# What if the speed of light were 100 times higher?

Imagine the speed of light is 100 times that in our universe. Light from the moon takes about 1/100th of a second, the sunlight reaches our eyes in about 4 seconds, from nearby Alpha Centauri in about 16 days, and from the galactic center in about 260 years.

Assuming the laws of relativity would be scaled up to the higher value of $c$, would that make it easier to travel to other worlds?

Besides being awesome, would there be any other important considerations that I should keep in mind?

Edit: In light of the first few responses, if at all possible, I would like to assume scenarios where the universe does not burn down horribly. But perhaps such a fast propagation of causality leaves me with no outs...

• Energy per unit of mass would be quite a lot larger (E=mc^2). I don't know the implications of this, except maybe that WWII would have ended the world. Feb 12, 2015 at 2:37
• @DaaaahWhoosh Or perhaps in that universe the formula is E=mc^2/100 :) Feb 12, 2015 at 2:38
• Added bonus: MMORPG latency times go way donw. Feb 12, 2015 at 16:36
• This sounds like a perfect questions for XKCD's "What If" blog. Feb 12, 2015 at 16:55
• @SerbanTanasa I think you mean E=(mc^2)/10000, or E=m(c/100)^2 Feb 13, 2015 at 1:29

## 7 Answers

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 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).

• The size of macroscopic stuff scales with the lengths of bonds between atoms, and crystal structure. This presumably scales the same way as the Bohr atom radius with changing $\epsilon_0$. It's not hard to imagine the possibility of atoms getting "bigger" but not farther apart, as macroscopic stuff has a lot of empty space. (Or am I mixing up the "lots of empty space" thing being only when you count electrons and nuclei as taking space, not whole atoms? (i.e. electron shells / orbitals / probability densities)) Feb 15, 2015 at 7:16
• @Peter Cordes: "Or am I mixing up the "lots of empty space" thing being only when you count electrons and nuclei as taking space, not whole atoms?" Yes. If you look at a scanning tunnelling microscope image of a surface, you'll see that the atoms are densely packed. Indeed, covalent bonding depends on the atomic orbitals to overlap (so that electrons can be "shared" between atoms). And so does electric conductance of metals (so that valence electrons can move freely from one atom to another). Feb 15, 2015 at 7:43
• The industrial revolution might never have had an electrical component, on a world with 10k lower $\mu_0$. Steam turbines and internal combustion would work the same, though. Probably power grids would be in the form of pipes carrying some kind of fuel, rather than wires carrying electricity. I'm not sure what kind of non-magnetic electricity generation we'd use once we discovered electronics. Maybe fuel cells, flow batteries, or photovoltaics. Feb 15, 2015 at 22:27
• @PeterCordes: You raise some good points. So in short, a higher speed of light would result in a steampunk world. That's an interesting aspect! However the critical current in superconductors is because of the critical magnetic field and thus would be correspondingly higher. Feb 15, 2015 at 22:34
• Without the magnetic field, wouldn't Earth not be protected from space radiation? Then, there couldn't be humans, or much life (at least life as we know it). Is this true? Apr 11, 2018 at 0:37

The speed of light is a squared constant in $e=mc^2$, so multiplying it by 100 means atomic reactions — nuclear bombs and plants, and solar fusion — will be approximately 10,000 times more powerful. I suspect that this would either:

1. Make it impossible for a star's gravity to hold it together against its fusion core unless it's super-massive.
2. Or make it so stars expand more (greater internal pressure from fusion vs the constriction force of gravity).

Either of which would probably make our form of life impossible. Certainly our solar system wouldn't exists in its current form.

• I recently heard a talk where the speaker mentioned a technology being thought of which utilizes the blast from atomic or hydrogen bombs being fired behind the spaceship to accelerate the ship. If one could use this technique, I guess that higher velocities should be possible in such a world. Feb 12, 2015 at 7:28
• @InvisiblePanda: the speaker was probably referencing Project Orion project (not to be confused with the contemporary, capsule project of the same name). Regardless, as this answer correctly implies, you have to have an intelligent life capable of building such a ship in the first place. Feb 12, 2015 at 8:04
• -1 Actually it would make all known element unstable. Physics would be VERY VERY different. I doubt that stars would even form. en.wikipedia.org/wiki/Fine-structure_constant
– Aron
Feb 13, 2015 at 3:30
• Or it means that these reactions have 10,000 times less change in mass. We're talking about binding energy, not the rest energy of protons and neutrons - this isn't antimatter. Feb 14, 2015 at 19:46
• This is backwards. The strength of nuclear reactions is not set by $E = mc^2$, but rather the amount to which they affect mass is set thereby. The energies involved are based on the relative strengths of and balances between the forces operating within a nucleus - namely the competition between the residual strong and electromagnetic interactions (and to a lesser extent, the weak interaction which powers beta decays). If the strengths of these forces remain the same, the result is not that nuclear reactions become 10,000x more powerful, but that they only change masses 1/10,000 as much. Dec 4, 2018 at 18:48

Would that make it easier to travel to other worlds?

In terms of regular (rocket powered) space-flight, I don't think so. The distances between stars are so huge that the amount of fuel we need to approach speeds where special relativity becomes important is much, much, larger than the spaceship itself.

A quick Wikipedia search on Lorentz factor shows that you need to get to ~87% of the speed of light before time appears to slowed by half.

With the current speed of light, to get to that speed, a 100 tonne spaceship will need 9.2 million, million, GJ of energy.

If you were to bump up c by a factor of 100, you should be able to ignore Lorentz factors. Instead, you'd only need 3.4 million, million GJ. I have no idea what that is in practical terms, but I expect it's still a lot.

would there be any other important considerations that I should keep in mind?

Magnetic and/or electric fields would be influenced as well. The speed of light is can be expressed as the result of other fundamental constants in nature; the permeability and the permittivity of space. Because these are all related, you'll have to change one (or both) of these too.

That will effect motors, and electronics. I won't comment on how they will effect them. As I really can't grok the physics behind it.

• Since somebody mentioned nuclear propulsion in another comment - according to George Dysons book on Project Orion it was estimated that it would have taken some 25 million bombs (with yields between 5 and 15 kilotons) to get to the nearest star with in a human lifetime, and that number does not include braking (so you'd just woosh by) or the journey back. As you say that would indeed be a lot of fuel to carry.
– user412
Feb 12, 2015 at 8:37
• c is a factor in the equation that determines the energy output of a given nuclear warhead, though, so Project Orion's bomb-powered craft just had its thrust increased by a huge amount, which would reduce the number of bombs you'd have to carry... Feb 12, 2015 at 10:35
• "Instead, you'd only need 3.4 million, million GJ. I have no idea what that is in practical terms" 1 kWh = 3.6 MJ. Thus, if my powers of ten are not off, 3.4e12 GJ = 3.4e15 MJ = 3.4e15 kWh ~ 390,000 GW continuous for one full year. 9.2e12 GJ is almost three times that at right about one million gigawatts continuous for one year. The 2008 world energy consumption (all sources) was about 144,000 TWh (about 16400 GW continuous) says Wikipedia. So even your lower figure is about 24 times global energy consumption.
– user
Feb 12, 2015 at 12:00
• @anaximander, the practial limit to the yield for Orion bombs is what ship and crew can absorb (this is the reason to consider 5KT bombs even when much bigger yields where available). So I'm not sure how much an Orion-Type craft would benefit from the changed physics.
– user412
Feb 12, 2015 at 16:18
• @anaximander, c more correctly is a factor of the mass-equivalence of energy. How much energy is released from a nuclear reaction is determined by the mass-change before and after. Feb 13, 2015 at 0:48

Radiation would be more energetic. Visible light (~1000 nanometres) would be as dangerously ionizing as X-ray radiation is on earth (~10 nanometres). UV light would be like gamma rays. You'd need some really intense sun-block to walk outdoors.

Not exactly sure how the eyes' photoreceptors work, but it could be that the visible light photons would be too energetic and would just pass right through without being captured, and you might instead be seeing in entirely different far-infrared wavelengths instead. Either that, or you'd still see in visible light, but the brightness would seem WAY higher.

Seems like so many of these questions end with "you'd see a really lovely light show, and then die in a really horrible way".

• Rats! So either we're stuck at a measly 300,000km/s or we blow up all the stars? It's just not fair. Feb 12, 2015 at 14:00
• This plays well with my idea that all distances are proportionally larger. Visible light would have wavelength 100 times longer.
– Vi.
Feb 13, 2015 at 17:28
• You would, indeed, be unable to see what is currently known as "visible light", if you define that term by frequency. If you define it by wavelength, you'd still be seeing that same wavelength of light. However, that light that is now the same wavelength as real-world visible light is, for frequency-based definitions, in the UV direction, not towards the IR. Not that you'd be seeing actual UV, by frequency-based definitions, you'd be well beyond that range, and into the x-ray portion of the spectrum. Feb 14, 2015 at 17:05
• Good call on the wavelength/frequency issue. Now I want to know which one our rods and cones care about. I suspect probably wavelength, because apertures... no clue how to test that though. If both are relevant (say, if we need the light to fit through a certain aperture, but also to have a certain energy so's not to just pass right through the receptor) then we might be blind. Thinking about it, the light would refract differently through our lenses, too, wouldn't it? Feb 15, 2015 at 3:34
• I think more likely the organic compounds that have their electrons affected by photons "care about" photon energy. Depending on which physical constants change to produce the change in the speed of light, your photoreceptors might or might not be tuned to a higher energy. celtschk's answer makes a good case for keeping $\epsilon_0$ fixed, and just letting $\mu_0$ change, which should mean same frequency = same energy. (and the scales of time and space don't change, either.) Wavelengths would get longer by a factor of 100, but that's still far smaller than the diameter of a pupil. Feb 15, 2015 at 22:41

I'm not physicist so I might be wrong, but I don't think the other answers are correct.

In fact, I think that if the speed of light suddenly got 100 times higher, absolutely nothing would change. We even might not be able to realize it has changed.

In our daily lives we perceive space and time as two separate things; but in reality, they are the same exact thing, called spacetime. Everything in the universe, including light and ourselves, always move through spacetime at c, the speed of light.

Space and time are however orthogonal, and this allows us to move in either as different speeds, as long as the total spacetime travel speed is always c; never less, never more.

So, if you are not moving through space or moving very slowly (like ourselves) you move through time at near the speed of light. If you travel at near the speed of light, you don't travel through time. (Light never travels through time, and thus only travels through space at maximum speed, c; this happens because it has no mass)

With all that said, if c was 100 times higher, time would also be 100 times as fast for us. The chemical reactions in our brain would happen more quickly; but this means we will think "faster" so I don't think we would even realize it.

Some other answers said atomic bombs and stuff like that would be much more powerful. But is it true? I don't think so; more energy is released, but in much less time as time is quicker, so it would feel exactly the same.

In short, I am not a physicist and I may be wrong, but from my understanding c is a constant that affects everything, and thus if it increases or decreases everything increases or decreases with it leading to no observable changes. In fact - from my understanding - it could even be constantly changing and we would have no way to know.

In fact, thinking of it a bit more, it's just not possible to say that c = c * 100. Since c is m/s, if it travels 100 times more meters, time will be 100 times quicker; so it becomes c = 100m / 100s which has no change.

• From a physicist: you're wrong. (Sorry to be blunt!) Or more precisely, it sounds like you're talking about the situation where the scale of spacetime has been increased by 100. You're right about certain things not changing in that case, but that's not what the question asks. Feb 12, 2015 at 11:20
• @DavidZ and OP Good points, I'll have to ponder that for a while. Could it be that attempting to change c would alter all dimensions of the Minkowski space? Feb 12, 2015 at 14:20
• No, it just alters the ratio between the space and time dimensions. It also alters lots of other physical effects that depend on that ratio. Feb 12, 2015 at 19:31
• If the speed of light did not affect anything, no one would ever be able to measure it. Feb 13, 2015 at 0:49
• @EmilioMBumachar You're looking at this from a different POV - c is speed, that is distance per time. If the space time changes while preserving the ratio of distance per time, speed of light will remain the same. That's basically what spacetime is talking about. However, as DavidZ noted, while c would stay the same, some other things will not - because, in a way, the units changed - but we can only measure the ratio (because to use, the units aren't some absolute values, we can only measure them in relative terms). Feb 13, 2015 at 13:06

Suddenly computer networks and computers in general can be made a lot faster (or at least networks can have less latency).

• Fibre optics I can see being faster, would standard electronic circuits go any faster though? Feb 12, 2015 at 13:25
• @TimB It poses a limit that we are not too far away from. I am computer scientist, but no expert in hardware. My educated guess is: yes, at least it opens up the potential. Feb 12, 2015 at 14:43
• Not very constructive...
– Jax
Feb 12, 2015 at 18:21
• @DustinJackson I think this qualifies as an "important consideration" per the asker's last sentence. Feb 12, 2015 at 19:51
• @DustinJackson Now that I think about it, although the effects may not be so great on earth (I think they would, but nvm), suddendly we can communicate a lot better with our spacecraft and potential space colonies. If the earth-moon is suddenly only 0.01 seconds, we can basically just attach it to the Internet (still not great latency, but way better!). Mars' closest distance is 3 lightminutes, max. distance is 21 light-minutes. Suddenly you have a round-trip time of something like 3-20 seconds, not great, but hey! Feb 13, 2015 at 10:39

Having looked it up, my understanding is now the expected result is stars would burn faster, releasing more energy.

Increasing the speed of light appears (perhaps it doesn't have to be this way--hard to say) to decrease the binding energies at the same ratio so reactions drive normally; however the consequence of a higher speed of light is nuclear reactions run faster at the same energy levels, and energy from gravity wells doesn't change so fast.

This yields hotter stars in smaller sizes. KSP anybody?

• I would love to see your working on that; binding energy had crossed my mind, but I know very little on it, and didn't get far with Wikipedia. Feb 13, 2015 at 3:07
• It appears from the nuclear binding energy setup that the energy is the active term and the mass change is the result from that. I'm sorry, but there really can never be any more than that. A more sophisticated answer will mean the same. Feb 13, 2015 at 3:26
• Wouldn't that be hotter starts with lower masses? Stars exist in an equilibrium between gravitational pressure and the pressure from the fusion-generated heat. So if mass remained constant, and so did gravitational force (big if, of course), the volume of the star would have to increase, and its surface temperature would go down. So same mass, more energy output, but more volume and a lower surface temperature. Feb 13, 2015 at 13:11
• Luaan: If you cross-compute for constant energy output (remember he doesn't want a disaster scenario if avoidable) you get lower mass which in turn means lower diameter. This increases the number of stars available for life. Feb 13, 2015 at 16:26
• I don't see them being actually any hotter. Yes, lower binding energy means easier, and thus faster, reaction rates, but remember, those same binding energies are where the energy output of the reaction comes from in the first place. It seems to me that you'd be burning through more atoms per second, but the total energy those atoms released would stay the same, because each individual atom reacted would yield less. Feb 14, 2015 at 17:15