Einstein was noted for his thought experiments. He would think up a situation and then mentally chew on it for long periods of time. Sometimes he would come up with some really great stuff.
Maybe I will too … or maybe not but let’s not let a lack of formal education in this area and two beers stand in the way.
Got your feet up? Here’s one for ya.
Current theory says that if a bunch of aliens rockets up Canterbury Drive and past my house at close to the speed of light (relative to me), that dilation of space/time will occur according to the formula:
delta = 1 / sqrt( 1 – V2/C2)
- V is our relative velocity, close to the speed of light, and
- C is the speed of light
- delta is going to be a multiplier we’ll use in just a second
Notice that, in this formula as V gets close to C, V2/C2 approaches 1. When that happens, 1 – V2/C2 gets really, really small. And since that’s in the denominator, the answer, delta, starts getting really, really big.
In other words, when our relative velocity (to each other) is close to the speed of light, that multiplier (delta) gets really big.
What do we do with the multiplier?
Well, if I hold up a ruler as that alien space ship whizzes by — insert sound of Jetsons here — their space ship will appear to shrink (become squished) in the direction of movement. The delta (multiplier) tells us how much it will appear to shrink.
If the aliens are in a long rocket, it will appear to me to be shortened, squished or mashed almost completely flat in the direction of travel.
That’s how a high relative (to each other) velocity affects space.
And it affects time, too.
If there’s a window in the side of the alien’s spacecraft and I can see inside as they shoot past — assuming they measure time with the same kind of clocks we use; maybe they picked one up on their last visit — time passing on their clock will appear to me to be slowed down.
That’s the time effect.
Now, here’s the question.
Inside the spaceship, all the aliens are all traveling at the same speed. They see time passing normally inside the spaceship. They see distance (within their spaceship) as perfectly normal. Time, distance, mass, everything inside the spaceship appears and feels normal.
So, if they have their engine turned on and that engine is still squirting out the same amount of mass that it did when they started, then their perception of the acceleration is also unchanged. Action and reaction, you know?
According to their perceptions they are accelerating at, let’s say 1G, and have been doing so for, well, how about for a very, very long time.
So here’s the question.
According to their perception, how fast can they go? Assuming they don’t run out of gas or whatever they’re using for fuel, won’t they just, according to their perceptions, just keep accelerating faster and faster and faster?
Couldn’t they, given enough fuel, accelerate right up through all the Warp numbers ever heard in Star Trek?
Put yourself in the spaceship now.
Let’s say you have a telescope, a really good one, and you are looking out the back toward home as you rocket away from Earth. As you go faster and faster away from home, time (on Earth) will seem to be going slower and slower.
And if you accelerate as you move away and continue building up speed, at some point your velocity, relative to Earth, will approach C and, as far as you can see, time will slows or stop back on Earth.
But of course, back here we’re all fine and time is moving along just like normal. It’s only our perception of each others time, space, mass and energy that’s messed up.
And if you keep accelerating — remember, your acceleration is a function of the mass your spaceships squirts out the back, and that’s a relative motion — you will continue to accelerate, right up and then through C, as perceived as the relative motion between you and Earth.
C is not the limit to how fast you can go. It just, and I mean this quite literally, “looks” that way.
How about another beer?