## Instead of trying to achieve the speed of light why not just make spacecraft go a certain mph?

Question

For example make a drive that will power a spacecraft go 200,000 or more piles per second, forget about the speed of light.

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General Physics
4 years
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## Answer ( 1 )

The answer has to do with space and time and energy. There’s a certain theoretical minimum amount of energy required, if you want to accelerate a mass “m” from zero to a given speed “v”. For centuries, we thought that amount of energy was:

E = ½mv²

(This was based on our classical understanding of work, force, distance, and time.)

Then along came Einstein. He demonstrated convincingly that the universal constant “c” (a.k.a. “the speed of light”) was woven deeply into the structure of space and time. So much so, that a lot of our classical formulas involving time and motion and distance and energy, had to be revised. It turns out that the revised formula for the energy required to accelerate a mass to speed “v” looks like this:

E = mc²((1/√(1−v²/c²))−1)

These two formulas look really different; so the obvious question is, “How could we have gone for centuries without noticing the discrepancy?” Well, it turns out, if you graph these two formulas, they line up together almost perfectly until “v” reaches many millions of miles per hour. The fact is, at the everyday speeds in our everyday world — and even at the speeds of planetary orbits, which are “only” tens of thousands of mph — the two formulas both give you almost exactly the same answer for “E”. In fact, for most everyday engineering work, the “½mv²” formula is still used (because the math is simpler).

(Here’s a graph I found: https://upload.wikimedia.org/wikipedia/c… The green curve is the “classical” energy formula, and the red curve is the formula as revised by Einstein. The “speed” at the bottom is shown as a fraction of “c”; so “0.5” means half the speed of light.)

When “v” is so fast that it’s a significant fraction of “c”, then the two graphs really start to diverge, and in particular, the “E” in the second formula (the _correct_ formula) becomes much, much greater than the “E” in the first formula. Experimentally, when we’ve accelerated (subatomic) particles to nearly the speed of light, we’ve found that the energy requirements follow the red curve rather than the green one.

And indeed, as you can see in the “revised” formula, when v=c, you get a zero in the denominator, which means “E” becomes INFINITE. In the graph, you can see the red curve trending straight upward at that point.

What this means is that, according to our current understanding of the structure of space and time and energy, it would require an INFINITE amount of energy to get any mass to reach speed “c”. The only things that can travel at speed “c” are mass less particles (like photons).