Q: Why is the speed of light the value that it is?
Submitted By: Craig, 81 days, 11 hours, 24 minutes ago
We know that the speed of light in a given medium is a constant and that the speed of light in a vacuum appears to be an absolute limit and that E=mc^2. However, can anyone prove to me mathematically (ie without resorting to experiments that measure the speed of light or deduce it from interference patterns etc) why c is the value that it is and not some other value? Is there a way of deriving c from first principles which shows it to be the only rate that electromagnetic radiation can propagate at in this universe and why? i.e. We can prove without resorting to measurement why PI is the value that it is, can the same not be true for c?
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Planck Length
Submitted By: enisoc ( 79 days, 14 hours, 4 minutes ago )
It is theorized as a property of our universe that there exists a certain distance (on the order of 10^-35 meters), called the Planck length, that is the smallest unit of length that has any meaning. In other words, no measurement of distance can ever be made with an error less than the Planck length. This can be interpreted to mean that essentially space is discretely quantized (you might even say digital), such that there is a non-zero, finite minimum distance between any two points. Similarly, the theoretical smallest possible measurement of time is called the Planck time, and it is on the order of 10^-44 seconds. Since speed is distance per unit time, we can then think of the speed of a particle as being a measure of the probability that it will advance from one discrete point to the next one, a Planck length away in some direction, in a given Planck time. Assuming that the particle is lucky enough to achieve a 1.0 probability of advancing, we can calculate its speed as being one Planck length per Planck time, as follows:
(approximate values from http://en.wikipedia.org/wiki/Planck_units )
speed = l_P / t_P = 1.61624*10^-35 m / 5.39121*10^-44 s = 299,791,698 m/s
This is then the fastest speed that anything in the universe can hope to achieve without "cheating" (that is, without skipping from one point in space to a non-adjacent point some distance away in a single Planck time). You may also recognize it as approximately the speed of light in vacuum, allowing for rounding errors.
To be continued... (post size limit)
(approximate values from http://en.wikipedia.org/wiki/Planck_units )
speed = l_P / t_P = 1.61624*10^-35 m / 5.39121*10^-44 s = 299,791,698 m/s
This is then the fastest speed that anything in the universe can hope to achieve without "cheating" (that is, without skipping from one point in space to a non-adjacent point some distance away in a single Planck time). You may also recognize it as approximately the speed of light in vacuum, allowing for rounding errors.
To be continued... (post size limit)
Submitted By: enisoc
Of course, this doesn't answer anything really, because now we need to explain why the Planck length and time are the values they are. These values can be theoretically deduced from the fact that it is impossible to measure length at such a small scale that doing so would require probing the target with a photon so energetic that it would create a black hole on impact and thus defeat the possibility of obtaining a measurement (the photon being unable to escape from the newly formed black hole). This in turn relies upon the gravitational constant, which must be either experimentally measured or calculated from other experimentally measured values. On the other hand, if we express the gravitational constant in terms of units based on the Planck length, its value is simply 1. So where does that leave us?
to be continued again...
Submitted By: enisoc
If we accept that our universe is such that space and time are quantized into discrete non-zero smallest steps, then of course there must be some numerical value for those steps. The question then is not, "why are the steps the size that they are," but rather, "why is everything else in the universe the size that it is, relative to the smallest units possible?" When we find values for these constants in terms of our invented units, such as SI, we are only answering the question of how our contrived units relate to the "natural" units of the universe. Why our units are the size that they are is a matter of history.
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Speed of light may have changed
Submitted By: Craig ( 68 days, 2 hours, 19 minutes ago )
Some more info on this from <a href="http://www.newscientist.com/article/dn6092.html">New Scientist</a>
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Because it isn't any of the other values
Submitted By: porcupine ( 46 days, 19 hours, 58 minutes ago )
Zen rocks