Mass Established by Relative Motion: Implications in GR?

[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

 

[dacruick]

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

 

[jaketodd]

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

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

 

[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.

 

[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.

 

[D H]

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.

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.

 

[Naty1]

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?

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

..."mass" is defined in two different ways in special relativity: one way defines mass ("rest mass" or "invariant mass") as an invariant quantity which is the same for all observers in all reference frames; in the other definition, the measure of mass ("relativistic mass") is dependent on the velocity of the observer...

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

 

[jtbell]

First, take an arbitrary object and call its mass 1 unit.

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

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

 

[phinds]

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

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

 

[D H]

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

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.

 

[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.

 

[jaketodd]

This is getting interesting =)

 

[D H]

Your argument holds at best in Newtonian mechanics. As soon as quantum mechanics comes into play the scale invariance of mass is broken.

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.

 

[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.

 

[sophiecentaur]

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

Perhaps 'self referential' would be an appropriate description.

 

[jaketodd]

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.

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

Thanks,

Jake

 

[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.

 

[jaketodd]

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.

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

 

[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.

 

[jaketodd]

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).

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

 

[chrisbaird]

Feynmann touches on this in his lectures. If you were to contact intelligent life on a distant star and try to describe what humans look like, you couldn't just say humans are about two meters tall. You would have revert to an absolute unit scale instead of a relative one and tell them that humans 10^23 (or some number) hydrogen atoms. In the same way, an absolute mass scale would be in units of the mass of one hydrogen atom.

 

[jaketodd]

Feynmann touches on this in his lectures. If you were to contact intelligent life on a distant star and try to describe what humans look like, you couldn't just say humans are about two meters tall. You would have revert to an absolute unit scale instead of a relative one and tell them that humans 10^23 (or some number) hydrogen atoms. In the same way, an absolute mass scale would be in units of the mass of one hydrogen atom.

I disagree: What if their planet is more massive? Then hydrogen atoms would weigh more to them.

As for length, if their planet is more massive, then things with the same amount of hydrogen atoms as here would be shorter because of the added gravity condensing the hydrogen atoms.

Same thing for time: If their planet is more massive, then time would move more slowly for them.

However now, I think you could say "Our planet is made of X-many of these atoms, and Y-many of these other atoms, etc. and our planet is moving Z-fast along such and such a vector relative to the motion of your planet."

Jake

 

[DrDu]

I disagree: What if their planet is more massive? Then hydrogen atoms would weigh more to them.

Yes, but their mass would be the same.

 

[DrDu]

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

In that sense, the existence of virtual W and Z bosons or some equivalent carriers of weak interaction was already deduced from beta decay. Only in the 1980´s the corresponding free particles were generated and detected in large colliders.
Once you know the parameters like mass and charge(s) of the free particles, you can calculate all the forces due to the exchange of virtual particles, too.

 

[jaketodd]

Yes, but their mass would be the same.

You would need something to compare it to - like how much that mass weighs in a defined context. Mass only manifests in contexts. You have to define the other variables in two contexts in order to compare. You could do that by specifying how many atoms make up your planet, and what type of atoms they are. I don't think you could just say the mass is X, and they would have any idea what that is.

 

[jaketodd]

In that sense, the existence of virtual W and Z bosons or some equivalent carriers of weak interaction was already deduced from beta decay. Only in the 1980´s the corresponding free particles were generated and detected in large colliders.
Once you know the parameters like mass and charge(s) of the free particles, you can calculate all the forces due to the exchange of virtual particles, too.

Ok, but isn't the use of virtual particles a good indication that we don't have the full picture yet? Things behaving as if a certain thing is there, but not being able to find them seems to indicate that to me.

 

[DrDu]

You would need something to compare it to - like how much that mass weighs in a defined context. Mass only manifests in contexts.

If we tell them that an average earthling weights as much as 70 000 moles of hydrogen atoms they will have quite a clear idea of what mass this corresponds too. Any balance on which you put one mole of hydrogen atoms on one side of the balance will yield a mass of 1 g on the other irrespective of the planet in the field of which you use the balance.

 

[jaketodd]

If we tell them that an average earthling weights as much as 70 000 moles of hydrogen atoms they will have quite a clear idea of what mass this corresponds too. Any balance on which you put one mole of hydrogen atoms on one side of the balance will yield a mass of 1 g on the other irrespective of the planet in the field of which you use the balance.

Good point! About my other post please?

Jake

 

[Drakkith]

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

The W & Z Bosons have actually been detected by particle colliders. This is because they are real, and similar to photons, their virtual counterparts are what are considered to be exchanged during interactions.

I disagree: What if their planet is more massive? Then hydrogen atoms would weigh more to them.

Weight and mass are not the same thing. Mass is always the same no matter where you at. A 1 kilogram block is still 1 kilogram whether it's on the Moon, the Earth, or another planet.

As for length, if their planet is more massive, then things with the same amount of hydrogen atoms as here would be shorter because of the added gravity condensing the hydrogen atoms.

If you isolate a hydrogen atom then you can measure it's size which shouldn't change in different gravity.

Same thing for time: If their planet is more massive, then time would move more slowly for them.

On a planetary scale, the effect of time dilation is very small. About a difference on the order of microseconds per day.

 

[jaketodd]

The only question left in this thread is if having to use virtual particles to model interactions shows that we don't have the whole picture yet - I mean: Stuff that we haven't found to exist, and instead things acting as if those stuffs were there.

Thanks all,

Jake

 

[Drakkith]

The only question left in this thread is if having to use virtual particles to model interactions shows that we don't have the whole picture yet - I mean: Stuff that we haven't found to exist, and instead things acting as if those stuffs were there.

Thanks all,

Jake

To my limited knowledge on the subject, virtual particles are a result of doing the math a certain way. Whether this actually means anything or not is beyond me. It certainly works though.

 

[jaketodd]

To my limited knowledge on the subject, virtual particles are a result of doing the math a certain way. Whether this actually means anything or not is beyond me. It certainly works though.

Yes it works, but not being able to detect the particles leaves me wondering.

 

[Drakkith]

Yes it works, but not being able to detect the particles leaves me wondering.

I look at it like one of the following:
1) There aren't actually an virtual particles, it's just a mathematical construct or whatever
2) They aren't detectable because if they were they would have to be real and thus not virtual. So kind of like trying to figure out the position and momentum of a particle down to any precision, it just isn't possible.

 

[jaketodd]

I look at it like one of the following:
1) There aren't actually an virtual particles, it's just a mathematical construct or whatever
2) They aren't detectable because if they were they would have to be real and thus not virtual. So kind of like trying to figure out the position and momentum of a particle down to any precision, it just isn't possible.

So this takes a turn to the Uncertainty Principle. I forget, but aren't all quantities there; it's just not possible for us to measure the two pairs of information at the same time, which the UP lays out? If we broaden the UP to cover virtual particles, and there is a pair of information, one of which is detecting a virtual particle, then we should be able to detect them if we forget about the other piece of information. But a) is there even a pair of information for virtual particles, and b) is it possible to ignore the piece of information that would lead to detection of virtual particles, so they'd be particles, not virtual particles? Well wait a second, in the UP, there is the relation between energy and time. We can get the time of our virtual particles interacting if we ignore their energy? But we can't measure the energy of our virtual particles because they are traveling at the speed of light (virtual photons, for example) and thus time stands still for them, so they remain virtual?

Jake

 

[Drakkith]

I tried answering again, but I can't explain it well enough. I suggest making a thread in the Quantum Physics forum for this jaketodd. Try the FAQ there as well along with searching for related threads. There should be plenty.