Tuesday, November 07, 2006

In Space, No One Can Hear You Sing Happy Birthday

UPDATE: I realized later this week that the following narrative is deeply flawed. Bridges are not merely teleportation devices. For more commentary, see the newer post here.

For those blog readers not familiar with general relativity, here is a more detailed example of how Bridges allow time travel.

Note this is not "time travel" as in some stories, where people move back and forth in history. What happens is much less dramatic: objects do not age consistently in space, and Bridges let you see this happen quite clearly.

(Thanks to this site for doing the math for me. I just used their calculations for my own application.)

Consider a spaceship that leaves Earth, and accelerates at 2 g's for 100 days, until it is moving at about six-tenths the speed of light. It is heading for a destination six light-years away. But because it is moving at a relativistic speed this distance, from the point of view of the spaceship, shrinks to only 4.8 light-years.

From the point of view of the spaceship, this trip takes 8 years (4.8 divided by 0.6). From the point of view of someone watching from Earth, the trip takes 10 years (6 divided by 0.6).

Now, complicate the scenario by assuming the spaceship has a Bridge going back to Earth. In fact, you are the spaceship's pilot, but you live at home and only pilot it as a "day job". According to your watch, you spend half your time on Earth, and half you time at work on the spaceship.

When do you celebrate your birthday?

From the point of view of your friends on Earth, you do this every year from the Earth's point of view. You have ten birthdays during the journey's duration with a party on Earth involving chocolate cake. Of these terrestial celebrations, people on board the spaceship looking back at Earth through super-telescopes only see four of them (the light from the other six birthday parties is still on it's way from Earth to the destination).

From the point of view of your friends in the spaceship, you have a birthday every year from their point of view. You have eight birthdays during the journey's duration with a party on the spaceship involving vanilla cake. Of these celebrations, people on Earth looking at the spaceship through super-telescopes only see two of them (the light from the other six birthday parties is still on it's way from Earth to the destination).

So how many years older are you when you arrive at the destination? Two? Four? Eight? Ten? Or maybe 18, since you've eaten a total of that many birthday cakes?

Clearly not two or four: those are artificial constructs of the fact that light is still en route. No one in either point of view thinks you have really had so few birthdays. But the other answers are somewhat defensible.

Also, any other number greater than eight could be a defensible answer if we had yet another Bridge going to a location visited often with a third point of view. After all, some spaceship pilots might have a more active social life than you do!

Traditionally, physicists say that an object's "true" age is its age from its own point of view. But the fictional existence Bridges destroys the concept of an object "having" a meaningful point of view. Remember that you spent half your time on Earth and half on the spaceship -- neither point of view was inherently more "yours" than the other.

(Of course, you wear a watch and it measures your personal passing through time. But only things with you at all moments during that journey experienced aging as you did. Your body still gets old and wears out in the normal human way, but to other people not following you through Bridges to work and back your rate of aging seems jumpy. Watches are nice, but the fact remains that if every room in your house is actually on a different planet then you have no idea when to pay your annual property tax; the government must either give up property taxes or do taxes separately on each planet when a year passes in its point of view.)

So the existence of Bridges does not allow you to do as paradoxical a thing as going back in history to kill your own grandfather before he had any children. But it does at least mean nothing has an absolute "age". Your library books can still have a due dates, but you might have only eight days to read a book that the library thinks you checked out for ten.

One almost-final note: having a home away from home at a location moving at relativistic speeds unfortunately only means that while there your friends and family left behind perceive you as having lost time. You can't catch up on sleep by taking a Bridge someplace to get a few extra hours for rest.

This seems backwards to real physicists, but we can check by going back to our first scenario. From the point of view of the Earth, six years after you arrive at your destination all the light moving from the spaceship to the Earth during the journey will have finally arrived. At that point, from the Earth point of view, sixteen years have passed but they only saw you eat eight vanilla birthday cakes. So through telescopes your friends and family see that you age half as fast on the spaceship. But they know that's a trick of the light, because a few minutes after you arrived (six years earlier) you took a Bridge home and told them in person of your successful end to the journey.

As a final note, remember the grandfather issue? Well, if you let your own kids play on spaceships (which, after all, can move at a lot more than six-tenths the speed of light) you might be approached a surprisingly short time later by adult grandchildren you never new you had. That's not really time travel. It's just that your own kids are so bad a keeping in touch (sigh), and light moves so slowly...