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If you were to have a theoretical object that could double itself along a chain so you would start off with 1 then it doubles to two, four, eight etc eventually the width of the object would be such a large increase the end would move a huge distance but each individual component only moves relatively to the piece it is connected to.

Could you use this object to push against a solid object and a projectile to accelerate past the speed of light?

Charles Bryant
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1 Answers1

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You are actually close to something that is very important in physics, and your intuition is mostly right.

A rigid pole that doubles its length every so often does not exist. However, in most modern theories of cosmology the universe itself is expanding. This means that a given area of vacuum (say 1 meter across) will grow exponentially with time, so will double in length over some (very long) timescale, then double again in the same time then again and again. This doubling again and again is very much like your proposed "doubling pole".

Now, a consequence of this model of universal expansion is that their are some places in the universe we can never reach. Imagine some galaxy that is "far far away". This galaxy is so far in fact that even though the distance between us and it will take a very long time to double the rate of extra space produced by this doubling is faster than the speed of light (which is the maximum speed we can travel).

To understand why this is an analogy might help. Imagine that you earn 3 dollars per day (this represents you travelling at light speed, $3\times 10^8 m/s$), if you have a loan that grows by 1% per day then (for a sufficiently large dept, in this case over 300 dollars) the amount of money you owe will grow faster than you can possibly pay it off - because of the power of compound interest. The 300 dollars is the distance you initially had to cover, the 1% interest is the expansion of the universe.

So their are galaxies that are, in a sense, moving away from us faster than the speed of light by roughly the mechanism you describe. In fact everything beyond the "Hubble Radius" is effectively receeding from us faster than lightspeed because of the "compound interest".

For more material see:

https://en.wikipedia.org/wiki/Expansion_of_the_universe

and:

https://en.wikipedia.org/wiki/Hubble_volume

Dast
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