Difference between inertia and momentum?

[Philip Wood]

Absolutely no intention to cause acrimony.

 

[Studiot]

Not you Philip

 

[russ_watters]

What you are missing is, for example, a TV broadcast of some football game where the announcer talks about some running back having a lot of inertia because he was running so fast. When used in a lay sense, people do use the term "inertia" to sometimes mean mass and sometimes mean momentum.

Ok, I see - it isn't that the two terms are interchangeable, it is that they are often incorrectly used interchangeably.

That lay sense is the only sense that counts because the term "inertia" is rarely used in a technical sense.

I am against allowing laypeople to corrupt the definition of a word even if scientists no longer use that word. Incorrect usage should be corrected, not seen as a reason to discard the word.

Re Galileo's law of inertia, aka Newton's first law. It is important to remember the context of the time. Aristotelean physics was the dominant world view prior to Newton. The Aristotelean point of view was that objects naturally "wanted" to be at rest. Galileo, later reinforced by Newton, turned this point of view upside down. Objects naturally "want" to remain in the same state they were in unless acted upon by an external force.

Understood, but since everyone has to start somewhere with the learning of physics, don't most people have to learn what you just said? Doesn't that require exposure to the word "inertia"?

The law of inertia is a qualitative law. There is no quantitative measure of what constitutes "inertia" in that law. If a net force does not act on an object, the object continues along its merry way, unchanged. If a net force does act on an object, the object does changes behavior, but in some unspecified way. The law of inertia is moot on this. You need to look to the second law to quantitatively determine how a force change the behavior of some object. The second law does not use the term "inertia". It is phrased in terms of either momentum or mass and acceleration, depending on whose reading you are reading. But never inertia.

It sounds like you are saying mass and inertia are not proportional? That inertia is qualitative only? That it is improper to say an object with more mass than another has more inertia? Is this, from the wiki on "inertia" incorrect?

Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. It is proportional to an object's mass.

And from a student site?:

Mass as a Measure of the Amount of Inertia
All objects resist changes in their state of motion. All objects have this tendency - they have inertia. But do some objects have more of a tendency to resist changes than others? Absolutely yes! The tendency of an object to resist changes in its state of motion varies with mass. Mass is that quantity that is solely dependent upon the inertia of an object. The more inertia that an object has, the more mass that it has. A more massive object has a greater tendency to resist changes in its state of motion.

http://www.physicsclassroom.com/class/newtlaws/U2L1b.cfm

It is ambiguous (does it mean "mass" or "momentum?)

Based on the above it seems pretty clear to me that it doesn't mean momentum and is proportional to (is an effect of) mass.

Inertia is IMHO a term we should stamp out...
and outdated (do we really need to keep fighting against Aristotelean physics ~300 years after Newton, ~400 after Galileo?).

No fighting required - I get that as a subject advances, the language evolves, but I think students need to learn that history and understand the evolution of the terms.

 

[RedX]

Inertia is mass. Mass is scalar, the same no matter how fast observer.
Momentum is vector. Momentum depends on velocity of observer.

Something similar happens when we consider elementary particles transforming though their abstract gauge group as they propagate in time. Their inertia is expressed with a mass matrix and when this is diagonalized we have the physical particles. This is why/how for example "hyper-charge" and "weak isospin" combine to give electrical charge. It is in the inertia of the elementary particles which breaks the gauge symmetry by failing to align with the gauge charges. Along this same vein, neutrino flavor oscillations are analogous to the precession process I mentioned for free rotating objects... the mass matrix is not diagonal in the same basis as is the "flavor matrix".

Ok, maybe that's TMI but some may find it interesting.

I find that interesting, but I'm not sure I follow. How do particles transform through their gauge group as they propagate in time? Don't mass matrices transform under say U(n), while gauge groups tend to be of the SU(n) and U(1) type?

Don't hypercharge and weak isospin combine because choosing a vacuum state preserves the symmetry of transformations generated by that particular combination of generators? So for example although W¹ and W² don't have a definite charge, W^{\pm}=W^1 \pm i W^2 do have definite charge, and you're saying this is only because W^{\pm} have definite mass/are the mass eigenstates? I'm troubled by that imaginary combination, but don't W¹ and W² have the same mass anyway, so that any linear combo would also have the same mass?

Also, what gauge group corresponds to neutrino oscillations, if it's inertia that corresponds to failing to align to gauge charges?

 

[jambaugh]

I find that interesting, but I'm not sure I follow. How do particles transform through their gauge group as they propagate in time?

That is what the gauge potential (affine connection) determines.
D_\mu = \partial_\mu + iW_\mu

Don't hypercharge and weak isospin combine because choosing a vacuum state preserves the symmetry of transformations generated by that particular combination of generators?

Yes, but the reason that this choice of vacuum doesn't preserve ALL the gauge groups is the breaking of the symmetry (for the ground state=vacuum) via e.g. the Higgs mechanism which determines the inertia of the physical particles.

In the discussion here people keep speaking of "no momentum for stationary particles" which is not correct in the relativistic setting where momentum -> momentum-energy.

Here's a more concrete analogue. Consider light moving through a transparent material. The coupling of light to the matterial gives the photons an effective mass and they travel at less than c. This effective mass can be seen as coming from the inertia of the charge carriers of the material (it's inertia) to the e-m field of the light.

Now break the symmetry (in this case rotation sym), consider a birefringent crystal. Since the crystal couples differently to different photon polarizations you get different effective masses for the two transverse polarizations relative to the crystal alignment. The vertical photons and horizontal photons, while in this crystal behave like distinct types of particles with different masses.

This is an imperfect analogue since one is breaking a non-gauge symmetry but I think it shows some of the features.

So for example although W¹ and W² don't have a definite charge, W^{\pm}=W^1 \pm i W^2 do have definite charge, and you're saying this is only because W^{\pm} have definite mass/are the mass eigenstates? I'm troubled by that imaginary combination, but don't W¹ and W² have the same mass anyway, so that any linear combo would also have the same mass?

You have the W^1, W^2 and W^3 modes of the SU(2) gauge field, or in a different basis W^{\pm},W^0. Each modulo iso-rotations.

In the absence of symmetry breaking we'd have a continuum of superpositions of weak bosons, each massless, as well as massless hyper-photons. Apply the Higgs field, which creates a non-trivial weak-isospin-hypercharge vacuum. As with the analogue of the birefringent crystal, the masses of the gauge bosons are no-longer exactly zero but one has a mass matrix. In its eigen-spaces we have W^{\pm} (realtive to a particular isospin direction I_z) and we have the photon and the weak boson Z_0 as superpositions of the hyper-photon and W^0 boson fields which have respective 0 and non-zero "eigen-masses".

This also causes the leptons to split into heavier electrons/muons/tauons, vs lighter neutrinos.

Also, what gauge group corresponds to neutrino oscillations, if it's inertia that corresponds to failing to align to gauge charges?

This is a bit more strained but one supposes a separate SU(3) flavor mixing "symmetry" manifesting at a much higher energy. It breaks in a similar fashion as above giving e.g. electrons, muons, and tauons different masses. There is a distinction since we do not see manifest gauge bosons for the flavor group (unless this broken SU(3) is restored inside the nucleon somehow and it is the same as the color gauge...wild speculation there!)

But ultimately for neutrinos to oscillate they must a.) have masses and b.) the eigen-masses must be superpositions of the flavors identified with the quarks and non-neutrino leptons. In other words the mass matrix for one half of the weak doublets must be different slightly than for the other half of the weak doublets. The flavor spectrum which gives eigen-masses for electrons, muons, and tauons must not quite give eigen-masses for the corresonding neutrinos. So as these propagate they must oscillate through the flavors. This oscillation is at the "beat frequency" for their distinct phase frequencies given momentum is conserved but masses are distinct.

 

[ravisastry]

can interia be applicable to force fields also ?