We sometimes say that dogs are living in the now. Sometimes we say that of people who live in the moment and don’t think much about the future (or about the consequences). Whether we mean that as a compliment — as we generally do with dogs — or as an oblique implication of shallowness depends on the point we’re making.
There is the tale of the ant and grasshopper; it divides people into workers who plan for the future and players who live in the now. The former, of course, are the social role models the tale holds heroic. The grasshopper is a shifty lay-about, a ne’er do well, a loafer and a moocher, but that’s not the point.
The point is our sense of «now» and of time.
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!
A couple of readers have asked about the diagrams in this series of Special Relativity posts. I created them with the freeware 3D ray tracing application, POV-Ray. The diagrams are actually three-dimensional “scenes” designed to be viewed as flat pieces. If some of the “dots” look more like little spheres, that’s because they are!
I wrote some introductory posts a while ago (here, here, and here). You can read those if you want more details about the application.
For a little (optional!) Friday fun, I thought I’d share some POV-Ray images that have a bit more “dimension” to them.
My Special Relativity “icon”!
This week I’ve introduced you to time-space diagrams. They’re the foundation of everything that follows in this series, so I hope you’re feeling very comfortable with them.
I also introduced you to space-time events, and I apologize for any confusion in calling the diagrams “time-space” and the events “space-time.” Six of one, half-dozen of the other. I wanted to stress the time component of the diagrams, whereas space-time is the more usual general term.
Today we wrap up the week with some important diagram details.
Last time I introduced you to the idea of a space-time event. In physics, an “event” has the same meaning as when Hollywood blares out about a “major motion picture event” — that is to say, nothing at all special — just something that happens at a specified location and time.
If you attend a social event, it has a location and a time. When we talk about space-time events, all we mean is a specific location and a specific time (hence the name, space-time event).
Today we’ll explore some interesting aspects of such events.
The last two posts introduced and explored the concept of time-space diagrams. This time I’ll complete that exploration by using them to consider motion from two points of view. This will be an exercise in application of our diagrams.
I’m going to connect that application with something I stressed last week: that motion has a symmetrical component. It’s perfectly valid to think of the world moving past the train as it is to think of the train moving through the world.
It happens that here our dueling points of view are resolved by something else I discussed last week. See if you spot it before I mention it.