# How Do Relative Velocities Transform in Special Relativity?

• wansui
In summary, the conversation is about the speed of different objects in different reference frames. A is moving to the left at a speed of 0.9c relative to E, while B is moving to the right at a speed of 0.7c relative to E. The questions asked are: What is the speed of B in the reference frame of A? What is the speed of E in the reference frame of A? What is the speed of A in the reference frame of B? What is the speed of E in the reference frame of B? The equations for calculating speed in special relativity can be found at the provided link and the concept of speed being symmetrical between reference frames is also mentioned.
wansui
If A is moving to the left at a speed of 0.9c relative to E, B is moving to the right at a speed of 0.7c relative to E.

In the reference frame of A, what is the speed of B?
In the reference frame of A, what is the speed of E?
In the reference frame of B, what is the speed of A?
In the reference frame of B, what is the speed of E?:uhh:

http://www.math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html

Try to see if you can answer your own questions using the equations there, and then post again if you're still having trouble. Also, note that speed in special relativity is symmetrical between any two reference frames--if in my frame you are moving at speed v relative to me, then in your frame I will also be moving at speed v relative to you.

I would like to clarify that "special velocity" is not a commonly used term in physics. However, based on the given information, we can use the principles of special relativity to determine the speeds in different reference frames.

In the reference frame of A, the speed of B can be calculated using the relativistic velocity addition formula: VBA = (VBE + VAE)/(1 + (VBE*VAE)/c^2), where VBA is the velocity of B as seen by A, VBE is the velocity of B relative to E, and VAE is the velocity of A relative to E. Plugging in the values, we get VBA = (-0.7c + 0.9c)/(1 + (-0.7c*0.9c)/c^2) = 0.98c. This means that in A's reference frame, B appears to be moving to the left at a speed of 0.98c.

In the reference frame of A, the speed of E can be calculated using the same formula as above, but with the values of VBE and VAE swapped. This gives us VAE = (VAB + VBE)/(1 + (VAB*VBE)/c^2) = (-0.9c + 0.7c)/(1 + (-0.9c*0.7c)/c^2) = -0.92c. This means that in A's reference frame, E appears to be moving to the right at a speed of 0.92c.

In the reference frame of B, the speed of A can be calculated using the same formula as above, but with the values of VAB and VBE swapped. This gives us VAB = (VAE + VBE)/(1 + (VAE*VBE)/c^2) = (-0.92c + 0.7c)/(1 + (-0.92c*0.7c)/c^2) = -0.98c. This means that in B's reference frame, A appears to be moving to the left at a speed of 0.98c.

In the reference frame of B, the speed of E can be calculated using the relativistic velocity addition formula: VEB = (VAE + VAB)/(1 + (VAE*VAB)/c^2) = (-0.

## 1. What is special velocity?

Special velocity, also known as relativistic velocity, is the speed at which an object is moving relative to an observer. It takes into account the effects of special relativity, which states that the laws of physics should remain the same for all observers in uniform motion.

## 2. How is special velocity different from regular velocity?

Special velocity takes into account the effects of special relativity, such as time dilation and length contraction, which regular velocity does not. This means that as an object approaches the speed of light, its special velocity will increase while its regular velocity remains constant.

## 3. What is the maximum special velocity an object can reach?

The maximum special velocity an object can reach is the speed of light, which is approximately 299,792,458 meters per second. According to special relativity, it is impossible for any object with mass to reach or exceed this speed.

## 4. How is special velocity calculated?

Special velocity is calculated using the equation v = c * tanh(tanθ), where v is the special velocity, c is the speed of light, and θ is the object's regular velocity measured as a fraction of the speed of light. This equation takes into account the effects of special relativity on an object's velocity.

## 5. What are some applications of special velocity?

Special velocity is important in many areas of physics, including astrophysics, particle physics, and nuclear physics. It is also crucial for understanding the behavior of objects traveling at high speeds, such as spacecrafts and particles accelerated in particle accelerators. Additionally, special velocity plays a role in the theory of relativity, which has had a significant impact on our understanding of the universe.

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