If you say you want to make the speed of light 100 times as high, you have to say what you want to keep constant. I'll assume you want to keep constant the sizes of things (because if light is 100 times as fast, but all things are 100 times as large, the apparent speed is again the same), and also keep the time scales of physical processes (again, because if light goes 100 times as fast, but you also live 100 times as fast, you've won nothing).

Summary

I think by carefully adjusting the constants, you could make it so that most things stay more or less the same. However, there will be inevitable changes in the details, especially forget about earth magnetic field (and associated effects, like polar lights), permanent magnets, magnetic hard disks, golden gold and liquid mercury.

Edit: As Peter Cordes mentioned in the comments, also a lot of electric technology (especially motors and generators, as well as coils for circuits) depend on magnetic fields. This would have negatively affected all electric technology, and might result in a steampunk-like world (because steam engines obviously don't rely on magnetic fields).

How would physics have to be changed?

Let's first start with Maxwell's equations, which actually determine the speed of light [note: I'll use SI units throughout; some argumentations would have to be adapted for other unit systems, because they have less constants into which to incorporate the effects, but the ultimate effects would of course be the same].

In Maxwell's equations, there are two constants, $\epsilon_0$ which effectively determines the strength of an electric field generated by a charge density $\rho$ via the source equation $$\operatorname{div} \vec E = \rho/\epsilon_0$$ and $\mu_0$ which effectively determines the strength of the magnetic field generated by a current density $\vec j$ via $$\operatorname{curl} \vec B=\mu_0 \vec j$$ (note that unlike in the electric case this is not the complete Maxwell equation).

Maxwell's equations (the parts which I omitted above) predict electromagnetic waves going with the speed $$c = \frac{1}{\sqrt{\epsilon_0\mu_0}}$$ So you see, to modify the speed of light, you have to modify either the electric or the magnetic field a charge/current generates. For example, you could reduce both electromagnetic constants by a factor 1/100; that would make electric fields 100 times as strong (remember, $\epsilon_0$ is in the denominator of the source equation) and magnetic fields 1/100 as strong. Alternatively you could leave $\epsilon_0$ unchanged, but apply a factor 1/10000 to $\mu_0$, thus only (massively) weakening all magnetic fields, or vice versa, making electric fields much stronger but leaving magnetic fields unchanged. Indeed, you could even make one of them larger while reducing the other even more at the same time. So you see we have a certain freedom here, which we have to solve in another way.

So let's now look at the condition that sizes should remain the same. Well, the relevant size is, of course, the size of atoms, which basically can be written in terms of the Bohr radius, $$a_0 = \frac{4\pi\epsilon_0\hbar^2}{m_e e^2}$$ where $m_e$ is the electron's mass, $e$ is its charge, and $\hbar$ is Planck's (reduced) constant. This, of course, means we've got yet another constant we can play with, so this alone won't help us. So let's look at the second condition, that time scales also should be kept constants. Now quantum mechanics tells us that time scales are given by $\hbar/E$ where $E$ is an energy scale; for atomic processes (and thus also for chemistry and thus life) the relevant energy scale is given by the Rydberg energy, $$Ry = \frac{e^2}{2(4\pi\epsilon_0)a_0}$$ That means, the time scale can be characterized by $$\tau = \frac{2\hbar(4\pi\epsilon_0)a_0}{e^2}$$ If we want to keep both $a_0$ and $\tau$ (that is, sizes and time scales) constant, we need to keep both $\hbar$ and $\epsilon_0$ unchanged. Remembering the discussion above, this means we have to give $\mu_0$ a factor of $10000$.

So what would be the result?

The most direct change would be that magnetic fields would be much weaker, by a factor of 10000. Basically, forget about the magnetic field of earth. Also, forget about permanent magnets; they will be too weak to be of any use. Also, magnetic storage will probably not be a feasible way to store information. Actually, given that the very existence of ferromagnetism depends on sufficiently strong magnetic interaction, I'm not sure if there would be any ferromagnetism; if it existed, it would be a low-temperature phenomenon.

For further effects, let's look at the most important constant in electromagnetism: The fine structure constant, $\alpha = \frac{e^2}{4\pi\epsilon_0\hbar c}$ Since $c$ is the only constant which changes is $c$, this would mean that $\alpha$ is only 1/100 as large as in our world. Which is not that surprising, given that the name of that constant comes from its relevance for the atomic fine structure, which is caused by relativistic effects. With a higher speed of light, of course you expect relativistic effects to be reduced. Note that the dominant energies in atoms would not be changed (that's a direct consequence from neither $\hbar$ nor the relevant time scales being changed).

Well, given this, we come to a very visible (and surprising) effect of a much higher speed of light:

Gold would no longer be golden!

And moreover, mercury would no longer be liquid either. Note that relativistic effects are important mostly for heavy elements, so the properties of the most important elements for life (especially hydrogen, oxygen, nitrogen and carbon) should not be substantially changed; life would probably not be affected.

However I'm not sure what it would do with nuclear physics which is much more dominated by relativistic effects; mass defects would certainly be much more pronounced, but it might possibly alter the whole nuclear stability properties. On the other hand, one might evade that problem by adjusting some other fundamental constants relevant for nuclear physics.

Since the energy scales would be kept constant, $E=mc^2$ would mean a 10000-fold increase of the energy per mass; so a matter-antimatter annihilation would increase correspondingly. Whether nuclear processes also show this additional energy would again depend on the adjustments to nuclear physics; my bet would be that if you make them so that the stable isotopes remain the same, you'd also get approximately the same energy out of your nuclear processes. But that's just a guess; I don't know enough about nuclear physics to really say.

Given that in General Relativity, energy and momentum are the source of gravitation, a higher energy would also imply stronger gravitation; however you've got yet again a constant you can modify to avoid this: Just make the gravitational constant smaller by an appropriate amount.

And of course, you'd only get relativistic effects at high speeds; that's after all the whole point of it. So you'd get fast communication over wide distances, and also possibly very fast space travel (although we are still far from even reaching relativistic speeds for spaceships within our "slow-light" universe).

posted about 9 years ago

celtschk‭

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