# Is Mass Circular?

1. Dec 21, 2011

### jaketodd

We establish the mass of something by how much the earth pulls on it. We establish the mass of the earth by, for example, how much the sun effects the earth's motion. We establish the mass of the sun by how much it pulls on planets - and we're back to planets, which is already stated to be used to establish the mass of something.

Is it really circular like this, or did I miss something? If I didn't miss something, then what are the implications? Is it that we can only talk of relative masses within the same reference frame; there is no absolute mass for anything? Is this already stated in General Relativity?

Cheers,

Jake

2. Dec 21, 2011

### dacruick

Good question, I'm interested to see what some of the PF gurus say. Although I think you meant cyclical not circular.

3. Dec 21, 2011

### jaketodd

Thanks! I'm looking forward to what they say too.

4. Dec 21, 2011

### espen180

Yes, you can only talk about relative masses. First, take an arbitrary object and call its mass 1 unit. Then you can measure other objects' masses in terms of that unit by comparing them to the unit mass using Newton's 2nd law.

This process doesn't need gravity to be defined, it just needs a method of systematically applying a given force to different objects.

5. Dec 21, 2011

### Nabeshin

It's important to recall that gravitational and inertial mass are, as far as we know, the exact same quantity. That is, the mass which appears in Newton's law of gravitation (F=GMm/r^2) is the same as the one which appears in Newton's 2nd law (F=ma). So you have two ways of measuring mass -- either push on something, or see how much it is affected by gravity.

As espen180 notes, the mass scale is indeed relative. Specifically, we define a platinum-iridium cylinder sitting in France to be one kilogram, and we measure everything relative to this mass.

Note: The same could be said of lengths. We only measure lengths relative to other lengths, so I think your question is really more fundamentally one of defining your system of units.

6. Dec 21, 2011

### D H

Staff Emeritus
That's not quite right. We determine the mass of the Sun (better: the product of the gravitational constant and the mass of the Sun) by the orbits of the planets about the Sun. The planets are so much smaller than the Sun that, to first order, their masses just don't amount to much. Even the largest planet of the planets, Jupiter, has a mass that is only about 1/1000 that of the Sun.

Looking to the orbit of a planet compared to that of a tiny test mass is a lousy way to assess the mass of a planet. Much better is to look at how small objects orbit that planet. This gives have a good picture of the masses (G*mass) of all but Mercury and Venus.

There is a problem here. While the product G*M can be observed to very high degree of precision, mass cannot. The masses of the Sun and the planets are computed by dividing the observed planetary gravitational coefficient μ (G*M) by G. G is arguably the least well known of physical constants. Astronomers have assessed μ for the sun and several of the planets to nine or more decimal places. G: A lousy four decimal places.

7. Dec 21, 2011

### Naty1

Depends on your definition of mass....generally modern usage is that REST mass IS absolute.

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

Last edited: Dec 21, 2011
8. Dec 21, 2011

### Staff: Mentor

We happen to use this object, whose mass is defined to be one kilogram, exactly.

http://www.bipm.org/en/scientific/mass/pictures_mass/prototype.html [Broken]

All other mass measurements must ultimately come down to a comparison with this object, through a chain of intermediate objects.

Last edited by a moderator: May 5, 2017
9. Dec 21, 2011

### phinds

No, he clearly meant circular. Cyclical would make no sense in this context.

10. Dec 21, 2011

### D H

Staff Emeritus
Kinda sorta.

There are multiple mass standards that are loosely connected to the kilogram prototype. That kilogram prototype is the standard by which human-scale mass is assessed. Things that can be weighed on scales. At the atomic scale, the mass of a carbon-12 atom is the standard. There is a connection between the human scale and atomic scale of masses, Avogadro's constant. Currently this is measured experimentally.

This may change. As of the last meeting of the BIPM, plans are officially afoot (finally!) to tie the atomic and human scale mass conventions. Avogadro's number will become a defined constant, as will the Plank constant h, the elementary charge e, and the Boltzmann constant k.

At the other extreme are planetary and larger masses. Just as atoms are too small to balance against the kilogram prototype, these objects are too large. The connection between the kilogram prototype and these large objects is the universal gravitational constant G. While mass isn't directly observable at these large scales, the product μ=G*M is very observable.

11. Dec 22, 2011

### DrDu

Your argument holds at best in Newtonian mechanics. As soon as quantum mechanics comes into play the scale invariance of mass is broken. The size of an atom depends on the ratio of the charge and the mass of the electron and these cannot be scaled independently from each other. On the other hand the mass of the neutron determines how large a neutron star can be maximally before it collapses into a black hole, so you cannot scale large objects arbitrarily.

12. Dec 22, 2011

### jaketodd

This is getting interesting =)

13. Dec 22, 2011

### D H

Staff Emeritus
Huh?

The concept of mass is still applicable at the atomic and subatomic scales. Yes, mass is no longer additive, but I never said it was. The BIMP is quite aware of quantum mechanics. Why would they even think of making e, h, and k defined constants if the concept of mass didn't carry over to the atomic and subatomic scales?

Edit
Link to Resolution #1 of the 24th meeting of the CGPM: http://www.bipm.org/en/CGPM/db/24/1/

So who are the BIPM and the CGPM? The BIPM (International Bureau of Weights and Measures) are the keepers of the metric system. That kilogram prototype that jtbell mentioned in post #8 is the responsibility of the BIPM. Resolution #1, when/if accepted, would get rid of that prototype. The CGPM (General Conference on Weights and Measures) meets every four years, more or less, and makes recommendations to the BIPM. This resolution is huge. It is something that has brewing for decades.

Last edited: Dec 22, 2011
14. Dec 23, 2011

### DrDu

Dear D H, I was referring to the question of the original poster, not your reply. I also didn't want to imply that mass is no longer applicable in quantum mechanics.
The point I wanted to make is the following: For Newton, there is no fundamental difference between an apple and a planet (neither is there in general relativity). For Newton, both obey the same equations of motion.
Especially Newton cannot explain why there are no apple trees of galactic dimension nor suns of the mass of an apple. This underlying absolute scale is provided by quantum mechanics, only, finally probably by symmetry breaking via the Higgs mechanism which sets the mass of the electron and other elementary particles.

15. Dec 23, 2011

### sophiecentaur

Perhaps 'self referential' would be an appropriate description.

16. Dec 23, 2011

### jaketodd

Would you be so kind as to explain that in more detail? I'm very curious.

Thanks,

Jake

17. Dec 25, 2011

### DrDu

I´ll try, although I am not the specialist on that topic.
It is believed that the mass of most particles like e.g. the electron is due to scattering from the Higgs field, which, even in the vacuum, has a non-vanishing value. Nobody knows why the value of the Higgs field is as big as it is (if it exists at all, experiments at CERN are about to verify its existence experimentally). Probably its value is pure chance and there may even be regions in our universe where it has other values.
Anyhow, if it's value was 0, electrons would be massless and they would appear in two versions, right handed and left handed electrons. When the field is non-zero, a right handed electron can get scattered from the Higgs field into a left handed electron and vice versa.
How does that lead to mass? The energy of a massless particle goes linearly to 0 when we reduce its momentum (or wavenumber). In the case of light this leads to the familiar proportionality of frequency and inverse wavelength.
For a massive particle, the limiting value of energy when the momentum goes to zero (which is equivalent in this case to it´s velocity going to 0) is it´s mass ( up to the famous factor c squared of Einstein). In the case of the electron interacting with the Higgs field, there is some interaction energy present even when the momentum of the electron vanishes, which hence is it´s mass.

18. Dec 26, 2011

### jaketodd

First of all, thank you! Second, how was the Higgs field thought up? It sounds like it may be as baseless as string theory; absolutely zero empirical data supporting it. I have that book, which The Economist called "One of the most important books of the year," called "The Rise of String Theory; The Fall of Science."

Thanks,

Jake

19. Dec 26, 2011

### DrDu

The idea of symmetry breaking by the Higgs field has been taken over from condensed matter physics, namely the physics of superconductors. The Higgs mechanism explains quite a lot of observations and many of it´s predictions have been confirmed experimentally by now.
Namely the unification of weak and electromagnetic forces. This unification is explained by both forces being related by a symmetry. After this symmetry had been postulated, the carriers of the field (besides the photon, which obviously was known before) were subsequently confirmed experimentally (namely the vector bosons W and Z).
However, this symmetry is "broken", like e.g. the magnetic field in a magnet could in principle point in any direction, but in fact, in each magnet you will find only one realization of the direction of the magnetic field.
According to a theorem by Goldstone, a broken symmetry should leave some signature in the form of a massless particle, the "Goldstone boson". However, there is no corresponding particle.
The Higgs mechanism explains quite nicely how this particle actually gets a mass (and also the other particles).
So somehow the Higgs mechanism is the easiest way to save the concept of broken symmetry which has already been confirmed experimentally.

20. Dec 27, 2011

### jaketodd

I may easily be mistaken, however: Isn't the carrier of the EM force virtual photons? I've heard it said that, in this context, photons aren't actually detected - just the easiest way to model the interaction.

If that is all there is there, then are the W & Z bosons just as virtual, or have they actually been found and their properties experimentally identified (instead of them just being a convenient model)?

Thanks,

Jake