To Boldly Go Where …

20120508-113303.jpgPreviously in “Armchair Physics“, I said that if you were on-board a spacecraft that was under constant acceleration, you could continue to accelerate indefinitely.

The “limit” of the speed of light is an observational, or relative to something else, limit. That is, if you stand in your backyard and, looking up at the sky, observe something that is moving extremely fast (relative to you), you will be unable to measure (perceive) its velocity as greater than the speed of light. Also, at that same relative-to-you velocity, you would measure its mass as approaching infinity and, if there were a clock on-board that fast moving object, you would see that clock as nearly standing still.

But what if you change your viewpoint? What if you are on-board that fast moving object?

“Beam me up, Scotty!”

You can now look out a window from the spaceship and see Earth moving in the opposite direction. Using a telescope from your perch in that spaceship moving at or very close to the speed of light, you would see clocks on Earth as stopped and the Earth’s mass as infinite.

But you personally, on board that fast moving spaceship, would be unchanged. You wouldn’t weigh more than normal and the second hand in your wrist watch would still be ticking along at the normal rate (to you) just fine.

As you see it, everything would be normal.

If you then decide to fire up the engines, it would start spewing stuff out the back end and you would accelerate. And if you kept the engine running long enough, eventually you would be moving, relative to where you started, at a velocity faster than the speed of light.

“Warp Factor Two, Mr. Sulu!”

How long would that take?

Here’s the formula: v = u + at, where

  • v = Current velocity
  • u = Initial velocity
  • a = Acceleration
  • t = Time (duration)

So, if we take a standing start (u = 0) and accelerate with 1G — the same as you feel right now on your bottom pushing down into that chair — and keep it up for not quite a year (353.8231859 days or 30,570,323 seconds), you would then be going faster than the speed of light … relative to where you started from, that is.

Cool!

You could say that relativistic effects are a problem only if you relate.

Another way of viewing this is to say that each of us drags along our own little private bubble of space and time, and it is only when one object’s space-time interacts with another object’s space-time do we run into these mind-bending issues.

But there is one problem with the scenario I’ve described. That problem is fuel.

Sir Isaac Newton said that if you want to go faster, you have to throw something out the back. The more you throw out the back and the harder you throw it, the greater will be your acceleration.

You need mass to throw, and energy to throw it. And you need enough of both to keep doing that for a long time.

I suspect you’ll agree that, even without running the numbers, that’s gonna be a big pile of coal to cart along into space. And worse, you’re gonna have to accelerate that coal so it comes along with you. At the very beginning when you have all that coal on-board, you’re gonna have to burn a huge amount of it to get everything moving.

That’s why the first stage of rockets are so big — they have to lift not only the payload, but also all the fuel that’s gonna be burned through the remainder of the launch. The liquid oxygen and liquid hydrogen burned by the Saturn V’s first stage to start Apollo 11 on its trip to the moon was HEAVY!

In your spaceship and as your fuel supply burns down, it won’t take quite as much to keep up the 1G acceleration. But, oh brother, those first few months you’re gonna be shoveling like mad to keep the engines fed.

Don’t forget that all this is what it looks and feels like to you on that accelerating spaceship. Your mass, your time, your space looks entirely normal and all the physical laws of space and time apply just fine — within your frame of reference.

Someone looking on from the outside is gonna see (and measure) things very differently. Relativity is “relative”.

To keep ourselves from getting distracted, let’s close that window on the spaceship so you can’t look out.

Just keep shoveling; just keep the acceleration going.

And, come New Years day, your velocity will be up to 1.03 times the speed of light. You will then be traveling ever so slightly faster than the speed of light, relative to when you started.

Keep it up and, on your second anniversary in space, you will be moving away from Earth at 2X the speed of light.

Neat!

If only we could solve that darn fuel problem…

Uhm, how much is gas where you live?

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