The reality of Relative Velocities in Special Relativity

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Discussion Overview

The discussion revolves around the concept of relative velocities in the context of Special Relativity, specifically focusing on the calculations of relative speeds between two objects moving at significant fractions of the speed of light. Participants explore the implications of these calculations, the validity of the velocity addition formula, and the nature of measurements in relativistic contexts.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes a scenario with observer O and objects A and B moving at speeds of 0.5c and 0.3c, respectively, and discusses the calculation of relative speed.
  • Another participant calculates the relative speed of A as 3/17c, but later acknowledges an error in their calculation.
  • There is a discussion about the ability of observer B to measure A's speed relative to themselves, questioning the initial assumption that B cannot provide this information.
  • Participants mention that the rules for velocity addition in Special Relativity have not been extensively tested with macroscopic objects, although one participant cites the Fizeau experiment as evidence of testing.
  • One participant raises a question about whether the relative velocity equation can yield a speed greater than c when both input velocities are less than c, expressing confidence that it cannot.
  • Another participant confirms that the velocity addition formula, derived from Lorentz transformations, does not allow for speeds to exceed the speed of light.
  • Several participants engage in light-hearted banter regarding calculation errors, with acknowledgments of mistakes and humorous remarks about calculators.

Areas of Agreement / Disagreement

Participants express differing views on the testing of velocity addition rules and the ability of observers to measure relative speeds. While some participants agree on the implications of the velocity addition formula, the discussion contains unresolved questions regarding the calculations and assumptions made.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about observer capabilities and the extent of experimental validation of the velocity addition formula. Some mathematical steps and definitions remain unresolved.

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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