Ed Lu’s Journal: Entry #13: Relativity

After
our 6 months in space, we will have actually aged slightly
less than everyone else on the ground because of an effect
called time dilation. It isn’t by much (about 0.007 seconds),
but it is one side benefit of flying in space! For a little
change of pace, I decided to write this letter for the physicists
and engineers out there. The beginning part is more general,
but if you haven’t studied university level physics some of
the details may be a bit obscure. Hopefully though you’ll
still find this interesting, and who knows, maybe it will
inspire you to learn more about relativity!

As Einstein
first figured out, the concepts of length, energy, mass, and
time all depend on how fast you are moving. The reason is
the observed experimental fact that no matter how fast you
are moving, if you measure the speed of light you always get
the same value (this is another way of saying you can’t measure
your own absolute speed, but rather only relative to something
else). Think about two different people who are each moving
at different speeds while each simultaneously measures the
speed of a light beam. They will each measure the same speed
of light, even though they themselves are moving relative
to one another. The only way this can be possible is if one’s
standards of both length and time (what you use when you measure
speed) depend on your relative speed. In fact, if you stand
on the ground and watch somebody else fly past, you will say
that their clocks are moving slower and that they have shrunk.
The speed of time depends on your relative speed. This effect
is called time dilation. Similarly, the length of an object
(along the direction of motion) also shrinks. These effects
are really small for speeds much less than the speed of light
(300,000 km/sec), which is why nobody ever noticed it before
the beginning part of the 20th century. This result has been
verified thousands of times with thousands of different experiments
since then and is now considered an established fact. But
what I started to wonder was if it is possible for me to observe
a relativistic effect using a simple experiment (and no elaborate
hardware) up here. After all we are moving at what is by everyday
standards really fast (18,000 MPH). The problem is that by
relativistic standards we are still moving incredibly slow,
only about 3E-5 times the speed of light (this number is usually
referred to as beta). For small beta, the time dilation effect
that causes clocks to move slower goes as beta squared over
2, or about 5E-10,which is a really, really small effect.

Since
we are up here for a long time, the first thought was to see
if there was a way to measure the time dilation directly.
Since there are pi E7 seconds in a year, after 6 months moving
at beta 3E-5 we only get a difference of about 7E-3 seconds
between our clocks and those on the ground. This is pretty
tough to measure since you need two clocks (one on the ground
and one here) that are stable and accurate enough over 6 months
to distinguish the difference. There are clocks this accurate,
but we don’t have one on board, and besides, the goal was
to see if I could measure the effect without a special apparatus.
Similarly, the length contraction that the Space Station undergoes
due to its orbital speed is also tiny, about 2.5E-6 cm. You
can’t measure it from onboard anyhow, since everything here
is also moving at the same speed, and therefore is also shrunk
by the same fraction. Our onboard GPS receivers that we use
for navigation do have to take into account relativity when
calculating our position and velocity, but I can’t really
claim credit for that.

The next
thought was to look for Doppler shifts, as it is pretty easy
to measure frequencies. The problem is that the first order
Doppler shift (the term that goes as beta) is exactly the
same as the ordinary Galilean Doppler shift. So that doesn’t
really count as a relativistic effect. So once again, we are
looking for a second order beta squared effect on top of the
first order effect. And again I couldn’t figure out a way
to do that up here. We do have basic lab equipment (voltmeters,
oscilloscopes, signal generators, etc.), but a few part in
10^10 effect is pretty hard to see. After thinking about it
for months, I haven’t managed to come up with any good ideas.
Perhaps somebody out there has a good idea that one of the
future crews could try in their spare time for fun.
Which
way is up all depends on which way you look at it.

But while
I haven’t found a way to observe a direct relativistic effect,
in a desperate attempt to claim some sort of victory, I can
sort of argue that I have been able to observe another effect
that does depend upon relativity. We know that light carries
energy and momentum. If you consider that light is made up
of massless particles (photons), then the fact that photons
carry momentum is a relativistic effect. Of course, you can
always argue that even classical non-relativistic waves carry
both energy and momentum – but for the purposes of trying
to claim at least a partial victory I am going to stick to
the particle interpretation.

And in
fact it does seem to be possible to observe light pressure
up here. Our drink packages come wrapped in a very thin silvery
reflective film. I cut a small square of this film, and placed
it inside our glovebox – a chamber we use to run certain experiments.
The glovebox has a transparent face and is fully enclosed,
so it should be free from air currents inside. After much
practice, I can manage to release the small square, and get
it to float fairly motionless while I close up the glovebox.
Then by shining a flashlight in through the front, I find
that I can slowly accelerate the reflective film square. After
shining the flashlight on it for about 30 seconds, the square
will be moving a few tenths of a centimeter per second. One
thing I am not sure of is that this effect is due to radiation
pressure. As my friend Pawan pointed out, any small differential
heating between one side of the film and the other could cause
a force from air molecules ricocheting off the film slightly
faster on one side. But since the film is extremely thin,
the differential temperature from the illuminated side to
the other side should be small. In addition, the film is a
reflective silver color and so should reflect most of the
light rather than absorbing it and heating up.

My very
rough order of magnitude calculations are that the acceleration
is about right for the expected light pressure. I don’t know
the mass of the piece of film exactly, but estimated it by
guessing that if stacked up there would be roughly 500 layers
in a centimeter, and assuming a density of twice that of water.
I then estimated that the flashlight (one of those big ones
with 4 D-cells) puts out about one-tenth the light per unit
area as sunlight (I measured this by using the light-meter
from a camera). The solar illumination is about 1 kilowatt
per square meter, so I used a value of 100 Watts per square
meter for the flashlight. By my calculations after 30 seconds
that should lead to a velocity of order a half mm per second
– which is pretty close given the uncertainties in all my
estimates. I’ve been trying to figure out a way to experimentally
rule out differential heating, but I am running out of time
– we only have a few days until Expedition 8 gets here! I
guess it will have to wait until my next flight.

So there
you have it, partial victory, in a sort of legalese fashion.
Well, even if I am wrong, at least I’ll be 0.007 seconds younger
than everyone else when I get home!

This is
the glovebox with the reflective film square floating inside
and the flashlight floating outside.