I believe I know the answer to this but I don’t have the math to show it: If the speed of light were low, could I take advantage of time-dilation to travel great distances in my lifetime?
Suppose “c” was, say, 60 miles per hour. That means it would be physically impossible for me to get to New York in under 30 hours, ground time. But if I accelerate my car up to near 60 mph, the distance would be relativistically contracted and I would experience only one hour of travel time. Press the accelerator a little more and I could get to Alpha Centauri in a month.
I believe what would actually happen is that the mass increase would kill the idea. It would take more and more energy for me to accelerate close to 60 mph. I wouldn’t be able to get any significant time-dilation without burning up 10-to-the-something tanks of gas. Correct?
(Also, there is the problem that Earth would be a black hole, and so would the sun, and I would be frozen to death if it weren’t for the fact that life and I could never have arisen in the first place.)
Would a car even start if the speed of light is 60 MPH? Electricity travels at just under the speed of light, and starting a car requires the electrical system. Even if you could start it, it would probably run horribly because you couldn’t tune the spark plugs nearly as finely, and the Pistons would be at relativistic speed the whOle time the engine was running.
The Big Bang occurred about 13.8 billion years ago. C is about 671 million MPH. So if you’re slowing everything down by a factor of 10 million, we’re only a thousand years or so past the Big Bang. There’s probably just dust very slowly floating around in space right now.
The Lorentz factor, sqrt(1 - v^2/c^2), controls both the time dilation you would experience at a given speed, and the energy required to put into your car to attain that speed. The factor only depends on the ratio between your speed and the speed of light.
So it’s probably fair to say that if you need to get to 99.9% of the speed of light to get the time dilation required to make your trip in reasonable time, your car would be just as capable of achieving that in your “c = 60mph” scenario as it is in the real “c ~= 300 000 km/s” world. I.e. not very capable at all.
It occurred to me after the OP: Energy/mass is c-squared, so decreasing c greatly decreases the energy needed to get to relativistic speeds. Maybe the ideas isn’t dead!
This question reminds me of Redshift Rendezvous by John Stith. It is set on a spaceship whose ftl drive makes the effective value of c quite low inside the spaceship - so that normal activities have to take relativistic effects into account. It’s a mystery, and pretty good.
If one were not equal to one, then everything would be possible. But, alas, one is equal to one. And c is just a really funny way of writing the number one. It’s no more meaningful to speak of the value of c being different than it is to speak of the value of one being different.
Agreed. The intuitive way I look at it is that the speed of light in a vacuum should actually be regarded as effectively infinite. We measure a particular finite speed, c, because of the intrinsic nature of spacetime.