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I'm unsure how to interpret the "linearly extrapolated" retarded position of gravity, or electromagnetic field as well. I've read up on as many explanations of this as possible and am still confused. So, I've set up this thought experiment and would appreciate a straightforward answer and explanation if possible.

In the below diagram, an Observer is living on the Blue circle. The observer is using a large mass on an extremely well calibrated scale and observing the difference in measured weight as large objects flies "overhead". (Such as how the moon affects our weight as it passes overhead)

Minkowski diagram slice of space

In this diagram, the X axis represents Distance (space) and the Y axis represents Time.

The Black circle and the Green Circle are two objects that are traveling in space.

The SOLID black objects represents the linearly extrapolated path of the black circle. However, a massive off-gassing event causes the actual path of black object to follow the path of the hollow black circle. This can't be observed by the Blue Circle at the time of his measurements, since the speed of light propagates at 45 degrees in this diagram along the orange line A.

In the first scenario, the Blue Circle is moving along path GREEN ARROW, and regards the green grid as his time and distance.

In the second scenario, the Blue Circle is moving along path RED ARROW, and regards the red grid as his time and distance.

If the observer uses newton's formula for gravity, lacking knowledge of general relativity, then:

Which "distance" to the black object when plugged into Newtown's formula will most closely match what he calculates in both scenarios?

A, B1, B2, C1, C2?

Is it B1 and C1 (The linear extrapolated position) for the observer in the scenarios, the actual position (B2 and C2) of the object, or the retarded position of A?

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    $\begingroup$ You have way too many misconceptions in this question. The question is only interesting if you are checking the hollow black circle's motion, in which case, yes, the interesting behaviour happens because of the solid black circles. The issue that is being raised, should be considered in the SR EM level; that is, your grasp of the phenomenon is not strong on the SR level, you will just get confused even before you tried to understand it in fake GR. The answer is not A. GR straight up tells you that the relative speeds matter. You should learn things properly and not attempt to confuse yourself. $\endgroup$
    – naturallyInconsistent
    Commented Aug 28 at 18:20
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    $\begingroup$ Hello, thank you for the insulting reply :) You have no idea what my level of understanding is in SR. I've asked a (albeit annoyingly over-complicated) question, because I've arrived at this "paradoxical" problem while tackling smaller questions. This question includes several "what ifs" wrapped into one - for that I apologize. However, if you can provide a straightforward answer, then please be my guest and share your knowledge. For someone living in 1913, using a Minkowski-style diagram and using Newton's gravitation formula, my question would be considered extremely valid. Can you answer? $\endgroup$
    – Mr. Green
    Commented Aug 28 at 20:21
  • $\begingroup$ AND - If you carefully read my question again, you will notice that the hollow black circle IS the correct path of the black circle, and the "interesting behavior" is exactly what I'm asking about, because the solid black circle is the "linearly extrapolated" position of the black circle. $\endgroup$
    – Mr. Green
    Commented Aug 28 at 20:24
  • $\begingroup$ Yes, I read your question carefully. The issue is that you should be considering this in the EM setting, so not Newtonian gravitational interaction, before you consider gravity. But long story short, it really should be B1 and C1, not A. It is simply the norm that different observers would see different things. You should also note that the energy and momentum of the solid black circle is different to the two observers, yet we don't make a fuss about that. $\endgroup$
    – naturallyInconsistent
    Commented Aug 29 at 0:07
  • $\begingroup$ So, it really is B1 and C1 (The linear extrapolated position) for the observer in the scenarios, not the actual position (B2 and C2) and not the retarded position of A? Thanks I appreciate the answer, next time just ANSWER the question instead of being coy, and not as a comment please. $\endgroup$
    – Mr. Green
    Commented Aug 29 at 14:21

2 Answers 2

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Keep in mind that an observer or object on a spacetime diagram traces out a line or curve, and is not a point. (Unless the observer is born and immediately dies). So in a correct spacetime diagram, there will be a line connecting the three black points, and a parallel line running through the white circle of the observer. Then it's hopefully clear that the spatial distance (which is measured by drawing a line from one line to the other along your red "constant time" lines) doesn't change with time. So in scenario 2 there is no distinction between using A, B1, C1 to measure distance.

In scenario 1, assuming you're dealing with electromagnetism or weak relativistic gravity, then to get the field at the observer at the origin, you want to use the position of the black dot "now" in the frame of the observer, or in other words where the object would have been if it kept moving with the same constant velocity at the intersection with the past light cone. So, you're looking for the intersection of a horizontal green line going through the observer, and the black line that should be connecting the three black circles. That intersection will be at C1.

I find Scenario 2 is more intuitive in the frame where the observer is moving and the star is initially stationary, before accelerating due to the mass ejection event. (But of course you can use any inertial frame you want since the physics is equivalent). The observer is approaching a stationary star, and finding the field (assume we're talking about a electromagnetic or weak gravitational field) is steadily increasing as they get closer and closer. The observer can't know that the mass ejection event happened until there light has traveled from the mass ejection event to the observer, so before that happens, the correct distance to use to compute the field that the observer measures is the distance from the observer to the position of the star as if it had never moved.

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  • $\begingroup$ Thanks for answering. For clarity: The objects all travel along their respective lines as shown. The circles are different points along those lines, shown for emphasis. "In scenario 2 there is no distinction between using A, B1, C1 to measure distance." I agree. For scenario 1, the solid black circle is the linearly extrapolated position and the actual position on the "now" line is the the hollow black circle. $\endgroup$
    – Mr. Green
    Commented Sep 3 at 17:40
  • $\begingroup$ So, to be super clear, your answer seems to say the following: 1.) The blue observers in both scenarios will measure a different amount of force exerted from the Black Circle based on their relative velocities, even though they are in the same place and time on the space time diagram? And 2.) In both scenarios, the observer is pulled towards the linearly extrapolated position and not the ACTUAL position of the black circle, even though this might look very odd to a third party observer. Is this both correct? $\endgroup$
    – Mr. Green
    Commented Sep 3 at 17:41
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The position of a gravitating object is its position as seen by the observer. Seen means the same opticaly (EM) and gravitationaly. The observer is not extrapolating the position of the black ball, it waits to see what happens and moves accordingly. So at t=0 it's A, at t=1 it's wherever the black ball is. There is no absolute "when" in SR. Stuff happen when you see them happen. You don't extrapolate anything when looking at the sky, the same goes for gravity.

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  • $\begingroup$ Are you sure? All the things I've read on general relativity state it is the "linearly extrapolated" position and not the "retarded" position (the location you can see with your eyes) $\endgroup$
    – Mr. Green
    Commented Sep 3 at 4:14
  • $\begingroup$ Do you have a link pls? $\endgroup$
    – Alien from future
    Commented Sep 3 at 22:58
  • $\begingroup$ math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html "....a calculation shows that the force on A points not towards B's retarded position, but towards B's "linearly extrapolated" retarded position." $\endgroup$
    – Mr. Green
    Commented Sep 4 at 15:49

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