5 ms·

Stupid question: given General Relativity, and in particular that all reference frames are equally valid, including rotating and accelerating ones, in what sens

Stupid question: given General Relativity, and in particular that all reference frames are equally valid, including rotating and accelerating ones, in what sense is heliocentrism more 'true' than geocentrism? E.g. you can pick a geocentric reference frame and all the math works out (albeit you'd need to define large fictitious forces, etc., but again, they are only 'fictitious' from the perspective of a different reference frame; in the chosen frame they look quite real!). Isn't the choice between geocentrism and heliocentrism purely one of convenience, and we can simply pick and choose whichever reference frame is most convenient for calculation purposes? For example, if I'm interested in things happening in daily life, I pick a reference frame at rest with respect to the ground beneath my feet. If I am figuring out satellite orbits, I use a geocentric frame. If I'm calculating a trip to Mars, I use a heliocentric frame (perhaps a rotating one). If so, why do we still define heliocentrism to be more correct? Is the argument really an implicit throwback to Newtonian absolute space and time, which Relativity rejected?

kevinwang 10y ago
I think most simply, the entire solar system revolves around the sun and not the earth.
- smallnamespace 10y ago
  Isn't that simply begging the question though? If you adopt a geocentric reference frame, then the Sun appears to rotate around the Earth, and all the other planets also appear to follow epicyclic paths around the Earth. You can predict the motions of every planet and star equally well, the equations are just different. So again, why is one more 'correct' than the other, besides calculational simplicity?
  - hsitz 10y ago
    The simple answer of why one is more correct, is because it's deemed as correct by the scientific community, which comprises the scientific experts on that issue. The larger issue you raise is one that was especially prominent in mid-20th century philosophy of science, specifically in Thomas Kuhn's concept of a "paradigm shift". A radically new scientific theory does not displace an existing theory because it is more "correct", since ad hoc modifications (e.g., epicycles) can always be made to the existing theory to account for new evidence that appears not to fit. However, at some point the existing theory will come to have so much baggage, and the new theory will explain the world so much more elegantly (e.g., with calculational simplicity) that the new theory will overthrow the old one and become the new "paradigm". Note that this is not because the old theory could not accommodate all the facts; any old theory can if you modify it enough, but at some point when you have to make all sorts of strange adjustments to the existing (old) theory it just becomes wildly implausible when compared with the new theory. At some point scientific consensus changes and the the new "paradigm" is accepted. You can read more about this at Wikipedia: https://en.wikipedia.org/wiki/Copernican_Revolution https://en.wikipedia.org/wiki/Copernican_Revolution https://en.wikipedia.org/wiki/The_Structure_of_Scientific_Revolutions https://en.wikipedia.org/wiki/The_Structure_of_Scientific_Re... https://en.wikipedia.org/wiki/Thomas_Kuhn https://en.wikipedia.org/wiki/Thomas_Kuhn
  - loteck 10y ago
    I'll admit I'm way out of my depth here! But wouldn't the fact the planets experience orbital decay that ultimately cause them to be pulled into the star they are orbiting, mean that heliocentric is "more correct" when discussing a planet's relation to a star?
    - DSMan195276 10y ago
      You could still calculate that with an earth-centric approach, it just might not be fun. As far as the physics go, it doesn't care which point or body you pick to be non-moving - the math all works out, it's just relative to a different point. And with that, there's no spot in the universe you can point at and say "That point is not moving", so there's no "fundamental zero" we can compare everything to. Perhaps the point is that "more correct" is subjective. Both approaches will give you the right answer, it's just that heliocentric makes finding the answer easier.
  - lmkg 10y ago
    Geocentrism and Heliocentrism are not just calculation frameworks for making observations of the sky. They are also an attempt to create a model of the fundamental rules that govern the heavens, and then to create observable predictions based on those rules. Heliocentrism is the better model of the two, because the paths of the planets are dominated by force of gravitational attraction to the sun. This force is what you model, regardless of your frame of reference. You can use this model to create observational predictions for any point in the solar system, but the forces that your modeling are essentially the heliocentric ones. But to your larger point: In my grade-school science class, we were all taught that heliocentrism was itself supplanted by the discovery that the sun is rotating around the galaxy, and that modern cosmology doesn't center around anything at all. Heliocentrism is still more accurate than the geocentrism that it replaces, but is still regarded as a stepping-stone to modern theories.
  - Jarwain 10y ago
    I've always thought of the difference between geocentric and heliocentric to be an ego thing. Setting Earth as the center of the Universe works great, for everyone on Earth. It enforces the idea that Earth, and through that, Humans, are so important that the Universe is really centered on the Earth. Maybe this is the case, maybe its not. To assume that the Earth is the center because of us is pretty egocentric. Heliocentric places it in a more objective way, I guess? Changes the reference point to be consistent with the known laws/theory/whatever of gravity. It could also be a scaling thing as well. Applying the equations to planets while setting a reference point based on our sun would provide equations that are more easily adaptable to other galaxies or solar systems that also have planets rotating around the sun. Sure, we could try and create formulas that describe the motion of other galaxies in reference to the Earth, but that would fall apart if the Earth stopped existing.
spaceheeder 10y ago
Not a physicist so my answer may be totally wrong, but my first _guess_ would be that geocentrism necessitates unequally valid reference frames. You would need different equations to represent the movements of Venus and Mars relative to Earth as you would need to represent their movements relative to each other. Or at least it certainly seems to me like you would at first guess. Perhaps you could use matrix algebra to apply geocentric laws of motion to all reference frames, and then simply translate them into a reference frame where Earth is the "actual" center of things? But then you're just admitting that Earth isn't the "actual" center of things.
Chinjut 10y ago
I think the answer is precisely the realization that heliocentrism is a convenient framework for specifying the correct relationships. If one formulated their geocentrism-with-epicycles model to be precisely equivalent to heliocentrism in all physically observable details, just with Earth as the origin to their coordinate system, and acknowledged this equivalence, then that would be perfectly correct as well, albeit unduly cumbersomely framed. But the useful thing is that insight, that what happens is equivalent to the clean heliocentric model, whatever coordinates you might prefer to think of it in terms of.
- mannykannot 10y ago
  Is it possible for a geocentric, epicyclic model to get the 3D positions of the solar system bodies approximately correct, as opposed to just their angular motion with respect to Earth?
  - mannykannot 10y ago
    I cannot edit my post any more , but I can still reply to it, and it seems the answer is yes: https://www.youtube.com/watch?v=QVuU2YCwHjw https://www.youtube.com/watch?v=QVuU2YCwHjw - but you need eccentricity to get the speeds right: https://www.youtube.com/watch?v=qHmjGUxWRAI https://www.youtube.com/watch?v=qHmjGUxWRAI (10 minutes in.) Furthermore, the result is not equivalent to the heliocentric model because it has many more parameters.
gabriel34 10y ago
Newtonian physics allows different frames of reference. Non inertial frames of reference need pseudo-forces. Einstein's relativity deals with non absolute space and time, that is, time speeds up or slows down depending on your 'frame of reference', the only thing remaining constant is the speed of light in a vaccum. The choice isn't purely one of convenience because assuming 'heliocentrism' allows for a more elegant and universal set of equations to explain everything, from quarks to galaxies.
jules 10y ago
The modern view is indeed that there is no preferred reference frame. It's just a matter of choosing a coordinate system. If you wanted to make a distinction you could say that the laws have a simpler form in a heliocentric coordinate system, but this is only really true if you make certain approximations.
onlyrealcuzzo 10y ago
Are these "large fictitious forces" the same thing as Dark Matter today? That would be pretty interesting, if so.
- raattgift 10y ago
  That's a good question, but the short answer is no. Fictitious forces relate to particular choices of coordinate systems (and their origins). For example, the centrifugal force is an easy way to think about the tendency to be pulled "down" by an astronaut aboard a spinning space station; that astronaut can think of a set of cylindrical coordinates with the origin at the centre of rotation of the station, or of a set of Cartesian coordinates with the origin at some point on the "floor" and centrifugal force is simply natural-seeming. However, if the astronaut uses a non-rotating set of Cartesian coordinates whose origin is outside the entire station, for example, centrifugal force no longer seems very natural as an explanation. Alternatively, close inspection of the path traced by a dropped tablet would also conflict with expectations from a real centrifugal force. Careful study of the movement of stars in the outer reaches of certain types of rotating galaxies threw up a surprise: the linear velocities of stars orbiting far from the centre should be much faster in order to maintain their roughly circular orbits than observational evidence of their speed allows. This difference does not change with a change of coordinates, so it is not an artifact of a choice of coordinate systems. Thus it is not really fixable with a fictitious force; so far the only "fix" we know is to either use known real forces that are generated by the non-gravitational content of the universe (possibly adding not-previously-known matter) or to keep the matter content constant but modify one or more forces. (Hybrid approaches are also possible). The space for introducing truly new long-range forces has been heavily constrained by experiment on Earth, and a "fifth force" is essentially ruled out. We have not yet ruled out many viable forms of previously undetected matter, however some forms are no longer plausible. Dark Matter introduces invisible mass far from the centres of galaxies that help to suspend these surprisingly slow-moving stars. Modifications of gravity have also been proposed that bend the trajectories of such stars less towards the centres of their galaxies. Dark Matter also explains the peculiar velocities of galaxies within several clusters; they move as if attracted to unseen mass in the cluster. Previously mentioned modifications of gravity have to be further modified to incorporate these observational results. Collisionless Dark Matter also explains the behaviour of several known (past) galactic collisions where gravitational lensing preceeds the visible matter and especially the energetic gas and dust that collided as the galaxies passed through one another. This so far has not been fixable by yet more modifications of gravity, however people are trying that approach too (e.g. https://arxiv.org/abs/1606.09128 https://arxiv.org/abs/1606.09128).
ziotom78 10y ago
You're right, mathematically speaking the two systems are the same. As a matter of fact, the calculations that describe the attitude of a spacecraft flying not far from the Earth are usually expressed in a geocentrical reference frame. It's much simpler, yet produces the same result you would get using the heliocentric frame. The real disadvantage of the geocentric system is that it is a barren model: it does not allow science to advance. It is able to explain the motion of planets with exceptional precision, but it does so by using a mathematical construction (the epicycles) that does not lead to a deeper understanding of the inner laws of nature. On the other side, the heliocentric model (when corrected with Kepler's idea of using ellipses instead of Copernicus' circles and epicycles) was a big step towards the bigger understanding of gravitation that was produced by Newton's law of gravitation.
caf 10y ago
When you're dealing with the motion of objects close to the Earth, a geocentric reference frame is entirely appropriate. However, when examining the motion of the planets a heliocentric reference frame is "more correct" in that the motion of the planets in that reference frame suggests a deeper truth: that the primary influence on the motion of the planets is somehow the Sun.
deleted 10y ago
[deleted]
mannykannot 10y ago
Of all the answers offered here, the only ones that get to the heart of the matter are those that make the distinction between inertial (non-accelerating) frames of reference, and those that rotate (and therefore have at least centripetal acceleration). In Newtonian and post-Newtonian mechanics, only inertial frames are equivalent. A geocentric frame (with a rotating Earth) spins the whole universe once a year; fix the Earth's spin, and you set the universe spinning once a day.
- raattgift 10y ago
  You can have accelerating frames of reference in Special Relativity; for example, one can set Rindler coordinates on a body that is uniformly accelerating. Addtionally, you can have locally inertial frames of reference that are inequivalent. Consider two space stations orbiting Earth at different altitudes. The occupants are in free-fall in both cases, but there is a relative acceleration between them. Rotating frames of reference tend to distract users into confusing coordinate artifacts with physical ones. As a trivial example, suppose we vary the Minkowski metric by introducing a rotation into Cartesian coordinates: dS^2 = -\left(1 - \omega^2 ({x}^2 + {y}^2) \right){dt}^2 + 2 \omega (- y dx dt + x dy dt) + {dx}^2 + {dy}^2 + {dz}^2. Here a non-massless object far from the origin will have |d\vec{x}/dt| > 1, or in other words a coordinate velocity greater than c. This is essentially the same as your last sentence. However, when we calculate the four-velocity \eta^\mu of any non-massless object, even far from the origin, we will see that dS^2 < 0 for all nearby points along its worldline. In other words, there is no superluminal motion -- there is just movement against a set of coordinates, and a different choice in coordinates will vary that. We can certainly do Standard Model physics (or classical particle dynamics) in a rotating system of coordinates, using a number of approaches. However, it is usually easier to use a different system of coordinates, and even better to abandon the idea of using any global system of coordinates in a spacetime that is not Riemann flat.
raattgift 10y ago
It's not a stupid question. General Relativity does not have global frames of reference. Borrowing from Special Relativity, an inertial frame of reference is on in which the Poincaré isometry group applies at every point in the frame of reference, and that means that fundamental physical constants do not change with translations, rotations or Lorentz boosts. That is, as you move back and forth along the spacelike axes, or rotate clockwise or counterclockwise around them, or acquire boosts, or move futureward, some set of constants are invariant; in pure SR the constants are the spacetime intervals -- the distance from one event to another. In the Standard Model of Particle Physics, there are other invariants, such as the fundamental charge and the speed at which a massless particle moves. Special Relativity is a theory with global inertial frames of reference. General Relativity has no global frames of reference at all, except in the (flat, Minkowski) spacetime of Special Relativity. Instead, GR has the concept of the LIF -- the _locally_ inertial frame -- which exists everywhere in the tightest possible definition of local (specifically, in the local section of the fibre bundle, or in the limit where spacetime intervals go to zero), but only exists in _some_ bigger regions of spacetime (those that are flat -- or at least effectively flat, in the Wilson sense of an effective field theory). None of this has to do with sets of coordinates; even in SR you can choose among a variety of coordinate systems (e.g., polar coordinates, Cartesian coordinates) and place the coordinate system's origin anywhere. Using different coordinates even in the spacetime of Special Relativity can help focus on aspects of a system under study, and indeed one can even use Rindler coordinates in Special Relativity to consider systems that include acceleration, or more often to treat a uniformly accelerating object as at rest at the coordinates' origin point. In GR covariance is introduced to express all physical laws in arbitrary coordinates. Arbitrariness here certainly includes systems in which spacelike _coordinate_ distances (or the period of an oscillator) vary with position, or even in which the speed of light _against a set of coordinates_ varies with direction. The Einstein Field Equations are written in a form that is independent of the choice of coordinates; they stay in that form even under a change of coordinates -- this is the generally covariant form. Newtonian physics, for example, can become much more complicated when you make a change of coordinates -- in this discussion, in dealing with planetary orbits under a change from a sun-centric polar coordinate system, or even a sun-centric Cartesian coordinate system to an Earth-centric system. In General Relativity the same Einstein Field Equation (EFE) form is used. The calculational price for covariance is high -- the EFEs are ten non-linear partial differential equations. Even today that's heavy calculating. So anywhere one could get a decently correct answer using Special Relativity or Newtonian mechanics, especially where one can make a good choice of coordinates, you'd choose to do that instead. Where bodies move slowly against the chosen coordinates compared to how light moves against the same system of coordinates, and where the distances between massive bodies is large, the errors will be small to negligible. So, to recap, "Isn't the choice between geocentrism and heliocentrism purely one of convenience, and we can simply pick and choose whichever [coordinate system] is most convenient for calculation purposes?" Yes, essentially, but one has to be wary about artifacts of the coordinate system that vary under a change of coordinates. A classic example involves latitude-longitude coordinates on Earth: there is a coordinate singularity at each pole, but the singularity goes away upon a change of coordinates (e.g. to local East-North-Up coordinates, or ECEF coordinates, or Cartesian coordinates with any number of possible choices of origin). Likewise, epicycles in planetary orbits change or vanish under different systems of coordinates, and so are unphysical. I changed "reference frame" to "[coordinate system]" there to capture what an observer is doing: laying out an observer-centric set of coordinates. No such set of coordinates is the correct one, but any observer can choose manifestly useless sets of coordinates or draw incorrect conclusions from the motions of objects against one particular set of coordinates (not just what system of coordinates, but also where the origin is).

kevinwang 10y ago

I think most simply, the entire solar system revolves around the sun and not the earth.

smallnamespace 10y ago
Isn't that simply begging the question though? If you adopt a geocentric reference frame, then the Sun appears to rotate around the Earth, and all the other planets also appear to follow epicyclic paths around the Earth. You can predict the motions of every planet and star equally well, the equations are just different. So again, why is one more 'correct' than the other, besides calculational simplicity?
- hsitz 10y ago
  The simple answer of why one is more correct, is because it's deemed as correct by the scientific community, which comprises the scientific experts on that issue. The larger issue you raise is one that was especially prominent in mid-20th century philosophy of science, specifically in Thomas Kuhn's concept of a "paradigm shift". A radically new scientific theory does not displace an existing theory because it is more "correct", since ad hoc modifications (e.g., epicycles) can always be made to the existing theory to account for new evidence that appears not to fit. However, at some point the existing theory will come to have so much baggage, and the new theory will explain the world so much more elegantly (e.g., with calculational simplicity) that the new theory will overthrow the old one and become the new "paradigm". Note that this is not because the old theory could not accommodate all the facts; any old theory can if you modify it enough, but at some point when you have to make all sorts of strange adjustments to the existing (old) theory it just becomes wildly implausible when compared with the new theory. At some point scientific consensus changes and the the new "paradigm" is accepted. You can read more about this at Wikipedia: https://en.wikipedia.org/wiki/Copernican_Revolution https://en.wikipedia.org/wiki/Copernican_Revolution https://en.wikipedia.org/wiki/The_Structure_of_Scientific_Revolutions https://en.wikipedia.org/wiki/The_Structure_of_Scientific_Re... https://en.wikipedia.org/wiki/Thomas_Kuhn https://en.wikipedia.org/wiki/Thomas_Kuhn
- loteck 10y ago
  I'll admit I'm way out of my depth here! But wouldn't the fact the planets experience orbital decay that ultimately cause them to be pulled into the star they are orbiting, mean that heliocentric is "more correct" when discussing a planet's relation to a star?
  - DSMan195276 10y ago
    You could still calculate that with an earth-centric approach, it just might not be fun. As far as the physics go, it doesn't care which point or body you pick to be non-moving - the math all works out, it's just relative to a different point. And with that, there's no spot in the universe you can point at and say "That point is not moving", so there's no "fundamental zero" we can compare everything to. Perhaps the point is that "more correct" is subjective. Both approaches will give you the right answer, it's just that heliocentric makes finding the answer easier.
- lmkg 10y ago
  Geocentrism and Heliocentrism are not just calculation frameworks for making observations of the sky. They are also an attempt to create a model of the fundamental rules that govern the heavens, and then to create observable predictions based on those rules. Heliocentrism is the better model of the two, because the paths of the planets are dominated by force of gravitational attraction to the sun. This force is what you model, regardless of your frame of reference. You can use this model to create observational predictions for any point in the solar system, but the forces that your modeling are essentially the heliocentric ones. But to your larger point: In my grade-school science class, we were all taught that heliocentrism was itself supplanted by the discovery that the sun is rotating around the galaxy, and that modern cosmology doesn't center around anything at all. Heliocentrism is still more accurate than the geocentrism that it replaces, but is still regarded as a stepping-stone to modern theories.
- Jarwain 10y ago
  I've always thought of the difference between geocentric and heliocentric to be an ego thing. Setting Earth as the center of the Universe works great, for everyone on Earth. It enforces the idea that Earth, and through that, Humans, are so important that the Universe is really centered on the Earth. Maybe this is the case, maybe its not. To assume that the Earth is the center because of us is pretty egocentric. Heliocentric places it in a more objective way, I guess? Changes the reference point to be consistent with the known laws/theory/whatever of gravity. It could also be a scaling thing as well. Applying the equations to planets while setting a reference point based on our sun would provide equations that are more easily adaptable to other galaxies or solar systems that also have planets rotating around the sun. Sure, we could try and create formulas that describe the motion of other galaxies in reference to the Earth, but that would fall apart if the Earth stopped existing.

spaceheeder 10y ago

Not a physicist so my answer may be totally wrong, but my first _guess_ would be that geocentrism necessitates unequally valid reference frames. You would need different equations to represent the movements of Venus and Mars relative to Earth as you would need to represent their movements relative to each other. Or at least it certainly seems to me like you would at first guess. Perhaps you could use matrix algebra to apply geocentric laws of motion to all reference frames, and then simply translate them into a reference frame where Earth is the "actual" center of things? But then you're just admitting that Earth isn't the "actual" center of things.

Chinjut 10y ago

I think the answer is precisely the realization that heliocentrism is a convenient framework for specifying the correct relationships. If one formulated their geocentrism-with-epicycles model to be precisely equivalent to heliocentrism in all physically observable details, just with Earth as the origin to their coordinate system, and acknowledged this equivalence, then that would be perfectly correct as well, albeit unduly cumbersomely framed. But the useful thing is that insight, that what happens is equivalent to the clean heliocentric model, whatever coordinates you might prefer to think of it in terms of.

mannykannot 10y ago
Is it possible for a geocentric, epicyclic model to get the 3D positions of the solar system bodies approximately correct, as opposed to just their angular motion with respect to Earth?
- mannykannot 10y ago
  I cannot edit my post any more , but I can still reply to it, and it seems the answer is yes: https://www.youtube.com/watch?v=QVuU2YCwHjw https://www.youtube.com/watch?v=QVuU2YCwHjw - but you need eccentricity to get the speeds right: https://www.youtube.com/watch?v=qHmjGUxWRAI https://www.youtube.com/watch?v=qHmjGUxWRAI (10 minutes in.) Furthermore, the result is not equivalent to the heliocentric model because it has many more parameters.

gabriel34 10y ago

Newtonian physics allows different frames of reference. Non inertial frames of reference need pseudo-forces. Einstein's relativity deals with non absolute space and time, that is, time speeds up or slows down depending on your 'frame of reference', the only thing remaining constant is the speed of light in a vaccum. The choice isn't purely one of convenience because assuming 'heliocentrism' allows for a more elegant and universal set of equations to explain everything, from quarks to galaxies.

jules 10y ago

The modern view is indeed that there is no preferred reference frame. It's just a matter of choosing a coordinate system. If you wanted to make a distinction you could say that the laws have a simpler form in a heliocentric coordinate system, but this is only really true if you make certain approximations.

onlyrealcuzzo 10y ago

Are these "large fictitious forces" the same thing as Dark Matter today? That would be pretty interesting, if so.

raattgift 10y ago
That's a good question, but the short answer is no. Fictitious forces relate to particular choices of coordinate systems (and their origins). For example, the centrifugal force is an easy way to think about the tendency to be pulled "down" by an astronaut aboard a spinning space station; that astronaut can think of a set of cylindrical coordinates with the origin at the centre of rotation of the station, or of a set of Cartesian coordinates with the origin at some point on the "floor" and centrifugal force is simply natural-seeming. However, if the astronaut uses a non-rotating set of Cartesian coordinates whose origin is outside the entire station, for example, centrifugal force no longer seems very natural as an explanation. Alternatively, close inspection of the path traced by a dropped tablet would also conflict with expectations from a real centrifugal force. Careful study of the movement of stars in the outer reaches of certain types of rotating galaxies threw up a surprise: the linear velocities of stars orbiting far from the centre should be much faster in order to maintain their roughly circular orbits than observational evidence of their speed allows. This difference does not change with a change of coordinates, so it is not an artifact of a choice of coordinate systems. Thus it is not really fixable with a fictitious force; so far the only "fix" we know is to either use known real forces that are generated by the non-gravitational content of the universe (possibly adding not-previously-known matter) or to keep the matter content constant but modify one or more forces. (Hybrid approaches are also possible). The space for introducing truly new long-range forces has been heavily constrained by experiment on Earth, and a "fifth force" is essentially ruled out. We have not yet ruled out many viable forms of previously undetected matter, however some forms are no longer plausible. Dark Matter introduces invisible mass far from the centres of galaxies that help to suspend these surprisingly slow-moving stars. Modifications of gravity have also been proposed that bend the trajectories of such stars less towards the centres of their galaxies. Dark Matter also explains the peculiar velocities of galaxies within several clusters; they move as if attracted to unseen mass in the cluster. Previously mentioned modifications of gravity have to be further modified to incorporate these observational results. Collisionless Dark Matter also explains the behaviour of several known (past) galactic collisions where gravitational lensing preceeds the visible matter and especially the energetic gas and dust that collided as the galaxies passed through one another. This so far has not been fixable by yet more modifications of gravity, however people are trying that approach too (e.g. https://arxiv.org/abs/1606.09128 https://arxiv.org/abs/1606.09128).

ziotom78 10y ago

You're right, mathematically speaking the two systems are the same. As a matter of fact, the calculations that describe the attitude of a spacecraft flying not far from the Earth are usually expressed in a geocentrical reference frame. It's much simpler, yet produces the same result you would get using the heliocentric frame. The real disadvantage of the geocentric system is that it is a barren model: it does not allow science to advance. It is able to explain the motion of planets with exceptional precision, but it does so by using a mathematical construction (the epicycles) that does not lead to a deeper understanding of the inner laws of nature. On the other side, the heliocentric model (when corrected with Kepler's idea of using ellipses instead of Copernicus' circles and epicycles) was a big step towards the bigger understanding of gravitation that was produced by Newton's law of gravitation.

caf 10y ago

When you're dealing with the motion of objects close to the Earth, a geocentric reference frame is entirely appropriate. However, when examining the motion of the planets a heliocentric reference frame is "more correct" in that the motion of the planets in that reference frame suggests a deeper truth: that the primary influence on the motion of the planets is somehow the Sun.

deleted 10y ago

[deleted]

mannykannot 10y ago

Of all the answers offered here, the only ones that get to the heart of the matter are those that make the distinction between inertial (non-accelerating) frames of reference, and those that rotate (and therefore have at least centripetal acceleration). In Newtonian and post-Newtonian mechanics, only inertial frames are equivalent. A geocentric frame (with a rotating Earth) spins the whole universe once a year; fix the Earth's spin, and you set the universe spinning once a day.

raattgift 10y ago
You can have accelerating frames of reference in Special Relativity; for example, one can set Rindler coordinates on a body that is uniformly accelerating. Addtionally, you can have locally inertial frames of reference that are inequivalent. Consider two space stations orbiting Earth at different altitudes. The occupants are in free-fall in both cases, but there is a relative acceleration between them. Rotating frames of reference tend to distract users into confusing coordinate artifacts with physical ones. As a trivial example, suppose we vary the Minkowski metric by introducing a rotation into Cartesian coordinates: dS^2 = -\left(1 - \omega^2 ({x}^2 + {y}^2) \right){dt}^2 + 2 \omega (- y dx dt + x dy dt) + {dx}^2 + {dy}^2 + {dz}^2. Here a non-massless object far from the origin will have |d\vec{x}/dt| > 1, or in other words a coordinate velocity greater than c. This is essentially the same as your last sentence. However, when we calculate the four-velocity \eta^\mu of any non-massless object, even far from the origin, we will see that dS^2 < 0 for all nearby points along its worldline. In other words, there is no superluminal motion -- there is just movement against a set of coordinates, and a different choice in coordinates will vary that. We can certainly do Standard Model physics (or classical particle dynamics) in a rotating system of coordinates, using a number of approaches. However, it is usually easier to use a different system of coordinates, and even better to abandon the idea of using any global system of coordinates in a spacetime that is not Riemann flat.

raattgift 10y ago

It's not a stupid question. General Relativity does not have global frames of reference. Borrowing from Special Relativity, an inertial frame of reference is on in which the Poincaré isometry group applies at every point in the frame of reference, and that means that fundamental physical constants do not change with translations, rotations or Lorentz boosts. That is, as you move back and forth along the spacelike axes, or rotate clockwise or counterclockwise around them, or acquire boosts, or move futureward, some set of constants are invariant; in pure SR the constants are the spacetime intervals -- the distance from one event to another. In the Standard Model of Particle Physics, there are other invariants, such as the fundamental charge and the speed at which a massless particle moves. Special Relativity is a theory with global inertial frames of reference. General Relativity has no global frames of reference at all, except in the (flat, Minkowski) spacetime of Special Relativity. Instead, GR has the concept of the LIF -- the _locally_ inertial frame -- which exists everywhere in the tightest possible definition of local (specifically, in the local section of the fibre bundle, or in the limit where spacetime intervals go to zero), but only exists in _some_ bigger regions of spacetime (those that are flat -- or at least effectively flat, in the Wilson sense of an effective field theory). None of this has to do with sets of coordinates; even in SR you can choose among a variety of coordinate systems (e.g., polar coordinates, Cartesian coordinates) and place the coordinate system's origin anywhere. Using different coordinates even in the spacetime of Special Relativity can help focus on aspects of a system under study, and indeed one can even use Rindler coordinates in Special Relativity to consider systems that include acceleration, or more often to treat a uniformly accelerating object as at rest at the coordinates' origin point. In GR covariance is introduced to express all physical laws in arbitrary coordinates. Arbitrariness here certainly includes systems in which spacelike _coordinate_ distances (or the period of an oscillator) vary with position, or even in which the speed of light _against a set of coordinates_ varies with direction. The Einstein Field Equations are written in a form that is independent of the choice of coordinates; they stay in that form even under a change of coordinates -- this is the generally covariant form. Newtonian physics, for example, can become much more complicated when you make a change of coordinates -- in this discussion, in dealing with planetary orbits under a change from a sun-centric polar coordinate system, or even a sun-centric Cartesian coordinate system to an Earth-centric system. In General Relativity the same Einstein Field Equation (EFE) form is used. The calculational price for covariance is high -- the EFEs are ten non-linear partial differential equations. Even today that's heavy calculating. So anywhere one could get a decently correct answer using Special Relativity or Newtonian mechanics, especially where one can make a good choice of coordinates, you'd choose to do that instead. Where bodies move slowly against the chosen coordinates compared to how light moves against the same system of coordinates, and where the distances between massive bodies is large, the errors will be small to negligible. So, to recap, "Isn't the choice between geocentrism and heliocentrism purely one of convenience, and we can simply pick and choose whichever [coordinate system] is most convenient for calculation purposes?" Yes, essentially, but one has to be wary about artifacts of the coordinate system that vary under a change of coordinates. A classic example involves latitude-longitude coordinates on Earth: there is a coordinate singularity at each pole, but the singularity goes away upon a change of coordinates (e.g. to local East-North-Up coordinates, or ECEF coordinates, or Cartesian coordinates with any number of possible choices of origin). Likewise, epicycles in planetary orbits change or vanish under different systems of coordinates, and so are unphysical. I changed "reference frame" to "[coordinate system]" there to capture what an observer is doing: laying out an observer-centric set of coordinates. No such set of coordinates is the correct one, but any observer can choose manifestly useless sets of coordinates or draw incorrect conclusions from the motions of objects against one particular set of coordinates (not just what system of coordinates, but also where the origin is).