The reality of Relative Velocities in Special Relativity

In summary, 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.
  • #1
Quarlep
257
4
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.
 
Physics news on Phys.org
  • #2
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:
  • #3
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).
 
  • #4
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.
 
  • #5
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.
 
  • #6
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.
 
  • #7
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:
 
  • #8
PeterDonis said:
Oops, you're right! I multiplied instead of subtracted. :oops:
Blame it on the calculator! Those buttons are so close together.
 
  • #9
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. ;)
 

Related to The reality of Relative Velocities in Special Relativity

What is special relativity?

Special relativity is a theory developed by Albert Einstein that explains the relationship between space and time in the absence of gravity. It is based on two main principles: the constancy of the speed of light and the relativity of simultaneity.

What is the concept of relative velocity in special relativity?

Relative velocity in special relativity refers to the speed of an object relative to a specific observer. This means that the velocity of an object can change depending on the frame of reference of the observer. In special relativity, the concept of relative velocity is essential for understanding the effects of time dilation and length contraction.

How does special relativity explain the relationship between time and space?

Special relativity states that the laws of physics should be the same for all observers in uniform motion, regardless of their relative velocity. This means that time and space are not absolute, but are relative concepts that depend on the observer's frame of reference. This theory also predicts that time can appear to pass at different rates for observers in different frames of reference.

What is the formula for calculating relative velocity in special relativity?

The formula for calculating relative velocity in special relativity is given by v = (u + v') / (1 + uv'/c^2), where v is the relative velocity, u is the velocity of the first object, v' is the velocity of the second object, and c is the speed of light. This formula takes into account the effects of time dilation and length contraction.

What are some real-life examples of relative velocities in special relativity?

One famous example is the observation of muons, which are subatomic particles with a very short half-life. When they are created in the upper atmosphere and travel towards Earth, their relative velocity causes them to experience time dilation, allowing them to reach the surface of the Earth before they decay. This phenomenon has been confirmed through experiments and is a direct result of special relativity.

Similar threads

  • Special and General Relativity
Replies
17
Views
674
  • Special and General Relativity
Replies
15
Views
935
  • Special and General Relativity
Replies
21
Views
707
Replies
32
Views
959
  • Special and General Relativity
2
Replies
35
Views
2K
  • Special and General Relativity
Replies
21
Views
1K
  • Special and General Relativity
Replies
20
Views
858
  • Special and General Relativity
2
Replies
57
Views
4K
  • Special and General Relativity
Replies
17
Views
954
  • Special and General Relativity
Replies
9
Views
1K
Back
Top