## Celebrating Einstein

### How High Up Is That Place?  How Far In The Future Is That Event?(continued)

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E.  Spacetime

We have indicated that, if space and time have the kind of interrelationship indicated by Minkowski's diagrams, anything that travels at a particular finite speed (the speed of light in a vacuum) turns out to have the same speed in any frame of reference.  Einstein's discovery was the reverse.  Knowing from various experiments that the speed of light in a vacuum evidently was the same in every frame of reference, Einstein worked out mathematically how space and time have to change with one's velocity in interrelated ways so that the speed of light in a vacuum does stay the same.  Some of these changes turn out to be, for the velocities we're accustomed to traveling, too small to notice but drastically and obviously different for much higher speeds.

Minkowski diagrams illustrate that space and time are not separate things, but are different features of a whole.  As Minkowski put it, "Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."  Space and time are related somewhat as vertical and horizontal directions in space are related, in a single continuum now known as "spacetime".  There are differences.  Note how the vertical and horizontal directions change in the same direction in our "earth-and-balloon" diagrams, while the changes in space and time directions are opposite in the Minkowski diagrams.  And we obviously perceive space quite differently from the way we perceive time.  Nonetheless, the situations are similar.  "Past" and "future" turn out to be opposite directions in spacetime, just as "up" and "down", or "right" and "left" are.  And which way is "future" turns out to depend on one's frame of reference, just as which way is "up" depends on where one stands.

We have only introduced some key concepts of relativity theory here without going into all the reasoning that led to them, or the many experiments that confirm them.  If you would like to learn about the theory in more detail, the references at the end of this article offer plenty of insight.

The Universe and Dr. Einstein by Lincoln Barnett
A journalist's account of Einstein's theories, including Special Relativity.

The Evolution of Physics by Albert Einstein and Leopold Infeld
Traces the main ideas of physics from Galileo to modern quantum theory in four chapters.  Relativity theory is one of the main subjects of chapter three.  Remarkably, this book only has two equations in it:  2 x 2 = 4 and 3 x 3 = 9!

Relativity and Common Sense by Hermann Bondi
Einstein's relativity theory is often considered revolutionary, through Einstein himself simply considered it a logical conclusion of the ordinary theory of his own time.  Bondi takes the same point of view, and demonstrates how relativity is simply an extension of common-sense ideas.

Relativity:  The Special and the General Theory by Albert Einstein
Einstein's original paper on relativity, "On the Electrodynamics of Moving Bodies", made use of calculus, but in this book Einstein showed a way to arrive at the same conclusions using a more direct approach.  Incidentally, if you've ever wondered what uses there are for algebra and the Pythagorean theorem, this book shows one of them.

"On the Electrodynamics of Moving Bodies" [exit federal site] by Albert Einstein
English translation of the original paper in HTML.  Links at the bottom of the page to PDF version and to zipped PostScript and LaTeX versions.

The Priniciple of Relativity by A. Einstein, H.A. Lorentz, H. Weyl, and H. Minkowski, with notes by A. Sommerfeld
Original articles on relativity, in English or English translation, including Einstein's first two papers on Special Relativity, and Minkowski's address on "Space and Time", in which he introduced his diagrams to show the geometric relationship.

The Meaning of Relativity by Albert Einstein
Advanced mathematical treatment of both the Special and General Theories of Relativity and Einstein's attempts to extend them.

The Light Cone: an illuminating introduction to relativity [exit federal site] by Rob Salgado
We've only touched on the relationship between space and time in this article.  Salgado explains the relationship in more detail, illustrating it with computer-animated versions of space-time diagrams, and takes you step-by-step from our knowledge before Einstein through Special Relativity to General Relativity.

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Prepared by Dr. William Watson, Physicist
DOE Office of Scientific and Technical Information