Inertial vs Gravitational Mass "mystery"?

[Ghost117]

Hi everyone,

I read in a first year textbook (K&K) that the reason why "gravitational mass is proportional to inertial mass" is a big "mystery"...

Can someone please explain why this is a mystery?

Thanks

 

[A.T.]

Can someone please explain why this is a mystery?

Because we don't know it.

 

[dextercioby]

It's one of the postulates of classical Newtonian mechanics. Can't really do without.

 

[Ghost117]

Why is inertial mass "operationally distinct" from gravitational mass in the first place? Isn't mass just the amount of 'stuff' that makes up an object? All equations we input mass into require the same Kg value, don't they?

 

[A.T.]

Why is inertial mass "operationally distinct" from gravitational mass in the first place? Isn't mass just the amount of 'stuff' that makes up an object?

Replacing the word "mass" with the word "stuff" doesn't offer any new insight. You just have "gravitational stuff" vs. "inertial stuff".

 

[mfb]

Why is inertial mass "operationally distinct" from gravitational mass in the first place? Isn't mass just the amount of 'stuff' that makes up an object? All equations we input mass into require the same Kg value, don't they?

Compare it to electromagnetism, where the "gravitational charge" is replaced by the electric charge, and inertial mass is still inertial mass. There is no special reason why electric charge and mass should be proportional - and in fact they are not. Why is this different for gravity?

 

[Ghost117]

@A.T.

That's my point though, why make the distinction at all? But mfb's question is starting to clarify this...

@mfb
I think I'm starting to get it... So you're really asking: why is M present in both

and

while it's absent from the formula for electric charge?

 

[A.T.]

You're really asking: why is M present in both

and

while it's absent from the formula for electric charge?

Or, why is charge absent from the formula for gravitational attraction?

 

[A.T.]

That's my point though, why make the distinction at all?

Why don't make a distinction, because observation tells us they are the same. But it doesn't tell why they are the same.

 

[Ghost117]

"Or, why is charge absent from the formula for gravitational attraction?"​

Hmm... because Gravity isn't unified with Electromagnetism (yet)... ?

But even if it was, wouldn't the same question exist? Couldn't we just ask "why is M present in all 3 formulas" ?

... I guess maybe that's the mystery: why should the same value exist in completely separate formulas at all...

If that is the mystery, that's definitely interesting

 

[A.T.]

But even if it was, wouldn't the same question exist?

Yes, the "why?" is always a "mystery" in physics.

 

[Ghost117]

hmmm... yea, it's definitely one of those mysteries then...

Thanks everyone :)

 

[MrRobotoToo]

General relativity provides a resolution of sorts.

Q: Why do all objects fall identically in the same gravitational field, regardless of their mass?

A: Because they're following a geodesic through curved spacetime. A geodesic is a geodesic is a geodesic: it doesn't depend on the peculiarities of the objects that move along it.

 

[Ghost117]

General relativity provides a resolution of sorts.

Q: Why do all objects fall identically in the same gravitational field, regardless of their mass?

A: Because they're following a geodesic through curved spacetime. A geodesic is a geodesic is a geodesic: it doesn't depend on the peculiarities of the objects that move along it.

I guess I'll put this question on the shelf, till I get to GR...

 

[Matterwave]

General relativity provides a resolution of sorts.

Q: Why do all objects fall identically in the same gravitational field, regardless of their mass?

A: Because they're following a geodesic through curved spacetime. A geodesic is a geodesic is a geodesic: it doesn't depend on the peculiarities of the objects that move along it.

That gravity can be modeled by space-time curvature is a direct consequence of the equivalence principle (inertial mass = gravitational mass), so it's really more of a chicken-or-egg thing in GR.

 

[Buckleymanor]

Replacing the word "mass" with the word "stuff" doesn't offer any new insight. You just have "gravitational stuff" vs. "inertial stuff".

Ghost117 goes onto say in his post that all the equations we input mass into require the same KG values.May-be you missed that or don't consider that this allso offers any insight.
If you consider that inertial mass is measured by the KG values that we impose upon them which in turn is from the gravitational values we have found by weighing them using KG, then it's not really surprising that there is no difference between the two.
You might get some subtle arguments that say that inertial and gravitational mass could be different depending where in the universe they are measured.
It's doubtfull if the local unit of measurment is used whatever that might be:)

 

[harrylin]

"Or, why is charge absent from the formula for gravitational attraction?"​

[..] Couldn't we just ask "why is M present in all 3 formulas" ?
... I guess maybe that's the mystery: why should the same value exist in completely separate formulas at all...
If that is the mystery, that's definitely interesting

Ghost117 goes onto say in his post that all the equations we input mass into require the same KG values.[..] If you consider that inertial mass is measured by the KG values that we impose upon them which in turn is from the gravitational values we have found by weighing them using KG, then it's not really surprising that there is no difference between the two.[..]

Indeed - it's also a mystery to me, why matter has both the properties of gravitation and inertia.
However, with that given, I cannot find a mystery in two stones weighing twice as much as one stone, and also resisting acceleration twice as much. Consequently Newton assumed (argued) that they are proportional. Thus it remains a mystery to me why, at least in classical mechanics, for some people the proportionality is a mystery - or even a "big mystery"...

 

[DrStupid]

That gravity can be modeled by space-time curvature is a direct consequence of the equivalence principle (inertial mass = gravitational mass)

Can you explain this within GR?

 

[Matterwave]

Can you explain this within GR?

What do you mean? Do you mean "can GR explain the equivalence principle?" In that case, no, the equivalence principle is a foundational principle of GR, and just like the principle of relativity is not explained by SR, but simply taken as experimental fact, the equivalence principle is similarly taken as experimental fact in GR.

However, I can explain why equivalence principle leads to space-time curvature model of gravity. This is because all things fall along geodesics. There can be no "gravity shielding" like there can be for the E&M force (neutral particles are not affected by it) and so the equivalence principle gives you the ability to formulate a theory in which all things fall in the same way. In this way, the theory of gravity can be modeled as intrinsic to the background gravitational field and independent of the object on which it is acting. If you tried, for example, to formulate a space-time curvature formulation of E&M, you would have to explain why different things fall differently...and so the space-time curvature would be different depending on the charge of the object that is falling through it. This would not be a very useful theory.

 

[Ghost117]

If you tried, for example, to formulate a space-time curvature formulation of E&M, you would have to explain why different things fall differently...and so the space-time curvature would be different depending on the charge of the object that is falling through it. This would not be a very useful theory.

But wouldn't that allow control over 'gravity'? I mean, if we could control the curvature of spacetime via the electrical charge of an object, then that should grant us control over gravity, no? ... Or maybe I'm misunderstanding what you said?

 

[DrStupid]

What do you mean?

I mean a closed line of argument from "inertial mass = gravitational mass" to "gravity can be modeled by space-time curvature" without using classical mechanics. You could start with the definitions of inertial and gravitational mass in GR.

However, I can explain why equivalence principle leads to space-time curvature model of gravity. This is because all things fall along geodesics.

Where does this comes from? Does it result from the weak equivalence principle and if yes how?

There can be no "gravity shielding" like there can be for the E&M force

ditto

and so the equivalence principle gives you the ability to formulate a theory in which all things fall in the same way.

Is the equivalence principle sufficient for this purpose or do I need something else?

 

[mfb]

But wouldn't that allow control over 'gravity'? I mean, if we could control the curvature of spacetime via the electrical charge of an object, then that should grant us control over gravity, no? ... Or maybe I'm misunderstanding what you said?

Do you have "control" over gravity just because you can move masses around? This is the same question.

 

[Ghost117]

Do you have "control" over gravity just because you can move masses around? This is the same question.

No, but if we could control the curvature of spacetime with electromagnetic forces, then we wouldn't need to move masses around, and this would give us control over gravity, no? Wouldn't this be a direct consequence of what Matterwave described as " a space-time curvature formulation of E&M" ?

 

[Matterwave]

But wouldn't that allow control over 'gravity'? I mean, if we could control the curvature of spacetime via the electrical charge of an object, then that should grant us control over gravity, no? ... Or maybe I'm misunderstanding what you said?

You misunderstood what I said. My point was not that the E&M force allows us to "control space-time curvature", it's that the E&M force is not a good candidate to be described by a "space-time curvature" theory. Unlike the gravity.

 

[Ghost117]

Thanks for clarifying Matterwave

 

[Matterwave]

I mean a closed line of argument from "inertial mass = gravitational mass" to "gravity can be modeled by space-time curvature" without using classical mechanics. You could start with the definitions of inertial and gravitational mass in GR.
Where does this comes from? Does it result from the weak equivalence principle and if yes how?
ditto
Is the equivalence principle sufficient for this purpose or do I need something else?

That gravity can be modeled by a "space-time curvature" theory requires the stronger form of the equivalence principle, either the strong equivalence principle, or at least the Einstein equivalence principle. You need not only that masses fall the same way, but that other fields behave the same way under the influences of local gravity as they do under acceleration. We must not be able to tell with local measurements whether our (boxed off from the outside) laboratory is floating in the vacuum of space or if its free-falling in a gravitational field. This requires things like light (in terms of single streaming photons), which has no inertial mass and no gravitational mass, to fall the same way when it is in a gravitational field.

Whether the equivalence (strong) is sufficient to derive a "space-time curvature" theory of gravity, depends on the exact specifics of what we mean by a "space-time curvature theory". It is not sufficient to derive GR, for example, because GR also relies on the principle of (local) relativity, as well as the principle of the constancy of the (local) speed of light (the postulates of SR). In addition, the constants within the Einstein Field Equations are derived from matching GR to Newtonian gravity in the weak field limit. So, the equivalence principle itself is certainly not enough to derive GR. However, the equivalence principle gives us a strong indication that some "space-time curvature" theory is possible. It won't narrow down which of a whole class of theories is correct; however. There are different "curvature" theories that obey the equivalence principle.

 

[DrStupid]

That gravity can be modeled by a "space-time curvature" theory requires the stronger form of the equivalence principle, either the strong equivalence principle, or at least the Einstein equivalence principle.

That means the original statement was wrong?

 

[David Carroll]

Is it a "mystery" because it is paradoxical that two massive objects attracted toward each other should both experience resistance to their respective accelerations due to their masses and experience increased attraction due to their masses? It's not paradoxical for the other fields because given a field strength, more mass resists acceleration quite simply, I imagine. Does inertial mass even figure into equations for force between two massive objects gravitationally attracted to each other?

 

[Matterwave]

That means the original statement was wrong?

If you insist that I was wrong when I said "equivalence principle" and not "the Einstein equivalence principle", then sure, I was wrong. :)

 

[atyy]

If you insist that I was wrong when I said "equivalence principle" and not "the Einstein equivalence principle", then sure, I was wrong. :)

Are there theories that satisfy the weak EP and are not metric theories?

 

[Matterwave]

Are there theories that satisfy the weak EP and are not metric theories?

I think...Newton's theory of gravity and his laws of motion? I mean that's where the weak EP originated anyways.

But I think people are reading too much into what I'm saying. I was trying to only say that the (strong) EP gives us an inclination that a space-time curvature theory is possible, and useful. I don't think I said the EP means that ONLY a space-time curvature theory is possible. This is certainly false, since one can model GR as a spin-2 tensor field with non-linear field equations on top of a flat background space-time... If I gave anybody that impression, then I apologize for being unclear.

 

[atyy]

I think...Newton's theory of gravity and his laws of motion? I mean that's where the weak EP originated anyways.

But I think people are reading too much into what I'm saying. I was trying to only say that the (strong) EP gives us an inclination that a space-time curvature theory is possible, and useful. I don't think I said the EP means that ONLY a space-time curvature theory is possible. This is certainly false, since one can model GR as a spin-2 tensor field with non-linear field equations on top of a flat background space-time... If I gave anybody that impression, then I apologize for being unclear.

I thought Newton-Cartan theory? http://en.wikipedia.org/wiki/Newton–Cartan_theory

Maybe you are "wrong", but not for the right reason?

 

[Matterwave]

I thought Newton-Cartan theory? http://en.wikipedia.org/wiki/Newton–Cartan_theory

Maybe you are "wrong", but not for the right reason?

I'm not sure what that means. XD

 

[DrStupid]

If you insist that I was wrong when I said "equivalence principle" and not "the Einstein equivalence principle", then sure, I was wrong. :)

That alone wouldn't be a problem. It was the addition "(inertial mass = gravitational mass)" that confused me in this context. I don't even know what that means in GR.

 

[Matterwave]

That alone wouldn't be a problem. It was the addition "(inertial mass = gravitational mass)" that confused me in this context. I don't even know what that means in GR.

That IS the weak equivalence principle. It means that two (small) objects will fall at the same rate when they are in the same gravitational field regardless of their mass.

This is the form of the equivalence principle that is so famously tested in the Eötvös experiment:

http://en.wikipedia.org/wiki/Eötvös_experiment
http://en.wikipedia.org/wiki/Equivalence_principle#Tests_of_the_weak_equivalence_principle