Some questions regarding speed of light?

[supermankid]

My understanding:
Relative to stationary body, the speed of light is 3*10^8[m/s]
In all intertial frame of reference the speed of light remains constant:
menaing, if I travel in rocketship @ 0.5*c, the light coming out of my rocketship will also travel at 3*10^8[m/s]. The law of physics remains same everywhere in universe.
So, c is same for faster/ slower/ stationary bodies.

But I have difficulty understanding a point, the maximum cosmic limit is c.
(Do they mean it with reference to a stationary object?)

Considering two accelerating bodies:
If two of them are moving at 0.6*c the speed of light.
The relative speed of them for each other would be 1.2*c (correct me if my assumption is wrong).
If the light is beamed from one of these two directed to the other, the light would never reach the other because they would always travel faster than the speed of light?
Second, the maximum relative speed could be bigger than c.??!

 

[cpsinkule]

velocities do not add like u+v in relativity. the velocity addition formula ensures that the sum of any 2 velocities is never greater than c

 

[supermankid]

velocities do not add like u+v in relativity. the velocity addition formula ensures that the sum of any 2 velocities is never greater than c

Some more details would be nice. I am not hard core physics kid but interested a lot.
So, let's get it this way. It works on earth, if two bodies travel at 5m/s. One would see the other @ speed of 10m/s.
When or at what speed this classical concept stops working and relativity takes over ?
How can this simple phenomenon be explained by relativity and also the above mentioned in my original question.

I am highly expecting, someone could throw some light to my question with very high speed :)?

 

[cpsinkule]

there are several things you need to understand before the law will make sense. in special relativity, you cannot detect your own motion, assuming you are not subject to any forces or accelerations. the most you could possibly say is that you are moving relative to something else. the composition law for velocities in special relativity requires two observers (inertial frames) for which the object in question is moving relative to both. it makes no sense to ask the question "if i shoot a bullet with speed v and I am moving at speed u, what is the speed of the bullet?" because the statement "i am moving at speed u" has no meaning unless you specify what you are moving relative to. if you understand that part we can continue.

if you and a different observer are moving relative to one another with velocity u=.9c (to make it simpler I will assume it is co-linear motion ) and that other observer fires a bullet from a gun and measures it's velocity as v=.5c then you will measure the velocity of the bullet given by the addition law of velocities
w=u+v/[1+(uv/c²)]≈.96c which is less than the speed of light. from the formula, it should be clear that no matter how large u and v are, there sum defined this way can never exceed c. in the limiting case, if u=.5c and v=c the law gives the composite velocity w=c as the answer, which is another statement that light will always be seen as moving with speed c by any observer.

 

[A.T.]

if two bodies travel at 5m/s. One would see the other @ speed of 10m/s

Not exactly:
https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity

 

[supermankid]

COOOOOOL...thanks MODs. This is interesting. I don't understand intuitively but I believe it from the formulae...

Can I ask you for a favor? I am engineering student...but I sooo want to understand relativity...
Would you recommend me some books, article,(website/blogs/archive) to get to understand it...
I want to grasp the idea of how these formulae came about and what are the basis for these formula...

 

[anorlunda]

COOOOOOL...thanks MODs. This is interesting. I don't understand intuitively but I believe it from the formulae...

Can I ask you for a favor? I am engineering student...but I sooo want to understand relativity...
Would you recommend me some books, article,(website/blogs/archive) to get to understand it...
I want to grasp the idea of how these formulae came about and what are the basis for these formula...

I highly recommend Professor Susskind's video course. He is a master teacher.

 

[HallsofIvy]

My understanding:
Relative to stationary body, the speed of light is 3*10^8[m/s]

Your first sentence indicates that you do NOT understand! There is NO body that is "stationary" of itself. The speed of light is that speed relative to any object.

In all intertial frame of reference the speed of light remains constant:
menaing, if I travel in rocketship @ 0.5*c, the light coming out of my rocketship will also travel at 3*10^8[m/s].

The same error. if you are traveling in a rocketship @ 0.5c relative to some given frame of reference, the light coming out of your rocketship will also travel at 3*10^8 [m/s] relative to that same frame of reference.

The law of physics remains same everywhere in universe.
So, c is same for faster/ slower/ stationary bodies.

But I have difficulty understanding a point, the maximum cosmic limit is c.
(Do they mean it with reference to a stationary object?)

There is NO stationary object!

Considering two accelerating bodies:
If two of them are moving at 0.6*c the speed of light.

You said "accelerating bodies" so they can't be moving at any constant speed!

The relative speed of them for each other would be 1.2*c (correct me if my assumption is wrong).

Yes, you are wrong. If you see two objects moving toward each other with, relative to you, 0.6c then they would each be approaching the other at
[tex]\frac{0.6c+ 0.6c}{1+ \frac{(0.6c)(0.6c)}{c^2}}= \frac{1.2c}{1.36}= 0.88c[/tex]

If the light is beamed from one of these two directed to the other, the light would never reach the other because they would always travel faster than the speed of light?
Second, the maximum relative speed could be bigger than c.??!

 

[vanhees71]

COOOOOOL...thanks MODs. This is interesting. I don't understand intuitively but I believe it from the formulae...

Can I ask you for a favor? I am engineering student...but I sooo want to understand relativity...
Would you recommend me some books, article,(website/blogs/archive) to get to understand it...
I want to grasp the idea of how these formulae came about and what are the basis for these formula...

Here's the beginning of my special-relativity FAQ:

http://fias.uni-frankfurt.de/~hees/pf-faq/srt.pdf