The reality of Relative Velocities in Special Relativity

Quarlep · Jan 21, 2015

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 · Jan 21, 2015

Quarlep said: ↑

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.

Quarlep said: ↑

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.]

Quarlep said: ↑

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.

Quarlep said: ↑

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.

Nugatory · Jan 21, 2015

PeterDonis said: ↑

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

They have, however, been tested. Google for "Fizeau velocity addition".

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

ghwellsjr · Jan 22, 2015

PeterDonis said: ↑

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.

Quarlep · Jan 22, 2015

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 · Jan 22, 2015

Quarlep said: ↑

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 · Jan 22, 2015

ghwellsjr said: ↑

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 · Jan 22, 2015

PeterDonis said: ↑

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

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

PeterDonis · Jan 22, 2015

ghwellsjr said: ↑

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

Unfortunately I did this one in my head...

phinds · Jan 22, 2015

PeterDonis said: ↑

Unfortunately I did this one in my head...

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

phyti · Jan 22, 2015

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 · Jan 22, 2015

phinds said: ↑

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. ;)

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The reality of Relative Velocities in Special Relativity

Quarlep

PeterDonis

Staff: Mentor

Nugatory

Staff: Mentor

ghwellsjr

Quarlep

Ibix

PeterDonis

Staff: Mentor

ghwellsjr

PeterDonis

Staff: Mentor

phinds

phyti

PeterDonis

Staff: Mentor

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