The Significance of c

The Significance of c

An earlier page discussed two conclusions of Einstein's Theory of Relativity:

"Light in a vacuum always travels at the same speed."
"Nothing can travel faster than the speed of light in a vacuum."

The first statement has several implications. One is that light of all wavelengths travels the same speed c in a vacuum. Highly-energetic gamma rays, low-energy radio waves, and all other types of electromagnetic radiation travel at 299,792,458 m/s when in a vacuum. When traveling through another medium, however, the speeds are not necessarily the same. Light of different energies and wavelengths will interact with matter differently, have different indices of refraction, and therefore travel at different speeds through a medium other than vacuum. We will not worry about the difference in this module, but will instead cover it along with other forms of dispersion in a different module.

The second statement above needs a bit more clarification. Some intangible things, such as shadows or projections, can move faster than c. (Suppose you could make an incredibly powerful laser that could shine all the way to Pluto. If you swing the laser, the location of the laser spot on Pluto would move much faster and could conceivably have a speed exceeding c.) Einstein's ultimate limit on speeds refers to the speed at which information can move from one point to another. Thus no physical particle can travel faster than c, lest information carried by that particle travel faster than c. (Using the previous example, the moving laser beam still has to travel to Pluto before the spot there will move, so the information "I have moved my laser" still does not travel faster than c.) This is why c is often called the ultimate speed limit of the universe. This limit, however, does not constrain the rate at which information is transferred but only the delay between the time at which information is sent and when it is received. The factors limiting the amount of information sent are discussed in the module on signal transfer.

The speed of light in vacuum is the ultimate speed limit of the universe

Note: Saying that no particles move faster than c does not mean that no particles will ever travel faster than light. In water, for example, light slows down more than some high-energy electrons do. Thus an electron may travel faster than light in water, although no electron will ever travel faster than c.

Another implication of the first statement above is that any measurement of c will yield the same value, even if two measurements are done in environments moving relative to each other. A scientist in a rocket moving at a constant speed away from earth will measure the speed of light in vacuum to be c, as will a scientist on earth who measures the speed of light in c inside the rocket. Further discussion of this topic is outside the scope of this module, but the inquisitive reader is encouraged to read more about it in some of the References.

Does anything change except the speed when light moves from one
medium to another? Continue to the next page to find out!