Oh, Mr. Einstein, you’re such a kidder!

So, here’s the deal:  my cousin Bert, who lives on the planet Schnipplefarq, and I have devised an experiment.  We have carefully synchronized our watches to Cosmic Mean Time.  I will leave Earth at a prearranged time in my spaceship, which travels at exactly one half the speed of light, making a bee-line for Bert’s house, where he will wait with his notebook to write down the results.  In my spaceship, I will have two items: a red laser pointer, and a high tech bean shooter capable of shooting a bean, also at exactly one half the speed of light.  At a pre-determined time, I will simultaneously point the laser at Bert’s house and press the button, and launch a bean, also at his house.

Since the speed of light is constant, according to Mr. Einstein, and the speed of the bean is relative to the speed of my spaceship, they should arrive at the same time.  Bert will have long since given up, of course, forgetting that our carefully synchronized watches will be way off, since time for me and my watch will pass more slowly than for him and his.

What should happen is that my red pointer light will arrive on time, but magically blue.  Bert, by that time, having decided that I’m hopelessly forgetful, will have put away his notebook and gone back into the house for a quick shot and a nap.  So he won’t notice when the bean also arrives at the same time, having increased to infinite mass due to travelling at the speed of light.  Which is just as well, since Bert, his shot glass, his comfy chair, and his planet will be annihilated by the collision.

Now, you might think what I find bothersome about all this is that time slows down for me, or that a bean could acquire infinite mass just by going real, real fast, but no.  Oh, it’s true that while I’m zipping along relative to Bert, he’s also zipping along relative to me, and why wouldn’t our time distortions cancel out, or that infinite mass would by definition have to include everything else out there, but that’s not it. It’s the concept of speed.

See, we happen to live on a planet that is way, way larger than we are, which gives us the illusion that it’s stationary, so when we think of speed, it’s relative to the great blob of  stuff under our feet.  If we go six mph, we mean six miles of earth has passed beneath us during an hour.  But the earth itself is not standing still.  It’s rotating at about 1,036 mph, and orbiting the sun at about 67,000 mph.  As if that’s not enough, the sun is moving through the galaxy at about 447,400 mph, and the galaxy is moving … well, you get the point.  You are really moving many, many thousands of miles per hour.  Plus six.

All of this speed, of course is relative to something else, us to the earth, the earth to the sun, and so on.  This means that it could be said that when we are moving six mph, the earth is moving that same speed relative to us.  Put another way, two cars, each going 30 mph relative to the earth, might be going anywhere from 0-60 relative to each other.

So what is the speed of light relative to?  According to Mr. E, nothing!  Or rather, itself.

Okay, let’s see.  If I wanted to measure the speed of light, I could count the number of some units of it that pass by during some time interval, like counting power poles from a train to figure out how fast it’s going.  That might be waves, but that’s dependent on frequency, and you get tautological pretty quick doing that.  Or it could be particles, but counting photons is worse than trying to figure the number of water molecules passing in a stream.  You’re left with bursts of light.  So you do that and get a good number.  Then Cousin Bert (still alive for the nonce) does the same thing, with the same bursts, while zooming past you at cosmic speeds.  And gets the same number.

What?  I don’t even know what speed means in that context.

Don’t even ask what would happen if I got the velocity upgrade for the pea shooter.

The mountains and the sea, Part 2

Ah, GPS!  What would we do without it?  Those satellites tell us exactly where we are. That’s what they do, isn’t it?

Well, not exactly.  In fact, the only thing a GPS satellite does is tell you what time it is up there.  For that to tell you where you are, two things are required: two perfectly synchronized clocks, one in the satellite and one in the receiver, and a way to tell exactly how long the signal from above takes to get to you.  The clocks in the satellites are atomic clocks; they’re be accurate for many millennia.  The clocks here are quartz clocks, like your fancy wristwatch; they’re cheaper and you can easily reset them if they get off, something you can’t do to the satellite clocks.  The satellites just send out regularly timed strings of pseudo-random numbers.  The necessary calculations to figure out where we are all done down here.  The receivers generate the same, and then compare the signals to get the lag.  Since we know the speed of light, which is the same as radio waves, calculating the precise distance is easy peasy.

A little sidebar of interest: you know those equations Einstein came up with you thought were only good for bombs and nuclear reactors?  Without them, GPS wouldn’t work worth a damn.  You see, the satellites orbit at about 12,000 miles, far enough for them to be moving significantly faster that anything on the surface of the earth.  So fast, in fact, that time actually slows down for them relative to the earth.  If you don’t take that into account, you’ll end up thinking you’re in the middle of the ocean somewhere.

Cool.  There are enough satellites (27) so that you can get at least 3 or 4 from anywhere on the planet, and can thus pinpoint your location by trilateration.  But there are issues.  The military, which originally developed GPS, also wanted to know the elevations as well as horizontal location.

Remember sea level?  Our lumpy egg of a planet drove us to turn that into an abstract surface, where all points on it had the same gravitational potential.  An easy way to think of that is to think of a surface where an object weighs exactly the same, no matter where it is (yes, if you want to lose weight, just climb a mountain).  This surface is called the geoid, and is less lumpy than earth as a whole, but lumpy all the same.  GPS gives you the actual surface of the earth, but you have to adjust that to sea level to get a useful elevation.  Shouldn’t be a problem, right?

Wrong.  Since the geoid is irregular, there’s no easy way to model it for the computers to work with.  The best we could do was a smoothish egg, kinda-sorta where we thought sea level was, but often significantly different.  What to do?  It turns out that traditional ways of measuring elevation, with spirit levels, was very, very good at arriving at the geoid.

Years ago, I worked as a land surveyor when the military was just developing GPS.  The Defense Department sent out memos to surveyors everywhere, requesting us to set up our receivers at known elevation points every chance we got, and report the official elevation along with the what the GPS receiver thought the elevation was.  It wasn’t too long before an accurate model of the geoid was available.

Now you know what that little flat box does when you tell it to go to Grandma’s house, by the mountains or the sea.

C

I don’t get it. C, that is. The speed of light.

I get that it’s supposed to be constant, and I get that the idea enables us to have GPS and all kinds of other wonderments, and I don’t even wonder why, since the universe gets to have any rules it wants, as far as I’m concerned. I just don’t get what it means that the speed of light is constant. Not light itself, mind you, but its speed. An attribute trumps the thing it’s attached to.

When you’re talking about speed, the first question that pops up is, relative to what? With light, it doesn’t matter, it’s the same regardless of what it’s measured against. If I’m standing still, and you’re moving, we will still get the same reading on our cosmic radar guns. As if that weren’t enough boggle for one topic, yours would arrive a little bluer or redder than mine, because, of course, the frequency, which I would have thought had some relation to speed, is not constant.

What exactly was Einstein on about when he was talking about the speed of light? Clearly, velocity, almost by definition, is what relates time to space, so I get why it should have a central place in a theory that regards space-time as a continuum. But velocity is an attribute, dammit! It has no existence outside of the thing it is a characteristic of. How can it possibly be the root phenomenon of reality as we know it?

Then again, I still don’t understand airline pricing, so maybe such things are just beyond my grasp.