What is mass fundamentally, beyond its effects?

[Drakkith]

If one thinks of mass as the quantity of matter...

That leads to problems. For example, 2 protons and 2 neutrons unbound in free space have MORE mass than when they are bound together in an alpha particle. Same number of particles, less mass.

 

[sophiecentaur]

Which does not really explain mass because: energy is defined as the ability to do work, and work is defined in terms of mass (the dimensions of energy are mass x distance^2 x sec^-2).

AM

But no quantity is 'explainable' in isolation. All that you can do is show how a certain set of relationships have some common factor and you then give that factor a name and call it a quantity. Science isn't really a set of things that have relationships; it's more the other way round, in as far as we observe phenomena and manufacture 'quantities' in our heads to explain the structure. Dimensional analysis it a simple way to approach the problem and gives us (or suggest to us) these quantities.
The temptation can be to approach Science as if it's based on a 'God says' / Leggo parts basis - looking for a structure on those terms. I really don't think there's much joy in that direction. It's the same as the Feynman objection to the 'why' question.

 

[craigi]

There is something very weird about mass.

We have the inertial mass and the gravitational mass. For a long time they were considered to be the same thing, but until Einstein there was no principle that showed their equivalence. I can think of no other property of matter that has such a deep dual purpose. It would seem reasonable to expect a fundamental reason that they are the same thing. This might offer the answer:

http://arxiv.org/abs/1001.0785

 

[DrStupid]

We have the inertial mass and the gravitational mass. For a long time they were considered to be the same thing

They are not the same thing and in GR there is no gravitational mass at all. Newton considered inertial mass and gravitational mass to be proportional (not identical) because it has been shown experimental:

"But I understand this quantity everywhere in what follows under the name of the body or of the mass. That becomes known through the weight of any body: for the proportion to the weight is to be found through experiments with the most accurate of pendulums set up, as will be shown later."
[Philosophiae Naturalis Principia Mathematica]

If you try to use gravitational mass in GR (even tough it makes no sense) it will appear to be equal to inertial mass for bodies at rest but not at very high velocities (see http://home.comcast.net/~peter.m.brown/ref/mass_articles/Olson_Guarino_1985.pdf )

 

[Andrew Mason]

But no quantity is 'explainable' in isolation. All that you can do is show how a certain set of relationships have some common factor and you then give that factor a name and call it a quantity. Science isn't really a set of things that have relationships; it's more the other way round, in as far as we observe phenomena and manufacture 'quantities' in our heads to explain the structure. Dimensional analysis it a simple way to approach the problem and gives us (or suggest to us) these quantities.
The temptation can be to approach Science as if it's based on a 'God says' / Leggo parts basis - looking for a structure on those terms. I really don't think there's much joy in that direction. It's the same as the Feynman objection to the 'why' question.

The "explanation" was sought by lendav_rott. My point was that "mass is energy" doesn't explain mass in terms of other concepts, since energy is defined in terms of mass.

We can explain distance and time in terms of concepts that we can readily perceive: space and changes in positions of things.

In a way, mass can be understood in terms of distance and time. Mass of a unit body of matter is perceived by the magnitude of its change in motion due to a specified interaction. This is the change per unit time of its position as measured in its pre-interaction reference frame.

AM

 

[sophiecentaur]

The "explanation" was sought by lendav_rott. My point was that "mass is energy" doesn't explain mass in terms of other concepts, since energy is defined in terms of mass.

We can explain distance and time in terms of concepts that we can readily perceive: space and changes in positions of things.

In a way, mass can be understood in terms of distance and time. Mass of a unit body of matter is perceived by the magnitude of its change in motion due to a specified interaction. This is the change per unit time of its position as measured in its pre-interaction reference frame.

AM

I would put it, rather, that we can show a relationship between - rather than "explain": that's one stage back in the process (Further from the answer to the 'why' question, if you like.
(I realized that you were not seeking an "explanation". I was endorsing your post. It's sometimes difficult not to appear to be disagreeing.)

 

[Aerion]

I've thought a lot about this, and I do think it is important to consider that our ideas about matter/mass/gravity are significantly influenced by the way our brain interprets data from the world. We think of matter as concrete, we associate matter with things. It is deceptively easy to think of particles as tiny balls of "stuff", and I think it is here that the confusion arrises. It seems more helpful to me to just think of particles as fields, with a central point where the field is most powerful, but nothing differentiating that center from the rest. There is no special part that could be "touched".

 

[lightarrow]

My point was that "mass is energy" doesn't explain mass in terms of other concepts, since energy is defined in terms of mass.

What do you mean? A photon's energy is defined as E = hf, the electrostatic field energy U in void is defined as U = eps_0 integral E^2dv where E = electric field, etc.

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[Andrew Mason]

What do you mean? A photon's energy is defined as E = hf, the electrostatic field energy U in void is defined as U = eps_0 integral E^2dv where E = electric field, etc.

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lightarrow

E=hf is not a definition. E relates to the ability of the photon to perform work on matter. Its ability to do work on matter is proportional to its frequency.

Energy has units of mass x distance^2/time^2 and it is defined as the ability to do work. Energy is not only defined in relation to mass - it only has meaning in relation to matter/mass.

AM

 

[lightarrow]

E=hf is not a definition. E relates to the ability of the photon to perform work on matter. Its ability to do work on matter is proportional to its frequency.

Energy has units of mass x distance^2/time^2 and it is defined as the ability to do work. Energy is not only defined in relation to mass - it only has meaning in relation to matter/mass.

AM

Sorry but it's your definition of energy that is not a definition at all. "Ability to do work"? Let's not joke...

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[Andrew Mason]

Sorry but it's your definition of energy that is not a definition at all. "Ability to do work"? Let's not joke...

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It is not exactly my definition. Work is defined in terms of force (mass x acceleration) and distance. If you have a better one, you should enlighten us.

AM

 

[lightarrow]

It is not exactly my definition. Work is defined in terms of force (mass x acceleration) and distance. If you have a better one, you should enlighten us.
AM

No, I don't mean to enlighten anyone, because it's impossible to give a definition of energy in a few words and which is comprehensive of all the forms of energy known.
About force, usually it's defined as dp/dt but you can define it with springs, as it were defined in the past. The concept of mass came after the concept of force, not before.

Having the concept of force as what is given from a compressed spring, you can define work as dW = Fdx, without need of knowing mass.

Of course nowadays we prefer to define F as dp/dt, because of convenience reasons.

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[Andrew Mason]

No, I don't mean to enlighten anyone, because it's impossible to give a definition of energy in a few words and which is comprehensive of all the forms of energy known.
About force, usually it's defined as dp/dt but you can define it with springs, as it were defined in the past. The concept of mass came after the concept of force, not before.

Having the concept of force as what is given from a compressed spring, you can define work as dW = Fdx, without need of knowing mass.

Of course nowadays we prefer to define F as dp/dt, because of convenience reasons.

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lightarrow

Actually F=dp/dt came from Newton but the concept of energy was not used until the early 19th Century.

While one can conceive of "force" independently of mass and acceleration (ie a compressed spring), the only way to experience a force is by its application to matter. And the only way to measure a force is by its interaction with matter e.g. the resulting acceleration of a mass. If you take a compressed spring and simply remove the constraint so that it expands freely (ie. without being in contact with a mass), it does no mechanical work at all.

AM

 

[lightarrow]

Actually F=dp/dt came from Newton but the concept of energy was not used until the early 19th Century.

Ok, but you wrote that energy is "the ability to do work" and then you wrote that "work is defined in terms of force (mass x acceleration) and distance" so having force you authomatically have energy, according to your definition.

While one can conceive of "force" independently of mass and acceleration (ie a compressed spring), the only way to experience a force is by its application to matter. And the only way to measure a force is by its interaction with matter e.g. the resulting acceleration of a mass.

I don't agree with that. If a laser beam is reflected off something (which has or not mass), its own momentum changes in a finite time, so we can say it experiences an average force that we could define as $$F = \Delta p/ \Delta t$$ and we know how to compute/measure the beam's momentum p from its power and lenght, for example.

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[Andrew Mason]

Ok, but you wrote that energy is "the ability to do work" and then you wrote that "work is defined in terms of force (mass x acceleration) and distance" so having force you automatically have energy, according to your definition.

No. You need to apply the force through a displacement. One does not require energy to maintain a static force. When you drive a screw to pull two boards tightly together, that binding force will last for a very long time. During that time, no energy is required to keep the boards tightly together.

I don't agree with that. If a laser beam is reflected off something (which has or not mass), its own momentum changes in a finite time, so we can say it experiences an average force that we could define as $$F = \Delta p/ \Delta t$$ and we know how to compute/measure the beam's momentum p from its power and lenght, for example.

The concept of force over time (impulse) does not apply to a photon.

The only way we can detect a photon is when it interacts with matter. What it is doing between the time it is emitted and the time it is received is unknowable.

Of course, a photon takes momentum from the matter that emits and delivers it to the matter that receives it.
The concept that a photon has momentum while it is a photon is a useful mathematical tool that helps us to visualize the transfer of momentum from one body to another and to preserve the principle of conservation of momentum.

AM

 

[lightarrow]

The concept of force over time (impulse) does not apply to a photon. The only way we can detect a photon is when it interacts with matter.

I have not mentioned photons at all.

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[Andrew Mason]

I have not mentioned photons at all.

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I assumed you were aware that a laser beam consists of a stream of (identical) photons.

AM

 

[lightarrow]

I assumed you were aware that a laser beam consists of a stream of (identical) photons.

AM

But I think this is irrelevant: I used (properly, improperly, don't know) simply the definition of force as Δp/Δt and the classical description of electromagnetic radiation.

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[lightarrow]

No. You need to apply the force through a displacement. One does not require energy to maintain a static force.

Maybe I didn't express myself clearly enough. Obviously there is the need of a displacement. But to define work we need force + displacement; since we already know how to define/make/measure a displacement, what is missing is the concept "force" and we were discussing about it for this reason. Having defined force we have everything we need to define work. This is what I intended.
Regards.

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[Andrew Mason]

Maybe I didn't express myself clearly enough. Obviously there is the need of a displacement. But to define work we need force + displacement; since we already know how to define/make/measure a displacement, what is missing is the concept "force" and we were discussing about it for this reason. Having defined force we have everything we need to define work. This is what I intended.
Regards.

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lightarrow

The issue is: how does one define a concept of force other than in relation to mass?
Force is implicitly defined in Newton's first law as something that causes a change in the motion of body i.e. a body of matter.The second law quantifies the force by relating the magnitude and direction of the force to the magnitude and direction of the acceleration of a mass.

You can suggest that it be standardized in relation to a standard spring but that only has meaning if there is mass involved. For example, I could say that a unit of force is the push provided by a standard spring with standard spring constant k compressed a by a standard displacement of x metres. But that unit of force can only exist if there is mass to push against. If it does not push on a mass, there is no force.

Similarly, if I punch with my fist in the air, I am not exerting force on anything (except a tiny force on the air). If I punch you, I may apply a force. If I punch a piece of paper with the same strength, I apply a much smaller force to the paper.

AM

 

[lightarrow]

The issue is: how does one define a concept of force other than in relation to mass?

To me the main issue was how to define energy, infact my first reply to you was about it.

Force is implicitly defined in Newton's first law as something that causes a change in the motion of body i.e. a body of matter. The second law quantifies the force by relating the magnitude and direction of the force to the magnitude and direction of the acceleration of a mass.

Ok, but how did they prove in the past, originally, that F = dp/dt (or F = ma), if force the first time was defined that way?

You can suggest that it be standardized in relation to a standard spring but that only has meaning if there is mass involved.

If a (powerful! ) laser beam is directed against a spring and reflected off, it compresses it.

Regards.

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[Andrew Mason]

To me the main issue was how to define energy, infact my first reply to you was about it.

Yes, of course. The main issue that you have raised is whether energy can be defined independently of mass. And in our discussion we have reduced that to an issue of whether force can be defined independently of mass.

Actually, all concepts involved in the concept of energy (mass, distance and time) require inertial reference frames and that requires mass.

Ok, but how did they prove in the past, originally, that F = dp/dt (or F = ma), if force the first time was defined that way?

F=ma follows from Galilean relativity and the first law. It can be shown that if force was not proportional to acceleration (assuming mass is constant) we would observe that the acceleration of the same body subjected to the same applied force depended on the motion of the reference frame in which it was observed.

If a (powerful! ) laser beam is directed against a spring and reflected off, it compresses it.

Yes. But the laser source has to be some body of matter.

In fact if the end of the spring simply absorbed the laser light, the spring would compress (but only half as much). And you would find that the impulse experienced by the source of the laser light was equal and opposite to the impulse received by the spring (half of the impulse experienced by the spring if there is total reflection).

AM

 

[DrStupid]

F=ma follows from Galilean relativity and the first law.

It follows from Galilean relativity, isotropy, definition of momentum, second law and third law.

It can be shown that if force was not proportional to acceleration (assuming mass is constant) we would observe that the acceleration of the same body subjected to the same applied force depended on the motion of the reference frame in which it was observed.

That would just show that force is frame dependent.

 

[Andrew Mason]

It follows from Galilean relativity, isotropy, definition of momentum, second law and third law.

Galilean relativity is premised upon time and space being the same for all inertial observers. Galilean relativity is an observable phenomenon: the laws of motion are the same in all inertial frames of reference, as was demonstrated by Galileo in experiments on moving ships. The second law follows from that. Conversely, if the second law was incorrect, one could show that Galilean relativity must be false.

That would just show that force is frame dependent.

In other words, it would show that the laws of motion would depend on the inertial reference frame of the observer. For example, the spot where a ball dropped from the top of the mast of a moving ship lands would depend on how fast the ship was moving. So it would violate Galilean relativity.

AM

 

[DrStupid]

In other words, it would show that the laws of motion would depend on the inertial reference frame of the observer.

In SR force is frame dependent but the laws of motion do not depend on the frame of the observer. That shows that your conclusion is not correct.

 

[Andrew Mason]

In SR force is frame dependent but the laws of motion do not depend on the frame of the observer. That shows that your conclusion is not correct.

No. That conclusion is based on the premise that time and space are the same for all inertial observers. So SR simply shows that the premises of Galilean Relativity are incorrect (but materially incorrect only when you are dealing with frames of reference moving at ~light speeds relative to each other).

AM

 

[lightarrow]

Yes, of course. The main issue that you have raised is whether energy can be defined independently of mass. And in our discussion we have reduced that to an issue of whether force can be defined independently of mass.

Actually, all concepts involved in the concept of energy (mass, distance and time) require inertial reference frames and that requires mass.

F=ma follows from Galilean relativity and the first law. It can be shown that if force was not proportional to acceleration (assuming mass is constant) we would observe that the acceleration of the same body subjected to the same applied force depended on the motion of the reference frame in which it was observed.

Yes. But the laser source has to be some body of matter.

Certainly but it's not relevant, I don't need to know what is mass, I only need a fixed support for the Laser source.

In fact if the end of the spring simply absorbed the laser light, the spring would compress (but only half as much). And you would find that the impulse experienced by the source of the laser light was equal and opposite to the impulse received by the spring (half of the impulse experienced by the spring if there is total reflection).

I only need to verify that an efficient mirror is put on the spring's end.

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[lightarrow]

F=ma follows from Galilean relativity and the first law. It can be shown that if force was not proportional to acceleration (assuming mass is constant) we would observe that the acceleration of the same body subjected to the same applied force depended on the motion of the reference frame in which it was observed.

I don't understand: didn't you wrote that you *define* force to be that? Which demonstration do you need?

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[DrStupid]

example

No. That conclusion is based on the premise that time and space are the same for all inertial observers. So SR simply shows that the premises of Galilean Relativity are incorrect (but materially incorrect only when you are dealing with frames of reference moving at ~light speeds relative to each other).

OK, than let me falsify your claim with a modification of Newton's laws that work with Galilean transformation:

The first law remains unchanged.

The second law shall define force as

$F := \dot p \cdot \left( {1 + \frac{{v^2 }}{{c^2 }}} \right)$

In order to keep momentum conserved the third law need to be adjusted accordingly:

$F_2 = - F_1 \cdot \frac{{c^2 + v_2^2 }}{{c^2 + v_1^2 }}$

That also applies to all natural laws dealing with forces, e.g. Newton's law of gravitation:

$F_g = G \cdot M \cdot m \cdot \frac{r}{{\left| r \right|^3 }} \cdot \left( {1 + \frac{{v^2 }}{{c^2 }}} \right)$

These laws of motion are independent from the frame of the observer and within the limits of classical mechanics they describe all observations correctly because the resulting equations of motions are identical with the results of Newton's original laws. But the modified force is neither proportional to acceleration nor frame independent. This counter example clearly shows that you are wrong.

 

[Andrew Mason]

I don't understand: didn't you wrote that you *define* force to be that? Which demonstration do you need?

I did not define force to be mass x acceleration. I just said that f=ma follows from the principle of Galilean Relativity and its premises.

AM