Q: What would the consequenses for our universe be if the speed of light was only about one hundred miles per hour?

Physicist: In terms of things like space travel, the difference between 100mph and light speed is academic.  Everything out there is really far apart.  The speed of light, “C”, is woven into the laws of the universe from top to bottom, mostly in the context of electro-magnetism.  Changing the speed of light would have profound effects on chemistry and the fundamental forces.

But those changes are boring.  What’s more interesting is the effects that special relativity would have on every day life.

For what follows, the speed of light is now C = 100 mph (161 km/h for our Canadian or otherwise foreign readers).

"Gamma" is a measure of how much velocity dilates time and shrinks distances. Most of the action happens beyond 90% of C.

Movement? Nopers: If you’ve taken intro physics you may have learned that the kinetic energy of an object is E=\frac{1}{2}mv^2.  But this is just a low-velocity approximation of the true equation (found by Einstein), which is E=\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}\approx mc^2+\frac{1}{2}mv^2+\frac{3}{8}m\frac{v^4}{c^2}+\cdots.

The first term is the famous rest mass energy (E=mc2), the second term is the regular kinetic energy, and the third, fourth, fifth (and so on) terms are only important when the velocity is a substantial fraction of light speed (so Newton can be forgiven for getting this one wrong).  But if C=100mph, then suddenly those later terms become important even at low speeds, and you’ll find that moving as fast as 0.01mph would require something like a rocket or a nuclear-powered car.

But that’s boring, so let’s pretend that it isn’t the case.

No long range communication: 100mph is about 45m/s, so having a conversation with someone who isn’t close at hand will result in really annoying delays.  It would be like those satellite interviews, only in person.  To send a message to someone on the other side of the world would take at least 5 days and 4 hours at the speed of light.

I’m ignoring the effects, by the way, of the Earth rotating at about 1,000 mph (at the equator).

Leave your watch at home: The act of walking around would cause you to lose about half a second for every mile you walk, which isn’t to bad.  But if you started moving around in a car at highway speeds (65 mph), then you could expect to lose about 17 seconds for every mile you travel.

“Super Speed”: One of the slick things about traveling at relativistic speeds is that, although you can only pass things at up to 100mph, you can actually cover more distance than the 100mph speed limit might imply.  There are two ways to look at this.

From your point of view the world around you undergoes length-contraction.  So, for example, at about 87mph you would see the world contracted by a factor of 2.  So while you’d see things pass by at 87mph, you’d be eating up distance as though you were traveling at 174mph (2 x 87mph).

From everyone else’s point of view, you’re traveling through time slower.  At 87mph they’d see your watch ticking at half the usual rate, so the trip will only take half the time it should.

Pretty colors: Even at running speed there would be enough relativistic doppler shift to change the colors around you.  If you were driving past a yellow field of grain, it would appear blue in front of you and fade to deep red as it passed behind you.

There are just a hell of a lot of other effects, so if you’re wondering about any of them, just ask in the comments.

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8 Responses to Q: What would the consequenses for our universe be if the speed of light was only about one hundred miles per hour?

  1. DonalH says:

    You say that there would be profound effects on chemistry. What are some examples? Would we even have organic compounds, life, or us?

  2. burens says:

    “…and you’ll find that moving as fast as 0.01mph would require something like a rocket or a nuclear-powered car.”

    You could also say for light to be forced to travel at 100 mp/h any movement in such a universe would have to be very energy demanding.

    Otherwise the light would travel faster.

  3. The Physicist Physicist says:

    By dropping the speed of light, the “magnetic permeability of space” will have to jump tremendously. Essentially, magnetism would be a much more important force. I would guess that electrons would only show up in pairs. So odd numbered elements might only show up in ionized forms.
    Beyond that I’d need a biochemist and a crazy ass big computer to look at the effects on protein folding, which is strongly influenced by magnetic interactions between different parts of the protein. I’d suspect that none, or almost none, of the proteins that exist in the world today could exist in a world with a very different light speed. However, in a world with a different C there might be all kinds of other fancy new amino acids and proteins.
    Again, this is all guesswork. For anything more complicated than a single hydrogen atom we need giant computers and experiments.

  4. Donald says:

    Interesting. Chemical reaction would go slower, so it could affect the biochemistry in living organisms, and the speed ofneural impulses. The heat from stars and the center from the earth would not be able to leave their source at the same speed either. But as long as the heat was released just as fast as new one was building up, it shouldn’t be a problem.
    I assume the inflation of the universe would still be the same. If so, the sky at night must be much darker, since the light from distant stars would require so many years to reach us.

    And what if the speed of light was a million times faster than it is today, instead of much slower. Then the universe would perhaps be more available for us than it is today. Travelling thousand times faster than the present speed of light should be possible, and require less energy than a spaceship who has reached 90 percent of the 300 000 km per sec of today.

  5. Berg says:

    Another consequence is that it would be very hard to kill someone with a gun. A bullet couldn’t have moved fast enough to kill someone. A bomb going off would be a cool sight. Falling from Empire State Building would probably not be that dangerous.
    Considering that the escape velocity from Earth’s gravity is about 11.2 km/s, one could say that most large objects would be some kind of black holes.

  6. The Physicist Physicist says:

    Classically momentum is P=mv. However, relativistically P=γmv. You can think of this as “things get heavier near light speed”. So while you might take a long time to fall off the empire state building, the end result would be about the same.

  7. Pingback: Q: How do velocities add? If I’m riding a beam of light and I throw a ball, why doesn’t the ball go faster than light? | Ask a Mathematician / Ask a Physicist

  8. christopher says:

    would a bomb be a cool sight? if the other forces are left alone, i would imagine the shockwave of heat and death would hit you at the same time the light emanating from the explosion hit you? so maybe it would look cool for a nanosecond or something.

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