Uncovering the Mystery of Mass: What is it?

[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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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

 

[Ssnow]

The quantity of matter confined in a (finite) space region?

 

[Andrew Mason]

example

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.

If you start with your premise that force is frame dependent, you are immediately in conflict with Galilean relativity. You are saying that a standard force unit (e.g a standard compression distance of a standard spring) depends on the frame of reference. That would violate the premise that distance is the same in all reference frames. All I am saying is that a standard force unit will be observed to accelerate a standard mass unit at the same rate in all inertial frames (non-relativistic).

Besides, it appears to me that all you are saying with your example is that Galilean relativity would be observed to be correct for frames moving at non-relativistic relative speeds, and that at such speeds $F=\dot{p}$ would be observed, to within a negligible margin of error.

AM

 

[DrStupid]

If you start with your premise that force is frame dependent, you are immediately in conflict with Galilean relativity.

No, I'm not. Please refer to my counter example above. With these modifications of the laws of motion force would be frame dependent without violating Galilean relativity.

You are saying that a standard force unit (e.g a standard compression distance of a standard spring) depends on the frame of reference.

No, I would say that this wouldn't be an appropriate standard force unit.

All I am saying is that a standard force unit will be observed to accelerate a standard mass unit at the same rate in all inertial frames (non-relativistic).

No, you are saying that

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

I will no longer spend any effort into the falsification of your claims because it is not my duty and it seems that it doesn't stop you from repeating them. You are responsible for proper justification. So please show me step by step how you get F=m·a from Galilean relativity and the first law.

Besides, it appears to me that all you are saying with your example is that Galilean relativity would be observed to be correct for frames moving at non-relativistic relative speeds, and that at such speeds $F=\dot{p}$ would be observed, to within a negligible margin of error.

That depends on the value of the universal constant c. It does not need to be the speed of light. With c=1m/s the difference between the original and the modified second law would be obvious even at walking speed.

 

[Andrew Mason]

No, I'm not. Please refer to my counter example above. With these modifications of the laws of motion force would be frame dependent without violating Galilean relativity.

The first law of motion (which is part of Galilean Relativity) says, in part, that a force applied to a body at rest will change that body's motion (ie. the body will experience a change in motion relative to its initial rest frame). And it says that all inertial reference frames are equivalent: the laws of motion are the same in all inertial reference frames.

So according to Galilean Relativity, the same physical interaction between two unit bodies will have the same result in all inertial frames of reference. Let's say that a standard interaction is the collision of two 1 kg steel balls, Ball A which is unconstrained and stationary, and Ball B which is moving at one unit of velocity in the rest frame of Ball A. Ball B is moving toward ball A at one unit of velocity immediately before it collides with Ball A. Galilean Relativity says that Ball A will experience the same change in motion whether the interaction takes place on a uniformly moving rail car or on a stopped rail car. If it did not, one would be able to differentiate between inertial reference frames, thereby destroying the basic postulate of Galilean Relativity.

The equivalence of inertial reference frames means that the graph of velocity vs time experienced by Ball A during the collision as measured in the frame of the rail car would be the same regardless of the (uniform) velocity of the rail car. Galilean Relativity also postulates that time and distance are the same in all inertial reference frames This means that the resulting change in velocity would be observed to be the same in all inertial reference frames. (This is just a matter of applying the Galilean transformation to the experiment).

I think we would both agree to this point. But if I am mistaken, let me know where we differ.

Now, let's involve the concept of force. By the First Law we know that Ball A experiences a force because it changes its motion. So let's attach a spring to Ball A and have Ball B move toward that spring at unit velocity and have a high speed camera record the interaction so we can measure the compression of the spring as a function of time.

Since the interaction is the same in all reference frames, the graph of spring compression vs. time will be the same regardless of how fast the rail car is uniformly moving. And since time and distance are the same for all inertial reference frames, the compression distance as a function of time will be the same for all inertial observers, regardless of how fast they are moving. So the area under that graph would be the same for all inertial observers. Since motion change when the spring compresses, we will say that the compression of the spring represents a force. We won't assume Hooke's law. We will just say that a force, F, at a given time is represented by the compression distance. The area under the graph is proportional to the impulse received by Ball A.

This shows that the impulse, $I=\int Fdt$ on Ball A is the same for all inertial observers. And since time is the same for all inertial observers, the time averaged force is the same. So let $I = \int Fdt = F_{avg}\Delta t$.

Now repeat the experiment with two unit balls, Ball A and Ball A', each undergoing simultaneous collisions with unit ball traveling at unit velocity. The change in motion of Ball A will be identical to the change in motion of Ball A'. So the change in momentum (product of no. of unit balls and velocity) is double. And, however you want to define force, the average force is doubled. And since the mass has doubled with the same change in velocity, momentum change has doubled.

Since the change in velocity of Ball A, $\Delta v$, is the same in all frames, this means that the average force, $F_{avg}$ multiplied by the time, is proportional to the change in momentum: $F_{avg}\Delta t \propto m\Delta v \rightarrow F \propto \dot{p}$.

You could also do the same experiment using a series of collisions, with the successive collisions taking place with a Ball B traveling at unit velocity with respect to the rest frame of Ball A moving at $v_i + \Delta v$. You can see in that case that doubling the duration of the same average force doubles the change in momentum. And since $\Delta t$ is doubled and the force is the same, $2\Delta v/2\Delta t = \Delta v/\Delta t$ is constant . Take any number of successive standard collisions and you can see that $n\Delta v/n\Delta t = \Delta v/\Delta t$ is constant. (ie. acceleration is constant)

Now if you take the limit as mass/time/unit velocity approach 0, you can see that a series of the same collisions, or any number of simultaneous collisions or any combination of these, has the same result: $Fdt \propto mdv$. So if the force is constant over time, dp/dt is constant. And if mass increases proportionally with force, the change in velocity per unit of time is the same.

And that is just Newton's second law.

No, I would say that this wouldn't be an appropriate standard force unit.

So why don't you suggest a standard force unit. One does not have to assume Hooke's law, as the above shows.

It would have to be something that can be considered constant over time and space in some reference frame. Your definition of force as $F=\dot{p}(1+v^2/c^2)$ makes it impossible to have such a constant force. So a spring maintained at the same compression distance and applied to a free body would experience a different force depending on the speed of the inertial reference frame in which the spring is situated. I am not sure why you would want to presume that the force changes when nothing observable changes.

I will no longer spend any effort into the falsification of your claims because it is not my duty and it seems that it doesn't stop you from repeating them. You are responsible for proper justification. So please show me step by step how you get F=m·a from Galilean relativity and the first law.

See above.AM

 

[lightarrow]

The quantity of matter confined in a (finite) space region?

"Matter" and "mass" are two different things.

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[lightarrow]

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.

Then I don't understand anything. In post #41 you wrote:
"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."
This and other statements you did made me think you define force as dp/dt or as m*a. Which is instead the definition of force you give?

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[DrStupid]

We will just say that a force, F, at a given time is represented by the compression distance.

Why?

 

[Andrew Mason]

Why?

It isn't really necessary. I just wanted to say that since all frames are equal, and the spring is compressed the same way for the same duration in all reference frames, Body A is subjected to the same time average force in all frames. Imagining a plot of compression vs. time simply helps one see that. The absolute symmetry of Galilean Relativity means that the forces must be the same for all identical time intervals for all inertial observers.

AM

 

[Andrew Mason]

"Matter" and "mass" are two different things.

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Yes, but not in classical mechanics. Newton's definition of mass as "quantity of matter" applies to classical mechanics.

AM

 

[Andrew Mason]

Then I don't understand anything. In post #41 you wrote:
"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."
This and other statements you did made me think you define force as dp/dt or as m*a. Which is instead the definition of force you give?

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lightarrow

I said work is defined as force x distance and Force = mass x acceleration. I am not defining force as mass x acceleration. All I said was that F=ma follows from Galilean Relativity.

AM