# Is the Relative Speed of Light Constant?

• jjaji
In summary: This is a matter of opinion, but I believe that the geometric picture makes the formulas easier to remember, and easier to use when generalizing to higher dimensions.In summary, the relative speed of light remains constant regardless of the observer's frame of reference. This means that the speed of light is always measured to be the same, no matter what the observer's velocity is. This is because all speeds are relative and there is no absolute speed. This concept can be understood using the Lorentz transformation and the hyperbolic-tangent formula, which describe how velocities add in Minkowski geometry.
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.

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.

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.

jjaji said:
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?

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?

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:
$$V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}$$

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.

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

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

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

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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

jjaji said:
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.

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jjaji said:
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.

## 1. What is the significance of the speed of light being constant?

The speed of light being constant is a fundamental principle in physics and is a cornerstone of the theory of relativity. It is a universal constant that is the same in all inertial frames of reference. This means that the speed of light is the same for all observers, regardless of their relative motion.

## 2. How is the constant speed of light measured?

The constant speed of light is measured using tools such as lasers and interferometers. These instruments use the principles of optical interference to accurately measure the speed of light. The current accepted value for the speed of light is 299,792,458 meters per second.

## 3. Has the speed of light always been constant?

It is currently believed that the speed of light has always been constant. While there are theories that suggest the speed of light may have been different in the past, there is currently no evidence to support these claims. The principle of the constant speed of light has been verified through numerous experiments and observations.

## 4. Does the constant speed of light apply to all forms of light?

Yes, the constant speed of light applies to all forms of electromagnetic radiation, including visible light, radio waves, and X-rays. This is because all forms of electromagnetic radiation travel at the same speed in a vacuum, regardless of their frequency or wavelength.

## 5. Can anything travel faster than the speed of light?

According to the theory of relativity, nothing can travel faster than the speed of light. This is because as an object approaches the speed of light, its mass increases infinitely, making it impossible to accelerate it any further. While there are theories that suggest ways to circumvent this limitation, they have not been proven and are not widely accepted in the scientific community.

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