Ptolemy or Copernicus, just a matter of convenience?

[Jim__]

TIME's excerpt from Hawking's new book:

A famous example of different pictures of reality is the model introduced around A.D. 150 by Ptolemy (ca. 85–ca. 165) to describe the motion of the celestial bodies. Ptolemy published his work in a treatise explaining reasons for thinking that the earth is spherical, motionless, positioned at the center of the universe, and negligibly small in comparison to the distance of the heavens.

This model seemed natural because we don't feel the earth under our feet moving (except in earthquakes or moments of passion). Ptolemy's model of the cosmos was adopted by the Catholic Church and held as official doctrine for fourteen hundred years. It was not until 1543 that an alternative model was put forward by Copernicus. So which is real? Although it is not uncommon for people to say Copernicus proved Ptolemy wrong, that is not true. As in the case of the goldfish, one can use either picture as a model of the universe. The real advantage of the Copernican system is that the mathematics is much simpler in the frame of reference in which the sun is at rest.

These examples bring us to a conclusion: There is no picture- or theory-independent concept of reality. Instead we adopt a view that we call model-dependent realism: the idea that a physical theory or world picture is a model (generally of a mathematical nature) and a set of rules that connect the elements of the model to observations. This provides a framework with which to interpret modern science.

Though realism may be a tempting viewpoint, what we know about modern physics makes it a difficult one to defend. For example, according to the principles of quantum physics, which is an accurate description of nature, a particle has neither a definite position nor a definite velocity unless and until those quantities are measured by an observer. In fact, in some cases individual objects don't even have an independent existence but rather exist only as part of an ensemble of many.

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Is Ptolemy's model valid? Can we use his model if we just re-work some other ideas, e.g. relativity? Is the choice of Copernicus just a convenience?

[Demeter]

1. Ptolemy's Model is like a mirage

It looks real to the naked eye, but it isn't correct.

[EmilyKent]

2. Well Aryabhata, a Hindu mathematician,

calculated the value of pi and the solar year's length, determined that the earth revolved around the sun and discovered the cause of eclipses about a thousand years before Copernicus.

[muriel_volestrangler]

8. Aristarchus suggested it in the 3rd century BC

http://www-istp.gsfc.nasa.gov/stargaze/Sarist.htm

involving eclipses as well.

[EmilyKent]

13. So we're agreed.

Ptolemy and Copernicus were late to the party. :rofl:

[yellowcanine]

3. Ptolomy had some weird complicated constructs to make his model work.

I speak of epicycles.

http://en.wikipedia.org/wiki/Deferent_and_epicycle

[BadgerKid]

4. First, you need to define "valid".

e.g., Did Ptolemy's model explain the data?
Did Ptolemy's model make observable predictions?
Was Ptolemy's model aesthetically pleasing to his audience?
Did Ptolemy's model contradict other observations?

Copernicus's model was revolutionary in thinking, although it cheesed off the Church, in the sense it shifted the model's frame of reference (pardon the accidental pun). On first thought I tend to doubt Einstein's relativity could be re-worked in an analagous fashion because the observer's and observee's points of view can already be interpreted through it. But who knows? Maybe some thinking outside of the box might lead to something!

[Jim__]

9. By "valid" I mean the Ptolemaic System could be used as a workable model today.

My reading of what Hawking is saying is that it could - only the math would be much more complex. That surprises me, but if that's what Hawking is saying, then I trust that he's right.

Maybe the more complex math is only theoretically feasible, but in reality, beyond what we could develop.

[leahcim]

5. Yes, it is just convenience.

You can reformulate Newtonian and relativistic mechanics in Earth's frame of reference, just as well as the Sun's.

In an Earth-centred Newtonian description of the solar system, the other planets orbit the Sun due to gravity, but the Sun-Earth interaction is too small to make something as massive as the sun orbit the earth. Fortunately in the earth-centred frame there are inertial forces (centrifugal and Coriolis forces) that permeate all of space to compensate and allow the sun to orbit the Earth in that frame.

In a Sun-centred frame, the inertial forces are much, much smaller (a small amount due to the Sun's non-inertial motion around the centre of the galaxy, and any non-inertial motion the galaxy itself is doing, but the effect is minuscule) so in that frame you can describe the entire system in terms of gravity.

So yes, the choice of reference frame is a convenience -- we pick a frame to eliminate the effect of inertial forces. The physics does work in all reference frames, though, just with more complicated math.

[Jim__]

11. Thanks. That's what I understand Hawking to be saying. But I wasn't sure. - n/t

[HiFructosePronSyrup]

6. No.

You can rework different reference frames for a geocentric model using newtonian physics. Although it's pretty fucking stupid, as Galileo pointed out.

But not if you take relativity into account.

[muriel_volestrangler]

7. What about angular velocity?

The angular velocity of the earth as it rotates around its axis can be easily detected without reference to objects beyond the atmosphere (eg Foucault's pendulum, or the Coriolis effect on things like artillery shells). But surely the angular velocity of the earth's rotation about the centre of the solar system, around a different axis, is measurable as well, if you have good enough instruments. Ptolemy's model wouldn't be able to cope with that.

You could say "I'll use Ptolemy's model, but then add on, to every object in the universe, a correction in its motion that just happens to account for this motion we detect that could be explained by assuming the earth is not fixed, but behaves like all the other bodies in the universe"; but that seems really perverse.

[Jim__]

10. My reading of Hawking is that it could be handled.

Presumably, we'd call it something else. But, if it couldn't be handled, then I would think that Ptolemy has been proven wrong. Hawking appears to be saying that's not the case.

[leahcim]

15. Perverse

Yes, it is perverse. But "perverse" and "impossible" are not the same thing.

In some cases it's not even all that perverse. If you're modelling global weather patterns, almost all of the forces are between the air and things fixed on the Earth, so it makes sense to pick your reference frame so that the Earth is fixed, assume gravity and the centrifugal force generally cancel each other out, and incorporate the Coriolis force into your model.

Even with your artillery shell example. If I'm firing shells at France with a gun placement in England, it still makes sense to work in the reference frame where England and France are stationary and say "a Coriolis force acts on my shell". Using an inertial reference frame, and modelling the non-constant motion of England and France relative to the centre of the galaxy would be a more complicated model.

[dimbear]

12. Ptolemy's method was perfectly valid, but under it the laws of

physics become incredibly complex and arbitrary. We choose the sun centered system because the laws of physics which come out of that assumption are simple and elegant.

[caraher]

14. Ptolemy's model isn't even about physics

It is not valid for the simplest possible reason - Earth and all the planets orbit the Sun. While yes, one could cook up all kinds of crazy theories that account for the apparent motion of planets across the sky, all observational evidence contradicts the fundamentally geometric model of Ptolemy (and any of it's possible variants).

Bear in mind that today, we not only know the directions to all the planets (all that anyone had until telescopes) but we also know distances. It's then a simple matter of mapping out the relative positions of the sun and planets, and you wind up with a heliocentric solar system. No reference frames, relativity, etc. required.

Hawking is, of course, correct that *Copernicus* didn't prove Ptolemy wrong. He simply provided what looks like a better model, but one which could - relative to the knowledge of the time - have turned out to be incorrect. But Hawking is not implying we don't know better today; it just took more than the work of Copernicus to definitively rule out the Ptolemaic system.

[Jim__]

16. I read Hawking to be saying something much stronger that that.

Sure, we can read that one sentence: Although it is not uncommon for people to say Copernicus proved Ptolemy wrong, that is not true to mean that at the time of Copernicus, Ptolemy had not been proved wrong. But, the next 2 sentences make the claim much stronger: As in the case of the goldfish, one can use either picture as a model of the universe. The real advantage of the Copernican system is that the mathematics is much simpler in the frame of reference in which the sun is at rest.

One can use. If your claim were true, he should be saying, one could have used.

And, in the case of the goldfish that he is citing (included in the excerpt linked in the OP), he is stating that the ability to formulate laws that correctly predict behavior is as good as we can hope for:

The goldfish view is not the same as our own, but goldfish could still formulate scientific laws governing the motion of the objects they observe outside their bowl. For example, due to the distortion, a freely moving object would be observed by the goldfish to move along a curved path. Nevertheless, the goldfish could formulate laws from their distorted frame of reference that would always hold true. Their laws would be more complicated than the laws in our frame, but simplicity is a matter of taste.

Obviously Hawking is not saying that we could arbitrarily use the Ptolemaic System - I'm guessing much of physics would have to be re-worked. But, I believe that he is saying our view of reality is just that, a view. We cannot know the actuality. We can't be sure that our view is not distorted, just as the view of the goldfish in a curved bowl is distorted.

Our view of reality is model-dependent:

These examples bring us to a conclusion: There is no picture- or theory-independent concept of reality. Instead we adopt a view that we call model-dependent realism: the idea that a physical theory or world picture is a model (generally of a mathematical nature) and a set of rules that connect the elements of the model to observations. This provides a framework with which to interpret modern science.

We can't do any better than that.

Clearly, I haven't done the math so I don't know that a Ptolemaic system would hold up. I am taking Hawking at his word. It's possible that he is deliberately misleading people who don't know better in order to sell more books, but that would be extremely disappointing.