# Cosmology at differing values of c?

1. Aug 3, 2007

### MarkeD

How would the Universe evolve under differing values of c?

c being the speed 3 x 10^8 m/s as defined, being the speed electromagnetic, and other massless forces propogate.

I'm interested in scenarios where c varies relative to the other constants of nature, I'm wondering if or how the anthropic principle can be applied to our observed value of c.

I've tried starting with considering how the universe would evolve if c=0, and a simple E=mc^2 indicates no energy and mass and a non-existent universe.

I'm wondering if the value of c today is an indication of how much energy was involved in the Big Bang. I'd be very interested in seeing what the esteemed members of this forum would speculate on such universes where c is greater or less than our value today. Is c so finely tuned as other constants such as the fine structure constant?

2. Aug 3, 2007

### marcus

I think it would help you rephrase the question and understand the answer if you would first recognize an important difference between two kinds of physical constants.

there are what are called DIMENSIONLESS constants. they would be the same in whatever system of units you use, essentially because they are ratios.

the fine structure constant is dimensionless. another way to say is that it is a "pure number". It is always 1/137 or more exactly 1/137.036...
or whatever no matter what units you use to measure.

by contrast the speed of light c is NOT a dimensionless number---it is a physical quantity, it doesnt have any number attached to it except by human convention (when we establish systems of units like the metric system that has no effect on nature, it is merely conventional)

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when people talk about adjusting the constants of nature so as to get other universes (some funny-looking, some uninhabitable, etc.) IT IS ALWAYS THE DIMENSIONLESS ONES THEY MEAN.
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another constant is 1836, the ratio of the proton mass to the electron mass.

another is 13 billion billion, the ratio of the Planck mass to the proton mass.

IF YOU CHANGED ANY OF THESE RATIOS EVEN SLIGHTLY IT WOULD MAKE A BIG DIFFERENCE. atoms would act different, they might all be radioactive, things would weigh different (if the earth and us still consisted of the same numbers of particles) or everything might just melt in a flash of light

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the dimensionless constants, the ratios, are what matter, if you want to fantasize about alternative universes.
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I would advise you to get to know what the key dimensionless constants are. There are about 30 of them that go into the standard setup of physics and cosmology.

Some are ratios of particle masses relative to the Planck mass.
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the metric system doesnt allow you to talk about making c different because the meter is defined as the distance light travels in 1/299792458 of a second. the meter is defined so that light HAS to go 299792458 meters in one second. this is in vacuum, the standard speed.

so you don't get anywhere by saying "what if light would go 1.5 x 108 meters a second?". it would simply amount to changing the definition of the meter and nothing else
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it doesnt mean anything to ask "What if the speed of light were only half as much?" unless you say relative to what other speed?. But most things in nature including our familiar speeds DEPEND on the speed of light. Assuming you could find some other speed in nature that doesnt depend in some way on the speed of light, and imagine changing the speed of light relative to that hypothetical speed, then you would be changing the DIMENSIONLESS number which is their ratio.

It always comes back to that, the meaningful fundamental proportions of our world are the ratios. The numbers that are unaffected by what units you use. There are 30 or so of them. Get to know some of them and exercise your imagination by picturing what if they were different----like if 1/137 were actually 1/136

Did you ever look at Martin Rees book "Just Six Numbers"
http://www.amazon.co.uk/Just-Six-Numbers-Universe-Science/dp/0753810220/
I never looked at it but it probably is about six of the most important ratios (i.e. dimensionless pure numbers).
If not, please let me know.

Last edited: Aug 4, 2007
3. Aug 4, 2007

### turbo

In His 1920 book on relativity, Einstein said that c must be variable with location because if the velocity of light in a vacuum was not variable, gravitational lensing could not occur.

http://www.bartleby.com/173/22.html

Unless you are willing to pit yourself against Einstein, you might consider that the speed of light in a vacuum is not constant, but variable, based on the properties of the space through which light propagates.

4. Aug 4, 2007

### Chronos

I agree with marcus. There is no observational evidence of variable 'c', or any other fundamental constant over time. The universe is confusing enough without introducing evolving constants. Einstein's remarks are easily misinterpretted.

Last edited: Aug 4, 2007
5. Aug 4, 2007

### turbo

Einstein's statements are simple and very easy to contemplate. The presence of embedded matter conditions space in its variable properties, including its refractive index.

The "observational evidence" of variable c is gravitational lensing, which Einstein modeled as refraction as per classical optics. It's easy to consider Einstein's field equations as if they have some independent reality - the tough part is to follow his path and determine the mechanics of GR, including the origin of gravitation, inertial effects, and the behavior of EM propagation, which plagued him to his death. His contemporaries satisfied themselves with his mathematical model for predicting the behavior of interacting massive bodies (GR) without understanding his dissatisfaction for that approximation.

6. Aug 4, 2007

### island

I agree with marcus and Chronos. Velocity isn't the same thing as absolute speed, and light cannot be measured to travel between any two points at absolute c only because curvature varies due to its constantly changing proximity to massive objects, so there is no such thing as a straight line, nor can there even a constantly curved trajectory between any two points in a less-than-absolute vacuum.

Einstein's statements do not conflict with this.

Last edited: Aug 4, 2007
7. Aug 5, 2007

### meopemuk

You might find it curious that the idea of the position-dependent speed of light can be described by a simple classical Hamiltonian. For example, in the field of a point mass M the Hamiltonian can be chosen as

$$H = cp - \frac{2GMp}{cr}$$

where $p = | \mathbf{p}|$ is photon's momentum and $r = | \mathbf{r}|$ is its distance from the mass M. The force acting on the photon at each point of its trajectory can be found from the Hamilton's equation of motion

$$\mathbf{F} = \frac{d \mathbf{p}}{dt} = - \frac{\partial H}{\partial \mathbf{r}} = - \frac{2GMp\mathbf{r}}{cr^3}$$

Assuming that in the 0th approximation the photon is moving along a linear path, and integrating this force (its component orthogonal to the path) along the path, one easily gets the usual light deflection angle.

The other Hamilton's equation of motion

$$\frac{d \mathbf{r}}{dt} = \frac{\partial H}{\partial \mathbf{p}} = \frac{\mathbf{p}}{p} (c - \frac{2GM}{cr})$$

suggests that in the field the speed of light reduces by the amount $2GMc^{-1}r^{-1}$. Again, by integrating this quantity along the linear photon's path one easily obtains the usual Shapiro time delay.

Eugene.

8. Aug 5, 2007

### MarkeD

Thank you for helping me ask the right questions and the book looks great, I've ordered it. I was aware of a similar sounding book if not the same being talked of at Uni and thats probably how this question originated. I was aware we take our definitions of a meter from the speed of light, so it will always be exactly defined as 3x10^8m/s.

From the book synopsis, I see the six numbers are:

nu (a ratio of the strength of electrical forces that hold atoms together compared to the force of gravity which is 10 to the 37th power)

epsilon (how firmly the atomic nuclei bind together which is 0.004)

omega (amount of material in the universe)

lambda (force of cosmic "antigravity" discovered in 1998, which is a very small number)

Q (ratio of two fundamental energies, which is 1/100,000)

delta (number of spatial dimensions in our universe)

I'd be interested in which of these c is involved, if not all of them.