Rømer and the speed of light 1676
Rømer's argumentation was the reason Descartes' view of instantaneous light propagation was abandoned in favor of the until now accepted view of light traveling at a high but finite speed. His arguments were quite simple, maybe a little too simple, but were universally accepted. By calculating the time it took for the closest moon of Jupiter to reappear from behind the planet, and multiplying the minimal differences between all the observations during a ten year period, Rømer was able to show that the differences when seen from different positions of the earth relative to Jupiter were far from negligible. He was then able to calculate the speed of light reasonably accurately, certainly for his time.
The question is whether the differences in the times of eclipse and reappearance of the moon cannot be interpreted differently, without involving the idea that it takes time for light to travel through space. We all know that when looking through the telescope at a planet like Jupiter, we do not see it rotating about its axis, or orbiting the sun. We get each time a snapshot of a frozen moment in time, and the changes to the images we receive occur in jumps without any intermediate states. This is understood as the effect of parallax, or more simply resolution. Because of the distance two points separated by relatively large distances will appear to our perception as one, and it takes time before we notice the difference between one position and another.
This is exactly the situation which Rømer is analyzing, but instead of understanding it as a case of parallax and resolution, he chooses a very specific approach. He considers the time it takes for astronomers to observe the disappearance or reappearance of Jupiter's moon as a fact that needs no further explanation. If we see the moon appearing at time t that is because the moon appeared at time t. And if we notice that when the earth is at another position, farther from Jupiter, and the moon appears or disappears at time t+x, then x must be caused by the longer distance between the earth and Jupiter.
This is much too easily discounting the fact that we only see immediately the differences between one view and another when we are very close to the object. It is not surprising that Jupiter's moon seems to appear or disappear at a later time than when the earth is closer to Jupiter. The larger the distance between the earth and Jupiter, the more time it will take us to notice a difference between two consecutive moments.
In other words, whatever Rømer and everybody after him might think, he did not prove that it takes time for light to travel through space, and his calculations concerning the speed of light, whatever their merit, are based on invalid arguments.
The question is whether the differences in the times of eclipse and reappearance of the moon cannot be interpreted differently, without involving the idea that it takes time for light to travel through space. We all know that when looking through the telescope at a planet like Jupiter, we do not see it rotating about its axis, or orbiting the sun. We get each time a snapshot of a frozen moment in time, and the changes to the images we receive occur in jumps without any intermediate states. This is understood as the effect of parallax, or more simply resolution. Because of the distance two points separated by relatively large distances will appear to our perception as one, and it takes time before we notice the difference between one position and another.
This is exactly the situation which Rømer is analyzing, but instead of understanding it as a case of parallax and resolution, he chooses a very specific approach. He considers the time it takes for astronomers to observe the disappearance or reappearance of Jupiter's moon as a fact that needs no further explanation. If we see the moon appearing at time t that is because the moon appeared at time t. And if we notice that when the earth is at another position, farther from Jupiter, and the moon appears or disappears at time t+x, then x must be caused by the longer distance between the earth and Jupiter.
This is much too easily discounting the fact that we only see immediately the differences between one view and another when we are very close to the object. It is not surprising that Jupiter's moon seems to appear or disappear at a later time than when the earth is closer to Jupiter. The larger the distance between the earth and Jupiter, the more time it will take us to notice a difference between two consecutive moments.
In other words, whatever Rømer and everybody after him might think, he did not prove that it takes time for light to travel through space, and his calculations concerning the speed of light, whatever their merit, are based on invalid arguments.
Comments (107)
Let's get down to earth in the time of Galileo who is still trying to sell his (stolen) invention to pay his many debts. An admiral of the Venicean navy is using the new revolutionary device, while a lower officer is staring at the horizon hoping to detect an enemy ship before, or at least not too long after his superior. The question is, what would determine the difference between the time the admiral detects the ship, and the time in which the lower officer does the same in turn? It is in fact a very simple operation: if the difference is equal to the time it takes the ship to get in visual range of the naked eye, then we can say that the telescope is showing the location of the ship in real time. If, on the other hand, the difference between the detection times is negligible, then we can say that the telescope allows us to see objects not there where they are, but where they were when their light started its travel towards us.
Now, let me ask you this. What would be the strategic advantage of seeing an enemy ship a few (milli) seconds earlier? Especially in the 17th century. Also, if it is correct, what does it mean that a telescope allows us to see distant objects in real time?
Well there is a lot here, and as I am not sure where you are headed, let's just begin by saying that the advantage of seeing a ship with greater clarity earlier than the Captain of a ship seeing you is the ability to make a decision whether to run or attack.
As for real-time, this leads to a total different discussion about the nature of time. Scientific time has to do with movement in space and the measurement of simultaneity.
But there is also duration (Bergson called real-time), which is the time we are experiencing as life.
Scientific time is homogenous and discontinuous. Duration is heterogeneous and continuous. What we mean by time and distance can get pretty hazy the more we dig into the nature of nature and the nature of perception.
I saw my second post more as a clarification of the problem posed in the first one. Are we allowed to speak of the speed of light as we do if we are able to perceive distant objects in real time? If looking through a powerful telescope had allowed Rømer to see in real time the reappearance of Jupiter's moon, would he have had any reason to believe that it takes time for the images to reach us? That would in fact mean that the admiral would hardly have any advantage on his officer ( a few milliseconds). Only if the admiral saw the enemy ship there where it was at that time does a telescope have any use for the military. Otherwise it would be just another scientific toy with no strategic significance.
Replace the enemy ship with Jupiter's moon and you would have to admit that Rømer 's calculations are meaningless.
As your example illustrates, one can take various views of this problem all of which result in approximately the same answer. Similarly with quantum mechanics vs. quantum interpretations. Different interpretations, same answers for practical purposes.
This is not to say that having a deeper understanding of the nature of perception, light and space is off no consequence. It probably has lots of consequences, but not related to some practical problems that are currently being solved using Romer's method or otherwise.
I honestly have no idea what you mean.
This is hardly surprising, after all nothing is visible in the dark: no light, no perception.
This still does not explain the complicated fact of perception. Light as a conditio sine qua non of vision does not mean that light needs to be reflected off objects into our eyes for us to see these objects.
Here is a simple example: a light beam directed away from me will still be visible, as will be the light at the end of a tunnel even if I am standing in complete darkness. It would be difficult to argue that light rays somehow are reaching my eyes when there is no indication of it whatsoever. Furthermore, light intensity diminishes with the square of the distance. After a while, light stops and darkness takes over. That does not mean that somebody who stands way beyond the illuminated area cannot see the light in the distance.
If we link these thoughts to the original discussion then we can wonder whether we are seeing the stars because their light takes time to reach our eyes, or if we see them just like we see a light on earth that does not shine beyond a very limited distance.
https://philpapers.org/bbs/thread.pl?tId=897#p8097
https://philpapers.org/bbs/thread.pl?tId=1002#p9701
https://philpapers.org/bbs/thread.pl?tId=1006#p9742
https://philpapers.org/bbs/thread.pl?tId=1011#p9778
https://philpapers.org/bbs/thread.pl?tId=1015#p9837
https://philpapers.org/bbs/thread.pl?tId=1021#p9877
https://philpapers.org/bbs/thread.pl?tId=1026#p9932
Concerning Bergson, I think I have read almost all of his books, in French, in high-school. He and Camus were my favorites. But then, I was very young.
Not if Rømer was wrong and we are seeing distant stars the way the admiral was seeing the enemy ship: there where we see them, and not as something shown by light rays traveling trillions of kilometers and taking millions of years to reach us . The question therefore whether Rømer was right in his assumptions has far-reaching consequences that go well beyond some ratiocinations about perception. That is why the discussion of his claims should not be considered as closed once for all. This is an attempt to reopen a discussion that scientists believe has been solved a very long time ago. I claim that they are wrong.
This was more or less what I was attempting to suggest. The nature of perception is far from a done deal. If you like Bergson, I think you'll appreciate Stephen Robbins analysis of Bergson on YouTube. Very astute, and like Bergson, way, way ahead of his times.
Thank you for the link.
Bergson dared put into question the idea that mathematics is the "language of nature" as Galileo announced so proudly. Since then we can say that Galileo has been the unchallenged champion and Bergson, in spite of his Nobel Prize, has been relegated to the "oubliettes". Like Bergson, I do not think that the language of Nature is Mathematics for the simple reason that mathematics is a human language and bears all our strengths and weaknesses. It is an indispensable tool for Science, with the emphasis on "tool".
Those are two pictures taken with a pinhole lens, attached to 3 sets of extension rings, and the whole attached to a Nikon body.
The red light you see is a laser pen directed towards the lens, as close to the center as I could position it. The second picture, where the spot is hardly visible, was taken with a shutter speed of 1/60s. The first one with 30 seconds.
There were more, showing the laser spot in different shape depending on the shutter time.
Here is another one (about 5 seconds exposure time).
The following shows that the shorter the exposure time, the less rings are visible, until they disappear all together. Here is one with 1s.
I have the following remarks that I hope will show that we should not take the established theories of light for granted.
1) Can the speed of light play a role in the differences we observe between one picture and the other?
2) Should we consider the dark bands as destructive interference patterns? Or are they simply the image of the laser lamp and its wiring?
The shots were taken at around 2 meters.
The pinhole diameter 0.25mm
Light is supposed to travel at 300.000 km/s. How could there be a difference of less than 1 second between a picture where the laser spot is visible, and another one where it is not, and that over a distance of 2 meters?
Even taking into account the imprecision of cameras and laser pens, all images should be as bright as they can be for the camera. Even the fastest time a modern camera can have, around 1/4000s, should make it possible for the laser light to travel 75 km, that is more than 35000 times the distance it has to travel from the pen to the camera. If we take a shutter speed of 1/400s light would be able to travel 750 kilometers, but it would still be unable to form an image on the sensor of the camera?
I am no mathematician, and I get my figures very easily wrong, so maybe that is one of those cases where a genius with numbers will shame me by pointing at simple but oh so fundamental mistakes. I will be waiting and ready to learn.
Theoretically, this laser light should cross the threshold unimpeded and hit the screen or sensor. But then, the same could be said of the part of any scene that happens to face the hole directly. We would get something like the infamous Spot of Poisson: every image should show in its center a bright spot that receives light unimpeded, even if the conditions, like shutter speed, make it difficult for the other rays to reach the sensor.
But then, that is not what is happening, is it? If anything we are confronted with the Anti Spot of Poisson. Even the light that should go unimpeded through the center of the hole, seems somehow to be diminished or even extinguished by a shorter shutter speed.
Where is Poisson when you need him?
I can not believe that this is the correct explanation. If a photon is capable of reaching the outer lens of a telescope; it is certainly capable of going a few more inches or feet and reaching a retina.
In fact the admiral with the telescope and the underling with his naked eyes must necessarily see exactly the same set of objects. The telescope simply magnifies an image so that it can be processed in detail by the eye/brain system; whereas the naked eye image can't be resolved in sufficient detail.
In other words the underling is looking for a tiny little spec that takes up only a tiny little spec's worth of retinal cells. The telescope makes it so that tiny little spec's worth of photons is spread out over a larger area of the retina.
It can't have anything to do with the fact that the telescope is a couple of feet long hence getting the photons first, if that's what you're saying.
A similar thing happens with photography. If I stand in one spot and take a picture with a wide-angle lens then a telephoto lens, the telephoto is simply cropping the field of view. If you had enough resolution you could shoot exactly the same shot with a wide angle lens and then crop it in the computer.
I'm no expert on telescopes or optics so if I'm missing something let me know. As I understand it, it's just about making a given set of photons take up a larger portion of the retina via telescopic magnification.
What you've produced is called an Airy Disk, which results from the light which diffracts when traveling through a very small aperture (comparable to it's wavelength) and is then redirected by your camera lens.
Regarding Romer, as far as I understand it, since he knew when the distance between Jupiter and the Earth was growing or shrinking (and by approximately how much), he was able to correlate changes in eclipse duration with distance gained or lost between the Earth and Jupiter during the actual eclipses.
Matters of resolution aren't problematic for his observations because the emergence of light after the eclipse was not dependent on having a detailed image, but merely the presence of light.
I'm not exactly sure what your main criticism of Romers analysis is. You suggest that there are these periods of no intermediate "updates" between the images we collect of distant moons, but in reality different photons are continuously and somewhat unpredictably (at very small time scales) striking our photo-receptors. Our ability to get continuous updates is limited only by our willingness to gather the photons with sufficient speed and at sufficient scales.
The way telescopes defeat the resolution problem is simply by gathering more photons and refocusing them into a size our own eyes can interpret. (bigger telescopes see farther because they gather more light from far away points which are slowly diffusing, thus increasing resolution).
Could you clarify exactly why it is that low resolution observations in Romers experiment makes an alternate model viable?
First, diffraction should not be a problem since we are talking about a 0.25mm aperture, with no lens. The different wavelengths are measured in nanometers.
Concerning your objection about my Rømer analysis you are assuming that which I think he had no right to do. If you assume that you are seeing the moment when a moon appears from behind Jupiter you have already decided that the difference between the times of observations can only come because of the distance and the speed of light. I do not know how to make it any clearer, but this obviously, as least to me, the case of a circular argument. Your theory has to be right for it to be right.
You seem to agree with me, so I am not sure what I should say. maybe you are right and what the admiral sees is such a tiny speck on his officer's retina that the latter is not conscious of it. I will remind you that beyond a certain distance even that speck will not be captured by the retina.
The point is: when the admiral sees the enemy ship,and maybe we should transpose this in a Star Wars decor, a ship some millions of light years ago. The question is, where is that ship when the admiral sees it in his telescope? Assuming some Star trek kind of warp drive, you still can divide the distance by its speed and predict how long it will take the ship to get within range. And that is only possible if you are seeing the ship there where it is, at the moment it is there.
Light diffracts as it travels as it travels around the edge of an object, in this case, the inside edges of your pinhole. How far away from the pinhole is the camera again? Two meters?
Since when does Nikon make a lens-less camera?
Quoting Hachem
The hypothesis is that the time difference is caused by a finite speed of light. The experiments and calculations based on that assumption lead to the creation of a model with repeatable predictive power. The fact that we can use the underlying assumptions to make reliable predictions is what lends credulity to this particular model.
If you have some other proposed mechanism for the deviations in eclipse duration I would love to hear it, but parallax can be accounted for and issues of resolution are not relevant.
Quoting Hachem
The theory needs to retain it's predictive power and to not be contradicted by some competing or better theory. If you're really looking to upset our physical and scientific understanding of light as non-instantaneous you might as well start with the best modern measurements and experimental evidence rather than digging up poor poor Romer...
1. The pinhole lens has a Nikon fitting but is not made by Nikon.
2. Your assumption of diffraction is not reasonable, Why should a collimated beam diffract when going through an empty opening?
3. Even assuming diffraction, the question still remains of why there should be such differences between the different images on the basis of shutter speed alone. I would very much like to see some calculations that take the speed of light into consideration, and explain to me the differences.
4. You are defending the theory or theories of light as they are taught. I have no problem with that. But referring to them is not enough. I will be very happy and obliged if you could show me where I went wrong, but appealing to authority is not enough.
Can you explain your setup in more detail? A laser pointer is shining at a mounted pinhole lens that is attached to a camera (a camera with a separate internal lens?). Or do you have a barrier of foil somewhere in-between the two meter gap between the camera and the laser pointer? (if so, where?).
If the diffraction pattern is caused by the pinhole, you should be able to see it projected onto the back wall (you might need to find the right distance to see the pattern clearly) without any need for a camera. If the diffraction pattern is caused by the glass lens of the camera, then using the pinhole as a pinhole projector will not reveal the diffraction pattern. You should be able to test this yourself!.
Quoting Hachem
When a photon passes close to the edge of something it can become diffracted (it's direction changed). The closer to the edge of the pinhole that a given photon is, the greater the angle of diffraction.
Quoting Hachem
The longer the shutter is open, the more photons the camera collects over a period of time, and so we see a cumulative sample of exactly where photons are striking the photo-receptors over that given period of time.
Quoting Hachem
I think the burden is on you to show where Romer went wrong, and I don't think you've sufficiently done that. You haven't addressed the main evidence for Romer's hypothesis (that the speed of light is finite) which is the reliability with which that model allows to make highly accurate predictions.
Where did Romer go wrong? Why is this interference pattern even pertinent to his observations?
The setting is exactly as I described it. A camera body to which were attached extension rings, empty tubes, usually to allow getting closer to the object. Here they lengthen the focal length and makes the image much darker, needing longer pressure times. The pinhole lens , known as a Holga pinhole lens. with a pinhole diameter of .25 mm, is attached to the tubes. There is no other lens involved. The light goes therefore through an empty hole. I could have used a self-made pinhole camera made out of a shoe box as it were.
As far as Romer is concerned, I am sorry but I do not feel like repeating myself. I will of course answer to any argument you might have that goes beyond simple appeal to authority.
I will clarify that nowhere do I claim that the speed of light is infinite. In fact I do not believe that is the case. if you had read what I wrote on the subject you would know that. It is because the speed of light is finite that the theory of light as we know does not make sense. If the speed of light was infinite then we could simply say that we see things where they are when they are there, and we see them immediately because, as Descartes thought, light is infinite.
I do not think that. Therefore, I say that the theory of light cannot explain vision and certainly cannot explain the fact that when we look through a telescope the object is there where we see it, when we see it. The same way we look at somebody coming down the road, still a few hundred meters away from us, and we know it will take some time for him to reach us. Light theory as it is can easily explain this last example, but it breaks down when it comes to distant objects and great distances.
Why does the contemporary assessment of the speed of light break down when it comes to distant objects and great distances?
When the captain looks through a telescope, he is seeing the light entering the telescope, which is more or less the same as the light that is entering the eyes of the sailor below. The captain can actually recognize the distant ship because the telescope gathers much more light from a wider area than a normal human eyeball does and so gains additional resolution. There is no contradiction of any kind. We don't see objects as they are even when using big telescopes, we see them as they were when those photons were originally emitted, and over long distances there are no issues. As long as we get a steady stream of photons to record even a single point of light is sufficient to measure the emergence of Jupiter's moon after an eclipse; resolution issues would not cause it to blip in and out of existence (and even if it did we simply get a bigger telescope and problem solved).
Where is the break down? Don't repeat yourself though, please try and make your argument clear this time...
Regarding your experiment: It's what happens when you shine a laser through a small aperture.
that is exactly what my pictures also show. Regarding my arguments, no I will not repeat them. I will wait for your objections that have to be about what I said, and not about what you think I said. Asking why when you apparently have not even taken the time to read what I wrote is tiring and it is a game I will not play. Quote what you do not agree with and say why you do not agree with it instead of simply asking again and again for clarifications.
OK, I will highlight the crucial points of error numbered, in bold and underlined and explain why they are errors down below
Quoting Hachem
1: We do see rotation of planets, especially when we have powerful telescopes. Planets and moons are so large and rotate relatively slowly though, so it's very hard to notice with the naked eye in real time (like trying to notice the movement of shadows due to the rotation of the earth). We definitely observe rotation and we definitely observe orbits.
2: Yes, there are "intermediate states". Photons tend to come very tightly packed one after the other, and so unless you want to get down to the time interval between photon strikes (which decreases as the light gathering aperture gets smaller) there is a practical continuous stream of photons to measure.
3: Parallax and resolution are not the same thing, and parallax has little or nothing to do with this experiment. Parallax is the apparent motion of objects due to changing perspectives of observation, which unless you can correct me has nothing to do with visible light after the emergence of Jupiter's moon following an eclipse. Resolution is not an issue either, as we do not need to see Jupiter's moon with any high degree of detail whatsoever, we just need to see when the light from it becomes visible after it's emergence from behind Jupiter.
4: We see differences in distant objects as light reflecting those differences reaches us. This has long been proven since the invention of more powerful optics and more sensitive measuring equipment. Low resolution and distant objects can sometimes be hard to analyze, but luckily, in this case, being obscured and then unobscured by a planet creates a strong flashing signal for us to look for and to measure.
5: In order for what you say here to be true, some sort of time dilation effect would need to be acting on the light coming from more distant places, effectively slowing it down and making it appear to move more and more slowly. This does happen to occur over unfathomably long enough distances, but luckily, again, we can see the emergence of Jupiter clear as day. No resolution issues, no parallax complications, and correcting for special/general relativity is of almost marginal consequence.
Now that I've laid out my objections more clearly, I can see that your argument rests entirely on the assumption that "it takes longer to notice changes in distant objects" despite the obvious fact that bigger telescopes mean more resolution, which can eliminate any setbacks caused by resolution blur. The "no intermediate states" bit is unsubstantiated and must result from a confused understanding of how we carry out astronomical observations...
Thank you for making the effort of stating more clearly your objections.
1. You might be right concerning the fact that with current telescopes we can see planets rotate. I honestly wouldn't know but I am willing to take your word for it.
Please do not forget that we are talking about the 17th century, and I do not think that the telescopes then, which were no better than cheap binoculars, would be capable of such a feast.
2. I will skip this point because I do not see its relevance nor how it could be used against me. I will just wait to hear more from you on this subject.
3. The distinction between parallax and resolution is an artificial one. In fact, parallax makes the lack of resolution evident since we need to move through space, and time, before we can distinguish two objects from each other. Having said that, both are considered as different phenomena, and the fact that I mention them at the same time does not mean I am not conscious of what separates them. I just think it is more a matter of degree and perspective than fundamental differences.
4. Is how you explain things while I am proposing an alternative approach that does justice to some phenomena that established light theories do not explain.
Vision is based on the assumption that we see objects because light reflected off these objects enter our eyes and impinge on our retina , I have given many examples in this thread and in Optics: some problematic concepts, why this view is erroneous, or at least incomplete. I will not repeat myself here neither.
5. It is not entirely clear to me what you mean by dilation effect, and have no idea whether I should agree with it or reject it. I will therefore abstain.
Quoting VagabondSpectre
Concerning the first part of this quote, this is as far as I can see an argument in my favor. We are capable of seeing objects as they really are, therefore with no delay. You reaffirm the idea by stating "bigger telescopes mean more resolution" which seems to indicate that we see distant objects as they are. I am curious as to how you reconcile the idea that telescopes give an accurate image of reality with the principle that it takes time for light to reach us (on that we agree), and that therefore the images we see represent an image of a moment in the past. All I am saying is that we are not looking at the past but at the world as it is now, and that is the puzzle we have to solve.
I do not have all the answers and you will certainly be able to ask questions for which I may have no answer. I do not consider my reflections as a complete and finished theory, but as a work in progress, and I will see where that gets me.
1: They had a few large telescopes in the 17th century, but again, we don't need to identify rotation, we just need to identify the lunar emergence from behind Jupiter.
2: It means that there is a continuous flow of photons, and the "snap-shot" effect you're trying to describe is a mere consequence of us actually taking snap-shots. No such effect has been demonstrated to exist or to be the cause for the variations in eclipse duration of Jupiter's moon.
3: The distinction between parallax and resolution is not artificial, they're two completely different phenomenon. I've explained what they both are and asked you how they could possibly be responsible for differences in measured eclipse duration. "There are no intermediate states" is demonstrably false with more and better measuring equipment...
4: I'm not going to dig through any thread but this one. Take responsibility for your own position and at the very least quote yourself. I don't recall where you pointed out any light phenomena that the current model cannot explain, not do i recall where you actually presented a theory of your own which was explanatory or predictive in any way. Please present the evidence for your own claims. "I've already presented it" is lazy and self-deceptive.
5: Due to the expansion of space described in the current cosmological model, over very great distances light is essentially stretched out as the space between photons expands. This is what actually gives rise to a definitive edge of the observable universe, because at sufficiently large distances the cumulative expansion of space exceeds the ability of light to ever reach the other end (like a road that grows faster than you can traverse it, you will never get to the end). This comes from Einsteins special and general relativity, both of which have been demonstrated to have stunning predictive power.
Quoting Hachem
Seeing an object with greater resolution doesn't mean we're also seeing them with less delay. That assumption doesn't follow from any logic I'm aware of.
why do you think better resolution means less time delay?
Why?
This has also been asked by VagabondSpectre. Maybe it seems obvious only to me, but greater distance blur objects, or points together. A simple example are two mountains that appear to be one from a distance, Craters on the moon that are kilometers wide and which are projected in much smaller images with the concomitant loss of details. That means in the case of eclipses or reappearance of moons from behind Jupiter that greater distances would make it more difficult for an observer to pinpoint the moment of disappearance or reappearance. I am sure it represents no problem now, telescopes are powerful enough for us to see the moons peeking from behind Jupiter. After all, if we can see the planets rotating, that should not present any difficulty.
I would be interested to know if Rømer's experiment have been re-done and what the results are. I mean the experiment itself whereby the exact times of eclipse and reappearance are compared, taking into considerations all relevant factors. If is has already happened I would appreciate a link or a reference.
@VagabondSpectre I may expect you to do your homework and referring to where I have handled some other matters is certainly not deceptive.
Also, size does not always matter, and the nice picture you show does not say anything about the quality of the lenses at that time.
I realize I have not answered all objections, but I will try sometimes later.
Here is the last of a series of six taken at the fastest shutter speed my camera can manage: 1/4000s.
You will notice that the rings become less and less visible.
It would be difficult to claim that diffraction has anything to do with the way the image is. The opening of a camera body is huge relative to the different wavelengths of light, and so is the sensor area.
This reinforces me in my conviction that what we are looking at is the image of the laser itself, but I am certainly open to suggestions.
You interpret "snap shot" as meaning a discontinuous flow of photons. I agree with you that it is highly unlikely. But then I do not think we see objects because of what had been called photons.
A central tenant of light theory is a straight beam carried by waves, and supported at the sides by wavelets. The Huygens Principle, fine tuned by Young, Fresnel, Maxwell and others is supposed to explain how light can go on indefinitely, and also how we see objects.
A simple refutation of the Huygens Principle I have dealt with in this discussion and the other one mentioned is the fact that we can see objects even when no visible light rays are entering our eyes.
We can see them from a completely dark corner, and therefore also from aside. I do not know how that is possible and what creates this "lateral" perception, but the Huygens Principle and the theory of light cannot account for it.
Maybe other electromagnetic waves than visible light are making it for us possible to see objects even when there is no light ray reaching our eyes. But then, if we can see objects whose light is directed away from us, the so-called wavelets that are supposed to sustain the main wave must use energy in all the other directions, weakening the main wave.
In fact, it is probably what is happening when we consider the fact that visible light weakens with distance until it disappears from sight altogether.
I have given many examples of this kind and I did not get any answer from all the objectors. But I have not lost hope yet.
3. We disagree on the differences and similarities between resolution and parallax, but we agree on the fact that resolution is involved when looking at the moons of Jupiter to determine the exact moment of their eclipse or reappearance. Maybe we should concentrate on that.
My theory, or rather my raw intuition, will be easily falsifiable. Imagine two observers, one near Earth, the other on Mars, looking at each other through powerful telescopes.
They can see when their colleague millions of kilometers away raises a board with a number on it. They must then raise a board, or type a number which shows up on an electronic board, a number that is one higher than the number they saw, or whatever formula they have agreed upon.
They will immediately be able to determine how fast the information has reached the other side. My prediction is that they will see it immediately, even though any other form of communication between Earth and Mars will be much slower than the speed of light.
edit: They could even play chess, like the characters in one of the sequels of Resident Evil. But they will have to acknowledge which move they have received from their opponent as soon as they see it.
And this one with 1/2000s.
edit: If you take a thin band of the central spot and the different rings, you will see that it is the same result as the one shown by two-split experiments and other images used to prove the wave theory of light.
edit2 The large oblique beam is I think the result of back and forth reflections of the prism that directs the image to the viewer. But I am not really sure.
The point of using Io was that the reappearance is obvious and effectively instantaneous. But anyhow, given that the relevant time difference between eclipses were in the order of minutes, a second or two would make no difference to the calculation.
I am afraid you are wrong. Romer's calculations were based on the average of observations made over 10 years! So it was a matter or seconds, or even less!
edit: it always looks instantaneous. One moment Io is indistinguishable from Jupiter, the next it is. That is the whole point in fact.
In fact the maximum delay was sixteen and a half minutes later than would have been expected if the speed of light were infinite.
I will go back and reread the op.
Here is another example of bad argumentation that has always been considered valid while it is wrong logically.
https://philpapers.org/post/20762
https://philpapers.org/post/20890
https://philpapers.org/post/21002
Look at the image on the screen that the M.I.T professor uses as a proof of destructive interference.
https://youtu.be/RRi4dv9KgCg?t=94
His argument is that by pushing on the plate he changes the distances between the screen and the dark and bright rings of the image, making them alternate. Those black rings are according to him the result of destructive interference. The problem is that in my experiments bright rings did not suddenly black rings when I changed the position of the laser. So, what the professor might be showing is simply two alternate images in time and space that give the impression that black has turned red, and vice versa.
Look at this image and tell me what it reminds you of.
https://youtu.be/qkQo6gig3tQ?t=55
Quoting Banno
Quoting Hachem
Quoting Banno
Again, a difference of even a few seconds, as might (conceivably, but I doubt it; having seen the such eclipses myself, I can vouch for their astonishingly instantaneous appearance) result from an issue with the resolution of the telescope being used, would have made little difference to the result.
So I suppose I have misunderstood your argument. Can you explain it to me with a bit more clarity?
After all, why post unless you would like to discuss your argument?
This seems to be the core of your 'argument'; but it remains oddly opaque. I know that I can see the rotation of Jupiter's red spot through even my modest telescope; although it is certainly not as bright as when I was a child. One does not see a series of snapshots. But even if one did, it is not clear why one would conclude that the changes to Jupiter occur without any intermediate state. Nor is it clear how this relates to parallax, nor to resolution - which, as has been pointed out, are two quite distinct things.
Perhaps one should conclude that this is not an argument at all.
For Romer, the situation was different, the differences between one observation and the other where probably more snapshot like. One moment Jupiter was alone, the other, there was a moon beside it.
Like when you are looking at somebody approaching you and you suddenly recognize the person. It would be very difficult to pinpoint a moment where that happened. And that is made even more difficult when large distances are involved. I would certainly like to avoid the resolution-parallax discussion again, what matters is that it takes longer for two objects which are very far away to appear as two objects, and not as one.
That is why I consider his conclusion that the speed of light is involved not as irrefutable.
Just as for Bradley, nobody is really interested in the correctness of the argumentation, it would be considered more like a historical curiosity.
I have a vested interest in showing that the wave theory of light is not as impregnable as one thinks, that is why I took time to analyze old texts and experiments like that of Romer, Bradley and others.
The images I have taken are also completely on topic. They show that another interpretation is possible of light phenomena that have always been considered as strong proofs for the correctness of the wave theory.
Because of the distances involved, Io is effectively a point source. So it is not at all "like looking at a large object slowly being drawn behind a curtain"; it is instantaneous. I invite you to check this out for yourself; all you need is a small telescope or even a decent pair of binoculars. There's one today: 21:14 UT, Io exits eclipse by Jupiter's shadow. (see http://www.skyandtelescope.com/wp-content/observing-tools/jupiter_moons/jupiter.html)
Simulations are very often, as in this case a pedagogical instrument.
Once again, I do not doubt that the speed of light is finite, even though I doubt that light, visible light, travels through space. I consider light as a local phenomenon caused by something which I will call, because I do not have any better alternative, electromagnetic waves, that probably travel through space.
I therefore believe that we see illuminated objects there where they are, and not because their light travels to us, which I find very improbable. We would have to explain how light turns visible, then invisible, and again visible. I still have to see convincing arguments for that which do not rely on my faith in science (which by the way remains strong).
Again, differences of a second or two would have negligible impact on a demonstration involving minutes. Issues of resolution or parallax would not result in such large delays.
I find it curious that you do not see the contradiction. Don't you find it strange that one moment Io is there and the other it is not? Isn't that what a snapshot is?
What you do not seem to accept is that those differences are based on observations. In other words on the fact that observers (or devices) are able to distinguish one object from another. And that in itself depends on distance and resolution, and yes, even parallax.
Your whole argumentation, as was Romer's, is to consider the fact of observation as beyond any discussion. Once you reject this premise the whole argumentation falls in the water.
Cheers.
can't win'em all
edit: I would like to thank you though for the opportunity you offered me to clarify some points. You did not make me change my mind, as I did not make you change yours. But that is is the risk and also the benefit of an open discussion.
You're misunderstanding Roemer's observation. At any constant distance between the Earth and Jupiter, the observed time between a Jovian moon's disappearance and re-appearance would be the same.
But what if the distance between Earth and Jupiter is different when the times of disappearance and re-appearance are recorded? That's when you have information from which to calculate the speed of light.
So, your criticism of the validity of Roemer's determination of the speed of light is based on a misunderstanding of how he made that determination.
Michael Ossipoff
The duration of the observed time during which a Jovian moon is eclipsed depends on the difference in the distance between Earth and Jupiter. at the times of that moon's disappearance and re-appearance.
The change in the observed eclipse duration, when the disappearance and re-appearance are first observed from a certain two distances, and then observed again at a different pair of distances, is what enables calculation of the speed of light.
Michael Ossipoff
...so that the two pairs of distances, for the two measurements, would give the greatest possible difference in observed eclipse-duration.
Michael Ossipoff
The whole argumentation is based on the idea that we see the (dis)appearance at the moment it happens, and that distance does not have any effect on our perception and observations.
I am afraid that is a circular argument that cannot be proven.
Please note that I am not discussing the speed of light, only Rømer's argument how to calculate it.
That would work too.
Michael Ossipoff
...whereas the time of an appearance could be predicted only by clock, and clocks weren't as accurate in Roemer's day.
Of course the clock's inaccuracy would affect the speed-determnation's accuracy anyway, but you still wouldn't want the added uncertainty about when the re-appearance happened. ...if you came back to the telescope some time after the re-appearance.
Michael Ossipoff.
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.
***
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.
The Earth's speed in orbit is about 18.5 miles per second.
At Denmark's latitude, the speed of the ground's movement with respect to the Earth's center is about 1/6 of a mile per second.
In fact, if the observation is made when Jupiter is on or near the meridian (a the observer's longitude), then of course the ground at that location would have even less speed with respect to Jupiter.
The limiting factor for Roemer's determination was the accuracy of clocks in his day.
For that matter, are you even sure that Roemer didn't take the Earth's rotational motion into account when determining the distances from him to Jupiter?
See above.
See above.
It would be better to use disappearances, because there's observational information about exactly when to expect them.
If you're saying that it's necessary to record the time of a moon-disappearance (behind Jupiter), then you're right. That's what Roemer did.
As noted above, it would be better to record the time of disappearances, because it's easier to know when to expect them.
Earlier in Roemer's century, Isasc Newton solved the differential equations of the Earth's orbit (at least for a two-body model, disregarding perturbations by other planets).
That made it possible to calculate the Earth's distance from Jupiter at any time.
Most likely, using the orbital solution method originated by Newton, calculated the date on which the Earth would have the greatest speed-component toward Jupiter, and the date on which the Earth would have the greatest speed-component away from Jupiter.
On each those two dates, he'd record the times of two successive disappearances of a moon behind Jupiter.
Then, by the orbital solution introduced by Newton, Roemer would calculate the distances between Earth and Jupiter, at the times of the four observations, mentioned in the paragraph before this one.
When the Earth is moving toward Jupiter, the 2nd eclipse beginning will happen when the Earth is closer to Jupiter. Light won't have as far to travel as far, and so the event will be recorded a bit earlier. and so the observed time between successive disappearances will be shorter (than it would be if the Earth and Jupiter were stationaryi).
When the Earth is moving away from Jupiter, the effect is opposite, and the observed time between successive dissappearances of that moon will be longer.
According to Wikipedia, Roemer measured a 7-minute difference in the duration between successive disappearances on the two dates.
...resulting from the different light-transit-times at different distances.
From that he could calculate the speed of light.
The accuracy of his lightspeed determination was limited by the accuracy of the clocks of his day.
Michael Ossipoff
.
Okay. I am not really worried about the accuracy, but about the principle.
If I understand you right, it is possible and legitimate to compare times at different locations? That 5 o'clock at location A on the orbit path, is the same as 5 o'clock (or another time) at location B?
The maximum delay measured was sixteen and a half minutes. In comparison, the second or two that it would take light to cross the width of the earth is irrelevant.
The errors you describe are infinitesimal, and hence irrelevant to the outcome of the experiment.
Again you do not understand my question. I do not care whether it is 7 or 70 minutes.
Maybe you should think about Einstein's thought experiment involving the synchronization of clocks. I am not saying relativity is involved at this level, I am just asking ( and remember, this is a discarded version), how times and clocks relates.
By his clock and calendar, and Newton's solution for planetary orbits, Roemer could calculate the Earth's position, and Jupiter's position, at each of the 4 observation-times...and thereby the distances between Earth and Jupiter at those times.
Roemer most likely would prefer to make his observations when Jupiter is at or near the meridian at his longitude. But of course it would have to also be times at which the sky is dark enough to observe Jupiter's moons.
The speed of the ground that Roemer stood on, with respect to the Earth's center, is about 100 times less than the Earth's orbital speed. The component of Roemer's ground's speed toward or away from Jupiter would be even less.
Roemer could have ignored the position of his ground, with respect to the Earth's center, due to Earth-rotation,.because his ground's rotational speed is only about 1/100 of the Earth's orbital speed, and his clock-inaccuracy was limiting his result-accuracy anyway.
It's common to disregard small errors when there are much bigger ones.
Or he could have taken into account the position of his ground with respect to the Earth's center. Maybes he did. ...unless he was sure that that error was swamped by the error caused by his clock's inaccuracy.
In either case, there isn't any error in principle.
Michael Ossipoff
In this case I was right to discard my first argumentation, and concentrate on the perception of the (dis)appearance of the moon.
On this point, I am afraid, you have not changed my mind.
Quoting Hachem
I did my best.
I'll just suggest that you re-read my description of Roemer's determination method, from a fresh perspective, instead of in terms of beliefs that you've previously formed regarding what Roemer did.
When you're convinced that you already know, you're cheating yourself out of the opportunity to find out.
Other than that, there's nothing that I can say that would help.
As I said, i did my best.
Michael Ossipoff
and I appreciate it. Thank you.
Do you accept the accuracy of the following?
https://www.projectpluto.com/jevent.htm#oct
Io is the innermost moon, I.
You apparently have trouble grasping my objection. There is no reason for me to reject these observations, I am not an astronomer.
What we are talking about is the epistemological value of those observations.
To put it as clearly as I am able:
1) You see the moon appear at time t1 while you are at positon p1 of the orbit.
2) you see the moon appear at time t2 while you are at position p2 of the orbit.
@Michael Ossipoff made it clear to me that I was right in doubting the validity of my first version in which I doubted whether it was possible to assume a common clock. So, looking at the times and trying to falsify Rømer's argumentation was wrong.
My objection concerns the fact of the observations themselves.
When you see the moon at t1p1, that is an observation that is determined by the resolution of your device and the distance to the moon.
That distance determines the moment at which the moon becomes distinguishable from Jupiter as a singular object.
The longer the distance from Jupiter, the longer it will take for Jupiter and the moon to become distinguishable.
My objection may be be invalid concerning modern telescopes. Maybe modern optical technology has made distance irrelevant. I would not know and defer to the experts on that point.
What is certain is that this was not the case in the 17th century, and that is why I dare claim that Rømer's argument is not the proof everybody thinks it is.
You are talking about seconds, at the very most, in a measurement of minutes.
Anyhow, the period of Io is 1.769138 days - agreed?
You still do not understand my point.
If I am right, you are, in such a situation, not measuring the speed of light, but the moment the moon appears or disappears for you.
All you can say is that when you are at p1, you see it at t1, and when you are at p2, you see it at t2. You cannot draw any conclusion about light.
That is what, I suppose, makes my analysis so difficult to accept.
You realise that this is not an argument?
I am saying that Rømer did not have an argument.
Roemer's main source of inaccuracy was the clocks of his day. I've said that several times already.
No one's claiming that Roemer's determination was dead-on accurate. He estimated 140,000 mi/sec. That estimate was low.
But it was pretty good anyway, especially when you remember that, before Roemer, the speed of light was completely unknown.
Is that your whole point, that Roemer didn't have the instrumentation to make a highly accurate determination? But you've been claiming that Roemer was wrong in principle.
...and your attempted justifications of that claim have been completely vague and without meaning. It isn't possible to answer your argument, because it isn't saying anything that means anything.
Look, in philosophy, the academics can be full of sh_ _, and I claim that they are.
But in the physical sciences, like astronomy, how likely is it that Roemer, an astronomer, and all the later astronomers and physicists, agree that Roemer's light-speed determination method is right in principle, but that you know better than all astronomers and physicists?
When you believe that you're right, and all the astronomers and physicists are wrong, about a matter of astronomy and physics, then could it be that you might want to reconsider your belief?
You'd be able to understand my description of Roemer's method, but you won't look past your pre-formed belief that you have the truth, and all the astronomers and physicists are wrong.
Michael Ossipoff
Too bad you have changed your style in favor of polemics. So be it.
Not, it is not a matter of how precise measurements are. In fact, it does not concern measurement at all, except in asking the question:
What are we exactly measuring?
You assume, like everybody else, that it is the speed of light. Once you accept this assumption any inexactitude becomes historically irrelevant. It becomes solely a matter of progress in the measurement process.
I am asking of you to do one step back, before you decide that it is light speed that it is being measured.
When you do that you can ask yourself again: what am I measuring?
What happens when I observe an event from position p1, and then observe the same event from p2?
If you take the way your observation takes place as irrelevant. That is, if you do not doubt an instant that when you see the event happening, it is happening not at that moment but because light needs time to reach you and make you see it. Then you have already assumed that which you wanted to prove, and the only thing that rests is count the seconds or the minutes between one event and the other.
So, in fact, I am saying that Rømer had already decided for himself that it takes time for events to reach us, and the matter of calculations was then easily resolved.
Apparently, I am unable to convince you that that was an illegitimate jump in his reasoning. That is why we keep going back and forth without anyone of us convincing the other.
For the last time, once you accept the main idea, that is now a given in modern science, then there is no reason to doubt the validity of Rømer's argument.
But you must remember that in his time, that was not obvious and had to be proven. Well, my claim is that he did not, and simply assumed it, then presented calculations and made it sound scientific.
Whether he was proven right afterwards, or not, is irrelevant. What matters is, was his argumentation valid when he made it?
My answer is NO!
No, Roemer didn't necessarily assume that light had a finite speed. His experiment depended on no such assumption and implied no such assumption.
Roemer's measurement could have yielded an infinite speed of light. ...which would have told Roemer that either light's speed is infinite, maybe just too high to be measured by Roemer's method. But Roemer's measurements indicated a finite speed of light, and that measured speed was reasonably accurate.
In short--Roemer didn't assume, and his experiment didn't depend on an assumption of, a finite speed of light. But that's what it found.
If light-speed were infinite, the observed times between eclipse-beginnings would have been unchanged.
Before Roemer, there'd been no measurement to indicate that. Galileo had tried to measure light's speed, but, light was too fast for its speed to be measured by Galileo's method. From Galileo's measurement, either light's speed was infinite, or it was too fast to be measured by Galileo's method.
Roemer's measurements could have likewise indicated an infinite light-speed, which would have indicated that light's speed is infinite, or too fast for Roemer's method to measure.
So, no--Roemer didn't just determine what he'd assumed. He didn't assume a finite light-speed. But he found one.
Michael Ossipoff
That is where our interpretations diverge. I say that his idea was not the only possibility, and he never gave any reason why it should be.
I will not repeat my arguments, it would be a waste of time for all of us.
Let us then agree to disagree. Unless you prefer insults and name calling.
You haven't given a an alternative interpretation of Roemer's results. ...at least not one with a decipherable meaning.
I didn't call you names. I just said that maybe you should reconsider whether you're right and all the astronomers and physicists are wrong.
If you're done, at least that's an improvement.
It would have been easier to just ignore you. But I didn't want to insult you in that manner. I wanted to be polite enough to take you seriously, enough to answer you, to try to explain the subject to you.
It turns out that you didn't deserve that politeness, respect or effort.
So yes, let's agree to disagree on whether you're right and all the astronomers and physicists are wrong.
Michael Ossipoff
I am really disappointed in your analytic insight. The discussion is not about the speed of light, nor about astronomy. It is about the historical validity of Rømer's argumentation.
Trying to fault my logic through facts is really irrelevant, and I am sure you already know that.
I am not judging facts, I am judging an argumentation.
Oh, the discussion is most definitely about the validity of Roemmer's method for determinig the speed of light. That's what Roemer's "argumentation" was about. :D
You've rambled at great length, but haven't told of anything wrong with Roemer's "argumentation" I told you what Roemer's "argumetation" was. You said he'd circularly pre-assumed his conclusion. I pointed out that his measurement and determination neither implied nor needed any such presumption.
So then you retreated to your vague statement that Roemer's "argumentation" was wrong. ...in ways that you haven't coherently, intelligibly disclosed :D
:D
Forgive me for bothering you with mere facts
When you've made up your mind, what do facts matter?
[/quote]
Judge away.
You haven't decipherably told what was wrong with Roemer's "argumentation".
...except that several times you tried to, and your objections were answered. So you're continuing to evasively dance around your failure to support your claim that you're right and everyone else, including all the astronomers and physicists, are wrong..
Anyway, as I said, I've devoted more than enough time to be polite enough to not ignore you, and to try to explain this subject to you. Discussion concluded.
Over and out.
Michael Ossipoff
I am curious what you will make out of this
if you need to ask you don't need to answer.
the discussion with both of you on this thread has come to an end. Why prolong it unnecessarily? We all know where each of us stands.
Well, no. Your argument remains obscure.
If I'm right, the Hachem was saying something that was true, though he wasn't right about Roemer getting it wrong. Roemer didn't get it wrong. Roemer's method was valid. But there was more to it than we were talking about.
Hachem said that Roemer was assuming a value for the speed of light, in order to find the speed of light.. That's true. Roemer's determination required an initial assumption of what the answer might be.
But no, that doesn't mean that Roemer used circular reasoning.
I was talking about, the fact that, as measured and calculated by Roemer, the speed of light is determinable from the duration between moon-eclipse beginnings when the Earth is moving toward Jupiter, and when the Earth is moving away from Jupiter. I wasn't getting into details of the actual mathematical technique, which involved more than I spoke of.
In algebra courses, and in the mathematical problems that people are most used to, the answer is in the form of a formula, or a completed calculation. Even when it's necessary to solve a system of linear equations, and a lengthy procedure needed, it's still a completed calculation. Disregarding any lack of precision of your calculator, the answer is exact, and is completely arrived at after a relatively short finite calculation.
That's referred to as an answer "in closed form". in terms of numbers and elementary functions (like the sine, cosine, log, etc. on a scientific calculator).
But that isn't possible for all mathematical problems.
In fact, for most problems with any complexity the situation is that there's an answer, but it isn't in closed form in terms of numbers and elementary functions. It isn't completely arrived at by a finite amount of calculation, as is the case with simpler problems.
Such problems require some sort of step-by-step numerical solution, a step-by-step iterative solution.
Because such problems are so common in physics, engineering and mathematics, those numerical solutions are a much-studied and discussed topic in mathematics.
What are some examples of both kinds of problems?--
Well, for the area of a circle, a formula can be derived, pi * R squared. And then, you can solve that formula for any of its variables in terms of the others.
An example of a relatively simple physics calculation is Force = Mass * Acceleration. If you know all but one of those quantities but one, then you can solve for the one that you don't know.
Likewise for Galileo's formulas for accelerated motion--formulas that relate acceleration, initial position, initial speed, and the object's speed and position at any subsequent time. If there's just one of those quantities whose value you don't know, then you can solve for it in terms of the other values.
An example of a problem solvable only iteratively, is a planet's position in its orbit at any time. If I remember correctly, when you solve the differential equations for a planetary orbit, as a two-body problem (no perturbations), you can get an exact solution, in closed form with regard to numbers and elementary functions, for the time at which the planet will reach a particular place in its orbit. But if you want to know where the planet will be at a particular time, the formula doesn't have a closed-form solution for that. You can only get an iterative numerical solution for where the planet will be at a certain time.
There are lots of map projections for which, if you know a latitude-longitude position you can calculate where that point will be on the map. You can transform from Lat/Lon to X/Y. And you can also transform from X/Y to Lat/Lon. ...and get an answer in closed form.
But there also a lot of map projections for which a closed-form solution is avalable only for [/i]one[/i] of those transformations, in one direction. If you want to transform in the other direction, you need to solve an equation by a step-by-step iterative method, based on an initial assumption.
And that's just talking about solving equations. Step-by-step methods are also needed for most complicated integrals and differential equations too.
When solving such an equation, you start with a first guess about the answer, and, from that, an iterative method gives you a better approximate answer. Repeating the iteration, you can get as close as you want to the correct solution.
As I said, there are well-known efficient methods for such problems. Several of those methods were well-known before Roemer's time.
So, given the duration between eclipse-beginnings, when the Earth is moving toward Jupiter,and when the Earth is moving away from Jupiter, it's possible to get an accurate answer for the speed of light. ...an answer as accurate as you want, by an iterative method that must start with an estimate of the answer.
So yes, Roemer had to start with an estimate of the answer that he sought. But the subsequent iterative procedure brought him as close as desired to the correct answer. (...with the understanding that he knew that his accuracy was limited by his clock's accuracy.)
And I'll just repeat that, not only did Roemer's llght-speed determination method need an iterative solution, but even the calculations of the positions of Earth and Jupiter any some particular time (something needed in Roemer's determination) needed an iterative solution too.
So a lot of iteration was needed. No one said that it was an easy solution, especially in those pre-computer days.
But Roemer's principle was valid, and his answer would have been completely accurate if his instruments were completely accurate.
(disregarding the round-off error that happens in big iterative calclulations)
Michael Ossipoff
I wish I could agree with you because it makes a lot of sense.
I am afraid that my interpretation is quite different.
You are still trying to justify the accuracy of the method in calculating the speed of light, while I consider it a secondary, technical problem. Which by the way you describe beautifully.
There are, or at least were, two possible solutions, or more, to the question as to why the moon appeared later when the distance was larger, and sooner when the distance was shorter.
The first alternative, the one chosen by Rømer, and since then, by everybody, is that light needs time to reach us. Once you assume that this is the right solution, the rest is simple math.
The second alternative, the one I presented, even if it is not necessarily the right solution, could not be excluded. According to that alternative, our perception of two distinct objects as distinct from each other depends on the distance between us and those objects. The farther the objects are the longer it takes for moving objects to appear distinct to us. The closer they are, the easier it is.
There may be other logically possible solutions, but that is the only one I could think of.
The discussion should not focus on which of those alternatives is now considered as the right one, but on the fact that Rømer in his time had no justification in choosing one and discarding the other.
In other words, if you can prove that distance in no way could affect the perception of the moon as a distinct object from Jupiter, then you will have proven this alternative wrong, and by extension my whole argumentation.
Two dots appear as two distinct dots from a distance smaller than or equal to x. If the distance is larger the two dots will appear as one.
To see them as two distinct dots from a larger distance, those two dots will have to be farther from each other than they were. The extra distance between them takes more time of course.
Now all you have to prove is that the distance between the moon and Jupiter was the same at all Earth positions on the orbit path. But I wonder if that is possible. More importantly whether it were possible in Rømer's time.
An extra problem is that it really sounds like begging the question: how can you determine that the distance between the two dots has (not) changed?
Anyway, good luck to you.
Romer didn't initially know or assume that light takes time to reach us. That was his conclusion when he found that the duration between successive eclipse-beginnings was different when the Earth is moving toward, instead of away from, Jupiter.
After he noticed that, then yes, he interpreted it as meaning that light propagates at a finite speed and takes time to reach us. Then, by a very laborious but valid process, he calculated the light-speed that is consistent with his observations.
So yes, as you said, he assumed the finite propagation-speed as the explanation for the differing observed duration between successive eclipse-beginnings.
Your point is that there could be a different physical theory to explain the observation. Sure, of course there can always be a different physical theory.
So, (at least) two theories that could be consistent with the observations:
1, Light propagates at a finite speed.
2 Light propagates at infinite speed, and our perception of two distinct objects as distinct from each other depends on the distance between us and those objects. The farther the objects are the longer it takes for moving objects to appear distinct to us. The closer they are, the easier it is.
But William of Ockham, in the lale 1200s or early 1300s, pointed out that, when there are two rival theories to explain an observation, the simpler one is preferable, and maybe even more likely to be the correct one.
Your alternative theory says that the distinct appearance of two objects as distinct is something that propagates at finite speed, and that the propagation of that observed-distinctness is some separate phenomenon, separate from light's propagation-rate. ...and that that happens in addition to light's propagation at an infinite speed.
It was already known that light propagates (at finite or infinite speed), and you're adding an additional phenomenon that also propagates--the ability of objects to appear distinct to us.
Your theory is more complicated than Roemer's, and requires an additional assumption, an additional physical property or fact that propagates. You're assuming something ,else to be going on, more than the propagation of light.
So Roemer's explanation is the simpler one.
Whether light was regarded as a wave or a particle, no waves or objects were known to move at infinite speed, and so it wouldn't have been surprising to Roemer when he got observational results consistent a finite light-speed.
But yes, all physical theories are just theories, and eventually one is better confirmed and supported than its rivals. So yes, Roemer couldn't have known for sure that some more complicated theory didn't obtain.
That has often been the case in physics. Newton had no way of knowing that the more complicated theories of relativity or quantum mechanics obtained. But it turned out that there were more ultimate and more complicated laws of motion, mechanics kinematics and dynamics that were different from what Newton proposed.
So the simple theory isn't always the one that's right. But often it is, and in Roemer's case, that happened to be so.
Michael Ossipoff
I think we can now safely close the discussion.