Relativity Facepalm
Sometimes there are no words available to describe
just how stupid something is.
Mike was one of those curious types who wanted to learn how everything
worked. He liked to read about science and often watched
documentaries. Lately he’d been reading about
relativity. He thought he understood parts of it but was
confused about the other parts. So he decided to travel to a
nearby university where he could ask one of the professors who taught
the subject...
Mike: “I’ve been reading a lot about relativity and find it
somewhat confusing. I was wondering if you could help me out.”
Professor: (chuckles) “Well it is tricky subject I’ll
admit. Many people have trouble adapting to it. I
also did at first. Let’s see if I can explain.”
Prof: “Relativity tells us a number of things.
First it tells us that all velocity is relative. Or as we
like to say, there are no preferred frames of reference.
Secondly it tells us that light moves at a constant speed relative to
all observes. As a result time slows down when travelling at
high speeds. Or as we sometimes phrase it: moving clocks run
slow.”
Mike: “OK, I understand the first part about velocity being
relative. But the second part is confusing. If I
have two clocks moving independently through space, which one can I say
is moving instead of standing still?”
Prof: “Allow me to draw a diagram.”
The professor picked up some paper and drew a diagram of the Earth with
two clocks on it.
Prof: “See these two clocks sitting on the Earth’s
surface? They are not moving with respect to each
other. So we can reasonably describe them both as motionless.”
Mike: “OK.”
Prof: “Now suddenly one of them launches into
space. It keeps accelerating until it reaches a speed of,
let’s say, 87 percent of lightspeed with respect to the other
clock. We can now determine the Space clock is ticking at
half the rate of the Earth clock.”
Mike thought about this for a while.
Mike: “So you’re saying acceleration causes the time
dilation?”
Prof: “No, acceleration has nothing to do with it.
We calculate the amount of time dilation based on velocity.”
Mike: “But isn’t the Earth clock also moving at 87 percent of
lightspeed relative to the other clock?”
Prof: “You could argue that. But remember, we
agreed earlier that both clocks were motionless. Or at least
relatively motionless. Now you’ll note the Earth clock has
not undergone any acceleration during that time. So it must
still be motionless, and therefore it would not have experienced time
dilation.”
Mike: “I’m a bit confused. It seems as though you
are using the Earth as a special reference point to measure velocities
against. Is that right?”
Prof: “Certainly not. Preferred reference frames
are strictly forbidden in relativity. My example would work
regardless of where the starting point was.”
Mike: “OK then, forget Earth. Pretend these two
clocks were the only things that existed in the Universe.
They are moving apart from each other. Does time dilation
apply here?”
Prof: “Of course.”
Mike: “So which clock experiences more dilation?”
Prof: “The one that’s moving faster.”
Mike: “But which one is that? I no longer have
anything to measure their velocities against, except each other.”
Prof: “OK, what are their respective velocities then?”
Mike: “I don’t know.”
Prof: “Well I can hardly answer your question without enough
information.”
Mike wore a confused expression.
Prof: “Alright. Let me see if I can help
further. Come have a look at this board.”
They walked over to a chalkboard. On it was a spacetime diagram
and the Lorentz transforms.
Prof: “These are the Lorentz transforms. They allow
us to calculate the exact amount of time dilation in any
situation. You’ll notice there are transformations for
distance as well as time. There is also an inverse set that
allows you to calculate it backward.”
Prof: “Many skilled mathematicians have checked them over and found
they are perfectly balanced. I have checked them myself.”
Mike looked over the chalkboard and scratched his head.
Mike: “So will these equations tell me which clock is moving?”
Prof: “Of course.”
Prof: “But first you need to specify which is motionless.”
Mike: “Uhh... OK. So if I specify the clock on the left as
motionless, then the one on the right experiences time dilation.”
Prof: “Correct.”
Mike: “But if I specify the clock on the right as motionless, then the
one on the left is running slower.”
Prof: “Also correct. As you note, all velocity is relative.”
Mike: “But if two people specify different clocks as motionless, we
determine that each clock runs slower than the other. That
sounds like a contradiction.”
Prof: “Not at all. Each clock will see the other as running
slower.”
Mike: “Now I’m confused. I thought time dilation was a real
thing, not a perception.”
Prof: “It’s a real perception, yes.”
Mike was now lost for words.
Prof: “In science, we need to be careful about what we
describe as ‘real’. Reality is what we measure. In
the end, it’s the experimental results that count.”
Mike: “Umm... go on.”
Prof: “Alright I can see you’re confused. Allow me to provide
some historical background.”
Prof: “The first problem that relativity was called on to
resolve is something called Maxwell’s Invariance. Come and
I’ll show you.”
They walked over to a bench. On it was a coil of wire
whose ends were connected to a current meter (an ‘ammeter’).
There was also a small bar magnet.
Prof: (picking up the coil and magnet) “If I hold the coil
still and move the magnet toward it, you’ll notice the ammeter shows
a current flowing.”
Mike: “OK”
Prof: “Alternatively, if I hold the magnet still and move the coil
toward the magnet, I register the same current flowing. This
tells us that velocity is relative. I can also get that
result by moving them toward each other, each at halfspeed.”
Mike: “Makes perfect sense.”
Prof: “Exactly. Maxwell’s equations tell us the induced
current will be a function of relative velocity only. Now
here’s where special relativity comes into it.”
Prof: “If we assume that the speed of light is constant for
each observer, this creates a problem. Because if I move the
magnet toward the coil, the coil would still see the electromagnetic
field from that magnet arriving at the speed of light. It
should make no difference whether the magnet was moving or not!”
Prof: “To get around it, we need to use Lorentz transforms to
shrink the apparent distance between the magnet and wire.
This perfectly resolves the problem and shows the transforms are
correct.”
Mike thought about this for a while.
Mike: “Well that’s interesting. But what if I don’t assume
that light’s speed is constant for the observer. It seems I
wouldn’t need to apply the transforms. Is that right?”
Prof: “That’s true. But really, this is not the
important experiment to consider.”
Prof: “The important experiment came later. It was
the Michelson Morley Interferometer. By putting light through
an apparatus in perpendicular directions, they noticed it made no
difference what the direction of travel through the assumed aether
was. This showed that the speed of light was constant for all
observers.”
Mike: “Yes I read about that. Apparently though,
there are a number of different explanations for the experiment that
don’t involve relativity. How do we know which is correct?”
Prof: “Well, because we have many other experiments to
support relativity. Probably the best one is the
GPS. It involves both special and general
relativity. The people who set it up noticed that it
precisely conforms to both predictions. As a result, it is
necessary for special adjustments to be made otherwise the system
wouldn’t work. In fact you might have used a GPS receiver to
come here. So your being here is proof that relativity is
true!”
Mike: “Wow that’s impressive evidence! So
how can we check the satellites and see how much time dilation has been
applied?”
Prof: “You can’t check them. The GPS is a military
setup, originally used to target missiles to the correct location, and
uses special encryption in the process. No average scientist
would be allowed to examine it closely.”
Mike: “Umm, so how can you confirm what the adjustments are?”
Prof: “We have been told what the adjustments are.
We take it on good faith that they are correct.”
Mike: “Hang on a tick. I thought you scientist guys
are supposed to be always crosschecking and validating each other’s
experiments.”
Prof: “Ordinarily yes. But the GPS has been
wellvalidated already. There are millions of people out
there using it. Also don’t forget there are hundreds of GPS
receiver manufacturers. They would be well aware of the
relativistic adjustments.”
Mike: “So they build the adjustments into their receivers?”
Prof: “No because the adjustments are done in the
satellites. There’s no need for manufacturers to build them into
the receivers.”
Mike: “So umm... how do we confirm what the adjustments are?”
Prof: “Like I said. The system works well and has
thus been wellconfirmed already.”
Mike had a feeling he was going round in circles.
Mike: “OK. Is there some other experiment we can
do? I mean, where we can confirm the results directly?”
Prof: “Absolutely. Probably the best one is the
muon decay experiment.”
Prof: “As luck would have it, one of my postgraduate
students is working on this right now, and using it to confirm the
accuracy of relativity. It’s taking place on a nearby
mountain. Here, let me give you the address. Tell
him I sent you.”
Mike: “Many thanks. I’ll do that.”
Mike drove out to the mountain where he met up with the experimenter.
Mike: “Hi there. The Professor sent me.
He tells me you are using muon decay experiments to confirm
relativity. Could you tell me how it works?”
Experimenter: “Sure. Muons are special particles
that are created at the top of the atmosphere and have a very short
lifespan. Even if a muon was going at the speed of light it
should only travel a short distance before decaying.”
Exp: “But instead we observe them going much
farther. Today I’m finding them going five times the distance
than classical mechanics would predict. This shows they are
experiencing time dilation.”
Mike thought about this for a while.
Mike: “OK. But what if the muons were going five
times the speed of light. Wouldn’t that also allow them to go
five times the distance before decaying?”
The experimenter appeared aghast.
Exp: “But that’s preposterous! Nobody would ever
consider such a possibility. You have no idea how many laws
of relativity that would be violating.”
Mike: “Uhhh, but aren’t you supposed to be using this
experiment to see if relativity is true or not?”
Exp: (regaining composure) “Well, sure. But
anyway what you’re proposing couldn’t be true, because we measure their
speed and know they are going slower than light.”
Exp: “Come over here and I’ll explain.”
They walked over to see the detecting equipment which had a large block
of iron over it.
Exp: “See this block of iron? This is what we use
to confirm the muons are going less than light speed.”
Mike: “How does it work. Is it some kind of radar
device?”
Exp: (laughs) “Not exactly. What is does is filter
out muons that are going less than a certain speed. We know
how much energy is required for lowspeed muons to penetrate a certain
thickness of metal. We just extend that to calculate the
required thickness for highspeed muons.”
Mike: “I read about this. Apparently for relativity
you need to use different energy equations, rather than the traditional
kinetic energy equation for classical mechanics.”
Exp: “I see you’ve been studying. Very good!”
Mike: “So which energy equation do you use? The
classical or relativistic one?”
Exp: “The relativistic of course. The classical
equation is only applicable for lowspeed situations. Here we
are dealing with highspeed particles. We need to rely on the
relativistic equation.”
Mike: “OK. But if you used the classical equation
you’d calculate speeds faster than light, correct?”
Exp: “That’s true. But like I said it’s the wrong
equation to use in this situation. This is a relativistic
scenario and we must use the proper equation.”
Mike: “So if I understand correctly, in order to use muon
decay to prove relativity you first need to assume relativity is true?”
Exp: “Yes. But everyone knows relativity is true so
it’s not really an issue.”
Exp: “There are other experiments I suggest you look
at. Like Maxwell’s invariance and the GPS. They are
useful for proving relativity. What I’m doing is just
confirming the extent of relativity.
At this point Mike found he had developed a headache and needed to
excuse himself. He later decided a scientific career was not for him and
took up a different hobby.
