Derive time for relativity (i know how but not sure what to do i got a idea

• seto6
In summary, the conversation discusses a problem involving Lorentz transformations and length contractions. The poster attempted to solve the problem by substituting equations, but needed help with setting up a derivative. Another poster suggested using the Lorentz relation for length contractions and explained how to derive the relation for uy to uy'.
seto6

Homework Equations

equation 37.23 37.30 are the following

37.23
x'=gama(x-vt) x= gamma(x'+vt')
t=gamma(t-vx/c2) t'=gamma(t'+vx'/c2)

37.30
u'=(u-v)/(1-uv/c2) u=(u'+v)/(1+uv/c2)

The Attempt at a Solution

i tried the following...

since d=vt... i solved fot t=d/v

so (x'/u')=gama(x-vt) /((u-v)/(1-uv/c2)) but its not working can someone tell me where I am going wrong

but... now i see that i would have to derive instead dividing

like...dx'/du'

but I am not sure how..

any1

could soneone help me set up dx/dv pls

If you know the Lorentz relation for the length contractions, you can substitute one into the other and solve for a relation between t and t' (you should also end up with a spatial dependence in there).

For the second part, you would not expect spatial contractions along the y-direction since it is orthogonal to the direction of the relative velocity. Though, you could still expect a time dilation; so the derivation for uy to uy' would be the same way as done with ux to ux', except that you do not need to take into account a length contraction for the y-direction.

can you tell me what this is Lorentz relation for the length contractions..mean the formula

What is the concept of time in relativity?

The concept of time in relativity is that it is not an absolute quantity, but rather a relative one. This means that time can appear to pass differently for different observers depending on their relative speeds and distances from each other.

How do you derive time in relativity?

The derivation of time in relativity involves using the equations of special relativity, specifically the time dilation equation t' = t/(sqrt(1-v^2/c^2)), where t' is the time measured by the observer and t is the time measured by the moving object. This equation takes into account the relative velocity between the observer and the object and shows how time is affected by it.

What is the role of the speed of light in deriving time in relativity?

The speed of light, denoted by c, plays a crucial role in deriving time in relativity. It is a constant that is the same for all observers, regardless of their relative velocities. This means that even though time may appear to pass differently for different observers, the speed of light remains constant and is a fundamental part of the equation for time dilation.

How does time dilation affect our perception of time?

Time dilation can affect our perception of time in the sense that it can make time appear to pass slower or faster depending on our relative speeds and distances from other objects. For example, someone traveling at high speeds will experience time passing slower compared to someone who is stationary. This can lead to the phenomenon of time seeming to pass faster or slower for different people in the same situation.

How is time in relativity different from time in classical physics?

In classical physics, time is considered an absolute quantity that is the same for all observers. However, in relativity, time is relative and can appear to pass differently for different observers. Additionally, the equations used to calculate time in classical physics do not take into account the effects of relative velocities, whereas in relativity, these effects are crucial in determining the passage of time.

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