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At macroscopic level we can observe inertia. But what explanations are there for Inertia at molecular/atomic/quantum level?

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  • $\begingroup$ What explanation is there for inertia at the macroscopic level? Why would it be different at a microscopic level? $\endgroup$ – Jon Custer Jun 15 at 11:01
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The basic concept remains the same: A given electrostatic field (for instance in a simple accelerator of the type Van de Graaf) will accelerate a beam of protons far less than it will accelerate a beam of electrons, because the protons have a heavier mass.

The detailed calculation is more complex than in the Newtonian description, because at speeds at which the relativistic effects become noticeable, they have to be take into account, but the basic idea is still the same.

Answering a question from the comments:

"Is inertia seen at macro level is the sum of inertia of all individual atoms?"

Yes, that is nearly exactly that (with a small nuance).

for one particle of mass M:

$$ f = m .a$$

for N identical particles of mass m:

$ f_i = m_i . a_i$ individually, for I = 1..N

Since they are identical:

$$m_i = m$$ $$a_i = a$$ $$f_i = f$$

for all i (for all particles).

If the relation $f = m.a$ is true for one particle accelerated on its own, then is is also true for each individual particle accelerated separately in a set of completely independent particles.

Summing up the N independent equations:

$$ f_1 + f_2 +... f_N = m_1 . a_1 +... + m_n . a_N$$ or $$ N. f = m . N . a$$

or $$F = M.a$$ with $F = f_1+...+ f_N$ and $M = m_1+...+ m_N$

Conclusion:

Since the the relationship between mass and acceleration is linear with respect to mass, accelerating to a given acceleration $a$ a body which is N times heavier than a particle of mass $m$ requires the application of N times a given force f, exactly as if the large body (of mass $M=N.m$) was made up of N smaller bodies of mass $m$.

In other words, your intuition is correct: The inertia (or mass) of a body is indeed the sum of the inertia of its constituent parts.

Another words, within the limits of classical mechanics, inertia is nothing else than a a measure of the amount of matter (the amount of "stuff") within a physical object: The more "stuff" there is in an object, the more harder you have to push to get it to move.

Or stated otherwise: "The more bricks you have in a bag, the harder it is to throw it".

Why is there a nuance a the subatomic level?

  1. Bonds (within atoms and nuclei) need energy and eat up a fraction of the mass. So the mass of a fissile Uranium isotope (${}^{235}U$) is slightly less than the mass of its constituent parts, the missing mass is borrowed by bonding forces and transformed into a bonding energy (the missing mass m becomes energy according to Einstein's formula ($E = mc^2$)

  2. At an even lower level, the mass of elementary particles (at least according to the standard model of elementary particles) arises from the degree of interaction of a particle with the Higgs field. So to formulate it naively, on one hand massive objects have mass because they contain a lot of particles, but on the other hand, the smallest particles know to this day, in the light of the standard model of elementary particles, acquire a part of their ("elementary") mass on one hand by interacting with the Higgs field with permeates all of space (the more they interact with the Higgs field, the more they are slowed down by said field), on the other hand the remainder of their mass being in the form of internal energy ($E = mc^2$).

How literally should you take "The Higgs boson gives other particles mass"?

One last nuance

The answer above implicitly assumes that mass is the only expression of inertia. In classical physics it is true. However more generally, the expression of inertia if really given by the momentum of a body. Particles with no mass, like the photon, have no mass, but they have momentum:

https://en.wikipedia.org/wiki/Photon#Relativistic_energy_and_momentum

$p=\frac{h\nu}{c}$

with $h$: Planck's contant and $c$: speed of light

Which explains why a beam of light can actually be bent by gravity (as if it was made up by particle with a non-zero mass), see gravitational lensing:

https://en.wikipedia.org/wiki/Gravitational_lens.

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  • $\begingroup$ At all scales, from a planet down to an elephant, down to an electron, the mass (inertia) m of a body measures its reluctance to accelerate under the influence of a force f, according to Newton’s law: $$ a = f / m $$ At a much lower level, mass (which still plays the same role) can be further shown to stem from a coupling of a particle with the Higgs field (hence giving an origin to the mechanism of mass, but without altering the notion of inertia) $\endgroup$ – Serge Hulne Jun 16 at 10:17
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If you are asking that the exact Classical Mechanic meaning of INERTIA get carried over to Quantum scales then the answer is NO. What is more important to know is that when you have two theoretical frameworks, it is very rare that the exact meaning of a property in a framework gets carried over to the other. And so this answer is not very important.

Classical Mechanics as a theoretical framework, is a deterministic framework, while the microscopic world is looked upon by Quantum Mechanics, which is a Probabilistic theory. The point here is these to theories are fundamentally different and so it is not surprising the definition in one not getting carried over to the other.


Now, if you are asking whether the notion/idea of inertia gets carried over to microscopic scales. Then the answer is a huge YES. The essential idea behind inertia is the fact that any system/body requires some sort of energy/perturbation to change its state once the system is in a stabilized form.

In the general scenario, stabilized form corresponds to equilibrium/ground states and so the notice of inertia can be refines as "any stationary system will indefinitely remain in that state unless acted upon by external perturbations". This notion is insanely fundamental that, it can directly be attributed to the Second Law of Thermodynamics.

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The wavefunction of a single atom may mean, the particle's velocity is uncertain/probabilistic. But when all the atoms are taken together to make a macroscopic object- I think that leads to a wavefunction which has more precise velocity, for that macroscopic body. The wavefunction concept can be neglected for a macroscopic object, and we can treat it classically.

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