Does the Earth move around the Sun?

[diegocas]

I always hear people saying "Ptolemy thought that the Sun moved around the Earth, but it is the other way around: the Earth moves around the Sun".
I think that's wrong. I think that Copernicus's theory is not "truer" than Ptolemy's. It is just that Copernicus's theory is simpler! But both theories are correct.
It is just a matter of defining your reference frame!
Am I right? If that's so, why is it that even science teachers, science documentaries, etc. say that Ptolemy was wrong and that Copernicus was right.
Thanks!

 

[K^2]

Both frames are valid, of course, but it's not just a matter of simplicity. If you choose Earth as your frame of reference, and have Sun rotate around it, then the Sun is undergoing extremely high centripetal acceleration with no corresponding force to account for it. You can, of course, make up a fictitious force to hold the Sun in "orbit" around Earth, and then make up even more complicated forces to keep all the planets moving the way they do. But by that point, Ptolemy's system is not just more complex, it also seems very arbitrary and forced. Which is not a good thing for any model trying to explain things.

But yes, it is possible to describe everything with Earth as the center of the universe and unmoving, and everything else moving around it.

 

[diegocas]

Again, I think that, in the end, it really is about simplicity. We like simplicty and we accept that the simplest explanation is the correct one (Ockham's razor principle). Putting the Sun in the center together with Newton's equations of motion and Universal Law of Gravitation makes a nice and quite acurate description of the solar system. But that does not make the sentence "The Sun moves around the Earth" less true.

 

[Dickfore]

From the standpoint of Kinematics, both reference frames (one where the Sun is stationary - heliocentric and the other where the Earth is fixed - geocentric) are perfectly acceptable for describing observational facts. In fact, reference frames where the Earth is fixed are used quite often in Astronomy even today (horizontal and equatorial coordinate system) since they are very convenient to describe the everyday position of the celestial objects in the Sky from different points on the Earth's surface at different times.

However, science is not satisfied with merely describing phenomena. Science aims to find causal connections between the observed phenomena and to predict the outcome of future events.

So, the most common observation is that all stars on the Sky make one turn in a day. Is this because the "celestial sphere" is turning with such a period "above our heads" or is it simply because that the ground below our feet is rotating. Since different celestial objects are very far away from the Earth and it seems highly improbable that some interaction can be communicated between all of them to subdue them to rotate around the Earth with a common period, even the Ancient people had recognized that the latter option is much more viable and accepted the notion of a spinning Earth.

Now comes the question of the motion of the Sun, Moon and planets (literally meaning "wandering" stars) relative to the background of "immobile stars" (i.e. canceling the effects of the Earth's rotation). The (visually) largest among them, namely the Sun and the Moon seem to move around the Earth. And, this is indeed true. If you are only concerned about these two objects, saying that they revolve around the Earth is a very good approximation of reality.

The problem comes, however, when explaining the motion of the other planets (Mercury, Venus, Mars, Jupiter and Saturn are the only ones visible with the naked eye). Ptolemy had assembled tables for the predicted positions of the planets assuming they perform complicated revolutions around a moving point (epicycle), which in itself revolves around the Earth. Over the course of the centuries, the differences between the predictions and the observations were so drastic, that these tables were rendered useless.

Enter Copernicus. What if the planets do not revolve around the Earth, but around the Sun and the Earth is just one among them? Copernicus assumed the trajectories to be circles, so his predictions were of little practical value, but, nevertheless, his model made much better predictions and was much simpler. It was up to Kepler, using the data from many years of observations made by Tycho Brahe, to find that the true trajectories were ellipses, that the planets moved with a constant sectoral speed and that the cubes of the major semiaxes of the orbits were in proportion to the squares of the periods.

But, the model is still based on observations and there is still no causal connection between these curious results. If one applies the Newton's Laws of Dynamics to this motion, one can arrive at the Law of Universal Acceleration. This was, of course, done by Isaac Newton.

There is one caveat, however. The Laws of Dynamics are valid only in so called Inertial reference frames. The First Law is an experimental test whether the reference frame we are using is inertial to a good degree of approximation. In the XIX century, the French scientist Leon Foucault constructed a pendulum that did not preserve its plane of oscillation relative to the Earth's surface, which was a direct demonstration that the Earth actually rotates.

After Newton's Law of Universal Gravitation was developed and Calculus was refined in a practical form, scientists could perform extensive calculations regarding the characteristics of the planet's (and Moon's) orbits. Particularly, they discovered anomalies in the trajectory of a newly discovered planet, Uranus and the French astronomer Le Verrier conjectured that these anomalies would be due to some unknown until that time celestial body and predicted its mass and trajectory. That body - Neptune was soon observed by the Berlin observatory. This was an unprecedented triumph of celestial mechanics, whereby a scientists had discovered a whole planet at the point of his pen.

 

[russ_watters]

Again, I think that, in the end, it really is about simplicity. We like simplicty and we accept that the simplest explanation is the correct one (Ockham's razor principle). Putting the Sun in the center together with Newton's equations of motion and Universal Law of Gravitation makes a nice and quite acurate description of the solar system. But that does not make the sentence "The Sun moves around the Earth" less true.

You're not quite getting the purpose of Occam's Razor and why a simpler theory really is better. The goal of science is to explain how things work and if you add assumptions for which there is no evidence, you create more questions than you answer and as a result have subtracted more from our understanding of the universe than you've added.

"The Sun moves around the Earth" is less true than "the Earth moves around the Sun" because the extra assumptions make it less consistent with reality.

 

[K^2]

But that does not make the sentence "The Sun moves around the Earth" less true.

No, it doesn't. It only makes it a far less useful one.

 

[diegocas]

The goal of science is to explain how things work and if you add assumptions for which there is no evidence, you create more questions than you answer...

I wonder: What is the fundamental evidence for F = ma? I know, of course, that almost every experiment confirms this equation. However, does that make it true or do we just accept it because it works, it is very simple and it explains lots and lots of phenomena?

I think the simplicity issue is not minor. I also think that the ultimate goal is to find some basic, very simple, principles that describe everything. However, that does not make them any more true than any other complicated system. They're just simpler, more general, useful principles.

 

[Pythagorean]

If you take ptolemy's view, you also have to account for the strange little loop-de-loops stars do if we're not rotating around the Sun.

 

[nonequilibrium]

What exactly is the scientific method, explicitly?

I tried to write it down, but it seems to be too hard... First I tried to make the first point that "What we see we accept as true", but then would take hallucinations into account. Then to exclude those I tried to formulate "We postulate there are observations independent of the observer and those are true", but then we'd come into conflict with special relativity (speed determines your perception/reality). Maybe the first axiom is something like... "We postulate the existence of an exterior world that we can observe independently of the observer -- if the observation is dependent of the observer, it has to be explained from outside the observer" (the latter would be talking about the fact that the velocity used to explain different observations in SR is a characteristic outside the mind of the observer). But jezus, even that axiom is not good enough for some interpretations of QM.

Okay I'm making a mess, feel free to ignore it, but I implore someone to try and write down the scientific method, I'm very curious!

 

[Dickfore]

The scientific method is a series of procedures and rules used for obtaining scientific knowledge, i.e. factual, objectively verifiable statements about the phenomena occurring in our environment.

 

[K^2]

I wonder: What is the fundamental evidence for F = ma?

It's not exactly F=ma. It's dp/dt=F. Force is equal to rate of change of momentum. That's actually the way Newton stated it orginally. Since p is roughly mv, dp/dt is roughly d(mv)/dt = (dm/dt)v + m(dv/dt) = ma, but only for v<<c. Near the speed of light, it becomes more complicated.

Net force is defined as dp/dt. I mean, how do you measure a force? You try to accelerate something with it.(You can use springs, but that's just a simpler way of measuring the force, not the definition of it. A spring scale must first be calibrated, which is usually done with a known weight, and gravitational weight is due to gravitational acceleration. So you still fall back on acceleration in the end.

So the only real question is why forces are additive. That is, we define F₁ and F₂ based on the amount of acceleration they cause. How do we know that if you apply both you get effect of F₁+F₂? Well, you know that action is equal to reaction. Say these two forces are caused by two separate objects. Each one experiences -F₁ and -F₂ respectively, and of course, experience corresponding change in momentum. To conserve momentum, the change in momentum of the object to which these two forces are applied must correspond to application of F₁+F₂.

How do you know that Newton's 3rd holds? Well, you apply the same idea of conservation of momentum to interaction of two bodies. Since momentum changes must be equal and opposite, so are the forces.

Just for completeness, if you have just one object, its momentum is going to be conserved. Hence, object in motion remains in motion.

Finally, how do we know that momentum is conserved? That's a more complicated question. It ultimately has to do with the fact that laws of physics are invariant under translation. But we are talking about Quantum Physics by this point. Unless there is a similar theorem in Classical Physics that I missed.

So that's all 3 Newton's Laws covered.

 

[Dickfore]

It's not exactly F=ma. It's dp/dt=F. Force is equal to rate of change of momentum. That's actually the way Newton stated it orginally. Since p is roughly mv, dp/dt is roughly d(mv)/dt = (dm/dt)v + m(dv/dt) = ma, but only for v<<c. Near the speed of light, it becomes more complicated.

Both statements are equivalent. Newton's second Law holds strictly for motion of "particles". This means, if a particle looses mass, then it ejects other particles by pushing on them. The ejected particles, by 3rd Newton's Law push back and this causes the particle to accelerate. But, a body with variable mass is not a single particle. It is a system of particles. Relativity has nothing to do with Newton's Laws as those hold only at speeds much lower than the speed of light.

Net force is defined as dp/dt. I mean, how do you measure a force? You try to accelerate something with it.(You can use springs, but that's just a simpler way of measuring the force, not the definition of it. A spring scale must first be calibrated, which is usually done with a known weight, and gravitational weight is due to gravitational acceleration. So you still fall back on acceleration in the end.
[/QOUTE]

It is a common misconception to state 2nd Newton's Law as a definition of force. This is not true. What this law says is that if such and such forces act on a particle it will have such and such acceleration, or, conversely, if the particle has acceleration, then the net force is so and so. It does not care what acts on the particle. Hence, the use of "free body diagrams".

So the only real question is why forces are additive. That is, we define F₁ and F₂ based on the amount of acceleration they cause. How do we know that if you apply both you get effect of F₁+F₂? Well, you know that action is equal to reaction. Say these two forces are caused by two separate objects. Each one experiences -F₁ and -F₂ respectively, and of course, experience corresponding change in momentum. To conserve momentum, the change in momentum of the object to which these two forces are applied must correspond to application of F₁+F₂.

This is a postulate about the forces and cannot be derived. It stems from previous studies in statics.

How do you know that Newton's 3rd holds? Well, you apply the same idea of conservation of momentum to interaction of two bodies. Since momentum changes must be equal and opposite, so are the forces.

In Newton's Dynamics, the conservation of momentum pf an isolated system of partricles is a consequence of the 3 Newton's laws.

Just for completeness, if you have just one object, its momentum is going to be conserved. Hence, object in motion remains in motion.

This only holds in Inertial reference frames. This is why First Newton's Law has content different than the other two and is not a simple consequence of them.

Finally, how do we know that momentum is conserved? That's a more complicated question. It ultimately has to do with the fact that laws of physics are invariant under translation. But we are talking about Quantum Physics by this point. Unless there is a similar theorem in Classical Physics that I missed.

So that's all 3 Newton's Laws covered.

Actually, Classical Physics covered these concepts fairly nicely.

 

[nonequilibrium]

The scientific method is a series of procedures and rules used for obtaining scientific knowledge, i.e. factual, objectively verifiable statements about the phenomena occurring in our environment.

You don't understand my point, you just used terms you assumed to be predefined, but in those definitions is exactly the hard part!

What is "factual"? "objectively"? "environment"?

And the use of the term "a series of procedures" isn't really clarifying on what those allowed ways of acting are.

 

[K^2]

Dickfore.

1) Fact that F=ma fails at v~c has nothing to do with dm/dt term. I took it to be zero in my derivation. See that equal sign? Meaning exactly equal? That's not where approximations took place. They took place when I took p to be roughly mv. That's an approximation.

2) Why don't you go ahead and define force, then?

3) Conservation of momentum does imply that forces are additive. I can show that as a general result.

4) Conservation of momentum is far more general than Newton's 3rd Law and follows from more fundamental principles. While Newtonian Physics takes it as a postulate, question I was answering is how these laws are confirmed. And while statistical argument might be compelling, an argument from a more general model will always win, because it will always be based on a greater sample.

5) In non-inertial frames there is such a thing as fictitious force. With fictitious forces in places, Newton's 1st holds.

6) Classical physics takes them as postulates. Not the same thing.

 

[nonequilibrium]

Something that always struck me as odd: if force is defined as F = ma, how is m defined? (or if m is defined by F = ma, how is F defined?)

 

[K^2]

How deep down that rabbit hole do you really want to go?

 

[nonequilibrium]

All the way down and then start digging some more -- we're physicists after all, aren't we?

 

[pallidin]

The Earth's moon moves around the earth, the Earth moves around the Sun, and that total system moves around the galaxy.
To my knowledge, our galaxy does not revolve around something(could be wrong)

 

[K^2]

All the way down and then start digging some more -- we're physicists after all, aren't we?

Alright. In that case, I would go all the way back to quantum mechanics.

Say you have a particle field. Let's diagonalize it with respect to momentum and energy.

k_i |\psi_i&gt;= \frac{1}{i}\frac{\partial}{\partial x}|\psi_i&gt;
\omega_i |\psi_i&gt;= i\frac{\partial}{\partial t}|\psi_i&gt;

That should give us continuum of states, so that we can define.

p = \hbar k
v_g = \frac{\partial k}{\partial \omega}
m_{rel} = p/v_g

Finally, we can define rest mass.

m = \lim_{v_g\to 0}m_{rel}

I think that should do it.

 

[nonequilibrium]

Oh jeez louise :) Thank you very much for the great reply, but sadly I haven't had any quantum yet. But I promise I'm bookmarking this to visit it once I did. I once was talking about it with another student and he suggested we could define mass by E = mc²; I found that an intelligent remark, but it seemed like you were "giving up" something which you could normally deduce.

Anyway, the fact you had to use QM brings up the following horrible question: before QM the laws of Newton were actually not even well-defined?

 

[K^2]

They were, but things were defined differently. 1kg was defined as the mass of 1 liter of water. Mass just being defined as the intrinsic property that relates momentum to velocity.

 

[nonequilibrium]

How was momentum defined?

 

[brainstorm]

The scientific method is a series of procedures and rules used for obtaining scientific knowledge, i.e. factual, objectively verifiable statements about the phenomena occurring in our environment.

I don't want to derail this thread, but this is a false view of science. Scientific method has to have some explicit recognition of empiricism and critical rigor. You can't just follow rules and procedures and come out with science. You have to take a critical position on some previously asserted knowledge-claim and come up with a research-design that links your critique to empirical observations and/or testing. This doesn't necessarily verify a knowledge-claim, but it may support it - and it can certainly render a false claim empirically untenable. If you break existing rules and procedures and still achieve these basic goals of critical theorizing and empirical testing, why wouldn't that constitute science?

 

[brainstorm]

While you're playing with the relativism of what revolves around what, consider the following:

If particles themselves are taken as the basis for measuring distance instead of space, then you could say that there is the same distance between the sun and the Earth as between a corresponding number of particles in Earth's atmosphere. You would just count the apparent distance between the particles in deep space as a side-effect of an increased ration between the speed of light and gravitation. I.e. you could say that light takes longer to go between particles in lower gravity, but that the particles are actually the same distance apart if gravity-level is controlled for.

If you looked at it in this way, the Earth and sun would actually be much closer and only appear more distant because of the relative constancy of the speed of light relative to changes in gravitation. If you looked at it in this way, neither Earth nor sun would really revolve around the other. They would just be layers/strata that drift in regular patterns relative to each other. The apparent rotation of the Earth could be chalked off to points of low gravitation between the two planes, sun and Earth, which cause the sunlight to bend inward before reaching the parts of the Earth-plane that have drifted out of gravitational alignment.

I like this perspective because it gives you Earth and sun as flat planes without anything revolving around anything else. However, given the standardization and pervasive elaboration of the heliocentric model of spherical heavenly bodies, it is very hard to think in terms of planar layers, even just as a thought experiment to see if it is even possible.

 

[K^2]

How was momentum defined?

"Quantity of motion" that is proportional to velocity.

 

[nonequilibrium]

That seems a kind of fishy definition? If I define the Ziblach with "It is a quantity that is proportional to the third derivative of distance", I haven't given an exact definition, have I (as it could be many a thing).

 

[K^2]

You only need to know two facts, both of which are experimental.

1) "Quantity of motion" is proportional to velocity.
2) Total "Quantity of motion" is conserved.

That's really all Newton had to go with. Defined slightly differently, but this is more compact.

Edit: So say you have an object A and you want to find it's mass. You know that mass is the proportionality constant between A's velocity and its momentum. You also know that proportionality constant for 1L of water is 1. So have a light container with 1L of water travel at some velocity, collide into A, and stick to it. You can now find A's mass by measuring final velocity.

 

[nonequilibrium]

Oh that's a nice summary, I like that, thank you very much.

 

[russ_watters]

I wonder: What is the fundamental evidence for F = ma? I know, of course, that almost every experiment confirms this equation. However, does that make it true or do we just accept it because it works, it is very simple and it explains lots and lots of phenomena?

It is true and we accept it because it works, is very simple and explainsn a lot of phenomena. That's all that can be asked of a scientific theory.

I think the simplicity issue is not minor. I also think that the ultimate goal is to find some basic, very simple, principles that describe everything. However, that does not make them any more true than any other complicated system. They're just simpler, more general, useful principles.

Whether "more useful" and "more true" are synonomous is something I think is true but it isn't something I'm interested in arguing about.

 

[brainstorm]

Whether "more useful" and "more true" are synonomous is something I think is true but it isn't something I'm interested in arguing about.

That's not really a useful statement then, is it? So does that make it false? . . . sorry, I couldn't resist pointing that out.

 

[Antiphon]

Scientific method: form a hypothesys that explains the data then formulate and perform experiments that attempt to disprove the hypothesys.

 

[nonequilibrium]

Antiphon - thanks for doing the effort, but my problem is more with the fundamental words like "data" -- what is considered "outside" of you? But I'll stop it, because I'm moving it way off-topic, but if anybody is interested in the matter, feel free to pm me :)

 

[brainstorm]

Antiphon - thanks for doing the effort, but my problem is more with the fundamental words like "data" -- what is considered "outside" of you? But I'll stop it, because I'm moving it way off-topic, but if anybody is interested in the matter, feel free to pm me :)

Why does data have to come from outside of you? If you are observing subjective events, the data comes from inside you. Data is another word for information. You can raise many issues regarding validity of the data. Sometimes you just have to think critically and pose specific issues instead of just saying you have "a problem with fundamental words like 'data'." Remaining vague in that way is really not good for anything except creating a haunted-house feeling.

 

[D H]

They were, but things were defined differently. 1kg was defined as the mass of 1 liter of water.

For about four years, yes. The kilogram has been defined in terms of the mass of a cylinder made of platinum and iridium since 1799. Quantum mechanics did not and has not changed the definition of the kilogram. The mass of a platinum-iridium prototype remains the definition of a kilogram to this day.

Basing things on prototypes has been been viewed as last resort for quite some time. Scientists have managed to move away from prototype-based definitions for everything but mass. People are trying to develop a more basic definition for mass, but accuracy remains problematic.

Mass just being defined as the intrinsic property that relates momentum to velocity.

What pray tell is momentum, then? How do you measure it? Momentum is a derived quantity. Mass is not defined as the intrinsic property that relates momentum to velocity. Mass is what it is, but we don't quite know what mass is yet. We have a good handle on it; mass is a form of bound energy.

Note well: This discussion is far removed from the topic of this thread.

 

[Cleonis]

I always hear people saying "Ptolemy thought that the Sun moved around the Earth, but it is the other way around: the Earth moves around the Sun".
I think that's wrong. I think that Copernicus's theory is not "truer" than Ptolemy's. It is just that Copernicus's theory is simpler! But both theories are correct.
It is just a matter of defining your reference frame!
Am I right? If that's so, why is it that even science teachers, science documentaries, etc. say that Ptolemy was wrong and that Copernicus was right.
Thanks!

Before I get to the main question let me first give some historical information.
The system that Copernicus devised does use the Sun as unmoving center. However, like all ancient astronomers Copernicus' research program was to model the motions of the planets in terms of uniform motion along perfect circles. In fact, Copernicus was more of a purist in using only the most elementary building forms (in a sense Ptolemy had used hybrid forms), and Copernicus ended up needing more epi-circles than Ptolemy had used.

Back then it was far from clear whether the Copernicus' system was simpler.
Now to the main question: "Heliocentric or geocentric, is it just a matter of defining your reference frame?"

For the answer to that question, let me recount what we expect from science. We expect from a scientific evaluation that all relevant information that is available is used . If you discard some information just because it happens to be inconvenient to you then you're not a scientist.

We need to consider the General Theory of Relativity, because currently that is the best theory we have.
Orbital mechanics is determined by gravitation. GR has the following in common with Newtonian mechanics: when it comes to orbits size matters.

Newtonian mechanics describes that heavier objects have more gravitational mass. GR describes that gravitational interaction is mediated by spacetime curvature and that heavier objects impose stronger spacetime curvature upon the surrounding space - size matters.

In this particular case the view in terms of GR is the same as the view in terms of Newtonian physics: the Sun and Jupiter are orbiting their common center of mass, and the Sun, being much heavier, is way closer to that common center of mass. (in fact, the common center of mass of Jupiter and the Sun lies just outside the Sun.)

Some people may argue as follows:
If you are in a space-capsule, orbiting a planet, and you use only the information you can gather from inside that space-craft, then you cannot discern whether you are in orbit or floating in outer space, far from any star. For inside the space-capsule all you can measure is that you are weightless, and you are weightless both in orbit and while floating in outer space.

But deliberately secluding yourself, depriving yourself of relevant information, is pointless. Science is information-based. You must always consider all the information that is available to the scientific community. Anything that is available to the community as a whole is available to you.

 

[brainstorm]

Some people may argue as follows:
If you are in a space-capsule, orbiting a planet, and you use only the information you can gather from inside that space-craft, then you cannot discern whether you are in orbit or floating in outer space, far from any star. For inside the space-capsule all you can measure is that you are weightless, and you are weightless both in orbit and while floating in outer space.

Are you sure there is absolutely no difference between these two situations? I have often wondered about the relevance of velocity relative to gravitation, even when free fall produces weightlessness. E.g. if you are orbitting a black hole near the event horizon, you are in free fall but you are approaching the speed of light as well. So the velocity needed to achieve orbit (i.e. sustained free-fall) is always relative the the speed of light, no, even at velocities where this has relatively little effect?

 

[K^2]

For about four years, yes. The kilogram has been defined in terms of the mass of a cylinder made of platinum and iridium since 1799. Quantum mechanics did not and has not changed the definition of the kilogram. The mass of a platinum-iridium prototype remains the definition of a kilogram to this day.

You can define 1kg any way you want it. Modern definition of what mass is, comes from field theory, and it is still a ratio of momentum to velocity. Period. Fact that we don't know the source of mass yet is a different matter entirely.

What pray tell is momentum, then? How do you measure it? Momentum is a derived quantity. Mass is not defined as the intrinsic property that relates momentum to velocity. Mass is what it is, but we don't quite know what mass is yet. We have a good handle on it; mass is a form of bound energy.

I've already defined it. In this thread. But to save you trouble of going out there and looking, I will repeat it. Strictly in classical mechanics sense, and assuming we can treat bodies as point-objects. If you want me to expand into rigid bodies, it can be done, but requires more work. This is sufficient illustration.

Following are definitions.
1) Momentum is a quantity proportional to velocity of a body.
2) Mass is a quantity that is proportionality constant for 1.
3) Momenta are additive.
4) Total momentum is conserved.

These are completely self-consistent and sufficient definitions for both quantities.

How do you measure momentum of a body? Measure it's mass first. How do you measure it's mass? I have already explained it in this thread. Take a body that you are willing to take as you standard of mass. You want it to be IPK? Fine. Use IPK. But it could be someone's grandma for all it matters.

Perform a perfectly inelastic collision between body with known mass and body with unknown mass. Knowing initial and final velocities and using definitions above, you can find the unknown mass. Now you can measure its momentum.

Of course, once you have some handle on gravity and elastic forces, you can just use a scale. But the above is necessary to get to that point, so there you have it.And notice how Newtonian Mechanics works perfectly well without understanding that mass and energy are in any way related. You don't need to know where quantity comes from to work with it. We don't have a first clue about what wave function is or what it does, except for knowing that it's perfectly linear. And look what we are doing with that seemingly insignificant fact.

 

[D H]

You can define 1kg any way you want it.

No, you can't. Metrology is a demanding science. The reason the kilogram prototype is still in use is that despite trying for a couple of centuries science has yet to come up with something better.

I've already defined it. In this thread. But to save you trouble of going out there and looking, I will repeat it. Strictly in classical mechanics sense, and assuming we can treat bodies as point-objects. If you want me to expand into rigid bodies, it can be done, but requires more work. This is sufficient illustration.

Following are definitions.
1) Momentum is a quantity proportional to velocity of a body.
2) Mass is a quantity that is proportionality constant for 1.
3) Momenta are additive.
4) Total momentum is conserved.

You haven't defined things, not scientifically. How do you measure momentum? What is your gold standard? If you can't measure it you are just doing philosophy.

The definition also has a big problem: What if the body isn't moving? Mass does not depend on motion.

 

[Cleonis]

Are you sure there is absolutely no difference between these two situations? I have often wondered about the relevance of velocity relative to gravitation, even when free fall produces weightlessness. E.g. if you are orbitting a black hole near the event horizon, you are in free fall but you are approaching the speed of light as well. So the velocity needed to achieve orbit (i.e. sustained free-fall) is always relative the the speed of light, no, even at velocities where this has relatively little effect?

Well, orbiting a (relatively small) black hole is an extreme example.

Firstly, in GR the relativity of inertial motion holds good at all locations. That means that all forms of being in the vicinity of a black hole are equivalent. (Either a black hole or any other extremely high density center of a gravitational well.) You can be in orbit around a high density gravitational well, or you can be in free fall straight towards it, in both cases the steep gravitational well gives rise to extreme tidal effect.

Still, With a sufficiently large black hole the radius of the event horizon is large enough so that even close to the event horizon tidal effects are minimal. If that is the case then onboard measurements will not detect effects. For instance, an onboard Michelson-Morley interferometer would not find orientation dependent differences in the propagation of light. That is, we do have that close to the event horizon the orbiting velocity approaches the speed of light, but that will not affect strictly local measuments of the speed of light; as long as tidal effects are below detection threshold a Michelson-Morley interferometer will give a null result.

Conversely, for any celestial body we have that sufficiently sensitive equipment (in orbit or in any way in vicinity) will detect tidal effects.

In terms of GR tidal effects are the only kind of gravitation effect that exists onboard a space-craft that is in the vicinity of a celestial body.

 

[K^2]

No, you can't. Metrology is a demanding science. The reason the kilogram prototype is still in use is that despite trying for a couple of centuries science has yet to come up with something better.

There might be no more convenient definition, but I can define 1kg as weight of my favorite chair, and all of the physics will follow, even if measurements cannot be made as precisely.

But your biggest problem is that you are trying to define a standard before you define the quantity. Here is your IPK. Here is a chunk of led I claim to also be 1kg. Prove me wrong. Your actions?

You haven't defined things, not scientifically. How do you measure momentum? What is your gold standard? If you can't measure it you are just doing philosophy.
These definitions are complete and experimentally verifiable. That's scientific definition.

And I told you exactly how to measure momentum. You take velocity and multiply by mass. Or are you suggesting that there is a momentumometer that Newton had but somehow misplaced?

The definition also has a big problem: What if the body isn't moving? Mass does not depend on motion.

Prove it. Prove to me that an object that is at rest and has no external forces acting on it has an inertial mass.

Theory doesn't ever need the mass of such an object, and so it is left without definition. But if you do need to define it, I have two words for you. Galilean Relativity.


Now tell me honestly, are you an engineer?

 

[D H]

There might be no more convenient definition, but I can define 1kg as weight of my favorite chair, and all of the physics will follow, even if measurements cannot be made as precisely.

No, it won't. The ability to measure things precisely is one of the hallmarks of physics, and one of the reason the term physics envy exists. For example, special relativity, general relativity, and quantum mechanics were accepted rather quickly given how radical a departure they represented from Newtonian mechanics in part because of precise measurements. Swapping a fairly precise, reproducible standard for mass with an imprecise and irreproducible one would destroy much of physics. The search for better standards for time, distance, charge helped push physics along.

And I told you exactly how to measure momentum. You take velocity and multiply by mass. Or are you suggesting that there is a momentumometer that Newton had but somehow misplaced?

That is not what you said. Your claims to date has been that momentum is a fundamental unit and that mass is a derived quantity. You used momentum to define mass in post #37 and now you are using momentum to define mass. Not good.

Now tell me honestly, are you an engineer?

What kind of backhanded, asinine, sophomoric question is this? Since we're being sophomoric here, tell me honestly, are you a sophomore?

 

[Cleonis]

D H and K^2,

a request: immerse yourself in the physicsforums blog entry https://www.physicsforums.com/blog.php?b=1594"

 

[K^2]

D H, you still can't define a standard before you define a quantity. It's absurd. Otherwise, I can bring something made of the same composition and claim it's 1kg. Or same shape and claim it's 1kg.

Define mass. Then you can try and define unit of mass.

And if you actually go back and follow what I said, you'll see that it is all entirely consistent. If you claim otherwise, please post quotes that contradict each other. Saying, "that's not what you said," is silly when everything is a matter of record.

Oh, and I am a Ph.D. Candidate in Theoretical Particle Physics.

Now please be so kind as to answer my query. Are you an engineer?

 

[D H]

Now to the main question: "Heliocentric or geocentric, is it just a matter of defining your reference frame?"

In a nutshell, yes.

We need to consider the General Theory of Relativity, because currently that is the best theory we have. Orbital mechanics is determined by gravitation. GR has the following in common with Newtonian mechanics: when it comes to orbits size matters.

But GR also says that all reference frames are equally valid. It's just a bit harder to understand/calculate/predict with a goofy choice of reference frames. Choosing a geocentric frame to describe the motion of the Sun, planet, and stars is a perfectly valid but completely goofy choice.

What Copernicus did was not so much to describe a better system; accurate Copernican model and Ptolemaic models were of comparable complexity. What Copernicus did was to begin freeing humanity from pre-scientific, mythological thinking. Copernicus' model was still plagued with a music of the spheres kind of thinking. Restricting motion to circles because circles are perfect is not scientific thinking. Freeing ourselves from pre-scientific thinking took a long time, and the process is far from complete (e.g., homoepathy).

One last point: The few kooks who do use GR to justify geocentricism are almost inevitably doing so in a fallacious manner. These kooks are the same ones who think that evolution doesn't exist and that the universe is a few thousand years old. In particular, these kooks (and yep, they are kooks) are claiming that geocentricism is the only valid point of view. That is a point of view that clearly is not supported by modern science.

 

[brainstorm]

One last point: The few kooks who do use GR to justify geocentricism are almost inevitably doing so in a fallacious manner. These kooks are the same ones who think that evolution doesn't exist and that the universe is a few thousand years old. In particular, these kooks (and yep, they are kooks) are claiming that geocentricism is the only valid point of view. That is a point of view that clearly is not supported by modern science.

My impression is that people who are using GR to justify geocentrism are doing so as an attempt to ground some kind of political epistemology of perspectival relativism. Maybe this is because they want to free humanity from the notion that thought has to be framed in fixed ways determined by (more) natural logics. It may seem more natural to look at planetary movement as being centered around the sun, but that does not undermine the ability to frame and chart heavenly motion vis-a-vis the Earth. The relevant point should be that epistemology is not naturally dependent on the behavior of observed natural systems or vice versa.

 

[Dickfore]

The unit of mass can be made precise. Even today, in mass spectroscopy, there is a unit of mass called atomic mass unit and is denoted by u.

It's definition is that it is exactly \frac{1}{12}th of the mass of the isotope ^{12}C. When expressed in SI units, its numerical value is:

<br /> u = 1.660\,538\,782(83) \times 10^{-27} \, \mathrm{kg}<br />

 

[Cleonis]

But GR also says that all reference frames are equally valid.

The above statement is not a necessary statement.
This is a difference between GR and SR that tends to go unrecognized.

For SR the physical equivalence of the members of the class of inertial coordinate systems is the very foundation. By contrast, axiom of GR is that for every point in spacetime there is local Lorentz invariance. That local invariance for all spacetime points is sufficient for GR.

In terms of GR it's natural/inevitable to work with a hierarchy of gravitational wells. Satellites are orbiting the Earth; For that system Earth is the center. Planets are orbiting the Sun, for that system the common center of mass of the solar system is the origin. The solar system orbits the center of mass of our Galaxy.

An exhaustive model of an entire Galaxy would model that hierarchy of gravitational wells. With enough mathematical ingenuity it would be possible to write down that model in terms of motion with respect to, say, the fourth planet of Aldebaran (assuming that star has planets.) But such a display of mathematical ability has no bearing on the physics taking place. No matter how the model is notated, the physical content of that model is that hierarchy of gravitational wells.

With enough mathematical ingenuity one can develop a way of representing motion that allows you to represent physics taking place with any choice of origin of your coordinate system (and whether the coordinate system rotates, etc, etc.) But that is not a statement about the physics taking place, it's just a statement about mathematical ingenuity.

It seems to me the following faulty syllogism is at work:
- SR has the equivalence of inertial frames as foundation.
- GR has superseded SR, with SR as limiting case.
Unjustified conclusion:
GR asserts equivalence of all frames of reference.


We have of course that GR has displaced SR. The introduction of GR was a revolutionaly displacement of its predecessor, just as SR displaced Newtonian mechanics. We have of course that GR took physics to a deeper level, but GR does not need - and hence does not assert - equivalence of all frames of reference.

 

[diegocas]

Thanks for all the replies to my post! There are quite interesting views about the subject.
I'm learning a lot about how physics (the science) works. However, as a mathematician, I should say that I'm a little impressed at how loosely defined certain physical notions are, namely, mass. (Please let me know if I'm wrong!) I thought there was more consensus about it, but I guessed the question is harder than it looks, even within GR, QM, etc.! Please, don't take that as an offense to physics, that's just how I feel because I'm a mathematician!
Please, keep the dicussion on! I'm learning a lot!
Thanks!

 

[Dickfore]

Well, Physics is most certainly not Mathematics. A definition in Physics does not bear the same content as a definition in Mathematics. This is mostly because Physics is founded on experiment and, ultimately, the base physical quantities are operationally defined.

And, if you think Mathematics is free of such paradoxes, how about set theory?

 

[diegocas]

In set theory, for example in Zermelo-Fraenkel set theory, you don't define the notions of "set" and "belongs to", you just assume that those notions exist and satisfy some properties (axioms). From that you work on formally. It is clearly stated what notions are defined and what primitive notions are left undefined.

I thought that when asking about what mass is, a physicist would say "In GR, mass is this... In QM it is this... In classical physics it is is..." Definite answers in each theory, although different in each realm of physics. However, I didn't see such clear-cut definitions (with the exception of K^2's posts).