Special Relativity Question (for a paper)

[NotAName]

SR, Do you calculate closing speed to determine light arrival time?

Please evaluate the paragraphs below... what I'm most concerned about the very last statement. Do I integrate the "motion" of the distant object to determine the arrival time of light or is that already in the calculation?

Thanks in advance!

According to SR, a traveller going to a star .5 lightyears away at .5C takes 1 year according to the stationary frame but the traveller only records .866 as much time elapsing for a total of .866 years to arrive. The traveller believes himself to be stationary and that the distant object is approaching at .5C from a distance of .433 lightyears away.

According to SR, a beam of light traveling to that distant star would take .5 years in the stationary frame and would take .433 years in the moving frame less the movement of the distant star for a total of .2165 years according to the moving observer.

 

[NotAName]

Is this too simple of a question? I'm surprised nobody cares to answer.

 

[HallsofIvy]

It's not that it is too simple, it's just not clear what your question is. What do you mean by "integrate the motion"? What "motion" function are you talking about?

 

[NotAName]

I'm sorry, I used bad terminology. I was just asking if the transformation already included the speed of light in it and it would therefore take .433 years total for light to reach the distant point.

Or should I calculate that light should reach the distant point at an effective 1.5C because the distant point is closing on my location.

And I further confused it by fat fingering the calculation... should have been .288 not .2165 (oops!)

Thanks

 

[asteriatic]

I would like to clarify that the calculation of light arrival time in Special Relativity does not involve the closing speed of the distant object. The calculation is based on the concept of time dilation, which states that time passes slower for objects moving at high speeds. In this scenario, the traveller experiences time passing slower due to their high velocity, resulting in a shorter perceived travel time. Similarly, the beam of light, which always travels at the speed of light, is not affected by the motion of the distant object. Therefore, the calculation of light arrival time is not dependent on the motion of the distant object, but rather on the relative velocity between the observer and the light.

Integrating the motion of the distant object is not necessary in this calculation, as the time dilation effect already takes into account the relative motion between the observer and the distant object. The last statement in the provided paragraphs may be misleading, as it suggests that the motion of the distant object affects the arrival time of light, when in fact it does not. It is important to understand that the concept of time dilation is a fundamental principle in Special Relativity and is crucial in accurately calculating light arrival time in moving frames.