# Inertial vs Gravitational Mass "mystery"?

1. Oct 6, 2014

### 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

2. Oct 6, 2014

### A.T.

Because we don't know it.

3. Oct 6, 2014

### dextercioby

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

4. Oct 6, 2014

### 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?

5. Oct 6, 2014

### A.T.

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

6. Oct 6, 2014

### Staff: Mentor

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?

7. Oct 6, 2014

### 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?

8. Oct 6, 2014

### A.T.

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

9. Oct 6, 2014

### A.T.

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

10. Oct 6, 2014

### 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

11. Oct 6, 2014

### A.T.

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

12. Oct 6, 2014

### Ghost117

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

Thanks everyone :)

13. Oct 6, 2014

### 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.

14. Oct 6, 2014

### Ghost117

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

15. Oct 6, 2014

### Matterwave

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.

16. Oct 7, 2014

### Buckleymanor

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:)

17. Oct 7, 2014

### harrylin

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"...

18. Oct 7, 2014

### DrStupid

Can you explain this within GR?

19. Oct 7, 2014

### Matterwave

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.

20. Oct 8, 2014

### Ghost117

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?

Last edited: Oct 8, 2014