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01/05/2004
How Time Flies
Happy New Year! Since last we met, I visited the Metropolitan
Museum of Art in New York and was attracted to a painting by
Signac, an artist of the pointillist school. The painting consists of
thousands of little dots or dashes. These little packets of paint
are quite evident if you’re close to the painting but disappear
when you move back far enough. Does time also come in little
packets that become less clear as one ages? I’m starting this
column on the day after my birthday, December 28, and by the
time I finish and post it the ball will have dropped at Times
Square. Both the ball drop and the birthday marked, with the
slightest tick of a clock, the passage of a whole year’s packet of
time.
When I was a kid in school, our clocks had minute hands that
didn’t move continuously but marked the passage of time in one-
minute intervals. On a warm day, we would eagerly await the
tick at 3:00 PM to set us free to grab our baseball gloves. Time
passed in those 1-minute packets. Today, our computers “tick”
in packets of millionths of a second or less. Whether our ticks
mark the passage of a year or a zillionth of a second, one can ask,
“What happens to time between the ticks?”
You say that’s a silly question? In a year or even a fraction of a
second, a lot goes on and time keeps passing smoothly between
those ticks. But wait a minute; is there a limit on how short the
time can be between ticks? Let’s go back a century to Max
Planck. (I once gave a plenary talk at a meeting at the Max
Planck Institute in Stuttgart, one of several Max Planck Institutes
in Germany.) Before 1900, light was thought to be a continuous
radiation of some sort. You would think that is the case just
looking at the light coming from the sun or a 100-watt bulb.
However, in 1900 Planck made the radical suggestion that light
and heat were emitted in “packets” (quanta) of radiation. We
know these packets as photons.
Planck’s suggestion gave birth to quantum mechanics. Einstein
hopped on Planck’s idea and showed that these packets of light
were responsible for the photoelectric effect. The photoelectric
effect occurs when a photon hits a metal and knocks an electron
out of its orbit, thus generating an electric current. This effect is
employed in the electric eyes used in automatic doors that open
when you approach them.
Planck said that the energy in a packet of light is equal to the
frequency of the light multiplied by a number that became
known as “Planck’s constant”. As quantum mechanics
developed, Planck’s constant played a very important role. For
example, the famous Heisenberg uncertainty principle says that
you can never measure absolutely precisely both the position and
velocity of an object. Planck’s constant sets the limit on how
precisely speed and position can be measured. Planck won the
Nobel Prize in 1918 and remained in Germany until his death in
1947. Sadly, his son Erwin was executed for taking part in the
failed plot to assassinate Adolph Hitler.
Einstein won his Nobel Prize for his work on Planck’s packets.
But instead of sticking to the tiny subatomic world of quantum
mechanics, Einstein turned his attention to the larger nature of
the universe and his theories of time and space. He showed that
gravity was a warping of something called spacetime. We three-
dimensional people find it difficult to visualize four-dimensional
spacetime. The standard crude way to explain gravity is to
pretend that spacetime is just a big flat rubber sheet held tightly
by some means. Now put a bowling ball on the rubber sheet.
The bowling ball will sink in and distort (warp) the spacetime
around it. Put a marble on the sheet and it will naturally be
attracted to the bowling ball by the dip in our sheet of spacetime.
This, hugely simplified, is gravity, a warping of spacetime.
Einstein’s spacetime, like the rubber sheet, is smooth and
continuous. There aren’t any breaks in the rubber sheet and time
“flows” continuously.
It’s ironic that Einstein won the Nobel for his work on Planck’s
packets. For much of the past century, the major goal of
theoretical physicists and of Einstein himself was to find a theory
that would unite Einstein’s smooth, continuous spacetime with
quantum mechanics and its weird, wildly discontinuous
menagerie of particles and interactions of the subatomic world.
One promising approach to melding the two worlds has been to
say that the fundamental units of everything are tiny strings.
This “string theory” says that fundamental particles such as
quarks and electrons are just various shapes and frequencies of
strings. But there’s a problem. These postulated strings are so
small that, if they do exist, we shall never be able to see them.
Although string theory seems to explain a lot, how will we ever
know if it’s true if we can’t see or measure the strings? Well, an
alternative theory has been getting a lot of attention, much of the
work being performed at a Canadian institution, the Perimeter
Institute for Theoretical Physics in Waterloo, Ontario. One
recent article on this “loop quantum gravity” theory is by
Perimeter researcher Lee Smolin in the January 2004 issue of
Scientific American. If you’re like me, just the term loop
quantum gravity is enough to scare me. I don’t have the foggiest
notion of the complexity of the theory. Suffice to say that it
purportedly takes experimentally proven ideas in both quantum
and relativity theories and goes on from there. Why the “loop”?
Apparently, the mathematics involves dealing with tiny loops in
spacetime.
Why do I even try to write about it? Some conclusions that fall
out of the theory seem to answer the questions posed above. For
example, (1) space and time do come in packets, (2) there is a
limit to the smallness of the interval between ticks and (3)
between ticks there is no time! How can time disappear between
ticks? Here’s where Planck comes back into the picture.
The loop theory predicts that there is an absolute minimum
length, the “Planck length”. In other words, like light, space
comes in packets. This means that nothing can have a dimension
smaller than the Planck length, which is derived from Planck’s
constant. This Planck length is pitifully small,
0.000000000000000000000000000000001616 centimeters (if I
counted correctly there are 32 zeros after the decimal point). The
way I interpret it, having an absolute minimum possible length
means that you can’t move an object or travel less than that
distance. We’re so big, it makes no difference but, if you have a
super tiny object, you can only move it in steps or multiples of
that Planck length. That is, the shortest possible trip in the world
is that Planck length. This sounds like the world of quantum
mechanics – you can be here or you can be there, but you can’t
be anywhere in between!
Knowing the shortest possible trip, we can ask, “What’s the
fastest possible trip?” Well, Einstein says we can’t move any
faster than the speed of light. So, let’s just divide the length of
our trip by our speed, that is, the Planck length by the speed of
light. What do we get? The answer is the “Planck time”,
0.00000000000000000000000000000000000000000005 seconds
(there should be 43 zeros after the decimal point). Since we have
just made the shortest possible trip in the shortest possible time,
isn’t that Planck time the shortest possible time between “ticks”?
What happens to time between these ticks? Nothing – there is no
time between these ticks! Even if we were super tiny beings
with super tiny clocks, I assume that we couldn’t measure any
time between ticks. For that matter, it seems to me that we also
couldn’t measure any space between the beginning and end of
our trip, even with super tiny rulers.
If this boggles your mind, as it does mine, you might rightly
question the importance and validity of such a loopy theory.
Besides, the numbers are so small that there is no chance that
we’ll ever be able to see or measure the smallest packets of
length and time. Isn’t the theory just like string theory in that,
even if true, it can’t be proved? On the contrary, say the loop
theorists. There is an experimental test that can be done and that
test may come in 2006. The loop quantum gravity theory
predicts that photons of light of different wavelengths (colors)
travel at very slightly different velocities through space.
The predicted difference in velocities is so small that this
difference can only be measured over very long, cosmic
distances and with photons of greatly differing energies. The
hope lies in a satellite scheduled for launch in 2006. This
“GLAST” satellite will search for gamma-ray bursts, cosmic
explosions that occur billions of light years away from us in the
far reaches of space. These gamma-ray photons are not visible to
our eyes but are much higher energy photons than visible light
photons. The test will be to spot a gamma-ray burst and see if
the gamma-rays of different energies arrive at different times as
the loop quantum gravity theory predicts.
This sounds to me like one awfully difficult experiment but I
wish the loop theorists all the best. In the interim, I hope to
enjoy seeing and reading about the adventures of another space
endeavor, the exploration of Mars. Go, Spirit, go! And that
picture of a comet taken last week in another space venture is
gorgeous. The year 2004 is off to a good start, scientifically at
least.
Allen F. Bortrum
NOTE: I’m back earlier than the promised January 8 posting
date. Next week I’ll return to the nominal Thursday posting,
with the actual posting typically on Wednesday afternoon.
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