# What's the secret behind v < c

#### topsquark

Forum Staff
The "chirality" I mentioned is very simple natural space property. Take a spiral spring or a drill and observe it carefully and you will get it.
Yes, of course. Classically speaking you are correct. I should have mentioned that I'm referring to the chiral properties of subatomic particles. My apologies.

In the whole course of derivation of SR, Einstein did not mention what light speed c exactly is. Actually, light speed has two different concepts: phase speed and group speed. It's impossible Einstein did not know that. I feel interesting.
Of course Einstein knew about phase and group speeds. He was referring to the group speed of light, which is labeled "c".

-Dan

#### neila9876

@dragon:
Nope, I can't find any proof about what Einstein mentioned about what c is. He bypassed that issue.

#### neila9876

What's the c calculated by that dragon with permitivity and permeability in his previous reply? Group speed or phase speed?

#### topsquark

Forum Staff
What's the c calculated by that dragon with permitivity and permeability in his previous reply? Group speed or phase speed?
Group.

-Dan

#### neila9876

@dragon:
I missed something in my last post, "empty space"...sorry.

#### topsquark

Forum Staff
No problem. Typically when the term "speed of a wave" is used we are referring to the group speed.

-Dan

#### neila9876

@dragon:
Why? How about in situation of single frequency wave? I wonder if my old textbook is outdated...

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#### neila9876

group vs phase

Phase speed is a natural concept. It's the true "light speed" in nature, for single frequency wave.
Whille group speed is an artificial method of calculation for multi frequency wave. It's approximation and changes with combination of frequencys.
Synthetic wave in man's eye actually is several single frequency wave in nature. It's man that sythesize it. Man often do that to complicate nature.
The light speed calculated with permitivity and permeability in empty space is applicable to any single frequency wave, it should be phase speed.

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#### topsquark

Forum Staff
Phase speed is a natural concept. It's the true "light speed" in nature, for single frequency wave.
Whille group speed is an artificial method of calculation for multi frequency wave. It's approximation and changes with combination of frequencys.
Synthetic wave in man's eye actually is several single frequency wave in nature. It's man that sythesize it. Man often do that to complicate nature.
The light speed calculated with permitivity and permeability in empty space is applicable to any single frequency wave, it should be phase speed.
A wave with a single frequency travels at a given speed which is just called the speed. If there are no other frequencies involved there is no distinction between a phase or group speed... you can call it what you like.

If there is more than one frequency then the speed of the envelope is called the group speed, and the speed of the waves inside the envelope is called the phase speed.

Mathematically we have
$$\displaystyle v_g = \dfrac{d \omega }{d k}$$

$$\displaystyle v_p = \dfrac{ \Delta \omega }{ \Delta k}$$

It is possible for the phase speed to be greater than the speed of light.

-Dan

#### neila9876

Actually, it’s not necessary to care too much about if c is phase speed or group speed or the specific value of c in SR. Just take it as a symbol. At last, the element γ reflects what it is. The symbol c is limit v. It means the limit of moving velocity of objects in 3D space. So, it can be only one value. It’s a universe constant.
Many experiments, e.g. acceleration of particles, etc, demonstrate such a limit of moving velocity ****** m/s does exist.
From the angle of light itself, measurements also demonstrate such a value ****** m/s does exist.