# Measuring relativistic mass

## Main Question or Discussion Point

Measuring the relativistic mass and energy
When we speak about a physical quantity we should define it and it is compulsory to propose a procedure of measuring it.
But how does one measure relativistic mass? The answer lies in the fact that relativistic mass (as well as proper mass) is never really measured directly, nor is energy measured directly. As Jammer1 wrote, “As in the last analysis all measurements in physics are kinematic in nature.” So, one does not measure mass nor energy. One calculates them from measured kinematic quantities. Suppose you know the strength of a uniform magnetic field B. Launch a charged particle, of magnitude charge q, into the field such that the velocity is perpendicular to the field lines. The charge will move in a circle of radius r. B is known while r and v are measurable. Then use the cyclotron relation p=qBr to find p. Then m=p/v. Multiply by c2 to get the relativistic energy of the particle E=mc2. We have indicated a measurement procedure for a physical quantity on which physicists wish to ban.2
References
1 Max Jammer, Concept of Mass in Classical and Modern Physics, (Harper and Row, 1964, Dover 1997)
2 Lev Okun, “The concept of mass,” Phys.Today, 42, 31-36 (1989)

Do you aggree with the lines above?

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bernhard.rothenstein said:
Do you aggree with the lines above?
I don't think I could have stated it better myself. One question remains though - How does one measure the relativistic mass of a particle with no charge?

Pete

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pmb_phy said:
I don't think I could have stated it better myself. One question remains though - How does one measure the relativistic mass of a particle with no charge?

Pete
Ummm, measure its momentum in a known momentum conservation situation? Like a calorimeter; see how far it penetrates some material of known density, such as water or armor-plate steel.

Ummm, measure its momentum in a known momentum conservation situation? Like a calorimeter; see how far it penetrates some material of known density, such as water or armor-plate steel.
And how do you propose to measure the momentum? Also, a calorimeter does not measure the energy, E, of a particle. It measures, K, the kinetic energy. If the proper mass of the particle is a known quantity then what you say is a sufficient method of measuring the mass of a particle.

Pete

robphy
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I have a few comments on this multi-faceted post.

bernhard.rothenstein said:
Measuring the relativistic mass and energy
When we speak about a physical quantity we should define it and it is compulsory to propose a procedure of measuring it.
This is usually called the "Operational Method".

bernhard.rothenstein said:
But how does one measure relativistic mass? The answer lies in the fact that relativistic mass (as well as proper mass) is never really measured directly, nor is energy measured directly. As Jammer1 wrote, “As in the last analysis all measurements in physics are kinematic in nature.”
I'll have to consult the reference for more elaboration of this point. I recall a profound statement I heard in graduate school: measurements are the results of inner products with one's measuring devices.

bernhard.rothenstein said:
So, one does not measure mass nor energy. One calculates them from measured kinematic quantities. Suppose you know the strength of a uniform magnetic field B. Launch a charged particle, of magnitude charge q, into the field such that the velocity is perpendicular to the field lines. The charge will move in a circle of radius r. B is known while r and v are measurable. Then use the cyclotron relation p=qBr to find p. Then m=p/v. Multiply by c2 to get the relativistic energy of the particle E=mc2.
It may be enlightening to express a measurement such as this in the way described above.

While your procedure may be one measurement method, I think it's fair to say that it may be unnecessarily complicated [for a theoretical discussion on foundations]. (To play the critic, I'll ask how all of these other quantities are defined.) I suspect there should be a simpler measurement that can be carried out in theory.

bernhard.rothenstein said:
We have indicated a measurement procedure for a physical quantity on which physicists wish to ban.2
I don't see the point of this statement. It seems to me, the issue of relativistic mass "which physicists wish to ban" arises not out of a failure to measure it or to define it... it is an issue of pedagogy.

bernhard.rothenstein said:
References
1 Max Jammer, Concept of Mass in Classical and Modern Physics, (Harper and Row, 1964, Dover 1997)
2 Lev Okun, “The concept of mass,” Phys.Today, 42, 31-36 (1989)

Do you aggree with the lines above?

I recall a profound statement I heard in graduate school: measurements are the results of inner products with one's measuring devices.

please explain me in detail what do you mean by the statemnt. it sounds attractive
thanks

Measuring the relativistic mass and energy
When we speak about a physical quantity we should define it and it is compulsory to propose a procedure of measuring it.
But how does one measure relativistic mass? The answer lies in the fact that relativistic mass (as well as proper mass) is never really measured directly, nor is energy measured directly. As Jammer1 wrote, “As in the last analysis all measurements in physics are kinematic in nature.” So, one does not measure mass nor energy. One calculates them from measured kinematic quantities. Suppose you know the strength of a uniform magnetic field B. Launch a charged particle, of magnitude charge q, into the field such that the velocity is perpendicular to the field lines. The charge will move in a circle of radius r. B is known while r and v are measurable. Then use the cyclotron relation p=qBr to find p. Then m=p/v. Multiply by c2 to get the relativistic energy of the particle E=mc2. We have indicated a measurement procedure for a physical quantity on which physicists wish to ban.2
References
1 Max Jammer, Concept of Mass in Classical and Modern Physics, (Harper and Row, 1964, Dover 1997)
2 Lev Okun, “The concept of mass,” Phys.Today, 42, 31-36 (1989)

Do you aggree with the lines above?
No, energy can be measured. Basically, let electron pass through two wire loop to measure its speed, then hit a target, measure the temperature change to get energy, it agree with the relativistic equation of energy

jtbell
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The answer lies in the fact that relativistic mass (as well as proper mass) is never really measured directly
Proper mass can be measured using the same techniques as measuring "the mass" in Newtonian mechanics. The most fundamental way of measuring the mass of an object is to put it on a balance in a uniform gravitational field, or in an accelerating reference frame if you prefer not to deal with gravity, and thereby compare its mass with a standard mass.