Expert: Philip A. Stahl - 7/10/2010

Question
Hello:

I love physics and the science that goes along with it especially when it comes to outer space.  Over the past 3 months I have been watching some shows that have been on our local cable stations called "The Universe" and "Into The Universe with Stephen Hawking" among others and I have many questions but will stick to this one for now. The question has two parts.

First. The speed of light.  186,000 miles per second. On one of the shows I saw last night they were explaining that because light travels at that speed we as humans see everything in "real time".  We get to experience events as they actually happen.  So that leads me to the first part of my question.  What if the speed of light suddenly slowed down to lets say 184,000 miles per second? What would or what do you think would happen? Second part of the question is the opposite.  What would happen if the speed of light suddenly increased to 189,000 miles per second?

The reason I am using small examples and not asking "what would happen if the speed of light dropped to 50,000 miles per second?" is because I can kind of understand what the effects would be on that large scale but on a smaller scale such as going from 186,000 to 184,000, would the effects be catastrophic?  Could we survive?

Thanks,

Paul

Answer
Your conjecture is interesting. So far as I can see the impact of such deviations in c as you describe would largely be of interest in two areas but possibly catastrophic in a third:

1)   the magnitude of the fine –structure constant (alpha) which ultimately governs the rate at which stars consume their nuclear fuel.

The dimensionless alpha (cgs units) is:   a(fs) = e^2/ h’c

Where h’ is the reduced Planck constant (h/ 2 pi0 and e the electronic charge.

Then we see from the above, that if c is larger a(fs) will be smaller, and if c is smaller than its established value then a(fs) will be larger. The latter will mean that we can expect faster evolution in more massive stars, less pronounced for sun-like stars.

2)   the energy associated with photons of particular wavelength (L), e.g.

The quantized energy E = hc/L

Thus, all quantized energies would change contingent on how c varies. This means atomic energy levels would change.

In addition, we know that: c = fL

And: L = c/f

So lower and higher values of c would have to be corrected for, say in red shift measurements.

In addition, relativistically, the space-time interval ([1 – {v_o/c)^2]  )would be affected, and all those critical computations contingent on it would have to also be adjusted.

3) Lastly, catastrophic consequences might be incepted as nuclear binding energies are affected (e.g. the so-called Q of nuclear reactions, e.g. Q = [mr + Mr - mp - Mp]c^2 where p subscripts denote products and r denote reactants)  which would affect fission rates, e.g. for radioactive elements, materials.

In addition, a higher or lower c would directly impact the solar luminosity (basic proton-proton fusion cycle energy production rate) with larger c yielding larger solar luminosity (even though a fraction of a percent) and lower c the converse. However, given that we already don’t know the full extent of solar variability, either of these may represent the proverbial “straw that breaks the camel’s back” especially the larger luminosity – when we already have global warming to deal with. (Some of the latest results disclose the ocean has increased in acidity by 30% since the onset of the Industrial Revolution, largely due to CO2 being absorbed to form carbonic acid, H2CO3).