The principle behind Inertia and it's connection to Equilibrium

Inertia is the tendency of a force-free body to remain in that state or it is something that opposes any act of changing its equilibrium state. Mass is a measure of inertia. I have some questions regarding inertia and equilibrium:

1) Is there a scientific explanation why inertia happens?

2) Is inertia a necessary criterion for equilibrium?
If so, then would it be applicable to less massive (I mean the fundamental particles that make up the matter) or massless particles also?

For example, the speed of light through vacuum is constant which means the photons are in equilibrium. But photons are massless entities. Do they too have inertia? If so is it necessary for equilibrium to be stated in terms of inertia?

• Please see our guide on writing good titles. – user10851 Apr 16 '16 at 18:27

Science never answers "why" questions, so in a strict sense there is no such explanation, but one can try to triangulate where we stand, at the moment.

In classical physics space, time and the existence of massive bodies are inexplicable pre-physical facts. Inertia then becomes an observed property of massive bodies that allows to differentiate them by their mass. Together with the observed homogeneity of space and time and the isotropy of space much of classical physics follows from there.

Relativity unifies space/time and energy/momentum (including rest mass) and inertia becomes a necessary property of systems with localized binding energy, but relativity alone can't describe the internal details of such systems. For that purpose we need quantum mechanics, more precisely quantum field theory. At this level we get to learn that the symmetry properties of spacetime have very profound consequences for matter and its interactions, but we are still short of having found a self-consistent explanation for spacetime itself. So one could say that among the classical mechanics triad space/time/matter, which is needed to "have a home for inertia", we have succeeded somewhat in understanding matter to some extent and we have (somewhat) unified space and time, but the fundamental object of "spacetime", which gives rise to all of this, is still not understood.

For me, and this is an opinion, of course, the fundamental question of "How does inertia really work?" (which goes beyond "What does inertia do?"), can not be successfully answered until we have made successful inroad into the "How does spacetime really work?" question. I do not expect rapid experimental and observational progress on that front because spacetime has turned out to be an extremely smooth object, so far... and we just don't have the right microscopes, yet, to see the structures in it that will get us towards a microscopic understanding.

Does one need inertia for equilibrium? No, but without it there can't be anything else. In classical physics inertia sets the velocity scale and without it dynamic equations are meaningless. In relativity all systems without rest-mass are moving at the same velocity in all observer systems, which is not very interesting. What makes the world so rich is the interplay between massive and massless fields. I believe the theoreticians can explain why one can't exist without the other, but I don't think that answers your question, either.

Newton's 1st law states, as you rightly say, that a force-free body maintains its state of motion. (This also holds in relativity.)

Newton's 2nd law states, that if there is a net force on the body, the body will accelerate in the direction of that force, $\vec{F}=m\vec{a}$. (This will be altered a bit in relativity, but for simplicity, let's stick with Newton.) As you see, for a given force, the acceleration $a$ is inversely proportional to inertia $m$, which here is a synonym for mass.

This has nothing to do with equilibrium.

In "main stream physics", you take this as a given fact: it is the inertia of a body which defines its mass. (Another definition of mass is by gravitation, but let's not get astray.)

In the past, however, there have been attempts to derive this inertial mass from something more fundamental. An attempt that I know of was by Mach who thought inertia came from the presence of all the other masses in the universe.

ps> Photons are special since they are quantum and relativistic. They have no rest mass and you can't accelerate them.

• "This has nothing to do with equilibrium."- How it has nothing to do with equilibrium? When there is no force, the object's energy (both kinetic and potential) remains constant which is one criteria of equilibrium states. Also the force is mass dependent. You need to apply two different forces to make two different masses to the same acceleration. So greater the mass, greater the force you need to change it's state. So greater the mass, greater is inertia – UKH Apr 14 '16 at 10:48
• Your initial question on equilibrium was: "Is inertia a necessary criterion for equilibrium?" The answer is no. Here is why: Take a mass $m$, at rest in a frame $R$, with two equal but opposite forces acting on it. Certainly, this mass is in equilibrium, ie it stays at rest. This is so no matter how big $m$ is. So you may take the $m\to 0$-limit of this result and you see that you get equilibrium even without mass/inertia. – Stesh Apr 14 '16 at 10:59
• Your conceptions about photons seem to be misguided. They are relativistic quantum objects that cannot be accelerated by acting upon them with an external force. They have no rest mass, $m=0$, but they do have energy, $E=h\nu$. They are absorbed/emitted by quantum processes involving charges. The only thing I can think of that acts on a photon in a "force-like manner" is gravitation. General Relativity tells you how to deal with that, and you end up with a photon still travelling at the speed of light $c$, but having another frequency. (Search for: gravitational red-shift) – Stesh Apr 14 '16 at 11:10
• Sorry that it seems my question misguided you. The question was not whether a photon can be accelerated. I just asked is there the phenomenon of inertia at the fundamental particle level. A photon could travel at the speed of light. It cannot be accelerated. So I thought a photon is having infinite inertia, even though it's rest mas is zero. This confusion is what I discussed through my question. But a particle like electron have only less mass which means it has a lesser inertia. So it is very much vulnerable to external force – UKH Apr 14 '16 at 11:35
• The particles at microscopic level behave a little bit differently. Applied in that case, the term inertia seems too be hardly confusing. So I just thought whether it is possible to give a microscopic description of what inertia is about. Thank you for sharing your knowledge with me. It was really informative. – UKH Apr 14 '16 at 11:38

Answer:1 Mass is just a form of potential energy of a gravity wave of relativistic bent time space and light is a gravitational wave of bent space, when it travels at the velocity of C, where time relativistically slows down. At that velocity (with time dilation) it makes a gravity wave into the photon. because it is traveling relativistic-ally it is slowing time and bending space. I hope this answer is enough to give answers to both your questions.

• I'am afraid that this is not an answer to my question. – UKH Apr 14 '16 at 10:45
• But you can interpret some relations for your answer from it – Mahin Apr 14 '16 at 16:20