# Different speeds of light w/ Planck Units

1. Feb 6, 2006

### pr0pensity

OK so my whining for help covers writing a paper about how things would be different if the speed of light was changed to 65 mph.

Right after getting the assignment I started thinking about dilations and all that. Then, I remembered planck's constant. Light would still have to have the same amount of energy, so the frequency would have to go up. Then I looked up a little more about planck's theorems and read about planck units.

so if c is changed in the planck units, everything is just scaled. space gets longer, time gets longer, charge decreases, etc etc pretty much there's just less energy if the speed of light decreases.

but if everything is just scaled, wouldn't it seem the same? wouldn't it seem like light still goes 300000 km/s?

the only way you would be able to tell any difference would be to compare two sections of the universe with different speeds of light, right?

my main question is about whether or not changing c would actually change the speed of light through space if everything is relatively unchanged.

2. Feb 6, 2006

### pervect

Staff Emeritus
It's not really a very well defined question, as I think you are starting to realize.

The first question is whether one is just changing the speed of light (i.e. one is imagining that perhaps the atmosphere has some very high refractive index), or whether one is actually changing 'c'.

Saying that one is going to change 'c' sounds like it should be unambiguous and make sense, but it's actually hard to say what this means outside the context of some particular model.

Probably the most direct interpretation of the question is to assume that the constant, c, used to define meter changes. This keeps the second unchanged, and makes the meter a huge number (in comparison to the standard meter). But this may not be the intent of the quesiton.

One can spend a lot of more or less useless time trying to define exactly what this question could mean.

There is one rather robust (and amusingly unexpected) consequnce that I am aware of (due to another poster, not on this board). If Earth's gravity and/or radius is assumed to not also be changed, i.e. the speed of light change is assumed not to be associated with a simple scale change (as I did above), and one assumes that everything else is the same but "c' is different, then the Earth must be a black hole, because it's escape velocity is greater than 65 miles/hour, i.e greater than c.

Which would mean that we would all die in a very short amount of time, certainly well before you finish writing your paper, as the Earth collapsed to a singularity and every human being on it was ripped apart by tidal forces.

(Well, on second thought, I suppose you could think of the Earth as being made of some sort of exotic matter, and imagine it to basically be a rather exotic entity known as a gravistar, and thus escape this fate.)

Last edited: Feb 6, 2006
3. Feb 6, 2006

### JesseM

This page has a good summary of why it does not really make sense to talk about changes in constants with units like the speed of light, and why it's better to talk about changes in dimensionless constants (constants with no units, like the ratio of a given particle's mass to the Planck mass).

4. Feb 7, 2006

### rbj

yup. first of all, "fundamental physical constants" are dimensionless constants such as $\alpha$ or $m_p/m_e$ or such. the speed of light, as we measure it with rods and clocks, is a human construct.

if no dimensionless constant had changed, it is meaningless to discuss what if some dimensionful constant (such as c or G) had changed. we could not tell if it had or not. but if a dimensionless constant such as $\alpha = e^2/(\hbar c 4 \pi \epsilon_0)$, we would know the difference, but it is not correct to ascribe that change to c or $\hbar$ or e. it's just a change in $\alpha$ (which has a real effect in the real world) and which of those components that changed is dependent only on how you decide to define your units to measure things. with Planck units, $c = (1 l_P)/(1 t_P)$ so neither c nor $\hbar$ would be measured to have changed. but e would appear to be different. but if you used Stoney units, then e would be constant and $\hbar$ would appear to have changed if $\alpha$ changed.

Last edited: Feb 7, 2006