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Ed Lu Letters - 10/24/03(2)



Submitted by Arthur - N1ORC
 
Expedition 7

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!

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