Rømer and the speed of light 1676 The first version of my objection was completely different. I started doubting its validity and after some time settled for a different approach.
I was not, and I am still not sure whether the idea of different times vs different positions in space made any sense.
I am presenting it here in the hope that your critical comments will help me better make up my mind.
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1) Rømer, and Huygens' drawing of Earth (p.8/22) moving on an orbit path is rather deceiving in its simplicity. What we have is a point on Earth, the observation point - and the location where the clock is situated- that continuously travels the circumference of the earth at the same time it is orbiting the sun. The path is more a spiral than an ellipse. We cannot therefore judge of the speed of light by taking two single points on the orbit path as landmarks. We have to take into account the whole distance traveled, and the time it took the observation point to move from A to B.
The only way to, justifiably, consider the straight line BC as the distance used to calculate the speed of light, would be to have two synchronized clocks, one at B, the other at C.
2) Furthermore, Rømer and Huygens assume that they are allowed to compare the times of observations. For them, observing Jupiter's moon at, say, 5 o'clock, when Earth is at position B, and then at, say, 5:10 when it is at position C, allows us to draw a conclusion about light speed. But 5 o'clock at B is not (necessarily) the same as 5 o'clock at C.
When timing the eclipse, the astronomer uses the same clock through the seasons. Even assuming a regular clock with no deviation whatsoever, 5 o'clock will indicate another position of earth relative to the sun at different points on the orbit path. The sun does not rise or set at the same time each day, due to the tilting of the earth. The two factors, appearance of Jupiter's moon, and the time indicated by the clock are only related to each other by the presence of an observer or a proxy device. The observer/machine relates a clock time to a physical event. Both events, the appearance and the clock time, are not causally related, so we need the mediation of the observer-machine.
3) Imagine you are Rømer, you have a 17th century atomic clock on your wrist, timing the appearance of Jupiter's moon each time it appears from behind its planet. You can now easily draw a graph with time and distance. That is in fact what Rømer's argumentation ultimately amounts to.
What is wrong with such a view?
Well, it is simply too... simple.
The whole point is the moment the observer (can be a machine) sees the moon reappearing from behind Jupiter. In our graph the observer is implicitly represented by the times shown on the clock, even though they are two absolutely distinct processes. In the case of a machine, programs and physical processes react to the detection of the moon, and then signal the clocking mechanism. As noted there are no causal links between what happens with the clock and the behavior of Jupiter's moon. Its appearance or disappearance have no effect on the functioning of the timing device.
Let us take an example where a causal link between two separate events can be clearly demonstrated. If a stone falls in a ponds, ripples are created on the surface of the water. It is impossible to have one without the other, while the (dis)appearance of the satellite is completely unrelated to the clocking mechanism, unless we create an artificial, technological, link between them. This link I call a proxy observer.
For Hume all events are in fact isolated events. What Hume, as far as I know, did not take into account is that we are able to control and manipulate some events better than others. We have no saying over the orbit of Jupiter's moons, or any other astronomic body, but we can decide what event we want detected and when a clocking mechanism should register it. So, even if we cannot prove the existence of causal links, and must be satisfied with empirical and statistical certainty, we can distinguish between events which we can control, and those we cannot.
Going back to our main theme, the speed of light, we can create correlations between events and timing processes. What we must realize is that we need at least two physical events and a timing procedure to obtain a meaningful set.
In the case in question, we need the appearance of Jupiter's moon linked to distance and time. And distance has to be the distance effectively traveled by the clock and the observer, and not a geometrical abstraction.
4) The conclusion that it takes longer for light to travel to C than to B is therefore not justified by Rømer-Huygen's argumentation. Even though more precise calculations might confirm their conclusion.