B Relativistic Mass of Sub-Atomic Particles: What Does it Mean?

[itoero]

"It is impossible to "weigh" a stationary electron, and so all practical measurements must be carried out on moving electrons. The same is true with any other sub-atomic particle. For particles like photons or gluons the situation is even more problematic since the very concept of a stationary or "at rest" massless particle lacks meaning."https://en.wikipedia.org/wiki/Electron_rest_mass

What do you think of this?

 

[Nugatory]

What do you think of this?

"Rest mass" is a clearly defined and very useful concept, and we can measure it by indirect means even if we cannot put the particle in question on a scale while it's not moving. It's the difference between the total energy and the kinetic energy, and this definition allows us to assign a rest mass of zero to particles like photons, which always move at the speed of light.

So I'd rate that Wikipedia quote as "incomplete and potentially misleading"

 

[Herman Trivilino]

"It is impossible to "weigh" a stationary electron, and so all practical measurements must be carried out on moving electrons.

Can you give us an example of one these practical measurements carried out on a moving electron?

Once you do that you'll see that it's possible to assign a mass $m$ or a mass $\gamma m$ to the particle, where $\gamma$ is a factor that depends only on the speed of the particle relative to some observer. It makes no difference what names you choose to give $m$ or $\gamma m$ because the values that they have are independent of the names you give them. So calling $m$ the rest mass is really just a silly thing to do, because the electron doesn't have to be at rest to determine its value. It's better to just call it the mass and forget about other kinds of mass, except when you choose to enter a conversation like this one to explain why that's all you need to do.

And the Principle of Relativity, by the way, tells us that we can always find a frame a reference where a massive (as opposed to massless) particle is at rest, regardless of its speed. So any distinction is arbitrary. Everyone, regardless of their speed relative to the particle, will measure the same value for $m$, but they will measure different values for $\gamma m$ which is all the more reason to use only the former. It's an example of an invariant quantity, that is, it has the same value in all inertial frames of reference.

 

[itoero]

Can you give us an example of one these practical measurements carried out on a moving electron?

Mass is the measure of an object's resistance to acceleration when a net force is applied. This implies you need momentum to measure mass.

This is my understanding of it, but I'm not a scientist:)...

What do you think about the speedlimit (c) of massless particles? Relativistic mass explains that. If kinetic energy isn't mass then there shouldn't be a speedlimit for massless particles.

 

[Nugatory]

Mass is the measure of an object's resistance to acceleration when a net force is applied. This implies you need momentum to measure mass.

That's a definition of "mass", but it's not the only one, it works well only in classical physics, and is pretty much unrelated to the energy-based definition of "rest mass".

Relativistic mass explains that. If kinetic energy isn't mass then there shouldn't be a speedlimit for massless particles.

Relativistic mass is not needed to explain the speed-of-light limit, for either massive or massless particles.

 

[Dale]

What do you think of this?

I think this is a perfect example of the reason why I prefer the term "invariant mass" instead of "rest mass". It is the same quantity, but the wording prevents this kind of misunderstanding.

 

[itoero]

That's a definition of "mass", but it's not the only one, it works well only in classical physics, and is pretty much unrelated to the energy-based definition of "rest mass".

What's an other definition of mass?

 

[itoero]

Relativistic mass is not needed to explain the speed-of-light limit, for either massive or massless particles.

How do you explain c without the use of relativistic mass?

 

[weirdoguy]

Relativistic mass is a concept that is not used that much in modern physics:
https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/

Kinetic energy goes to infinity when you approach c whether you consider relativistic mass or not, so I don't know why you think relativistic mass explains anything...

 

[DrStupid]

How do you explain c without the use of relativistic mass?

The original explanation are the Maxwell equations, which result in an invariant speed of plane electromagnetic waves in vacuum (no mass involved). Einstein genarlized that from electromagnetic waves to everything else by replacing Galilean transformation with Lorentz transformation (again no mass involved).

 

[Herman Trivilino]

Mass is the measure of an object's resistance to acceleration when a net force is applied.

This is a concept taught in introductory physics classes. It comes from this expression of Newton's 2nd Law: $a=\frac{F}{m}$. It's not wrong, it's just that it's an approximation that's valid only when speeds are small compared to $c$.

In the decade or two surrounding the year 1900 it became clear to researchers (who thanks to the invention of the vacuum pump were able to acclerate particles to high speeds) that it didn't seem to be true any more. They tried to rescue its validity by inventing different kinds of mass, but it gets really messy because the mass is different at different speeds, different for different directions of the force, and the direction of the acceleration is not parallel to the direction of the force.

Researchers quickly abandoned this attempt and instead of inventing new kinds of mass they modified the relationship between acceleration and force. The problem though, is that it took a hundred years, that is the decade or two surrounding the year 2000, for physics educators (who had the physics just as right, for the most part, as the researchers did) to fully catch on to the notion that different kinds of mass are not only not needed, but an impediment to learning.

Relativistic mass explains that. If kinetic energy isn't mass then there shouldn't be a speedlimit

Just because you can use an idea to explain something doesn't mean using that idea is the only way to provide the explanation. And by the way, it's incorrect to use relativistic mass in that particular explanation, you instead have to use one of those other kinds of mass I mentioned above, called longitudinal mass, if you want the explanation to correctly match what you measure happening when you accelerate massive (as opposed to massless) particles to high speeds.

A better way to explain why you can't accelerate a particle to light speed is to realize that if you have an invariant speed (that is a speed that's the same to all inertial observers regardless of their speed relative to each other) then that speed has to be a speed that you can never attain. It goes something like this. Chase after a light beam, not matter how fast you chase after it, it will always recede from you at speed $c$. Therefore you can never attain speed $c$.

Another way is to look at the relationship between kinetic energy and speed. You see then that for massive (as opposed to massless) particles their kinetic energy increases beyond all bounds as the speed approaches $c$.

You don't need relativistic mass for anything qualitative or quantitative. You're much better off spending the effort on learning about the geometry of spacetime because it will give you a clearer, and by the way a visual, understanding, as opposed to some pieces of misinformation that were cobbled together way back around 1900 before people really understood what's going on.

 

[itoero]

Relativistic mass is a concept that is not used that much in modern physics:
https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/

Kinetic energy goes to infinity when you approach c whether you consider relativistic mass or not, so I don't know why you think relativistic mass explains anything...

Kinetic energy doesn't go to infinity when photons approach c.

F=m.a The acceleration (a) increase the speed (v) which increases the speed dependent mass (m_rel). For a photon, the total mass (m) is the speed dependent mass (m_rel) which increases due to the acceleration (a).
The force (F) changes the momentum which decides the speedlimit(c).

So time causes the force (F) to increase due to the speed dependent mass (m_rel). You have a system in which force (F) decides c...force (F) is the limiting factor.

If speed dependent mass isn't calculated then F=ma, E=mc² and p=mv doesn't work for photons and gluons.

 

[jbriggs444]

If speed dependent mass isn't calculated then F=ma, E=mc² and p=mv doesn't work for photons and gluons.

If speed dependent mass is calculated then F=ma still does not work.

 

[itoero]

it's an approximation that's valid only when speeds are small compared to ccc.

Citation?

 

[PeterDonis]

Thread closed for moderation.

 

[berkeman]

After some Moderation, the thread is re-opened. Thank you to all trying to help the OP understand physics.

 

[Herman Trivilino]

Citation?

The Concept of Mass, by Lev B. Okun, Physics Today, June 1989, pp. 31 thru 36.

http://www.hysafe.org/science/KareemChin/PhysicsToday_v42_p31to36.pdf

Notice in particular equation (13) on page 33.

I also recommend pretty much any mainstream introductory calculus-based physics textbook written in the last 15 years or so.

 

[Dale]

Citation?

See equations 15.107 and 15.108 in Taylor's "Classical Mechanics"

Kinetic energy doesn't go to infinity when photons approach c.

Photons don't approach c, they always travel at c. Anything described as approaching c is necessarily massive.

As a massive particle approaches c (and a massive particle is the only kind of particle that can "approach c") the KE does go to infinity.

For a photon, the total mass (m) is the speed dependent mass (mrel) which increases due to the acceleration (a).

Photons don't accelerate.

 

[SiennaTheGr8]

https://en.wikipedia.org/wiki/Relativistic_mechanics#Force

 

[DrStupid]

Citation?

For the case that you don't believe in the references for the relativistic force, here the probably oldest available sources

for momentum http://cudl.lib.cam.ac.uk/view/PR-ADV-B-00039-00001/26

Def. II: p: = $q \cdot v$

(I am using the symbol q for "quantity of matter" instead of m in order to avoid confusions with invariant mass.)

and for force http://cudl.lib.cam.ac.uk/view/PR-ADV-B-00039-00001/46

Lex II: $F: = \dot p$

That results in $F = q \cdot \dot v + v \cdot \dot q$. The equation $F = q \cdot \dot v$ is a special case for constant q. It must not be used if q changes (for what reason ever). This is the case for the relativistic mass $q = \gamma \cdot m$. Included into the general equation for force and solved for acceleration it results in the equation mentioned by Mister T in #17. In this case F=m·a is just an aproximation for non-relativistic velocities.

 

[quiet]

I once asked the same question that started this thread. Among the help someone showed me what the basic laws applied to a rectangular waveguide, in the simplest mode of the guide. Based on Maxwell's theorem of the linear momentum of an electromagnetic wave p = \dfrac {E} {C} and just a hint of elementary mechanics, four things appear. 1) The guide is full of energy at rest for the cut-off frequency (mathematically, not in a practical radio installation). 2) For a higher frequency, the energy moves along the waveguide at the group velocity. In this case the energy is higher than in the rest condition. The relation between energy in motion and energy at rest is identical to the formula of special relativity. 3) The linear momentum, multiplied by the phase wavelength, gives a constant. If the energy contained in the guide is the minimum allowable by the electromagnetic field, that constant is the Planck constant. Then we obtain the formula of de Broglie that links \lambda_f=\dfrac{h}{p} being p the net amount of movement. Why the adjective net? Because the wave group is composed of elementary waves and each has its linear momentum. At rest the resultant is equal to zero. In motion the resultant is non-zero. 4) What an observer fixed to the walls of the guide sees as a wave group, another observer that moves with respect to the walls with a speed equal to the group speed, sees it as a standing wave. That is to say that the wave group is equivalent to a standing wave seen from another frame.

 

[1977ub]

Re: other methods besides applying momentum, how about using gravitation attraction to measure mass. You have a bunch of electrons in a confined area (somehow) and measure the acceleration due to gravity at some well-defined distance.

 

[Khashishi]

Compare the two statements
$$E^2 = m^2 c^4 + p^2 c^2$$
$$E = \gamma m c^2$$
They are both correct (but the second one can only be used for massive particles) and they show the relationship between energy and mass. $\gamma = \frac{1}{\sqrt{1-v^2/c^2}}$
$m$ is known as the mass. When the system is just one particle, then $m$ is also the rest mass. If there is more than one particle involved, the term rest mass is confusing and probably shouldn't be used. This is because the mass of the system can be different than the sum of the rest masses of the particles that make up the system. For example, the mass of a hydrogen atom is different than the mass of an electron + the mass of a proton. A better name in this scenario is the invariant mass, because the term invariant mass clues the reader in that the mass has a single value in all frames and therefore must be $m$.

Sometimes, $\gamma m$ is called the relativistic mass. It must never be called the mass, because that is an endless source of confusion. So many threads have been formed because of this confusion. There's no need to use the term relativistic mass. $\gamma m$ is more precise and does not lead to confusion.

 

[jerromyjon]

What's an other definition of mass?

How do you explain c without the use of relativistic mass?

"Another" definition is the energy bound as nucleons into particles.
"c" is the ultimate rate of transference of information.
Energy has mass and travels at a maximum of c, but energy has no rest mass.

 

[DrStupid]

There's no need to use the term relativistic mass. $\gamma m$ is more precise and does not lead to confusion.

E/c² is even better because it also works for m=0.

 

[Herman Trivilino]

Energy has mass and travels at a maximum of c, but energy has no rest mass.

Can you give an example of energy having mass? It seems that to do so you'd need to assign both energy and mass to some object, so energy and mass are both properties of that object. It wouldn't make sense to say that mass is a property of energy.

 

[Khashishi]

Energy has mass and travels at a maximum of c, but energy has no rest mass.

Wrong. See above.

 

[1977ub]

I used to think that mass and energy were both somehow present in an object, but it's more of an either/or, measurement wise, and it depends also on your frame how much of one you might get and how much of the other.

 

[Khashishi]

In relativity, it's useful to think of energy as part of an energy-momentum four-vector. Depending on your frame of reference, you see different components of the energy-momentum four-vector (that is, different energy and momentum), but the invariant interval (which is a generalization of the concept of length of a three-vector) doesn't change. The invariant interval of the energy-momentum four-vector is just the invariant mass.

This is analogous to simple directions in 3D. If you are going from point A to point B and you measure the displacement in steps forward and steps to the side, the result depends on which way you are facing. But the distance between A and B is fixed and doesn't depend on your facing. You can always calculate the distance from the displacement using the Pythagorean theorem. You wouldn't say stuff like "distance is a kind of horizontal step", so you shouldn't say "mass is a kind of energy".

 

[Herman Trivilino]

I used to think that mass and energy were both somehow present in an object, but it's more of an either/or, measurement wise,

Both are properties. Both can be measured. They are related by the relation $m^2=E^2-p^2$.

and it depends also on your frame how much of one you might get and how much of the other.

True for energy, but the mass is the same in all inertial frames of reference.

 

[jerromyjon]

Sometimes, γmγm\gamma m is called the relativistic mass. It must never be called the mass, because that is an endless source of confusion.

I'm sorry. I tend to think of gravitational influence as "mass". I don't have a better system of categorization.

 

[Dale]

I tend to think of gravitational influence as "mass".

Gravitation is a tensor, it can't be represented as a scalar

 

[Sorcerer]

Kinetic energy doesn't go to infinity when photons approach c.

F=m.a The acceleration (a) increase the speed (v) which increases the speed dependent mass (m_rel). For a photon, the total mass (m) is the speed dependent mass (m_rel) which increases due to the acceleration (a).
The force (F) changes the momentum which decides the speedlimit(c).

So time causes the force (F) to increase due to the speed dependent mass (m_rel). You have a system in which force (F) decides c...force (F) is the limiting factor.

If speed dependent mass isn't calculated then F=ma, E=mc² and p=mv doesn't work for photons and gluons.

Why would photons ever approach c? They are eternally at c in a vacuum.Anyway, here is the relativistic kinetic energy equation:

T = (γ - 1)mc²

where γ = 1/√(1 - v²/c²)This is using regular mass, and as you see, as v approaches c, T approaches infinity.

 

[nitsuj]

I'm reading about Bose-Einstein condensate, wow that adds some complexity to getting "my own" intuition for what mass "is" lol.

isotropic relative motion of bosonic atoms...okay I agree...invariant mass

 

[1977ub]

A compressed spring has a greater effective (relativistic) mass than uncompressed.

Is it correct to say that it has a greater *rest* mass? After all, all particles are at rest.

Have particles (photons) been literally added to the spring by compressing it ?

 

[Nugatory]

A compressed spring has a greater effective (relativistic) mass than uncompressed

It has greater mass. The qualifications "effective" and "relativistic" in this context are somewhere between meaningless, potentially confusing, and just plain wrong.

Is it correct to say that it has a greater *rest* mass?

Yes, and this is equivalent to saying that it has "greater mass". The qualifier "rest" is redundant, although widely used for historical reasons.

Have particles (photons) been literally added to the spring by compressing it ?

No. Energy was added to it.

 

[Dale]

A compressed spring has a greater effective (relativistic) mass than uncompressed.

Is it correct to say that it has a greater *rest* mass? After all, all particles are at rest.

Yes, although I would say it has a greater "invariant mass" rather than "rest mass"

Have particles (photons) been literally added to the spring by compressing it ?

The rest mass of a system can be greater than the sum of the masses of the constituent particles. So it is not that there are more particles, but just the system is in a more massive configuration.

 

[1977ub]

When you are compressing a spring, does this imply that somehow in the process photonic electromagnetic energy is being absorbed by the totality of the spring particle system?

 

[Nugatory]

When you are compressing a spring, does this imply that somehow in the process photonic electromagnetic energy is being absorbed by the totality of the spring particle system?

The words "photonic electromagnetic energy" don't mean much of anything, so the question as asked doesn't have any sensible answer.

When you compress the spring you're doing work on it, and that adds energy to it. Some of that energy shows up as heat; a real (as opposed to an ideal) spring warms up from very slightly from internal friction as it flexes. Some of that energy is stored as potential energy as the atoms in the spring are pushed a bit closer to one against the electromagnetic forces that tend to hold them in place in the uncompressed spring; this energy is released when the spring is uncompressed again.

(This might be a good time to mention that photons are part of quantum electrodynamics, while special relativity is based on classical electrodynamics; there are no photons in SR and thinking about them will just confuse and mislead you. I am speaking with tongue only slightly in cheek when I say that you should do your best to forget that you ever heard the word "photon" until after you've learned SR and then ordinary non-relativistic QM.
I am not speaking with tongue in cheek when I say that whenever you find yourself tempted to say "photon" in a relativity discussion you should substitute the phrase "flash of light".)

 

[1977ub]

When potential energy is added to a system, does this imply that must arrive via some one of the fundamental particles and forces of physics? Or must it only be understood as being a feature of the "arrangement" of the molecules ?

 

[Nugatory]

When potential energy is added to a system, does this imply that must arrive via some one of the fundamental particles and forces of physics? Or must it only be understood as being a feature of the "arrangement" of the molecules ?

Generally you add potential energy to a system by moving some part of the system against some force. Lifting a weight against gravity, moving a charged particle against an electrostatic force, ...

This is all classical physics, which you need to learn and understand before you take on relativity.

 

[1977ub]

Perhaps these questions need to be in the quantum area. The nub of what I'm after is the increase in mass after potential energy increases. Is there any kind of nuts-and-bolts understanding of that. The "residual" effective mass/energy after removing mass from particles - in cases where nothing is moving, is it made of anything? In cases where potential energy increases due to moving two bodies away to increase gravitational potential, in quantum terms is the system absorbing a graviton or anything?

 

[Dale]

When potential energy is added to a system, does this imply that must arrive via some one of the fundamental particles and forces of physics? Or must it only be understood as being a feature of the "arrangement" of the molecules ?

The answer to this question doesn't really matter. If you are dealing with a system that is simple enough to be described in terms of the fundamental forces then use that. If it is a more complicated system then you approximate things until you get a tractable level of complexity and just don't worry about the fundamental level.

The nub of what I'm after is the increase in mass after potential energy increases. Is there any kind of nuts-and-bolts understanding of that.

You add two vectors and take their norm. I don't see how you can get more nuts and bolts than that. It doesn't matter if the system you are dealing with is quantum or classical. It is the same process either way.

 

[1977ub]

I can appreciate that it may not "matter" but that doesn't stop my mind from trying to analyze and model it in terms of what is here and what is there.

 

[Dale]

I can appreciate that it may not "matter" but that doesn't stop my mind from trying to analyze and model it in terms of what is here and what is there.

But you cannot accurately use QFT models until you actually learn QFT. Anything that you try to analyze about it now is done from a state of ignorance, and will be misleading at best. QFT shouldn't be done halfway, and until you are ready to do it correctly it is best to avoid it. At this level of study it will not be beneficial in any way.

In this thread in particular, you are attempting to apply QM instead of focusing on the simple classical and geometric fact that the norm of the sum of two vectors is different from the sum of the norm. A deep dive into QFT will not provide any additional insight. The resolution to your question is not quantum mechanical, it is geometrical.

 

[1977ub]

I've got something in a black box. Its mass is tested using inertia or gravitational field. Some of the things I can do to what is in there which increase effective mass are clearly a matter of *adding* *something* - say, put in some more mass, or shine some photons in. I wondered if other actions which may increase the measured mass of what is in there - such as separating the mass into two parts - also amounted to adding something to the box. If not, I can accept that.

 

[DrGreg]

I've got something in a black box. Its mass is tested using inertia or gravitational field. Some of the things I can do to what is in there which increase effective mass are clearly a matter of *adding* *something* - say, put in some more mass, or shine some photons in. I wondered if other actions which may increase the measured mass of what is in there - such as separating the mass into two parts - also amounted to adding something to the box. If not, I can accept that.

The mass of the box (i.e. the box and its contents) and the total energy of the box as measured by a frame in which the box is at rest are related by $E=mc^2$. So the only way the mass of the box can change is if energy passes through the walls of the box. Any changes within the box (e.g. conversion of potential energy to kinetic energy) cannot affect the mass of the box provided nothing is added or subtracted through the walls.

 

[1977ub]

I'm actually looking at the different ways one can open the box, do something which increases the effective mass of the box, and then closing it up. When, for example, I reach in and then move half the mass to one end and half the mass to the other end, and then close it up again, there will be a greater intertial and gravitational mass since we have increased the gravitational potential energy. Does this mean I left anything in particular in the box or no?

 

[Herman Trivilino]

The nub of what I'm after is the increase in mass after potential energy increases. Is there any kind of nuts-and-bolts understanding of that.

If the potential energy of the spring increases by $\frac{1}{2}kx^2$ then the mass of the spring increases by $\frac{1}{2}kx^2/c^2$.

This is an example of the Einstein mass-energy equivalence. You seem to be seeking some mechanism by which the energy is converted to mass, but that is a misconception. There is no conversion. The energy is mass.

 

[Nugatory]

I'm actually looking at the different ways one can open the box, do something which increases the effective mass of the box, and then closing it up. When, for example, I reach in and then move half the mass to one end and half the mass to the other end, and then close it up again, there will be a greater intertial and gravitational mass since we have increased the gravitational potential energy. Does this mean I left anything in particular in the box or no?

You added some energy to the box. Whether that counts as having "left anything in particular" or not depends on what you mean by that phrase.