MarkeD said:
Is c so finely tuned as other constants such as the fine structure constant?
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 doesn't 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 doesn't 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 10
8 meters a second?". it would simply amount to changing the definition of the meter and nothing else
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it doesn't 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 doesn't 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.com/dp/0753810220/?tag=pfamazon01-20
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.