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Speed of light and time



Ok where do I begin.

Oh yeah. =)

I read this somwhere. It's not entirely accurate but here goes:

"...how long to Andromeda at 1g using Newton's theory? We will add the condition that we wish to stop when we get there, if only to turn around and come back. The best time we can make is achieved by accelerating for the first half of the journey and decelerating for the second. The total time for the trip can be calculated to be some 2,065 years. Rather a long time really. Consider the same journey in an Einsteinian Universe. We now have a limited maximum speed (the speed of light), which at 1g is reached in 30,000,000 seconds, or a little under 354 days. After we reach this speed, how much longer will it take to reach Andromeda? The answer is no time at all! For the distance to Andromeda will have shrunk to zero for the spacecraft. However to the people back on Earth a considerable length of time would pass: some 2.2 million years."

So why would the universe age 2.2 million years if we traveled at the speed of light?! And why would it only age 2000 years if we traveled at a sublight speed!?!

Did I read this wrong? Is this guy an idiot, am I an idiot? am I trippin out! tell me whats up.

Yeh, you probably read it wrong, if it were written right in the first place. You aren't the only one who has trouble with relativity theory. Make sure that the account you are reading was written by some one actually schooled in the theory in the first place.

I think it takes 2.2 million years to get to Andromida at speed c.

However the spaceships passengers would only age about 2000 years due to the supposed effects of 'time dilation".

The time dialation, if you were traveling at "c" would be infinite for the universe outside your ship. You'd have no opportunity to "slow down" and stop off at Andromeda. The universe would advance to the Big Crunch instantly outside your ship. Here's the Lorentz Transformation for t':

Let t' = time dialation for the frame you are observing outside your ship (the rest of the universe)

t' = < (t - (v/c^2) * x)/(sqrt 1 - v^2/c^2)>

You can see in the divisor (sqrt 1 - v^2/c^2) that is v = c, then the formula becomes:

t' = <(t - (v/c^2) * x)/ 0>

t' = infinity

If v = 99.999999999% c, the time dialation is about 12,500,000 years. You'll eventually hit a point before v=c where the dialation takes you to the Big Crunch anyway.

You won't actually hit "c" because that last quanta of energy needed to push you over the "hump" will have an energy requirement greater than what is available in all the universe.

Hmmm...the "<"'s and ">"'s that you see in the formula are supposed to be square brackets, not "greater than" or "less than" symbols. Apparently the board doesn't handle brackets correctly.

I also didn't identify the term "t" in the formula.

Let t = proper time (your passage of time inside the ship)

In the numbers that I posted I set the value of "t", your proper time passage to one second. So, at 99.999999999% c, the K' frame (the universe outside your ship) experiences about 12,5000,000 years for every second of your proper time inside the ship.

Also "x" is the interval (distance) traveled by your ship in the "x" coordinate in 3-space (x,y,z). I set it to "1" in the formula. It's an arbitrary number. No matter what value you plug in for "x" the result is the same.
I searched madly after posting this for where I had found it. I did and It's a correct quote, but I guess he was talking about the 2000 year trip in terms of newtownian physics. He talks about it like way before the example so it's really confusing to read this if you didn't remeber everything on his webpage.

So sorry for wasting your time everyone =P

A slight correct in my results in the earlier post. Ack! I plugged in seconds as the unit of time for the space ship so the unit of time for the other frame is also seconds.

So, one second of proper time inside the ship equates to 12,500,000 seconds of time outside the ship. The ratio for any unit of time is 1:12,500,000.
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