Derivating a from v (lorentz transform)

In summary, The Lorentz transform is a mathematical equation used in the theory of special relativity to describe how an observer's measurements of space and time change when viewed from different reference frames. When we say "derive a from v" in the Lorentz transform, we are referring to the process of finding the mathematical relationship between the acceleration (a) of an object and its velocity (v) in different reference frames. It is used in science, particularly in the fields of physics and astronomy, to understand the effects of time dilation and length contraction at high speeds. The Lorentz transform is a fundamental component of Einstein's theory of special relativity, providing a mathematical framework for understanding the relative nature of time and space. It differs from
  • #1
mntb
19
0
v'=(v-u)/(1-vu/c^2), then dv'=? is it (dv-u)/(1-udv/c^2)?
 
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  • #2
Please don't double post. Also, any homework questions you have should go in the Homework section of PF (at the top of the main page).
 
  • #3


Yes, that is the correct derivative of the Lorentz transform. To obtain this result, we can use the quotient rule for differentiation:

dv'/dv = [(1-vu/c^2)(dv) - (v-u)(d(vu/c^2))/dv]/(1-vu/c^2)^2

= [(1-vu/c^2)(dv) - (v-u)(u/c^2)(dv)/dv]/(1-vu/c^2)^2

= (dv - (vu/c^2)(dv) - (vu/c^2)(u/c^2)(dv))/((1-vu/c^2)^2)

= (dv - vu^2/c^2)(dv)/((1-vu/c^2)^2)

= (dv - u(dv))/(1-vu/c^2)

= (dv - udv)/(1-vu/c^2)

Therefore, dv' = (dv - udv)/(1-vu/c^2). Great job!
 

1. What is the Lorentz transform?

The Lorentz transform is a mathematical equation used in the theory of special relativity to describe how an observer's measurements of space and time change when viewed from different reference frames.

2. What does it mean to "derive a from v" in the Lorentz transform?

When we say "derive a from v" in the Lorentz transform, we are referring to the process of finding the mathematical relationship between the acceleration (a) of an object and its velocity (v) in different reference frames.

3. How is the Lorentz transform used in science?

The Lorentz transform is used in science, particularly in the fields of physics and astronomy, to understand the effects of time dilation and length contraction at high speeds. It is also used in the development of theories and experiments related to special relativity.

4. What is the significance of the Lorentz transform in Einstein's theory of relativity?

The Lorentz transform is a fundamental component of Einstein's theory of special relativity. It provides a mathematical framework for understanding how time and space are relative to the observer and how they change when viewed from different reference frames.

5. How does the Lorentz transform differ from other mathematical equations used in physics?

The Lorentz transform differs from other equations used in physics because it takes into account the effects of special relativity, such as time dilation and length contraction, which are not accounted for in classical physics equations. It also has a more complex mathematical structure, involving hyperbolic trigonometry, to accurately describe these effects at high speeds.

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