This blog is nearly four years old (I started on July 4th, 2011). This post makes it exactly 500 posts here on Logos Con Carne. To commemorate it, I’m giving myself the 500 Odometer Award (which I built myself from various electrons I had laying around).
As part of the party, this post consists of miscellaneous odds and ends that have intrigued me lately. I’ll leave it to you to decide which are the odds and which are the ends.
We’re finally sliding into home plate in this series (it’s baseball season, so I get to use baseball metaphors now). After spending a lot of time looking into how Special Relativity works, we’re able to at last explore how it applies to the idea of faster-the-light travel.
Last time we saw that FTL radio seems hopeless — at least at communicating between frames of reference in motion with regard to each other. It’s possible there might be a loophole for FTL communication between matched frames. (If nothing else, it may be fertile background for some science fiction.)
Today we examine the idea of FTL motion — of “warp drive!”
Over the last five weeks I’ve tried to explain and explore Einstein’s Theory of Special Relativity. We’ve seen that motion, velocity, simultaneity, length, and even time, are all relative to your frame of reference and that motion changes the perceptions of those things for observers outside your frame.
All along I’ve teased the idea that the things I’m showing you demonstrate how the dream of faster-than-light (FTL) travel is (almost certainly) impossible. Despite a lot of science fiction, there probably isn’t any warp drive in our futures.
Now it’s (finally) time to find out just exactly why that is.
This week I’ve focused on the relativity of time under motion, and we’ve seen that moving very fast allows “time travel” into the future. Very handy if you don’t mind the one-way trip. What’s more, a spaceship capable of such a flight is physically possible, so it’s a “time machine” we know works!
On Monday I described how fast-moving, but short-lived, muons created high in the atmosphere live long enough to reach the ground due to time dilation. That’s just one place we see Special Relativity actually working exactly as Einstein described. For another, fast-moving particles at CERN have decay times showing they, too, have slow clocks.
As we’ll see today, light’s behavior requires time appear to run slower!
Last time we saw that Em non-paradoxically time-travels over three years into Al’s future by flying 12 light years at half the speed of light for just over two decades. Her journey completed, Em has aged only 20.8 years while Al has aged 24.
That may not seem like much of a gain, but Em was only moving really fast — not really, really fast. If she travels at 99% of light-speed, her round trip shortens to 1.7 years while Al doesn’t wait much longer than it takes light to make the six light-year round trip: 12.12 years! And at 99.9% c, Em’s whole trip takes her only half a year!
Today we break down dime tilation. I mean, time dilation!
So far this week we have Em taking a round-trip to planet Noether at half the speed of light. Upon her return she discovers that, while she’s aged 23.8 years, Al (who stayed home on Earth babysitting Theories) has aged 27. It took her well over twenty years to do it, but Em effectively traveled 3.2 years into the future.
Last time we saw that — so long as Em is in constant motion — there is symmetry between Al and Em with regard to who is moving and who isn’t. Both can claim the other is (or they are). Both views are valid. Until Em stops. Or starts, for that matter.
Today we look at Em’s “time shadow” — it’s a key to the puzzle!
Last time we watched friend Em make a six light-year trip to planet Noether while friend Al stays home on Earth working on Theories. It turns out that Al ages 27 years while Em ages only 23 (point 8). This is not due to special diet, but to Special Relativity slowing Em’s clock on account of her fast motion through space.
We also saw that once Em stops at Noether, this breaks the symmetry of the two valid points of view regarding their motion (Em and ship are moving vs Al, Earth, and space, are moving).
Today we examine the trip before that point, while it is symmetrical.
We’ve covered a great deal of ground in the last four weeks. (Writing a series of posts this long is a new experience for me! I hope you’re getting something out of it, too.) We’ve learned that motion, velocity, simultaneity, and length, are all relative to your frame of reference — motion changes your perception of these things. This week we’ll see that time is also relative — motion changes that, too!
So far we only needed a (very imaginary) train to demonstrate the effects of Special Relativity. An Earthly frame of reference was enough to illustrate how motion affects velocity, simultaneity, and length.
But when it comes to time, we’re gonna need spaceships!
Last time I focused on how it was possible for Al to see — even enclose in a tunnel — a train that appears shorter to him due to its motion. It turns out that the train Al sees is a stack of time slices of the train at different moments. As we’ve seen, lots of things look different in a moving frame.
Today I want to say a little about Em’s point of view, run some numbers, and take you through a little math (just one equation, I promise). Then, because it’s Friday (when I try to write about light), I’ll introduce you to light cones.
They’re not actually necessary, but they’re kinda cool.
Last time’s Too Long Train illustration demonstrates that length is relative. Observers moving at different rates measure the length of an object differently. The faster something moves in your frame of reference, the more its length contracts along the direction of motion.
In previous weeks we saw that motion, speed, and simultaneity, are relative; now we see that length is also relative. Next week I’ll talk about the relativity of time. Today I want to dig a little deeper into the length contraction part of Special Relativity.
It’ll be a factor when we get to the spaceships!