Understand Relativity & Lorentz Transformation - Aaron

[doaaron]

Hi all,I am trying to understand relativity and Lorentz Transformation more clearly but I have some problems. Assume that we have frame F' which is moving at velocity v with respect to F. Now assume we have an object, O, moving at velocity, w, with respect to F. Frame F has its own time, t, and the position of O is x = wt. Now, if I want to find the position of O in frame F', I need to apply the Lorentz Transformation to find x' and t'. The equation for t' is,

t' = γ(t - vx/c²)

My confusion is the term "x" in the above equation. This suggests that time experienced in F' depends on O, since x is the position of O. So if I were to introduce another object, P, moving at a velocity, u ≠ w with respect to F, then t' would be different for O and P. Intuitively, I would think that t' only depends on v. Please let me know where I have made my mistake.thanks,
Aaron

 

[ShayanJ]

This suggests that time experienced in F' depends on O, since x is the position of O.

It doesn't depend on O, but on O's position.

Excluding the above sentence, your only mistake is leaning towards your intuition which you acquired by living in a non-relativistic world and studying non-relativistic physics.

 

[doaaron]

Thanks for the reply. Actually I think I understand my mistake. x', t' simply describes a coordinate in frame F', so it is possible to calculate x', t' for each object, O, P etc.

thanks,
Aaron

 

[Matterwave]

Thanks for the reply. Actually I think I understand my mistake. x', t' simply describes a coordinate in frame F', so it is possible to calculate x', t' for each object, O, P etc.

thanks,
Aaron

Yes, the t' is the coordinate label for an event O in the primed frame. Or a different event K, it will have a similarly different set of coordinate labels.

 

[sardar]

Hi Aaron,

Your confusion is understandable as relativity can be a complex and abstract concept to grasp. Let me try to explain the concept of time dilation in the context of the Lorentz Transformation.

First, it is important to understand that time is relative and can be experienced differently by observers in different reference frames. This is the fundamental principle of relativity. In your example, frame F' is moving at a velocity v with respect to frame F. This means that the observers in frame F' will experience time differently compared to observers in frame F.

Now, let's consider the equation t' = γ(t - vx/c2) in more detail. The term "x" in this equation represents the position of the object O in frame F. This is used to calculate the time experienced by an observer in frame F' when they observe the object O at a specific position. This equation takes into account the relative velocity of frame F' with respect to frame F, as well as the distance between the observer in frame F' and the object O.

If we introduce another object P moving at a different velocity u with respect to frame F, then the equation for t' would change because the relative positions of the observer in frame F' and the object P would be different. However, the factor of time dilation, represented by γ, would remain the same as it is determined by the relative velocity of the two frames, F and F'.

In summary, the equation for t' takes into account both the relative velocity between the two frames and the position of the observed object. It may seem counterintuitive, but this is a fundamental concept of relativity. I hope this helps clear up your confusion. If you have any further questions, please don't hesitate to ask.

Best regards,