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Mass and inertia are interchangeable, but no intuitive explanation of mass being different for the various particles is known to me.

The question I have is: since mass and energy are interchangeable, what drives the change-over from mass to energy and vice versa? Further, does a mathematical model exist that details the change-over in a moment-by-moment way ( or even femto-second by femto-second manner ) so that the transition between the two states can actually be studied in slow motion if you will. Further, it would be most helpful that a layman's version of such mathematical model is readily available so as to bring arcane discussions into my comprehension. I only got a grade of "B" in calculus.

TomFosdick2019
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  • The Standard Model of particle physics has a different explanation of mass that involves the Higgs field. Your explanation would be considered non-mainstream as there are no mainstream theories about particles hooking into the fabric of spacetime. This is because spacetime isn’t really like a fabric at all. – G. Smith Jul 11 '19 at 02:49
  • relevant question and answers https://physics.stackexchange.com/q/489241/ – anna v Jul 11 '19 at 03:39
  • "You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don't move?" Mach's principle. – Cinaed Simson Jul 11 '19 at 04:34
  • The field of study of inertia is called classical mechanics. The origin of inertia is a transfer of energy and momentum according to the Least Action Principle. There is no mystery, only misconceptions in your question like, "relative to the fabric of spacetime". – safesphere Jul 11 '19 at 15:44
  • Mass is a (very concentrated) type of energy. – PM 2Ring Jul 13 '19 at 04:38
  • Your 2019-07-13 02:44:52Z edit has replaced the existing question with an entirely new one. However, the design of stackexchange is that when you want to ask a new question you don't replace an existing one: you start a new page. If you want to I can delete my answer (which addressed your previous question), so that stackexchange will allow you to delete this page. – Cleonis Jul 13 '19 at 07:27

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In order to go into your question I must first say some things about doing physics in general.

In the history of physics we see a progression to unification. A vivid example is the way Kepler's three laws of planetary motion were unified by Newton's laws of motion. Newton's law of universal gravity holds good universally: that is in itself sufficient reason to regard it proven beyond reasonable doubt. At the same time, gravity itself is unexplained

Throughout the history of physics you clearly see that succesful physicists never allowed themselves to be bogged down by insisting on ever deeper explanation. It's a judgement call; Newton did move beyond Kepler's laws, but Newton accepted gravity as is. You pick your battles.

Inertia

As far as I'm aware of, in mainstream physics inertia is regarded as something that must be granted as is, in order to frame any theory of motion. As explained above, probably that is the best possible attitude. If a problem has no prospect of making progress then don't let that bog you down.

The closest analogy for inertia that we have is an electromagnetic phenomenon that is called 'inductance'. A coil with self-induction will oppose change of current strength. When you apply an electromotive force you get a steady rise of current strength. If you have a current going, and you suddenly open the circuit, an electric spark will jump the gap, because the self-induction opposes change of current strength.

Some additional remarks:
In the comment section someone mentioned the Higgs field. I must emphasize: the Higgs field is not an attempt at accounting for inertia.

For instance, in the Standard Model neutrino's are described as having non-zero mass, but that mass is not described as arising through interaction with the Higgs field.

For more information see the 2007 article 'The origin of mass' by Jim Pivarski, particle physicist

Quote from Jim Pivarski:

[...] protons and neutrons are known to be made of quarks, bound by an incredibly strong force called The Strong Force. Converted into conventional units, quarks attract each other with forces typically greater than 15 tons. The potential and kinetic energy of the quark orbits account for 99% of the mass of protons and neutrons; only the last 1% is due to the mass of the quarks themselves. This is relativistic mass in an extreme case — we are made, almost entirely, out of the attraction of quarks.

About relativistic mass:
Relativistic physics describes that energy that is confined to a region of space has a corresponding inertial mass.

That is why I emphasize that the Higgs field is not an attempt at accounting for inertia.

Cleonis
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