Confused by Notation: Need Help Understanding c!

In summary, the conversation is discussing the equation c^2 = group velocity x phase velocity and questioning the meaning of c in this context. The participants also mention that this equation is not always true and that the group velocity and phase velocity may differ in certain cases. However, it is generally accepted that for light, c represents the speed of light. Some participants also suggest that c may be reserved for the speed of light or a constant, and that other velocities would be denoted as v. Overall, there is some ambiguity in the interpretation of this equation, but it is commonly understood to represent the relationship between group velocity and phase velocity.
  • #1
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Homework Statement



I'm just confused by notation in this question, because the textbook I use has different notation than my course notes and now I'm just not sure what anything means.

Homework Equations



Group velocity x Phase velocity = c^2

The Attempt at a Solution



What is c in this case? Is it the speed of light, or some other velocity?
I know it's a really stupid question...

Ta for any help though.
 
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  • #2
Well, I assume that it is the speed of light. But really, the equation is not true in general.
Yes, photons move at c in free space, so phase velocity is c in free space (but inside midiums, the speed would get lower.).
However, the group velocity, could actually be lower than c. even 0. Just for reference, this is called EIT.
So if it is someother speed, well, normally it would be denoted as v, instead of c. c is normally reserved for the speed of light, or constant.
I guess what the most important part of this equation is that group velocity and phase velocity are the same in most of the cases: so if it is light, then it is c^2; if it is something else, then it is v^2. It is kinda open interpretation.
 
  • #3
According to Wikipedia it is indeed the speed of light. I've never seen that particular equation before myself, but the derivation on Wikipedia looks reasonable...
 

1. What is the meaning of "c" in this context?

In mathematics and physics, "c" typically refers to the speed of light in a vacuum, which is approximately 299,792,458 meters per second.

2. How is "c" used in equations?

"c" is often used as a constant in equations, representing the speed of light. It can also be used to denote other constants, such as the speed of sound or the speed of a wave.

3. What does the "!" symbol mean in the notation?

The "!" symbol is typically used in mathematics to represent the factorial operation, which is the product of all positive integers less than or equal to a given number. In this context, it may be used to indicate a certain number of iterations or repetitions.

4. How does the notation differ from standard mathematical notation?

The notation used in this context may differ from standard mathematical notation, as it may be specific to a certain field or concept. It is always important to carefully read and understand the notation being used in order to correctly interpret equations and formulas.

5. Can you provide an example of this notation in use?

One example of this notation in use is in the equation E=mc², where "c" represents the speed of light and the superscript "2" indicates the operation of squaring. This equation is known as the famous mass-energy equivalence equation, proposed by Albert Einstein in his theory of relativity.

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