Newton said that all frame of reference are equally valid

[putongren]

I'm not sure if either Einstein or Newton said that all frame of reference are equally valid. That from my point of view, the laws of physics is the same from your point of view. All frame reference can be put on an equal footing. I was wondering, can one consider the geocentric view that the Earth as the center of the universe to be equally valid as the sun as the center? That the astronomical model that Ptolemy with epicycles can be viewed on a equal footing as the commonly accepted model where the sun is in the center of the solar system.

I know that it's tempting to say that because the sun center model is simpler and hence more elegant and "better". But I think that it is possible to construct an entire astronomical paradigm having the Earth as the origin of reference point. Please let me know what you think.

 

[dst]

I wondered this once. The thing is that the Earth and Sun and indeed, any two binary systems will orbit around their common center of mass. Given that the mass of the sun vastly outmeasures the mass of the Earth, this barycenter is for all intents and purposes, inside the Sun. Saying the planets orbit around the sun is only a slight approximation.

Yes, all reference frames are equally valid and likewise, you can take either Earth or Sun to be the orbital center. However, Jupiter does not orbit the Earth as an approximation, nor do the other 6 planets (sorry Pluto ). In effect we have a multiple body system in which one of those is, to put it concisely, bloody well huge.

If I remember correctly, the method used to manipulate scenarios like this is Lagrangian mechanics which doesn't change for anything and the information you can get is limited anyway.

 

[tonyh]

I'm not sure if either Einstein or Newton said that all frame of reference are equally valid. That from my point of view, the laws of physics is the same from your point of view. All frame reference can be put on an equal footing. I was wondering, can one consider the geocentric view that the Earth as the center of the universe to be equally valid as the sun as the center? That the astronomical model that Ptolemy with epicycles can be viewed on a equal footing as the commonly accepted model where the sun is in the center of the solar system.

I know that it's tempting to say that because the sun center model is simpler and hence more elegant and "better". But I think that it is possible to construct an entire astronomical paradigm having the Earth as the origin of reference point. Please let me know what you think.

I'm not sure about Einstein, but in the Newtonian scheme, the laws of physics must have the same form in all *inertial* frames. With the solar system, we immediately have a complication - the planets are all accelerating and so are *not* inertial frames. Nonetheless, the Ptolemic model was used successfully for many centuries, so the fact that Earth is a non inertial frame can't have made too much difference(?)
As to which of the two views is better, I suppose it comes down to which gives the best answers to our questions, i.e., which best describes our observations. It is a fact that the planets orbit the sun, and that the rest of the solar system does *not* orbit the Earth. Given this, surely we have to conclude that the Heliocentric view is 'better'.

 

[kenewbie]

Oooh, I can't remember what the answer to this "common objection" is, someone enlighten me.

If all frames are equally valid, can I not spin around on the spot, declare the sun the be doing the spinning, and thus make it travel faster than light?

k

 

[Nick89]

Oooh, I can't remember what the answer to this "common objection" is, someone enlighten me.

If all frames are equally valid, can I not spin around on the spot, declare the sun the be doing the spinning, and thus make it travel faster than light?

k

Here's a quote which explains is quite nicely, got it from:
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#14

Stand up in a clear space and spin round. It is not too difficult to turn at one revolution each two seconds. Suppose the Moon is on the horizon. How fast is it spinning round your head? It is about 385,000 km away, so the answer is 1.21 million km/s, which is more than four times the speed of light! It might sound ridiculous to say that the Moon is going round your head when really it is you who is turning, but according to general relativity all co-ordinate systems are equally valid, including rotating ones. So isn't the Moon going faster than the speed of light? This is quite difficult to account for.

What it comes down to is the fact that velocities in different places cannot be compared directly in general relativity. Notice that the Moon is not overtaking any light in its own locality. The speed of the Moon can only be compared to the speeds of other objects in its own local inertial frame. Indeed, the concept of speed is not a very useful one in general relativity, and this makes it difficult to define what "faster than light" means. Even the statement that "the speed of light is constant" is open to interpretation in general relativity. Einstein himself, on page 76 of his book "Relativity: the Special and the General Theory", wrote that the statement cannot claim unlimited validity. When there is no absolute definition of time and distance it is not so clear how speeds should be determined.

Nevertheless, the modern interpretation is that the speed of light is constant in general relativity and this statement is a tautology given that standard units of distance and time are tied together using the speed of light. The Moon is given to be moving slower than light because it remains within the "future light cone" propagating from its position at any instant.

 

[putongren]

I've read all your replies and went over it with a friend, and he said that it seems like each of us are answering slightly different questions and presupposing different things. Maybe if we each explain our positions a little further, we can get somewhere.
I'm sorry I do not have much background in this area. This question just popped into my mind out of nowhere one day. I guess this question has more to do with perspectives than anything else. I've read somewhere that there is no such thing as an privileged observer and that all perspective should be treated equally. As a consequence, do we treat the sun's perspective as the same as the earth's. I think in modern Astronomy, we just assume that the Earth is not the center and base everything on that.

 

[russ_watters]

I've read somewhere that there is no such thing as an privileged observer and that all perspective should be treated equally.

That is true. That's called the "principle of relativity".

As a consequence, do we treat the sun's perspective as the same as the earth's. I think in modern Astronomy, we just assume that the Earth is not the center and base everything on that.

That's not exactly what the principle of relativity means. The principle of relativity does allow you to treat objects as stationary or moving depending on your frame of reference. Ie, if you are driving in a car and you pass another car, you can treat the Earth as stationary and say you are moving at 65 mph while the person you passed was moving at 60mph. Or you could say the person you passed was stationary and you moved past him at 5 mph.

Now you could use Newton's law of gravity to construct a model of the earth-sun system using Earth as a stationary reference frame. But you'd find the model to be needlessly complicated. More importantly, that model wouldn't make much sense to someone on Mars or someone observing our solar system from the outside (and stationary wrt the stars). Depending on the purpose and precision of the calculations, you'd tend toward the conclusion that either the sun should be considered stationary or the barycenter of the system stationary. The calculations are simpler that way.

That the astronomical model that Ptolemy with epicycles can be viewed on a equal footing as the commonly accepted model where the sun is in the center of the solar system.

Ptolmey's model of the solar system was an ad hoc mathematical model only. It had to be custom-built for each new object detected (and built over time, through observation of entire cycles) and couldn't make any predictions (it basically just played-back pre-recorded motions) and thus was not a real theory of gravity - it was just a model. Contrasting that with Newton's theory, you can take the current position and motion vector (or two positions and the time between them) and model the entire motion of the system (for an object much smaller than the sun). You can also do things like observe the orbit and calculate the mass of the objects involved. Newton's theory has real predictive power. It is a real theory.

 

[jimvoit]

Newton explained the orbits.

I'm not sure if either Einstein or Newton said that all frame of reference are equally valid. That from my point of view, the laws of physics is the same from your point of view. All frame reference can be put on an equal footing. I was wondering, can one consider the geocentric view that the Earth as the center of the universe to be equally valid as the sun as the center? That the astronomical model that Ptolemy with epicycles can be viewed on a equal footing as the commonly accepted model where the sun is in the center of the solar system.

I know that it's tempting to say that because the sun center model is simpler and hence more elegant and "better". But I think that it is possible to construct an entire astronomical paradigm having the Earth as the origin of reference point. Please let me know what you think.

Newton gave an explanation for Keplers equations in terms of his gravitationsl force law and
thereby negated the epicycles upon epicycle Earth centered model.

 

[maverick_starstrider]

If one considered the Earth stationary it would no negate any of the laws of gravity, ultimately one would just get equations of motions for each celestial body in the new non-inertial reference frame. The equivilance of reference frames would not allow you to recover epicycles and such as a predictive model.

 

[maverick_starstrider]

To restate in a perhaps more informative way: To say that the 'sun' or the 'earth' is the center of the solar system is quite arbitrary. The physically important feature is that the 'center of mass' is the most natural reference frame and that as long as the math is done correctly one can change the governing relations through a coordinate transformation to place your 'center' wherever you want. This however does not change anything or validate in any way the geocentric belief (which is not predictive).

 

[putongren]

I'm not allowed to post URLs to other sites since I haven't made 15 posts yet. This is from the Conservapedia.com on the talk page of Geocentric Theory.

The use of a Geocentric or Heliocentric frame of reference is a matter of choice, and not a matter of scientific proof. Both Galileo and Einstein have relativistic principles which allow celestial mechanics to be viewed from virtually whatever location you like. Bartosz Milewski (2006) states in reference to the Geocentric Theory: "Looking at the predictions it made of planetary movements, it is pretty good. One could probably derive it nowadays from the heliocentric theory by changing the system of coordinates (since the system attached to the Earth is not inertial, one would have to use Einstein's general relativity to do that correctly). Maybe physicists would be forced to introduce more cycles upon cycles to account for all the anomalies—maybe infinitely many. So even though the two theories differ in complexity, they are presumably equivalent in their predictive power." [1] This is not a unique view: "If one treats the motions in the heavens as relative motions (whether Galilean relativity, Einstein's General Relativity, or other types), one can create a model of the cosmos which is consistent with observations from many (if not any) reference points.[2] I can supply a hundred other sources which say the same thing. This is not in doubt, it is a fact and needs to be made clear.

I think this section stands in contrast to what have been said thus far.

 

[billiards]

It depends on the problem...

The thing is there is no true centre, so if we feel obliged to use some kind of co-ordinate system we are free to define the origin as we wish. It just so happens that if you are looking at the orbits of all the planets, the mathematics is easier if we consider the sun to be at the origin in the sense that the number of terms in the equations of motion are reduced.

However, if you wanted to look at the path of an aeroplane flying from London to New York, it would be easiest to choose a different co-ordinate system - in fact a non-inertial, geocentric framework would be easiest (non-inertial because it spins in a geo-stationary sense).

So to summarize, although any co-ordinate system is equally valid, the best one to use is the one which keeps the mathematics the simplest, which depends entirely on the problem..

 

[D H]

It just so happens that if you are looking at the orbits of all the planets, the mathematics is easier if we consider the sun to be at the origin in the sense that the number of terms in the equations of motion are reduced.

A heliocentric frame is an accelerating (i.e., non-inertial) frame. Looking at the orbits of the planets is easiest in a barycentric frame. A barycentric frame is of course accelerating, but toward the center of the galaxy. The gradient of this acceleration is negligible over reasonably short distances (the span of the solar system) and thus can be safely ignored over reasonably short periods of time (thousands to millions of years).

That said, any reference frame can be used. Newton's second law is not valid in an accelerating frame, but it can be made to appear valid by introducing pseudo-forces called "third body effects". Sometimes the use of these pseudo-forces makes "more sense" than working in an inertial frame. For example, the space agencies inevitably use a geocentric frame to model the orbit of an artificial satellite around the Earth.

 

[jimvoit]

"Numquam ponenda est pluralitas sine necessitate"

 

[russ_watters]

I think this section stands in contrast to what have been said thus far.

Except for a couple of points, it fits pretty closely with what I said:

One could probably derive it nowadays from the heliocentric theory by changing the system of coordinates (since the system attached to the Earth is not inertial, one would have to use Einstein's general relativity to do that correctly). [emphasis added]

I said roughly the same thing. In any case, the reason no one does that is because it is a pointless thing to do.

Maybe physicists would be forced to introduce more cycles upon cycles to account for all the anomalies—maybe infinitely many. So even though the two theories differ in complexity, they are presumably equivalent in their predictive power."

He's mixing a few things here: Ptolmey's model wasn't based on Newton's gravity, so it isn't correct to say that you'd be using "epicycles" to build a geocentric, Newtonian model. Ptolmey's model had no predictive power beyond what each invidividual, custom model could do.

"If one treats the motions in the heavens as relative motions (whether Galilean relativity, Einstein's General Relativity, or other types), one can create a model of the cosmos which is consistent with observations from many (if not any) reference points.[2]

That's correct.

One other thing that may or may not be minor. I spent some time at BadAstronomy and there were some Geocentrists there. A distinction was made between a capital and lower case "g" in "geocentrism". A lower-case "g" was used for a "weak" form of geocentrism that simply fit with the idea that any point could be used as a reference. A capital "G" was used to denote the Earth being the one and only universally valid frame of reference, ie, Biblical Geocentrism.

What you were trying to link wasn't a valild reference anyway, so we would have deleted the link. Conservapedia is a site with an adjenda and what you quoted was an ok part of a talk page (not the actual article on geocentrism) who'se purpose was to push the quite incorrect Biblical type of Geocentrism.

Their biggest, most obvious flaw is the desire to have it both ways: they argue Relativity's version when it suits them (it supports the "weak" version - that any point can be considered the center), then try to discredit Relativity.

I hope you didn't come here to try to bring that discussion here...

 

[putongren]

Conservapedia is a site with an adjenda and what you quoted was an ok part of a talk page (not the actual article on geocentrism) who'se purpose was to push the quite incorrect Biblical type of Geocentrism.

Their biggest, most obvious flaw is the desire to have it both ways: they argue Relativity's version when it suits them (it supports the "weak" version - that any point can be considered the center), then try to discredit Relativity.

I hope you didn't come here to try to bring that discussion here...

Don't worry, I'm not here to argue Biblical type of Geocentrism or the weak version. However, I think I should reapproach the problem a little differently.

I have a little textbook called the "Introduction to Tensor Calculus, Relativity and Cosmology" and it said at the beginning of its preface that "The revolt against the ancient world view of a universe centered upon the earth, which was initiated by Copernicus and further developed by Kepler, Galileo and Newton, reached its natural termination in Einstein's theories of relativity. Starting from the concept that there exists a unique privileged observer of the cosmos, namely man himself, natural philosophy has journeyed to the opposite pole and now accepts as a fundamental principle that all observers are equivalent."

The work of Einstein, Newton, Kepler, and Galileo was built around the Copernicus Principle, that the universe does not center around the Earth. There is a natural progression of scientific ideas starting with "the revolt" against the Earth-centered model to Newton's theories, and then terminating with Einstein's theories. Galileo (I think) was the one that said that the Earth was not the center, Kepler then provided the empirical equations of the movement of the planets with the sun as the center. Newton arrived at his three laws using Galileo's and Kepler's work. The three laws of Newton are in accordance with the fundamental principle upon which the special theory of relativity is based. The physics that they used relies on the philosophical assumption that the Earth is the center. So my using Einstein's fundamental principle that all observers are equivalent hence the Earth-centered perspective is valid as the sun-centered one is not going to prove my case, so to speak, because Einstein's work assumes the Copernicus Principle to be correct (I used Einstein principle incorrectly anyway). It seems that I am using an argument to prove something in which the fundamental principle of that argument is already in contradiction with what I am trying to prove.

So anyway, I think I will start anew again. To further weaken my case, measurements of the effects of the cosmic microwave background radiation in the dynamics of distant astrophysical systems in 2000 proved the Copernican principle on a cosmological scale. However, there are some good news for the people against the Copernicus princple. I got this article on Wikipedia on the Copernican principle.

Results from Wilkinson Microwave Anisotropy Probe (WMAP) appear to run counter to Copernican expectations. The motion of the solar system, and the orientation of the plane of the ecliptic are aligned with features of the microwave sky, which on conventional thinking are caused by structure at the edge of the observable universe

Lawrence Krauss is quoted as follows in the referenced Edge.org article:

"But when you look at CMB map, you also see that the structure that is observed, is in fact, in a weird way, correlated with the plane of the Earth around the sun. Is this Copernicus coming back to haunt us? That's crazy. We're looking out at the whole universe. There's no way there should be a correlation of structure with our motion of the Earth around the sun — the plane of the Earth around the sun — the ecliptic. That would say we are truly the center of the universe."

It would be somewhat surprising if the WMAP alignments were a complete coincidence, but the anti-Copernican implications suggested by Krauss would be far more surprising, if true. Other possibilities are (i) that residual instrumental errors in WMAP cause the effect (ii) that unexpected microwave emission from within the solar system is contaminating the maps.

There is a slight chance that an experimental error occurred, but I'm betting that this is a genuine piece of evidence against the Copernican model.

After talking to a friend about the problem again, what he had to say was that you do not lose any information switching from the complicated model to the more "elegant" model. Sure, with the Copernican principle as the fundamental cornerstone, you get Newton's laws and the theory of relativities. And yes, Ptolmey was only a mathematical model that can only playback recorded movement and have no predictive power. But I feel that we haven't developed that unused paradigm. I'm not actually arguing for Geocentrism, all I'm saying is that it is wrong to point at a model and discard it just because people developed an entire science based on an alternative principle. I think that people are afraid of the philosophical implications on science and our place in the world.

 

[D H]

Wikipedia can be a great source. However, it must be taken with a grain of salt. Ideologues and crackpots are drawn to wikipedia like flies to balsamic vinegar. This article appears to be one such case. Look at the discussion for this page: http://en.wikipedia.org/wiki/Talk:Copernican_principle#Relevant_Information_Prejudicially_Removed":

On 20 Sept, 2007, someone going by the name of, "Chalnoth" removed the following text from the article, stating that; "Lawrence Krauss was in no way, shape, or form intimating that the Earth is at the center of the universe". Although the referenced Edge article makes clear that Krauss was not advocating that the observational data was correct, he was indeed confirming the direct observational implications of the WMAP anomalies, which have since been refined to include other galaxy systems in a similarly meaningful manner, as was anticipated might happen within the very text of the Wikipedia article. This person also removed other evidence from an article from CERN that was only confirmed by Krauss' statement, strongly indicating that "Chalnoth" is consciously attempting to prejudicially censor the evidence.

It helps to go to the source. The paragraph in the http://www.edge.org/3rd_culture/krauss06/krauss06.2_index.html" article following the paragraph quoted in the wikipedia article reads

The new results are either telling us that all of science is wrong and we're the center of the universe, or maybe the data is [noparse][/noparse]imply incorrect, or maybe it's telling us there's something weird about the microwave background results and that maybe, maybe there's something wrong with our theories on the larger scales. And of course as a theorist I'm certainly hoping it's the latter, because I want theory to be wrong, not right, because if it's wrong there's still work left for the rest of us.

 

[russ_watters]

So my using Einstein's fundamental principle that all observers are equivalent hence the Earth-centered perspective is valid as the sun-centered one is not going to prove my case, so to speak, because Einstein's work assumes the Copernicus Principle to be correct (I used Einstein principle incorrectly anyway). It seems that I am using an argument to prove something in which the fundamental principle of that argument is already in contradiction with what I am trying to prove.

Could you please state explicitly what it is you are trying to prove? You're making a lot of arguments, but I haven't seen anywhere where you have said exactly what it is your point is.

But I feel that we haven't developed that unused paradigm. I'm not actually arguing for Geocentrism, all I'm saying is that it is wrong to point at a model and discard it just because people developed an entire science based on an alternative principle. I think that people are afraid of the philosophical implications on science and our place in the world.

If that's your entire point, then it really is wrong. The problem is exactly what I said before: any model that will correctly predict the motions of the planets is necessarily reduceable to Newton's (or Einstein's, if your required precision is higher) theory. So not only do you not gain anything by doing geocentric calculations, you lose a lot in simplicity. It really is pointless - so the question is: why would you want to do that?

 

[jimvoit]

You are right on the mark. As William of Ockham said, "Numquam ponenda est pluralitas sine necessitate"