Tuesday, April 21, 2015

Relativity: Something You Might Not Have Realized

Einstein's theory of relativity means that the faster you go, the slower your time moves with relation to an observer who is not travelling at your velocity. At regular Earth speeds this is such a tiny fraction of a second that it doesn't matter much, but at interstellar speeds approaching the speed of light, the effect becomes noticeable. Most of you already knew something about this, but did you know what that time dilation actually means for space travel? It means that from a space traveler's point of view, objects are actually closer than you might think.

How far is the nearest star?

Proxima Centauri 4.24 light years. Thanks Google.

That's the hard and fast answer, but you might be surprised to know that it's not really hard and fast at all, and I'm not talking about star orbits.

Hop on a fast-moving spaceship and relativity is going to change your mind about how far it is to Proxima Centauri. Mission planners on Earth will say that for an object travelling at 0.5 c (half the speed of light) it will take just over 8 years to reach Proxima Centauri (exactly 8 years to travel 4 light years, assuming no time is spent accelerating or decelerating).

But the pilot of the spacecraft will tell you a different story. While travelling at 0.5c Proxima Centauri will actually be just 3.67 light years away. Travelling at a constant 0.5 c you'll get there in just 7.34 years. A round trip will take 14.68, but on Earth the spaceship will return right on time, 16.96 years later.

What happened? According to the space travelers, Proxima Centauri was more proximal than they thought. According to us on Earth, nothing changed. The distance shrank for the travelers, but not for us. How about that for strange? It's called "length contraction."


I thought that things shrinking (length contraction) was an optical illusion. But the text says that it is not. If not, then how does something shrink? Answer:

Time dilation and length contraction are not just optical illusions, but neither do they represent a physical contraction. These effects are the result of a measurement from a given inertial frame that is performed on body moving with respect to that frame. We assume that the measurements always take into account the finite travel time of light. Consider two observers moving relative to one another. You have no difficulty with the idea of their velocities being relative - each thinks the other is "really moving." In SR, time intervals and space intervals are also relative. You don't shrink or see your own clock run slow. The other observer sees your clocks slow and meter sticks contracted from his frame. Similarly you will observe his clocks slow and meters sticks short from your frame. The time dilation and length contraction are inherent properties of the way measurements must be performed in spacetime. (Source: http://www.astro.virginia.edu/~jh8h/Foundations/quest7.html)
Now what do you suppose this means for something travelling at the speed of light?

It means that distances become infinitely small. Zero in fact. For the light-speed object, not us. What does that mean? Suppose you were a photon. How would you experience time passing?

"If you want to be anthropomorphic about it, a photon doesn't experience the passage of time. To it, it is everywhere at once. (Source: http://www.astro.virginia.edu/~jh8h/Foundations/quest7.html)"

So there's some literal truth to the saying that "God is Light" if you want to point to something in our universe that is omnipresent, at least from its perspective. Of course, light isn't alive, sentient, or a deity, as far as I know, but it's still interesting to think about.

So what if you could move at the speed of light? I suppose you would be everywhere at once, too. Now there's a plane of existence for a real live deity.

Sources: http://www.astro.virginia.edu/~jh8h/Foundations/quest7.html http://www.orionsarm.com/fm_store/RTTCalc.htm http://science.nasa.gov/science-news/science-at-nasa/2006/22mar_telomeres/