train arrives here at 7 o'clock,'' I mean something like this: ``The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.''
It might appear possible to overcome all the difficulties attending the definition of ``time'' by substituting ``the position of the small hand of my watch'' for ``time.'' And in fact such a definition is satisfactory when we are concerned with defining a time exclusively for the place where the watch is located; but it is no longer satisfactory when we have to connect in time series of events occurring at different places, or—what comes to the same thing—to evaluate the times of events occurring at places remote from the watch.
We might, of course, content ourselves with time values determined by an observer stationed together with the watch at the origin of the co-ordinates, and co-ordinating the corresponding positions of the hands with light signals, given out by every event to be timed, and reaching him through empty space. But this co-ordination has the disadvantage that it is not independent of the standpoint of the observer with the watch or clock, as we know from experience. We arrive at a much more practical determination along the following line of thought.
If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B. But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an ``A time'' and a ``B time.'' We have not defined a common ``time'' for A and B, for the latter cannot be defined at all unless we establish by definition that the ``time'' required by light to travel from A to B equals the ``time'' it requires to travel from B to A. Let a ray of light start at the ``A time'' tA from A towards B, let it at the ``B time'' tB be reflected at B in the direction of A, and arrive again at A at the ``A time'' t'A.
In accordance with definition the two clocks synchronize if
tB - tA = t'A - tB
We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:
- If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
- If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.
Thus with the help of certain imaginary physical experiments we have settled what is to be understood by synchronous stationary clocks located at different places, and have evidently obtained a definition of ``simultaneous,'' or ``synchronous,'' and of ``time.'' The ``time'' of an event is that which is given simultaneously with the event by a stationary clock located at the place of the event, this clock being synchronous, and indeed synchronous for all time determinations, with a specified stationary clock.
In agreement with experience we further assume the quantity
2AB = c,
t'A - tA
to be a universal constant—the velocity of light in empty space.
It is essential to have time defined by means of stationary clocks in the stationary system, and the time now defined being appropriate to the stationary system we call it ``the time of the stationary system.''
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