# The reality of Relative Velocities in Special Relativity

Lets suppose we have a observer O and two objects A and B a speed is 0.5c and B speed is 0.3c than we can calculate other relative speed acoording to these informations.We know that (according this info B sees A going to 4/17c but we can pretty sure thats true because we cant ask. him How can O predict this speed or he know that theres special relativity and nothing is really what it seem.

PeterDonis
Mentor
we have a observer O and two objects A and B a speed is 0.5c and B speed is 0.3c than we can calculate other relative speed acoording to these informations

Yes.

We know that (according this info B sees A going to 4/17c

I calculate 3/17 for the speed of A relative to B (assuming they are both moving in the same direction relative to O)

[Edit: the above was incorrect.]

but we can pretty sure thats true because we cant ask. him

Why can't we ask B? B is an observer just like O and A; there's no reason why he can't directly measure A's speed relative to him.

How can O predict this speed or he know that theres special relativity and nothing is really what it seem.

The SR rules for velocity addition have not been extensively tested with macroscopic objects, true. But SR in general has been very extensively tested, and the results would make no sense if the SR rule for velocity addition were not true, since it forms a consistent part of the whole theoretical framework of SR.

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Nugatory
Mentor
The SR rules for velocity addition have not been extensively tested with macroscopic objects, true.

(PeterDonis knows this already, of course - this comment is for Quarlep).

ghwellsjr
Gold Member
I calculate 3/17 for the speed of A relative to B (assuming they are both moving in the same direction relative to O):

$$v_{AB} = \frac{v_A - v_B}{1 - v_A v_B} = \frac{0.5 - 0.3}{1 - 0.5 * 0.3} = \frac{0.15}{0.85} = \frac{3}{17}$$
You better get a new calculator. 0.5-0.3 is 0.2 not 0.15. The OP was correct.

I want to ask another question.Whatever I wrote in Relative velocity equation I get small then c isnt it.I mean the equation requires it.Lets suppose I have two velocities smaller than c than I put it this equation these velocity Is there a chance to get bigger than c I think theres no probability of that but I want to be sure.

Ibix
I want to ask another question.Whatever I wrote in Relative velocity equation I get small then c isnt it.I mean the equation requires it.Lets suppose I have two velocities smaller than c than I put it this equation these velocity Is there a chance to get bigger than c I think theres no probability of that but I want to be sure.
Correct. The velocity addition formula can be derived directly from the Lorentz transforms, which by definition don't allow anything moving below the speed of light to reach or exceed it.

PeterDonis
Mentor
You better get a new calculator. 0.5-0.3 is 0.2 not 0.15. The OP was correct.

Oops, you're right! I multiplied instead of subtracted.

ghwellsjr
Gold Member
Oops, you're right! I multiplied instead of subtracted.
Blame it on the calculator!!! Those buttons are so close together.

PeterDonis
Mentor
Blame it on the calculator!!! Those buttons are so close together.

Unfortunately I did this one in my head...

phinds
Gold Member
2021 Award
Unfortunately I did this one in my head...
Uh ... are the parts too close together? :D You could blame it on your hat.

Quarlep
I want to ask another question.Whatever I wrote in Relative velocity equation I get small then c isnt it.I mean the equation requires it.Lets suppose I have two velocities smaller than c than I put it this equation these velocity Is there a chance to get bigger than c I think theres no probability of that but I want to be sure.
You can check it yourself by substituting 1 for either of the values.

PeterDonis
Mentor
Uh ... are the parts too close together? :D You could blame it on your hat.

Not wearing one. I appreciate the effort to salvage my self-esteem, though. ;)