If I disregard the distinction between passive and active gravitational mass, then we generally associate two types of masses with an object, namely, inertial mass (mI) that appears in F=mIa and gravitational mass (mG) that appears in F=GmGM/r2 for the same object. While this is the theoretical explanation, these equations are meaningless writing unless we provide physical interpretations to those through experiments. Then comes the question that how we measure mI and mG of the same object whose motion is getting studied so as to verify the above equations. Therefore, the question arises whether the unit, in terms of which mI and mG will be expressed, itself is an inertial mass unit or a gravitational mass unit.
I shall be glad if anyone can explain this.
According to the equivalence of gravitational and inertial mass, it does not make sense to have two different units for two types of masses. I think that also from a historical and metrological point of view, the kilogram (and earlier types of units) were introduced as units for both types of mass, which were assumed to be identical even before the experimental proof of the 19th and 20th centuries. In metrological practice, the mass of a body is usually measured with a balance, i.e. as a gravitational mass, not with a pendulum as an inertial mass. But I would not conclude from this practice that the kilogram is the unit of the gravitational mass.
Hi Dr Abhishek Majhi . I think Inertial mass is a mass parameter giving the inertial resistance to acceleration of the body when responding to all types of force. Gravitational mass is determined by the strength of the gravitational force experienced by the body when in the gravitational field g.
See the link: https://www.britannica.com/science/inertial-mass
Also, mass is both a property of a physical body and a measure of its resistance to acceleration (rate of change of velocity with respect to time) when a net force is applied. An object's mass also determines the strength of its gravitational attraction to other bodies. The SI base unit of mass is the kilogram (kg). See the link: https://en.m.wikipedia.org/wiki/Mass
Also, See the link: https://www.bbc.co.uk/bitesize/guides/z37jng8/revision/3
Generally, they should be equal, but I mean that the inertial mass is more general as it does not depend on the gravitational constant (which is not precisely known) and on the mass of the attracting body. Anywhere in the universe, to measure the mass, just apply the force F and measure the acceleration.
“…If I disregard the distinction between passive and active gravitational mass, then we generally associate two types of masses with an object, namely, inertial mass (mI) that appears in F=mIa and gravitational mass (mG) that appears in F=GmGM/r2 for the same object….”
- yeah, the inertial and gravitational masses are fundamentally different, and so that
“……While this is the theoretical explanation, these equations are meaningless writing unless we provide physical interpretations to those through experiments. Then comes the question that how we measure mI and mG of the same object whose motion is getting studied so as to verify the above equations. …..”
- is again correct, with a small correction, though: in the formulae above there is no “theoretical explanation”, since any real scientific explanation is evidently possible only if the both masses are scientifically defined. What is principally impossible in the official physics, since in mainstream philosophy and sciences, including physics, the fundamental phenomena/notions “Matter” and “Inertia” are really completely transcendent/uncertain/irrational; and so any explanations in framework of the mainstream can be only some transcendent/uncertain/irrational mental construction.
The definitions of the phenomena above, and practically of all other fundamental phenomena/notions, are possible, and are given, only in the Shevchenko-Tokarevsky’s “The Information as Absolute” conception https://www.researchgate.net/publication/260930711_the_Information_as_Absolute DOI 10.5281/zenodo.268904, and the informational physical model, for first reading see https://www.researchgate.net/publication/342600304_The_informational_physical_model_some_fundamental_problems_in_physics DOI: 10.13140/RG.2.2.12325.73445/3, which is based on the conception.
Concretely real scientific explanation of the equivalence of inertial and gravitational masses is obtained in the initial 2007 Gravity model in the informational physical model above, see https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics ; https://arxiv.org/abs/0707.4657 , section 2.9 “Mediation of the forces in complex systems”:
- all particles are close-loop algorithms, which constantly run – cyclically ticking with a frequency ω, and so having energy E=ћω=mIc2; mIis inertial mass, c is the speed of light, and every particle has also completely symmetrical charge of the fundamental Nature force “Gravity” - “gravitational mass”, mG, – which [the charge] also is proportional to the same frequency ω; and so the masses are equivalent at least at statics.
Gravity is real Force, and acts on all/every material object – unlike other fundamental Nature forces [Weak, E/EM, and Strong Forces], which act only in some concrete cases - Gravity is completely universal and symmetrical Force, in Matter everything attracts everything,
- and to describe this force action on the material objects, whereas also everything in Matter has Inertia, and so inertial mass, whereas any force’s action is defined by the equation F=mIa, for the gravitational impact be the same as other forces for the same acceleration, a, in the corresponding equation, i.e. Newton’s gravity law, the corresponding coefficient – the gravitational constant G is introduced,
- so that both masses are measured in the same “kilogram”; though, again, that hasn’t explanation in official physics, and so it is introduced purely ad hoc, - so the thread question is quite natural.
More see the links above, to read some other SS posts on RG in attached PDF Gravity_detail_12 _03_21.pdf and the SS posts in
https://www.researchgate.net/post/Plancks_particle_Plancks_time_Plancks_lengthit is useful as well.
Cheers
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