# Velocity in Lorentz Transformations

• zimbabwe
In summary, the conversation discusses two Lorentz velocity equations and their usage in determining the velocity of a particle in different frames of reference. The first equation, v'=(v-u)/(1-vu/c^2), gives the velocity of a particle in frame of reference K' in terms of its velocity in frame of reference K. The second equation, v=(v'+u)/(1+v'u/c^2), gives the velocity of a particle in frame of reference K in terms of its velocity in frame of reference K'. The question posed involves two particles moving in opposite directions with known velocities, and the second equation is used to determine their relative speed.
zimbabwe
I'm reviewing for exams and don't understand when to use which Lorentz velocity equation to use.
one goes

v'=(v-u)/(1-vu/c^2)

and the second

v=(v'+u)/(1+v'u/c^2)

You should probably let us know some details such as how your coordinate systems are labeled i.e. is the unprimed system system 'stationary' or moving, and which direction the moving system is going in. Common usage could be assumed, but I'd prefer not to make that assumption.

It looks like you have a particle moving at velocity, v, in some frame of reference, K. Then, you consider another frame of reference, K', moving at velocity, u. Then, the equations tell you the velocity of the particle, v', as seen in K' in terms of v, and the velocity of the particle, v, as seen in K in terms of v'.

hmm ok here's the question

two particles move in opposite directions, with one particle at a speed .784c and the other 0.650c as measured by the laboratory. What is the speed of one particle relative to the other.

To get the right answer it's the second equation= .95c

v=(v'+u)/(1+v'u/c^2)
v'=.784c u=.650

the first equation gives .375, which doesn't fit anywhere. So i don't see what it would be used for.

## 1. What is the concept of velocity in Lorentz transformations?

The concept of velocity in Lorentz transformations is based on Einstein's theory of special relativity, which describes how the laws of physics are the same for all observers in uniform motion. In Lorentz transformations, velocity is relative and depends on the observer's frame of reference.

## 2. How do Lorentz transformations affect the calculation of velocity?

Lorentz transformations involve a mathematical formula that can be used to calculate the velocity of an object in different frames of reference. This formula takes into account the effects of time dilation and length contraction, which are consequences of special relativity.

## 3. What is the difference between velocity and relative velocity in Lorentz transformations?

In Lorentz transformations, velocity refers to the speed of an object in a specific frame of reference. Relative velocity, on the other hand, is the difference in velocity between two objects as observed by an observer in a given frame of reference. It takes into account the relative motion of the two objects.

## 4. How does the concept of velocity in Lorentz transformations relate to the speed of light?

According to Einstein's theory of special relativity, the speed of light is constant for all observers in any frame of reference. This means that the velocity of an object cannot exceed the speed of light, and the laws of physics are modified to accommodate this constant speed in different frames of reference.

## 5. Can Lorentz transformations be used to explain time travel or faster-than-light travel?

No, Lorentz transformations do not allow for time travel or faster-than-light travel. While the formulas involved in Lorentz transformations can produce seemingly strange results, such as time dilation and length contraction, the speed of light remains a fundamental limit in the universe and cannot be exceeded.

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