What would happen if the light-speed in vacuum was higher?

Question

I came across a rather interesting passage in a book attempting to debunk Darwin's Theory of Evolution from a Christian viewpoint. One thing the book suggested, was that various scientific ways to measure age of fossils and rocks could not be trusted, because they assume that the rate of decay to be constant - something the book the suggest may not be the case. I assuming it's referring to C-14 dating and similar methods...

The book then quote "an exciting theory(sic) in this context" by Barry Setterfield and Trevor Norman that the speed of light may not always have been constant. That they by comparing 160 measurements of the speed of light from the 1600's all the way to today (2000), got results that suggested that "the speed of light 8000 years ago ("surprisingly", just around the time God's supposedly created the Earth and then the universe...), was 10^7 times higher than what it is today". And according to the book; this change in the speed of light would change the decay-rate, thus invalidating the result of C-14 dating.

Personally, I think the change in "measured" c is rather due to initial wrong assumptions (eg. "the ether"), and measuring-errors due to primitive technology (especially if we start in 1600) - but what do I know...?

So, just out of curiosity; what would happen if the speed of light was 10^7 higher than it is?

• Would an increase of the speed of light change decay-rates?
• How would the decay-rate - and results depending on it (like C-14 dainging) - change?
• Would it change time - eg. would the length of a second increase?
• What other manifestation would such a huge increase in the speed of light cause (in physics)? Anything devastating and cataclysmic?
• What would happen if the increase was (a lot) less - and perhaps more survivable - which effects would it have on our lives?

I could perhaps also add that I once read a book trying to explain relativity and such to a layman in very simple terms, using alternate worlds with changed physics and then exploring what the result would be. In one of these worlds the speed of light was a lot less - so the books hero could actually bike fast enough to get the effect of closing in on c... and taking the train, caused time-distortion effects for the passengers (like "twin-in-rocked-going-close-to-c-doesn't-age" paradox).

As a side-note; the author of the book "debunking evolution", seems to have shifted to writing fantasy-books for kids/young-adults - probably a much better use of his "talents"...

Answer 1

Most chemical decay rates are determined by the fine-structure constant $\alpha$, wich indicates the coupling of electrons to the electromagnetic field. Similarly, most nuclear decays are given by the Fermi coupling $g$ of the weak interaction. These two dimensionless parameters are respectively given by the following combination of fundamental constants: $$ \alpha = \frac{1}{4 \pi \epsilon_0}\frac{e^2}{\hbar c} \approx \frac{1}{137} \quad \quad g^2 = \frac{8 G_f m_w^2}{\sqrt{2} \hbar^3 c^3} $$ You can see that if the speed of light would increase the coupling would decrease, making most decay processes go slower.

How we measure and perceive time would probably not change. We perceive time with respect to the rate at which certain electromagnetic processes take place. If the speed of light would increase such processes would go faster, but as a result, our perception of time would 'speed up'. Certain nuclear decay rates (such as e.g. beta decay) would appear to go slower with respect to this `new' measure of time.

We can measure the speed of light in the past, by looking at the decay rates of certain isotopes in the early universe. This can in principle be done by looking at clouds of gas, measuring their density, and looking at their spectrum to determine the decay rate of these isotopes. (Though this is in theory possible the error margins one would obtain from such a measurement are probably very large. I am not aware of whether such an accurate experiment has currently already been carried out).

Answer 2

Nothing would happen. Dimensional constants like $c$ can be put equal to 1, one can do physics without ever introducing units and dimensions perfectly well. I explain here how you can derive the classical limit of special relativity starting from special relativity in natural units, you then see clearly that $c$ is actually a trivial scaling constant.

Answer 3

I believe that the question as you ask it is answered spot on by Count Iblis's Answer: nothing would happen because dimensioned constants can be rescaled through a change of units.

The enquiry I believe you mean to follow is an investigation of is what would happen if the ratio of the speed of light to time constants of other physical processes changed: e.g. the ratio of $c$ to a meter (length of a man's arm) per second (period of a heartbeat) - both physical objects and processes from our everyday World.

Jerry Schirmer, a distinguished user on this site and Ph.D. general relativist working as a software engineer makes the following excellent and elegant point that the size of $c$ in SI units, i.e. the ratio above, ultimately reflects roughly the ratio of sizes of energies released from nuclear to chemical reactions for comparable amounts of reactants, the latter releasing "everyday amounts" of energy, by dint of the rest mass total energy formula $m_0\,c^2$. Novel author, general relativist and gravitometer inventor (see Ch 16, Box 16.5 in Misner, Thorne and Wheeler, "Gravitation" for a design summary) Robert Forward also explored ideas similar to Jerry's in his novel "Dragon's Egg". The whole novel is essentially an answer to your question; a flavor of the ideas is given by the lifetime and evolution of the Cheela, a species of lifeform realized in nucleonic processes on the surface of a neutron star. Owing to the greatly higher speed and energy of these processes relative to chemical ones (represented by $c^2$), a Cheela lives out his/her (one of the protagonists is definitely spoken of as female) in forty human seconds. Nucleonic life springs from the Draco neutron star approximately 3000 BCE (human times), the first analogues of eukaryotes rise around 1000 BCE and the Cheela come onto the scene in the early 21st century. In 2032 CE the first Cheela co-operative skills arise and most of the story plays out between the 22nd of May and the 21st of June 2050 CE, a period spanning all of what we would recognize as a Cheela "civilization". Within a few days, Cheela technology vastly outstrips ours, they work out how to survive in low gravity environments and thus make contact with us.

So, in summary, $c$ controls the rate of nuclear processes relative to our everyday ones. This is what, I believe, YogiDMT means in his/her comment:

The universe would explode

i.e. if $c$ were much larger relative to $1{\rm ms^{-1}}$, the stars would exhaust their fuel much faster and quite possible life as we know it would not have had time to evolve.

Answer 4

The event horizon's or Schwarzschild radius would change and become smaller.

Answer 5

Many, many things would change, but time as we observe it would not change. Specifically, the speed at which cesium vibrates (this is used to define a second) would remain the same.

It's still an interesting question, though, so let's look at what would change. In no particular order...

If the speed of light were faster, then things like radios waves, which are light, would reach you faster. Things related to the speed of light, like electrical signals, would also reach you faster.

The speed of light also has significance in electrodynamics. For example, it can be produced from the fundamental constants $\epsilon_0$ and $\mu_0$, which respectively describe how easy it is for electric and magnetic fields to go through empty space.

Permittivity of free space: $$\epsilon_0 = 8.854 \cdot 10^{-12} \frac{s^4A^2}{m^3kg} $$

Permeability of free space: $$ \mu_0 = 1.2566 \cdot 10^{-6} \frac{m\space kg}{s^2A^2} $$

Together, they give the speed of light at follows

$$\sqrt \frac {1}{\epsilon_0 \mu_0} = c$$

So if c increased, then the product of $\epsilon_0$ and $\mu_0$ would decrease, which would change the values (although it cannot be known which ones would increase of decrease). Since these values are used in calculating the magnetic and electric forces, their strengths would change. This means that precision tools using magnetic or electric force would have to be re-calibrated (your hard drive, for example).

Relativity is another field that we would have to amend. In this domain, the speed of light is the cosmic speed limit; information of any kind is prohibited from moving faster than c. If the speed of light were to change, then relativistic effects would change. We would observe less time dilation, for one. For example, GPS satellites must record the time it takes light to reach them very accurately, for if it is even a microsecond off, the position would be off by several hundred meters. According to general relativity, the presence of a gravitational field affects the passage of time - the stronger the field, the slower time passes. And since the GPS satellites are farther from earth, they run slower than our clocks of earth. 44 $\mu s$ slower every day, to be precise. So your google maps would stop working.

There are, of course, many more things that would change, but to my eye, none of them would spell disaster; it's not like you wouldn't notice that your computer, cell phone, or for that matter most of our technology stop working optimally, but it most likes wouldn't cause mass destruction of our universe. We would just have to re-calibrate our electronics, and then enjoy some very fast internet.

Cheers.