A seam in the multiverse

Strange things happen at my house. Mostly computer stuff: the sound on my desktop refuses to mute when I ask — no, demand — it; printers mysteriously chat with each other in the dead of night and print out seemingly — only seemingly — incomprehensible reports on their meetings; my ebook, charged to within a nanometer of its battery’s capacity, is dead in the morning despite having been turned off, then charges up perfectly and is fine. It’s possible the ebook is an invited non-voting observer in the printer meetings, but it doesn’t seem to attend them all.

Well, ok, I thought, maybe Julian Assange is using my stuff to communicate with Putin, or something. There are oddly slow periods on the internet, and recently my router went on strike and I had to bring in a scab, which is working fine, but some of my other electronics are behaving strangely since the switch. I am willing to admit I can’t fully control my cyber-paramours. But this morning, the insurrection spread to something not even attached to the internet: my coffeepot.

My habit is to freshly grind some coffee at night before I go to bed, and get everything ready so that when I wake, all I have to do is poke a button, and Bob’s your uncle. Don’t laugh, I actually have an Uncle Bob, although he died at the age of five back in nineteen ought something or other. Anyway, this morning I smugly poked the button, ate my breakfast, and went to pour myself a delicious cuppa.

All I got was hot water.

Damn, I thought, I forgot to put in the coffee! It’s happened before, though rarely. So I opened the top, and, what the hell, there sat the filter, and in it was the proper amount of ground coffee, dry, as they say, as a bone. This is where String Theory, multiverses, and what-not come in. The design of the coffeepot is such that the heated water literally has nowhere else to go but through the coffee and into the pot, unless it clogs completely, in which case it would erupt all over the counter. Which it did not do.

You may have read a piece I posted recently about Shakespearean monkeys, in which I pointed out that, according to the theory of probability, there was no reason they couldn’t crank out, say, Henry V the minute they sat down rather than eons later. Similarly, if we are but one universe in a bubbly lather of multiverse, and if these bubbles, each containing it’s own set of physical laws, are bound to encroach on each other eventually, why not now, and why not at my house?

On the other hand, is it possible I inadvertently put the carafe, still full of water, in its place without first pouring the water in the reservoir?

Nah!

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.

Damn that Galileo!

I find myself thinking about Galileo, for no apparent reason, and his famous Tower of Pisa experiment, which he may or may not have actually performed.  You know the one: dropping two balls of unequal mass simultaneously to show that acceleration due to gravity is independent of mass.  In short, the two unequal balls arrive at the earth at the same time.  In physics, this is an example of what is known as the Weak Equivalence Principle (WEP), which I point out only for the pleasure of using such a silly term.

Despite being undeniably true, this is, to me, counterintuitive.  Think of the implications.  Suppose you are in the vacuum of space, maybe took a wrong turn on the way to the coffee shop, or something.  About ten feet away is a softball.  According to the WEP, you and the softball will move towards each other at exactly the same rate as you and the earth, if it were ten feet away.  Lucky for you, though, the damage inflicted by the softball will be considerably less than that inflicted by the earth in a similar situation.  Okay, the softball is much smaller and has much less mass than the earth, so what’s my point?

Let’s substitute something else for the softball, say, the moon.  By the magic of imagination, retracing your steps to see how you missed the coffee shop, you find yourself ten feet from the moon.  Once again, you and the moon move together at that same rate, independent of mass.  This time, though, you will definitely feel something when you finally make contact, because the moon is much, much bigger than a softball.  (Never thought you’d see that phrase in print, did you?)

We’ve all seen that footage of Neil Armstrong bouncing about on the moon.  I love that little tune that he sings, by the way.  Anyhow, it’s apparent that jumping that high on earth would result in much more jarring to the body.  But the moon, though smaller than the earth, is easily sufficiently massive to stop you cold when you hit it.  Remember, starting at ten feet away, you will strike the surface of the moon at exactly the same speed as you would on earth, coming to a full and immediate stop in both cases, or as close to full and immediate as measurable.  So why is there more damage to your poor, unsuspecting body when you do it on earth?

I remember reading a variation on this question years ago, in some “Ask the Scientist” thingie: if two cars of identical mass collide, how is the force different from one of those cars hitting a stationary wall?  Mr. Scientist, no doubt sighing inwardly, patiently explained that it had to do with the momentum of both masses.  To get the same force with just the one car, it would have to be going twice as fast, and even the thickest of us can see the difference there.  But what if you substitute a mountain for the wall?  Or drop the car from a sufficient height so that it’s going the same speed at impact as in the collision with the wall?  Even double the speed, to take account of the second car?

Or jump off a ten foot platform on the moon?

Don’t mind me; I still can’t see why levers work; and don’t even bring up pulleys.

Magic

Levers.  To me, they hold the key to all the mysteries of the universe.  Why does one thing follow the last?  Why is the speed of light – the speed of it, not light itself – immutable?  How can an attribute be more fundamental than the thing itself?  How can something come from nothing, and return to it?  How can two things as different as mass and distance be so intimately intertwined?

Everyone knows the formulae involved; that’s not what I’m talking about.  That work equals force times distance is definitional, and intuitively satisfying, given the ordinary meanings of the words in the equation.  We can relate to pushing a one ton weight a distance of, say, ten meters.  That’s work, by god!  But just between you and me, those aren’t really words; in this case, they’re mathematical terms masquerading as words:

 F = ma
W = Fd

For example, we accelerate a mass some distance by applying force to produce work, but we would never think of producing mass by dividing work by the product of acceleration and distance.  How would we even go about such a division?  Words literally fail us here!  Not so mathematics:

m = W/ad

The disturbing thing here is that it’s perfectly true.