Does the Earth move around the Sun?

[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:

$$u = 1.660\,538\,782(83) \times 10^{-27} \, \mathrm{kg}$$

 

[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).

 

[D H]

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 $^{12}C$.

Yep. An atomic mass-based mass standard certainly is one of the contenders. Unfortunately, physicists do not yet know what 1/12 of the mass of ¹²C is. As you noted, the published value, which is the value that you cited, has a 50 ppb uncertainty. This is largely due to the uncertainty in Planck's constant. Then there's the uncertainty in Avogadro's number. An mass standard that is only usable to particle physicists is of limited value. An atomic mass-based standard would require better definition of Avogadro's number (One solution: Just give it an ad hoc value), a way to accurately count the atoms in a largish sample, repeatability, cost, and all that.

There are a number of efforts underway to do the prototype-based mass standard in. One of them almost certainly will pay off, sometime. One thing is certain: It ain't going to happen any time soon. This is an international standard we're talking about, after all. There are claims to be validated, committees to be organized, documents to be written and reviewed, votes to be taken, ... Years.

 

[Dickfore]

Do you think a replication of the mass standard can be done with precision greater than 50 ppb?

 

[D H]

An order of magnitude better.

From http://www.bipm.org/en/scientific/mass/calibrations_mass/

1 kg prototypes in Pt/Ir
The primary role of the Mass Section is to provide traceability to the international prototype of the kilogram. We do this by maintaining a number of prototypes and other standards in Pt/Ir. A subset of these is used as working standards to calibrate national prototypes upon request. The remainder are used for quality control. The combined standard uncertainty currently assigned to the calibration of a national prototype is typically 0.005 mg.

1 kg mass standards in stainless steel
The BIPM offers a calibration service for 1 kg standards in stainless steel. This service is available free of charge to NMIs of Member States of the Metre Convention. The volume of the standard will be determined by hydrostatic weighing at the BIPM if this parameter is unknown (typical combined standard uncertainty obtained at the BIPM is 0.4 mm3 at 21.7 °C). However, the volumetric thermal expansion near room temperature must be supplied by the NMI or the manufacturer of the standard. If not already in our database, the BIPM will determine the location of the centre of gravity of the standard as well as its magnetic properties (volumetric magnetic susceptibility and axial permanent magnetization). The combined standard uncertainty currently assigned to the calibration of a 1 kg standard in stainless steel is typically 0.013 mg.​

The BIPM has long wanted a replacement for the prototype-based definition of the kilogram, but only if this replacement is accurate to within 20 ppb. In the case of an atomic-based standard, that 50 ppb error in the atomic mass unit itself is only a part of the error. Error will also creep in when the atomic mass unit is scaled up to human size. How do you know if you have 5×10²² atoms in a sample, versus 5×10²² plus 10¹⁷ atoms?

 

[Dickfore]

Ahh, I see. It's because the prototype has such a "big" mass compared to $u$ that the relative error is much smaller.