Readers who have
questions about relativity are invited to send them tome email@example.com.
will answer them on this page as time and tide permit.
Why can no particles move faster than
the speed of light?
To accelerate an
ordinaryparticle, such as an electron
or proton, to the speed of light would require an infinite amount of energy,
and to make it go faster than the speed of light would require an imaginary
amount of energy (and imaginary momentum). Since we have no supply of infinite
energy or of imaginary energy, we cannot accelerate an ordinary particle to a speed
faster than light. However, we can conceive the existence of hypothetical
extraordinary particles, called tachyons,
that always move at a speed faster than light and never slow down (to
decelerate a tachyon to a speed below the speed of light would require an
infinite amount of energy—the speed of light is a barrier for the deceleration
of tachyons just as it is a barrier for the acceleration of ordinary
particles). There are various physical problems with the tachyon idea. One
problem is the resulting instability of the vacuum. Tachyons can have positive
as well as negative energies, and that means that small thermal or quantum
fluctuations can spontaneously create tachyons of negative energy, with a
concomitant explosive release of positive energy throughout the entire
universe—obviously, this is not happening. Direct experimental searches for tachyons
have found no tachyons at all.
When the universe expands, do planets
and stars and galaxies expand? Or does only the space between them expand?
Planets, stars, planetary
systems, galaxies, and even bound clusters of galaxies do not expand. The
behavior of all these systems is controlled by the forces that their parts
exert on each other, and their internal motions are not affected by the
surrounding expanding universe. Only the empty space between the clusters of
galaxies expands. The universe grows like the shell of a turtle, which is built
of adjoining polygonal plates, each of which grows rings around its perimeter,
thereby increasing the size of the shell.
Consider two points on the equator, at
the leading and the trailing edges of the Earth in its translational motion,
and consider a distant pulsar located directly above the Earth’s North Pole. Is
it possible to synchronize two clocks at these points by means of a pulse of
light or radio waves received from such a distant pulsar? And would this
synchronization be independent of the velocity of light and of how the
translational motion of the Earth affects this velocity?
Since the paths of a pulse
from the distant pulsar to the two points on the equator are almost exactly
parallel, you might expect that the translational velocity of the Earth, at
right angles to these paths, has equal effects on the velocities of the
portions of the pulse reaching the two points, so these portions always remain
synchronized, regardless of the velocity of the pulse and of how the motion of
the Earth affects this velocity. However, this expectation is wrong, because the
paths from the pulsar to the two points are not exactly parallel—they form the two long sides of a very slender
isosceles triangle, and the velocities of the two portions of the pulse
therefore have (small) components along, or opposite to, the direction of
motion of the Earth. During the long travel of the pulse from the pulsar to the
two points, theses small velocity components accumulate a total time delay
equal to the travel time for a light pulse sent on a direct path from one point
to the other. Hence this method of synchronization is no better and no worse
than the use of a direct light signal from one point to the other, and it
depends on the velocity of light and on how the translational motion of the
Earth affects this velocity.
In the 1920s the philosopher Hans Reichenbach proposed an
alteration of the clock synchronization adopted by Einstein. In essence,
Reichenbach proposed to alter the settings of Einstein’s synchronized clocks by
a time-zone scheme. Moving, say, westward through a reference frame, he
proposed to set the clocks back (or forward) by a gradually increasing amount
(this is analogous to how the clocks are set in the Earth’s time zones; but, of
course, everybody understands that clocks with time-zone shifts are not
“really” synchronized). Is this Reichenbach scheme physically acceptable?
A reference frame with clocks
set a la Reichenbach can be used to describe physical phenomena, just as can a
reference frame with twisted x or y axes, or a reference frame with erratically
contracted length scales marked along its axes, or a wildly rotating and accelerated
reference frame. But, of course, the mathematical formulation of the laws of
physics becomes more complicated when the reference frame becomes more
complicated. Reichenbach’s scheme leaves the mathematical form of Newton’s First Law unchanged, but it messes up the
mathematical form of Newton’s
Second Law, by introducing an extra pseudoforce that depends on just how much
the clocks have been reset. Thus, a reference frame with clocks set a la
Reichenbach is a noninertial reference frame, but—in contrast to a rotating
noninertial reference frame—the noninertiality shows up only in the Second Law,
not in the First. Reichenbach, and many of his philosophical fellow travelers,
missed this point; they looked at the First Law, but never looked at the Second.
Is an electromagnetic field or an
electromagnetic wave, such as a radio wave, a form of matter?
Electromagnetic fields and
waves have energy, and hence have mass. They therefore must be regarded as a
form of matter. This view was first introduced by Einstein when he formulated
his theory of gravitation: “We make
a distinction hereafter between ‘gravitational field’ and ‘matter’ in this way,
that we denote everything but the gravitational field as ‘matter.’ Our use of
the word therefore includes not only matter in the ordinary sense, but the
electromagnetic field as well.” If we think of solids, liquids, gases, and
plasmas as the first four states of matter, then electromagnetic fields and waves
are the fifth state of matter.
What is spin?
Although spin is usually
thought of as a quantum-mechanical phenomenon, it first made its appearance in
classical physics, when it was recognized that a circularly polarized
electromagnetic wave carries not only energy but also angular momentum. The
ratio of energy to spin is equal to the angular frequency of the wave, exactly as
expected for a photon, for which the ratio of energy to angular momentum is
also equal to the angular frequency. The angular momentum of the circularly
polarized wave arises from a flow of energy within the wave—in the peripheral
part of the wave, the energy has a helical flow, that is, a circulation around
the axis of the wave in addition to the main flow along the direction of
propagation of the wave. More generally, all relativistic wave fields, except
for scalar waves, carry both energy and angular momentum. Thus, the spin of an
electron is merely the angular momentum arising from the helical flow of energy
within the Dirac wave field that describes the electron quantum-mechanically.