Minkowski on mathematician and physicist

十二月 19, 2012

Minkowski concluded this section with a remark that
clarifies his understanding of the basic motivations behind Einstein’s contribution to the
latest developments in electrodynamics: mathematicians—Minkowski said—accustomed
as they are to discuss many-dimensional manifolds and non-Euclidean geometries, will
have no serious difficulties in adapting their concept of time to the new one, implied by
the application of the Lorentz transformation; on the other hand, the task of making physical
sense out of the essence of these transformations had been addressed by Einstein in the
introduction to his 1905 relativity article.26


In general relativity, there is no gravitational force. Gravity is geometry

七月 28, 2012

In general relativity, there is no gravitational force. Gravity is geometry.

It’s similar for the clocks in the spaceship. The signal that the group at the front receives is “Doppler-shifted” to stretched waves because these scientists are moving away. Their detector counts fewer of these stretched waves per second, and the scientists conclude that the clock in the back of the ship runs more slowly than the clock at the front.
To confirm, the group of scientists at the back of the ship detects the light from the front clock. Because this group is accelerating toward the place where the signal was emitted, they detect a compressed wave, and their detector counts more of these waves per second. For them, the clock at the front runs faster than theirs. The two groups are in agreement about the clocks

Lorentz-Fitzgerald Contraction

七月 14, 2012

In 1889, the Irish physicist George Francis Fitzgerald proposed
a radical explanation of why the Michelson-Morley
experiment failed to detect the luminiferous ether. His
explanation came at a time when he, like most scientists,
firmly believed in the ether. Movement through the ether,
Fitzgerald said, shortened the arm of Michelson’s interferometer
just enough to cancel the decrease in the speed
of light caused by the ether wind. This length contraction
took place along the line of motion and was almost impossible
to detect because any meter stick used to measure it
would contract, too.
Two years after Fitzgerald published his proposal, Hendrik
Lorentz, a prominent Dutch physicist who was also a
staunch believer in the ether, developed the idea further.
The shortening of objects in motion relative to an observer
became known as the Lorentz-Fitzgerald contraction.
Lorentz also came up with a general method for transforming
the space and time coordinates of events from one
inertial frame of reference to another. The equations he
derived to do this are called Lorentz transformations, and
they proved useful to Einstein as he developed the special
Lorentz’s formulas for calculating time dilation and
length contraction are identical to those Einstein developed
for special relativity. Why, then, are Lorentz and Fitzgerald
not considered to be the authors of the theory of special
relativity? The answer lies in the two men’s wrong interpretation
of the Michelson-Morley experiment. According
to Lorentz and Fitzgerald, the ether existed and the speed
of light was constant relative to it. Einstein’s bold leap forward
was to ignore the ether and accept what Maxwell’s
equations were telling him: The speed of light is the same
for every observer. It is this key conclusion that led Einstein
to relativity—and kept Lorentz and Fitzgerald from discovering
it themselves.

Nevertheless, Einstein knew he owed much to the two
men’s groundbreaking ideas and was quick to recognize
them. In an after-dinner speech he delivered in California,
Einstein credited “the ideas of Lorentz and Fitzgerald, out
of which the Special Theory of Relativity developed.”

Special Relativity – Experimental Verification

三月 3, 2009

Special Relativity – Experimental Verification

Like any scientific theory, the theory of relativity must be confirmed by experiment. So far, relativity has passed all its experimental tests. The special theory predicts unusual behavior for objects traveling near the speed of light. So far no human has traveled near the speed of light. Physicists do, however, regularly accelerate subatomic particles with large particle accelerators like the recently canceled Superconducting Super Collider (SSC). Physicists also observe cosmic rays which are particles traveling near the speed of light coming from space. When these physicists try to predict the behavior of rapidly moving particles using classical Newtonian physics, the predictions are wrong. When they use the corrections for Lorentz contraction, time dilation, and mass increase required by special relativity, it works. For example, muons are very short lived subatomic particles with an average lifetime of about two millionths of a second. However when they are traveling near the speed of light physicists observe much longer apparent lifetimes for muons. Time dilation is occurring for the muons. As seen by the observer in the lab time moves more slowly for the muons traveling near the speed of light.

Time dilation and other relativistic effects are normally too small to measure at ordinary velocities. But what if we had sufficiently accurate clocks? In 1971 two physicists, J. C. Hafele and R. E. Keating used atomic clocks accurate to about one billionth of a second (one nanosecond) to measure the small time dilation that occurs while flying in a jet plane. They flew atomic clocks in a jet for 45 hours then compared the clock readings to a clock at rest in the laboratory. To within the accuracy of the clocks they used time dilation occurred for the clocks in the jet as predicted by relativity. Relativistic effects occur at ordinary velocities, but they are too small to measure without very precise instruments.

The formula E=mc2 predicts that matter can be converted directly to energy. Nuclear reactions that occur in the Sun, in nuclear reactors, and in nuclear weapons confirm this prediction experimentally.

Albert Einstein’s special theory of relativity fundamentally changed the way scientists characterize time and space. So far it has passed all experimental tests. It does not however mean that Newton’s law of physics is wrong. Newton’s laws are an approximation of relativity. In the approximation of small velocities, special relativity reduces to Newton’s laws.



Cutnell, John D., and Kenneth W. Johnson. Physics. 3rd ed. New York: Wiley, 1995.

Einstein, Albert. Relativity. New York: Crown, 1961.

Mould, R.A. Basic Relativity. Springer Verlag, 2001.

Hawking, Stephen. Black Holes and Baby Universes and Other Essays. New York: Bantam, 1993.

Schrödinger, Edwin. Space-Time Structure, Reprint Edition. Cambridge University Press, 2002.

Paul A. Heckert
K. Lee Lerner


. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

General relativity
—The part of Einstein’s theory of relativity that deals with accelerating (noninertial) reference frames.

Lorentz contraction
—An effect that occurs in special relativity; to an outside observer the length appears shorter for an object traveling near the speed of light.

Reference frames
—A system, consisting of both a set of coordinate axes and a clock, for locating an object’s (or event’s) position in both space and time.

—Space and time combined as one unified concept.

Special relativity
—The part of Einstein’s theory of relativity that deals only with nonaccelerating (inertial) reference frames.

Time dilation
—An effect that occurs in special relativity; to an outside observer time appears to slow down for an object traveling near the speed of light.

God did not play dice

十一月 17, 2007

‘Of the new rules in quantum mechanics, which appeared to mean that some essential part of nature was determined not absolutely but only in a statistical or probabilistic way , Einstein remarked that in his view God did not play dice. That was his rational for objecting to the foundations of quantum mechanics, and for insisiting that some more fundatmental theory must lie below its surface; he could not accept that the dear Lord would allow a probabilistic theory to be the whole truth about the way the world works. ‘ wrote David Lindley

Einstein in a nutshell

十月 26, 2007



Special relativity unlocked the secrets of the stars and revealed the fantastic quantities of energy stored deep inside the atom. But the seed of relativity was planted when Einstein was only 16 years old and asked himself a childlike question: What would a beam of light look like if you could race alongside it? According to Newton, you could catch up to any speeding object if you moved quickly enough. If you could catch up to a light wave, Einstein realized, it would look like a wave frozen in time. But even as a teenager, he knew that no one had ever seen a frozen light wave before. In fact, such a wave makes no physical sense.

When Einstein studied Maxwell’s theory of light, he found something that others missed—that the speed of light always appears the same, no matter how quickly you move. Einstein then boldly formulated the principle of special relativity: The speed of light is a constant in all inertial frames (frames that move at constant velocity).

No longer were space and time absolutes, as Newton thought. Space compresses and clocks tick at different speeds throughout the universe.