The reality of Relative Velocities in Special Relativity

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SUMMARY

The discussion centers on the calculation of relative velocities in the context of Special Relativity (SR). Observer O measures two objects, A and B, moving at speeds of 0.5c and 0.3c, respectively. The correct relative speed of A as observed by B is calculated using the velocity addition formula, yielding 3/17c. The conversation also emphasizes that the SR rules for velocity addition, derived from Lorentz transformations, ensure that no object can exceed the speed of light, c.

PREREQUISITES
  • Understanding of Special Relativity principles
  • Familiarity with Lorentz transformations
  • Knowledge of velocity addition formulas in physics
  • Basic arithmetic operations involving fractions and decimals
NEXT STEPS
  • Study the derivation of the Lorentz transformations
  • Learn about the implications of the speed of light as a cosmic speed limit
  • Explore practical applications of velocity addition in relativistic physics
  • Investigate experimental tests of Special Relativity, such as the Fizeau experiment
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Students of physics, educators teaching Special Relativity, and anyone interested in the mathematical foundations of relativistic motion.

Quarlep
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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 that's true because we can't ask. him How can O predict this speed or he know that there's special relativity and nothing is really what it seem.
 
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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 that's true because we can't 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 there's 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.
 
Last edited:
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).
 
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.
 
I want to ask another question.Whatever I wrote in Relative velocity equation I get small then c isn't 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 there's no probability of that but I want to be sure.
 
Quarlep said:
I want to ask another question.Whatever I wrote in Relative velocity equation I get small then c isn't 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 there's 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.
 
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. :oops:
 
PeterDonis said:
Oops, you're right! I multiplied instead of subtracted. :oops:
Blame it on the calculator! Those buttons are so close together.
 
ghwellsjr said:
Blame it on the calculator! Those buttons are so close together.

Unfortunately I did this one in my head... :eek:
 
  • #10
PeterDonis said:
Unfortunately I did this one in my head... :eek:
Uh ... are the parts too close together? :D You could blame it on your hat.
 
  • #11
Quarlep
I want to ask another question.Whatever I wrote in Relative velocity equation I get small then c isn't 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 there's no probability of that but I want to be sure.
You can check it yourself by substituting 1 for either of the values.
 
  • #12
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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