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# 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 light-speed with respect to the other clock.  We can now determine the Space clock is ticking at half the rate of the Earth clock.”

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 light-speed 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.”

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 space-time 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 half-speed.”

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:  “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 well-validated 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.”

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 well-confirmed 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 post-graduate 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:  “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 low-speed muons to penetrate a certain thickness of metal.  We just extend that to calculate the required thickness for high-speed muons.”

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 low-speed situations.  Here we are dealing with high-speed 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.

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