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’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!
The last two train examples (Lightning Strikes and Treaty Train) focused on how simultaneity is relative to motion. Our final train example focuses on how length is relative to motion. The faster something goes relative to you, the more it appears foreshortened along its direction of travel.
This example involves a train that, if it stopped halfway through, is too long for a tunnel — it would stick out both ends. But motion contracts length, so if the train goes fast enough, it becomes short enough to fit entirely inside the tunnel.
And it’s not an illusion; the train really does fit inside!