*Part 2 *
Subtle but Not Malicious The relativity of space and of time is a startling
conclusion. From the well-worn statement that the speed of light is
constant, we conclude that *space and time are in the eye of the
beholder. *Each
of us carries our own clock, our own monitor of thepassage of time. Each
clock is equally precise, yet when we move relative to one another, these
clocks do not agree. They fall out of synchronization; they measure
different amounts of elapsed time between two chosen events. The same is
true of distance. Each of us carries our own yardstick, our own monitor of
distance in space. Each yardstick is equally precise, yet when we move
relative to one another, these yardsticks do not agree; they measure
different distances between the locations of two specified events. If space
and time did not behave this way, the speed of light would not be constant
and would depend on the observer's state of motion. But it is constant;
space and time *do *behave this way. Space and time adjust themselves in an
exactly compensating manner so that observations of light's speed yield the
same result, regardless of the observer's velocity.
Getting the quantitative details of precisely how the measurements of
space and time differ is more involved, but requires only high school
algebra. It is not the depth of mathematics that makes Einstein's special
relativity challenging. It is the degree to which the ideas are
foreign and apparently
inconsistent with our everyday experiences. But once Einstein had the key
insight-the realization that he needed to break with the more than
two-hundred-year-old Newtonian perspective on space and time-it was not
hard to fill in the details. He was able to show precisely how one person's
measurements of distances and durations must differ from those of another
in order to ensure that each measures an identical value for the speed of
light.'
To get a fuller sense of what Einstein found, imagine that Bart, with heavy
heart, has carried out the mandatory retro -fitting of his skateboard,
which now has a maximum speed of 65 miles per hour. If he heads due north
at top speed-reading, whistling, yawning, and occasionally glancing at the
road-and then merges onto a highway pointing in a northeasterly direction.
his speed in the northward direction will be less than 65 miles per hour.
The reason is clear. Initially, all his speed was devoted to northward
motion, but when he shifted direction some of that speed was diverted into
eastward motion, leaving a little less for heading north. This extremely
simple idea actually allows us to capture the core insight of special
relativity. Here's how:
We are used to the fact that objects can move through space, but there
is another kind of motion that is equally important: objects also move
through time. Right now, the watch on your wrist and the clock on the wall
is ticking away, showing that you and everything around you are
relentlessly moving through time, relentlessly moving from one second to
the next and the next, Newton thought that motion through time was totally
separate from, motion through space-he thought these two kinds of motion
had nothing to do with each other. But Einstein found that they are
intimately linked. In fact, the revolutionary discovery of special
relativity is this:
“When you look at something like a parked car, which from your
viewpoint is stationary-not moving through space, that is-all of its motion
is through time. The car, its driver, the street, you, your clothes are all
moving through time in perfect synch: second followed by second, ticking
away uniformly. But if the car speeds away, some of its motion through time
is diverted into motion through space. {KR Motion is stationary only from
your eyes point of view but wrt the time passed , along with the earth it
was moving even along with you and that is the emotion in time} And just
as Bart's speed in the northward direction slowed down when he diverted
some of his northward motion into eastward motion, the speed of the car
through time slows down when it diverts some of its motion through time
into motion through space. This means that the car's progress through time
slows down and therefore time elapses more slowly for the moving car and
its driver than it elapses for you and everything else that remains
stationary.”
*That, in a nutshell, is special relativity.* In fact, we can be a bit
more precise and take the description one step further. Because of the
retro-fitting, Bart had no choice but to limit his top speed to 65 miles
per hour. This is important to the story, because if he sped up enough when
he angled northeast, he could have compensated for the speed diversion and
thereby maintained the same net speed toward the north. But with the
retro-fitting, no matter how hard he rammed the skateboard's engine, his
total speed-the combination of his speed toward the north and his speed
toward the east-remained fixed at the maximum of 65 miles per hour. And so
when he shifted his direction a bit toward the east, he necessarily caused
a decreased northward speed.
*Special relativity declares a similar moment for all motion: the
combined speed of any object's motion through space and its motion through
time 1s always precisely equal to the speed of light*. At first, you may
instinctively recoil from this statement since we are all used to the idea
that nothing but light can travel at light speed. But that familiar Idea
refers solely to motion through space. We are now talking about something
related, yet richer: an object's combined motion through space and time.
The key fact, Einstein discovered, is that these two kinds of motion are
always complementary. When the parked car you were looking at speeds away,
what really happens is that some of its light-speed motion is diverted from
motion through time into motion through space, keeping their combined total
unchanged. Such diversion unassailable means that the car's motion through
time slows down.
As an example, if Lisa had been able to see Bart's watch as he sped along
at 500 million miles per hour, she would have seen that it was ticking
about two-thirds as fast as her own. For every three hours that passed on
Lisa's watch, she would see that only two had passed on Bart's. His rapid
motion through space would have proved a significant drain on his speed
through time. Moreover, the maximum speed through space is reached when all
light-speed motion through time is fully diverted into light-speed motion
through space-one way of distancing why it is impossible to go through
space at greater than light speed. Light, which always travels at light
speed through space, is special in that it always achieves such total
diversion. And just as driving- due east leaves no motion for traveling
north, moving at light speed through space leaves no motion for traveling
through time! Time stops when traveling at the speed of light through space*.
A watch worn by a particle of light would not tick at all.:* it doesn't
age. As this description makes clear, the effects of special relativity
are most pronounced when speeds (through space) are a significant fraction
of light speed. But the unfamiliar, complementary nature of motion through
space and time always applies. The lesser the speed, the smaller the
deviation from pre-relativity physics-from common sense, that is but the
deviation is still there, to be sure Truly. This 1s not dexterous wordplay,
sleight of hand, or psychological illusion. This is how the universe works.
In 1971, Joseph Hafele and Richard Keating flew state-of-the-art
caesium-beam
atomic clocks around the world on a commercial Pan Am jet. When they
compared the clocks flown on the plane with identical clocks left
station-man. on the ground, they found that less time had elapsed on the
moving clocks. The difference is as tiny-a few hundred billionths of a
second-but it was precisely in accord with Einstein's discoveries. You
can't get much more nuts-and-bolts than that.
In 1908, word began to spread that newer, more refined experiments
were finding evidence for the aether. If that had been so, it would have
meant that there was an absolute standard of rest and that Einstein's
special relativity was wrong. On hearing this rumour, Einstein replied,
"Subtle is the Lord malicious He is not." Peering deeply into the workings
of nature to tease out insights into space and time as a profound
challenge, one that had gotten the better of everyone until Einstein. But
to allow such a startling and beautiful theory to exist, and yet to make it
irrelevant to the workings of the universe, that would be malicious.
Einstein would have none of it; he dismissed the new experiments. His
confidence was well placed. The experiments were ultimately shown to be
wrong, and the luminiferous aether evaporated from scientific discourse.
But what About the Bucket?
This is certainly a tidy story for light. Theory and experiment agree that
light needs no medium to carry its waves and that regardless of the motion
of either the source of light or the person observing, its speed is fixed
and unchanging. Every vantage point is on an equal footing with even
others. There is no absolute or preferred standard of rest. Great. But what
about the bucket? Remember, while many viewed the luminiferous aether as
the physical substance giving credible to Newton's absolute space, it had
nothing to do with why Newton introduced absolute space. Instead, after
wrangling with accelerated motion such as the spinning bucket, Newton saw
no option but to invoke some invisible background stuff with respect to
which motion could be unambiguously defined. Doing away with Relativity and
the Absolute aether did not do away with the bucket, so how did Einstein
and his special theory of relativity cope with the issue?
Well, truth be told, in special relativity, Einstein's main focus was
on a special kind of motion: constant-velocity motion. It was not until
1915, some ten years later, that he fully came to grips with more general,
accelerated motion, through his general theory of relativity. Even so,
Einstein and others repeatedly considered the question of rotating motion
using the insights of special relativity; they concluded, like Newton and
unlike Mach, that even In an otherwise completely empty universe you would
feel the outward pull from spinning-Homer would feel pressed against the
inner mall of a spinning bucket; the rope between the two whirling rocks
would pull taut.' Having dismantled Newton's absolute space and absolute
time, how did Einstein explain this?
The answer is surprising. Its name notwithstanding, Einstein's theory
does not proclaim that everything is relative. Special relativity does
claim that some things are relative: velocities are relative; distances
across space are relative; durations of elapsed time are relative. But the
theory actually introduces a grand, new, sweepingly absolute concept:
absolute spacetime. Absolute spacetime is as absolute for special
relativity as absolute space and absolute time were for Newton, and partly
for this reason Einstein did not suggest or particularly like the name
"relative theory." Instead, he and other physicists suggested invariance
theory stressing that the theory, at its core, involves something that
everyone agrees on, something that is not relative.
K Rajaram IRS 4724 5724 Part 2
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