Is the Relative Speed of Light Constant?

[jjaji]

I read somewhere that relative speed of light always remains constant. That is there is no difference between relative speed and absolute speed of light.
If we move with 99% velocity of light in the direction of light , the speed of light is NOT 1% of actual speed of light , It still remains 100% speed of light.

I would like to if above statement is correct.

 

[Doc Al]

All speeds are relative to something; an absolute speed has no meaning. But it's true: No matter what your speed, you will always measure the speed of light with respect to yourself to be the same.

If you are moving at 99% of lightspeed with respect to me, and you shine a beam of light in the direction of your motion, you and I will both measure that beam to move at speed c with respect to ourselves.

 

[jjaji]

I agree , but this is the same case with all other motion also.
Like .. I am traveling on moving body of speed X and i am throwing an object(A) with speed X in the same direction of my motion then the speed of A with respect to myself is X.

I think i need to put my question with more clarity.

Lets say , There are light beam L1 and spaceship S1 and an Observer O.
S1 is 99% speed of Light, both L1 and S1 starts at same instance of time

With respect to O , S1 travels 99% speed of L1
With respect to person in spaceship L1 is 1% greater speed than S1

What I understood from the book was L1 is always 100% speed of light relative to S1.
I know this is not logically sound.

 

[Doc Al]

I agree , but this is the same case with all other motion also.
Like .. I am traveling on moving body of speed X and i am throwing an object(A) with speed X in the same direction of my motion then the speed of A with respect to myself is X.

That's true, by definition--since you told us that you threw the object with speed X with respect to you. But it's not true that the speed of the object is X with respect to anyone, unless it's moving at light speed.

Lets say , There are light beam L1 and spaceship S1 and an Observer O.
S1 is 99% speed of Light, both L1 and S1 starts at same instance of time


With respect to O , S1 travels 99% speed of L1

OK.

With respect to person in spaceship L1 is 1% greater speed than S1

With respect to the spaceship, the speed of the S1 is zero and the speed of L1 is c.

What I understood from the book was L1 is always 100% speed of light relative to S1.

That's true.

I know this is not logically sound.

Why is that?

 

[jjaji]

With respect to the spaceship, the speed of the S1 is zero and the speed of L1 is c.

.

Yes , WRT to spaceship speed of S1 is zero. But i don't understnad why L1 is c with respect to spaceship

Lets say speed of A = 100 and B = 90 then relative speed of A WRT B is 10 and speed of B with respect to B =0 is that not the case? , can't we substitute A with c and B with speed of S1.

am i missing something?

 

[Doc Al]

What you're missing is that for high speeds (where relativistic effects cannot be ignored), velocities do not simply add like they do for low speeds.

For low speeds, velocities add like this:
$$V_{a/c} = V_{a/b} + V_{b/c}$$

But for high speeds, we must use relativistic addition of velocities:
$$V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}$$

 

[jtbell]

Just to nit-pick a bit: the second formula is always valid (both high and low speeds). The first formula is merely a very good approximation to the second one, for low speeds. jjaji, try calculating a few examples if you're not convinced of this.

 

[Doc Al]

I wouldn't call that a nit-pick, but an important clarification!

 

[jjaji]

How do we arrive at this expression ? Can you point me the theory behind it ? Pls post weblink if possible.

 

[Doc Al]

Try this: http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html"

 

[jjaji]

yes for low speed, denominator is almost equals to 1. I am curious how this formula is arrived at.

btw , I am working as a software engineer ,(had physics at graduate level) i just got very curious about SR and QM. so sometime i might ask some basic questions

 

[jtbell]

I am curious how this formula is arrived at.

That depends on where you're starting from, logically speaking. It can be derived from the Lorentz transformation:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/veltran.html#c1

Basically, all of relativistic kinematics (length contraction, time dilation, relativity of simultaneity, velocity addition) can be derived from the Lorentz transformation.

 

[robphy]

yes for low speed, denominator is almost equals to 1. I am curious how this formula is arrived at.

btw , I am working as a software engineer ,(had physics at graduate level) i just got very curious about SR and QM. so sometime i might ask some basic questions

The best way to think about the formula [in the case of motion in one spatial dimension]
is in terms of adding "angles" in Minkowski geometry (i.e. arc-length of the unit "circle" in Minkowski geometry) and interpreting "spatial velocity" as the hyperbolic-tangent of the "angle" multiplied by c. The formula is essentially an identity for the hyperbolic-tangent of a sum of two angles (as seen in Doc Al's link).

[In the more-general situation, it really amounts to trigonometry on the unit-hyperboloid.]

The methods above give a geometrical picture that underlies the algebraic formulas that are often (arguably, over-) emphasized in textbooks.