# What is the lower bound for lightspeed?

I am investigating the possibility of modifying the speed of light in my world. Assuming that the speed of light in a vacuum can (and in my world, is) modified, what lower bound exists that would permit humanity to exist?

Everyone has probably heard at least once that some values in Physics must be so precise that it could be compared to [insert absurdly precise example]. So is Light fine-tuned?

What would be the lower bound for light speed which still allows Human live? In following questions I want to address an upper bound and most notable effects.

Thanks to many physicists we know that light speed is very important for any part of fundamental Physics (Gravitation, Energy, Relativity, ...) At some light speeds Atoms might have so much energy that 1g of radioactive material would be enough to wipe out all human life.

• There aren't many on this particular site who could answer that, you might want to ask on Physics where it won't get closed as "Not about worldbuilding". VTC.: OT.: NAW. – Bitter dreggs. May 22 '19 at 17:12
• @JBH I've been noting thing new that I learn here as I go. I need a bigger notebook. – Bitter dreggs. May 22 '19 at 17:55
• @Hoyle'sghost You will eventually need a tome. – Ash May 22 '19 at 18:24
• @MrSpudtastic the lowest speed for light where Human life is still possible. – Soan May 22 '19 at 19:12
• @TylerS.Loeper At certain light speeds Human life will not be possible because Relativistic Physics would occur every time you moved. (this is only an example) – Soan May 22 '19 at 19:19

The fine-structure constant is the one controlling most of the properties allowing life as we know to exist.

It can be expressed as $$\alpha=k_e\cdot e^2 \over \hbar\cdot c$$, where

• $$k_e$$ is the Coulomb constant
• $$e$$ is the elementary charge
• $$c$$ is the speed of light in vacuum
• $$\hbar$$ is Planck constant

As you see, if you change $$c$$ you change $$\alpha$$, and that would make life impossible.

The anthropic principle is a controversial argument of why the fine-structure constant has the value it does: stable matter, and therefore life and intelligent beings, could not exist if its value were much different. For instance, were α to change by 4%, stellar fusion would not produce carbon, so that carbon-based life would be impossible. If α were greater than 0.1, stellar fusion would be impossible, and no place in the universe would be warm enough for life as we know it.

Therefore

What would be the lower bound for light speed which still allows Human live?

Exactly what it is: $$c$$

• So c is also fine-tuned? And you can only change it thousands of digits after the . ? – Soan May 22 '19 at 17:30
• @Soan, to help you with L.Dutch's answer: insofar as we understand the speed of light and insofar as present-day mathematics can accommodate the matter, there is one and only one speed of light: c. There is no lower bound. There is no upper bound. There is a single number: c. Not surprisingly, relativity states that this number is the moment when travel through the universe is perceived in the frame of the traveler as instantaneous. It may take light years in our time frame to travel, but in the time frame of light, it arrives at its destination instantly - regardless of distance. – JBH May 22 '19 at 17:45
• After researching a bit about the fine-structure constant I fail to see why it has this exact value in the first place and why it has to be this value. Could you please explain that to me? – Soan May 22 '19 at 18:00
• @Soan humans as we know it exist in a world where this value happen to lead to 1 planet out of maybe trillions to develop intelligent life. – Andrey May 22 '19 at 19:22
• @Andrey I know that it is highly unlikely but I just want to know if it would be possible with different light speeds. – Soan May 22 '19 at 19:27

From a purely classical point of view,

$$c = 1 / \sqrt {\varepsilon_0 \mu_0}$$

which means that if one were to change the speed of ligh $$c$$ one would have to change $$\varepsilon_0$$ (the vacuum [electric] permittivity), or $$\mu_0$$ (the vacuum [magnetic] permeability), or both, and, as an immediate effect, change the strength of all electromagnetic phenomena.

As it happens, chemistry is first and foremost an electromagnetic phenomenon. In a world with a different speed of light than ours the strength of electromagnetic phenomena is different than in ours and therefore the chemistry works in a different way than in ours. Different chemistry means different life, and, quite obviously, no humans. There may be life in such a world, even intelligent life, but there will most definitely be no humans.

You cannot have a different speed of light and the same chemistry. You cannot have a different speed of light and human life.

• Somehow I don't get c when using this formula: 299 796 878.9 instead of 299 792 458. I used the numbers from my Physics book (8,85418782 * 10^-12 and 1.2566 * 10^-6). Also, isn't $\mu_0$ defined as 4$pi$ * 10^-7? And because $pi$ is not precisely known we can't know if it is exactly c? Or how do we know that this formula is actually working? – Soan May 23 '19 at 11:51
• Light is electromagnatic waves. The solution for the propagation speed of electromagnatic waves in a vaccuum is given by the above formula on theoretical grounds from the formulas of a magnetic field induced by a changing electic field, and an electric field induced by a changing magnetic field. – Martijn May 23 '19 at 12:02
• @Soan: Things change. Nowadays $c$ is by definition exactly 299,792,458 meters per second. Everything else needs to adjust. As a consequence, $\mu_0$ is no longer $4\pi \times 10^{-7}$ H/m, but it's a physical constant which needs to be determined experimentally... And anyway, $\epsilon_0$ and $\mu_0$ vary (including their dimensionality) depending on the system of units of measurement; look how the electromagnetic formulas look in the various flavors of CGS. – AlexP May 23 '19 at 12:11
• So that means there is still wiggle room? But you said otherwise? Because apparently phisics still worked with different values for $\mu_0$ and $\varepsilon_0$ or what am I missing? – Soan May 23 '19 at 12:27
• @Soan: The physical reality did not change. What changed was the way we define our units of measurement. The state of technology is that we can measure time with very much greater accuracy than any other physical quantity; so we chose to define our unit of length based on the unit of time, the linkage being provided by choosing an exact value for the speed of light. As a consequence, $\mu_0$ is no longer defined to be $4\pi \times 10^{-7}$ H/m (in the SI system of units), but has been downgraded to an experimentally measured constant. – AlexP May 23 '19 at 12:35

The fine structure constant was identified as a result of Michelson and Morley's famous light-measuring experiment. This is the same experiment, whose same incredible results weren't able to be explained away as measurement or process error that caused us to question space and time itself, and ultimately accept that Lorentz contractions are the way the world works.

The answer to your question might be the same one : Galilean Relativity (also called Einstein's Relativity). The principle is this: within a local framework, the laws of physics continue always to apply the same way.

If the fine structure constant does vary, a similar preserving principle may apply keeping the universe as we know it ticking along just the same.

Here are some examples:

• Changing $$\alpha$$ causes the distance between electron orbitals grow tighter ($$r = {{\alpha \lambda} \over { 2\pi }}$$). Without any other changes, this means that the electromagnetic binding force $$F = {{k q_0 q_1} \over {r^2}}$$ increases. If binding forces become too high, chemistry as we know it falls apart.
• But what if the Coulomb constant $$k$$ contracts with $$\alpha$$ such that, locally, binding force remains the same irrelevant of the value of the fine structure constant? This outcome is predicted by the math if this relationship holds true : $$\alpha$$ = $${k e^2}\over{hc}$$, but it does require the local speed of light to remain the same.
• If space is quantized (required now for quantum gravity and some M theory, but not yet supported by any successful experiment), and if quantized space has any relationship to the fine structure constant, then while the local speed of light remains the same, it is possible that the relative speed of light an outside observer sees increases, while c remains unchanged locally, because you are iterating over smaller chunks of quantum space.

To sum up: nobody even knows if the fine structure constant changes. But if it does, it is possible for a principle of relativity to still apply that preserves the universe as we know it locally. That would mean there's no upper (or lower) limit.

C is the speed of light in a vacuum.

Light slows down when passes through transparent media by the factor of the index of refraction. The maximum theoretical refractive index value is \infty, which would bring the speed of light to ~0, but ~38 is the highest value engineered into a meta-material.

• Sorry didn't specify but I wanted to know what the theoretical lower bound of light in vacuum would be when I still want Humans to live. – Soan May 22 '19 at 18:16

Most constants in physics (all that have units, like c, units of speed) cannot be "changed", as you are just renaming the units. The speed of light is the relation between distance and time, so changing speed of light just changes the units of time (and/or distance), but all the physics remains the same. For example, theoretical physicists usually use natural (Plank) units, where c, and most important constants, are exactly 1. A completely different issue is the dimensionless constants, like the fine structure constant, approximately 1/137. These are the units you might want to change in your world if you want different physics.

https://en.wikipedia.org/wiki/Dimensionless_physical_constant

EDIT:

Then, if you want to change the speed of light, what you need to change is the dimensionless constants. It will change all the constants with dimensions, or at least their relation. The fine structure constant, for example, is defined as:

$$\alpha = \frac{e^2}{\hbar c \ 4 \pi \varepsilon_0}$$

and so,

$$c = \frac{e^2}{\hbar \alpha \ 4 \pi \varepsilon_0}$$

Doubling the the fine structure constant will half the speed of light, while keeping the other constants (e, the charge of the electron [or the proton]; $$\hbar$$, the Plank's constant; and $$\varepsilon_0$$, the permitivitty of free space). Of course, this will change another constants: for example, $$c =\frac {1}{\sqrt{\varepsilon_0 \mu_0}}$$, where $$\mu_0$$ is the permeability of free space (related to magnetism). Again, if the fine structure constant is doubled, the relation between the electric and magnetic force will change (magnetism would be 4 time stronger than in our world).

The point is that what you have to look is the relation between various forces; changing only a constant with dimensions, like the speed of light, without changing anything else, is only a change of units and so does not change the physics of the world.

Answering the initial question, what is the lower bound for lightspeed that permits humanity to exist? None, unless you change a lot of other things.

And if you change the dimensionless constants to change the speed of light? A lot of other constants (dimensionless; as said, the constants with dimensions are only relative to the system of units) will change. Which ones? The ratio of the speed of the electron in an orbit to the speed of light will change; the maximun number of protons in an atomic nucleus will change (it is around the inverse of the fine structure constant, 137 in our world; this could give a good limit, because nucleus will be more radioactive; in a world with a fine structure constant double as in our, and so with half the speed of light, palladium [Z=46] would be as radioactive as uranium in our world, Z=92, which would not exist; iodine would be highly radioactive; if $$\alpha$$ is multiplied by 4, vanadium would be as radioactive as uranium, and if $$\alpha$$ is multiplied by 8, carbon would be as radioactive as uranium, making life impossible). Then a possible lower limit is about 1/4th (but many changes would have to be made in human chemistry). But in that world stars would not exist, by the way, not as we know them. Citing wikipedia,

were $$\alpha$$ to change by 4%, stellar fusion would not produce carbon, so that carbon-based life would be impossible. If α were greater than 0.1, stellar fusion would be impossible, and no place in the universe would be warm enough for life as we know it.

You can try to check for other possible changes here: https://en.wikipedia.org/wiki/Fine-structure_constant#Physical_interpretations.

• Welcome to the site Carlos, when you have a few minutes, read up in our help center about how we work: How to Answer. Although what you say is quite true, it doesn't go far enough to really get to grips with the OP's question - but you can edit to expand how it might work and still be suitable for life. – Bitter dreggs. May 23 '19 at 12:35
• Our help center states, "World building includes geography, culture and creatures for the world, not to mention magic and planetary physics, in short, everything from the physics underlying your reality to the entire universe you want to build." In other words, this is the place you come to when you want to build a universe that doesn't comply with real-universe physics. Anything and everything is up for grabs. – JBH May 23 '19 at 18:04