# All mass is relativistic?

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## Main Question or Discussion Point

"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?

Related Special and General Relativity News on Phys.org
Nugatory
Mentor
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"

Mister T
Gold Member
"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.

jerromyjon and stoomart
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
Mentor
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.

jerromyjon
Dale
Mentor
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.

jerromyjon
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?

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?

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 vaccum (no mass involved). Einstein genarlized that from electromagnetic waves to everything else by replacing Galilean transformation with Lorentz transformation (again no mass involved).

Mister T
Gold Member
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.

SiennaTheGr8
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 (mrel). For a photon, the total mass (m) is the speed dependent mass (mrel) 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 (mrel). 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.

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jbriggs444
Homework Helper
2019 Award
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.

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

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PeterDonis
Mentor
2019 Award

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

Mister T
Gold Member
berkeman
Dale
Mentor
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.

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

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.)

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.

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, 1977ub and Dale
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.

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.

1977ub