[pavelrub]

There is so much wrong with this comment I don't even know where to begin. It will suffice to say that this is a huge conceptual muddle, and a great example of where conceptual confusion can lead us if we are not careful. You are confusing 'discovery' with 'giving new definitions', 'reality' with 'a mathematical model that describes...', physics with everyday language, and you also seems to be unaware of what 'orbit' and 'motion' actually mean: http://en.wikipedia.org/wiki/Orbit http://en.wikipedia.org/wiki/Motion_(physics)

It should be clear that it can never be the case that by using a new mathematical model we can come to the conclusion that "the earth is standing still". This would be equivalent to inventing a new theory of mind according to which people never get angry. At best, what we can achieve is a new interpretation of the words "standing still", different from what they actually means, under which the earth is doing something else. However, this would simply be a matter of choice, not of discovery, and a pretty bad one at that (see Wittgenstein's criticism of Freud).

[lutusp]

> It should be clear that it can never be the case that by using a new mathematical model we can come to the conclusion that "the earth is standing still".

Apart from the OP's many outright errors, this one suffers from the defect that it assumes there is only one possible frame of reference. One can obviously choose a frame of reference in which the earth is motionless, but relativity denies any special significance to a particular frame of reference -- indeed, that's what relativity means.

[waps]

Which is exactly the point. Whether the earth rotates depends on your frame of reference. You can pick one where it is, you can pick one where it isn't. Neither is "true". So saying the earth orbits the sun is a choice : it is not a true or false statement, just a statement reflecting an opinion. Occam's razor (as well as general mathematical practice) dictates that we declare this to be not true in that case (note the massive difference between "not true" and "false". Not true means you don't know it to be true AND you don't know it to be false either). But this is only possible in euclidean space, you have to transform space (change the normal/distance function) before you can choose a reference frame where there is rotation.

If you look at it in the original relative space, without an euclidean transformation, there's only 2 ways to see it : you can only pick reference frames where the earth is standing still entirely, or you pick reference frames where it is moving along a straight line. You cannot pick a reference frame in relativistic space that shows ellipsoid movement (like the one predicted by the Newtonian theory which is generally what people mean by "orbit").

So you can't actually pick reference frames to do whatever you want. In order to get something looking like an orbit you have to pick a reference frame where you not only have messed with the point of origin, but also projected the distances between objects to be invariant under the influence of gravity. Which they're not in reality (effectively you're claiming that distances everywhere in the universe are as they are at an earth-sun lagrange point, which is not true). Only by doing that transformation can you get an orbital pattern.

At that point, from a purely mathematical point of view you can analyze what other motions you could get that are equally true as saying it orbits. So you can say, you can put the origin point anywhere you like, moving, accelerating, whatever you want. In addition to that you can arbitrarily change the distance function. So you could make one where the earth spirals into the sun. Or spirals away from it (simply introduce a time component in the distance function). Hell, you could make one where the earth and the moon look like they're bouncing on the surface of the sun that looks like the disc in the discworld (put origin at the center of the sun, distance function is a the normal multiplied by the tangent of an angle that goes from the center of the sun to where the moon was 48 hours ago, and in the z direction all distances are zero). Hell, I bet that even if you demanded the reference frame be euclidean you could still make it look pretty silly (I think my spiraling examples would still be euclidean). Reasons for picking one over the other ? None.

Well, one : if you want to calculate the influence of the laws of physics inside our solar system, having an euclidean reference frame centered on the sun-planets lagrange point (which is not the center of the sun) is pretty useful, as it means you need 11 (number of planets) transformations to calculate the path of a satellite moving through the solar system, whereas a relativistic reference frame would require 12 transformations (imho because they don't change rotation they're simpler though).

Aside from the utilitarian choice, all those statements are simply equally true to saying that "the earth rotates around the sun". Just because we prefer one arbitrary kind of reference frame above others here on earth (ie. euclidean) doesn't make it any more real.

And yes, compared to objects "near infinity" the earth arrives at the same spot once a year, but that doesn't make it's path any less straight.

[lutusp]

> Whether the earth rotates depends on your frame of reference. You can pick one where it is, you can pick one where it isn't. Neither is "true".

No, both are true, yet you claimed that "3 in 4 hacker news readers don't know the earth doesn't orbit the sun at all" which is a false and ignorant claim.

> So saying the earth orbits the sun is a choice : it is not a true or false statement, just a statement reflecting an opinion.

False! Mathematical physics is as far from opinion as you can get, and it has vast amounts of supporting evidence.

> You cannot pick a reference frame in relativistic space that shows ellipsoid movement (like the one predicted by the Newtonian theory which is generally what people mean by "orbit").

Yes, you can! As I said earlier, sufficiently above the sun's north pole, you would see a classic Newtonian orbit, because of the choice of reference frame.

> you can only pick reference frames where the earth is standing still entirely, or you pick reference frames where it is moving along a straight line.

I just proved this claim to be false. But you know what? I'm not going to go through and correct all your false arguments (they're all false). I've had this exact experience more times than I care to remember. You don't know anything about physics or mathematics, your overall argument is post-modern ("It's all opinion"), and you're a waste of time.

If you actually understood the topic, you would use 10% of the words you use while being wrong, and your posts might become worth reading.

[waps]

> Yes, you can! As I said earlier, sufficiently above the sun's north pole, you would see a classic Newtonian orbit, because of the choice of reference frame.

No you would not. Here I assume a correct reference frame : the start point is above the sun's north pole, but it is in gravitational freefall, not artificially accelerated to the same relative position above the sun. If you looked at the earth moving and describe it's movement as an equation in relativistic space you'd get p = k * s + c (with k a real number, p s and c vectors).

This is not a rotation, obviously.

Intuitive observation would show rotation, but that's wrong, or at least that's not really what's happening. Note that your position "above the sun's north pole" is actually an accelerated movement at a point in time. As such it is not a reference frame that is at rest, and as such is not the type of reference frame you'd want to use for anything, unless of course you're using newtonian physics.

[pavelrub]

> Just because we prefer one arbitrary kind of reference frame above others here on earth (ie. euclidean) doesn't make it any more real.

You got it all backwards. Our preference for a certain reference frame is exactly what makes it real, because that's what 'real' means.

Certain frames of reference are almost useless, while others are very useful in our everyday life. This is why "I'm going to the store" is true, while "the store is moving toward me" is false: it is our application of those words in everyday life that defines what we would call 'true' and 'false' here.

It is ridiculous to claim that the above are equally true because supposedly we can choose our reference frame however we like: this is simply not what we mean when we talk about "true" and "false" here. By focusing too much on physical vocabulary, you are losing sight of what certain words mean in the first place.

If you develop a theory that says the fridge is moving toward me when I'm hungry (= I'm going to the fridge, from a different frame of reference) - you are not making a discovery, you are simply making up new definitions of existing words, and you are confused.

Also, mathematical models are just that - math, useful abstractions we can predict stuff with. Assigning to them an ontological status is a matter of choice and of personal belief, not of knowing anything about physics.

[lotharbot]

> "Occam's razor ... dictates that we declare this to be not true"

Note that Occam's razor does not actually have the authority to dictate anything. Occam's razor is a useful heuristic -- like frames of reference, you may treat it (or various similar heuristics) as true, but may also treat it as not true.

----

This whole exchange reminds me of one of my favorite Asimov essays, The Relativity of Wrong [0]. You can certainly make the argument that the reference frame "the earth goes around the sun" is not true, but it's less not-true than "the sun goes around the earth". "The earth goes around the sun" is a correct assessment of the relative behavior of the bodies in a reference frame which is in a sense arbitrary, while "the sun goes around the earth" is an incorrect assessment of the relative behavior of those bodies under either Euclidian or relativistic reference frames.

[0] http://chem.tufts.edu/answersinscience/relativityofwrong.htm