Can someone explain equivalence of gravity and inertia?

[Crazy Tosser]

I've been trying to put this together in my head for a while and it doesn't come out. For example, if there are more stars on one half of the sky, does it mean that a thrown object will travel faster in that direction? If the object is at the edge of the universe, does it mean it will not be able to move anywhere except towards the stars?

Thanks in advance :)
~Tosser

 

[akelleh]

hey tosser,

Gravity acts over long distances, but it's effects weaken the further you are from the source. If you're on earth, and throw an object in a direction where there are more stars, you won't see an effect on the object. This is because the gravitational force on the object from the stars is negligible.

 

[atyy]

They are not equivalent. It's gravitational mass and inertial mass that are equal.

For a particle with inertial mass m and electric charge q in the presence of another electric charge Q:
Qq/r²=ma

For a particle with inertial mass m and gravitational charge m in the presence of another electric charge M:
Mm/r²=ma

A mass m can have arbitrary electric charge, but it cannot have arbitrary gravitational charge. Its gravitational charge is always equal to its inertial mass.

 

[Naty1]

Can someone explain equivalence of gravity and inertia?

I don't think anyone knows why, but maybe somebody will post here.

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..if there are more stars on one half of the sky, does it mean that a thrown object will travel faster in that direction?

yes except (a) the Earth's gravitational field will overpower the effects of the entire universe(that's why you don't fly off Earth and into space and (b) there are a virtually identical number of planets,stars, and all other masses in each direction...we know that because the cosmic background microwave radiation is isotropic (uniform in all directions after correcting for Earth's motion)

If the object is at the edge of the universe, does it mean it will not be able to move anywhere except towards the stars?

You likely don't mean "move" you mean "be attracted by gravitational forces". but as far as is known the universe has no "edge", has no boundary...the universe has no "center"...all points are as much at the center as any other...

 

[Crazy Tosser]

A mass m can have arbitrary electric charge, but it cannot have arbitrary gravitational charge. Its gravitational charge is always equal to its inertial mass.

Thank you very much, it makes sense now. I guess I was just confused by the wording :)

P.S. I blame Gardner's book on relativity :P

 

[atyy]

Thank you very much, it makes sense now. I guess I was just confused by the wording :)

P.S. I blame Gardner's book on relativity :P

Actually, maybe Gardner was thinking of Mach's Principle, which postulates that inertial mass, even in eg. an electromagnetic situation, is determined by gravity between that object and the distant stars. Mach's Principle is not precisely formulated, and maybe not true, but it did inspire Einstein. It's the basis for many fun discussions!

Barbour edited a whole book about it:
http://www.platonia.com/index.html

Rovelli discusses it on p35,38:
http://www.cpt.univ-mrs.fr/~rovelli/book.pdf

 

[Jonathan Scott]

Actually, maybe Gardner was thinking of Mach's Principle, which postulates that inertial mass, even in eg. an electromagnetic situation, is determined by gravity between that object and the distant stars. Mach's Principle is not precisely formulated, and maybe not true, but it did inspire Einstein. It's the basis for many fun discussions!

Barbour edited a whole book about it:
http://www.platonia.com/index.html

Rovelli discusses it on p35,38:
http://www.cpt.univ-mrs.fr/~rovelli/book.pdf

I like Dennis Sciama's brilliant paper "On the Origin of Inertia" (from about 1953, but available http://adsabs.harvard.edu/abs/1953MNRAS.113...34S") where he constructs a simplified model of gravity based on analogies with electromagnetism and shows that it leads directly to inertia and rotational effects satisfying Mach's Principle. Basically, if you accelerate something relative to the masses of the universe, it feels a reaction force because of the relative acceleration of the universe!

Unfortunately, the equivalent result in General Relativity is not so easily demonstrated, and is thought to be only approximate.

 

[Pippo]

Can someone explain equivalence of gravity and inertia?

~Tosser

Put a ball on an elastic surface, trying to move it you can establish that the ball would like to remain in the original position (as the elastic surface has been distorted by the ball), this is the inertia, after that put another second ball on the same surface, you may see that the two balls move toward each other, this effect is the same as the gravity.
Now remove the term "elastic surface" and replace it with "space".

 

[Crazy Tosser]

Put a ball on an elastic surface, trying to move it you can establish that the ball would like to remain in the original position (as the elastic surface has been distorted by the ball), this is the inertia, after that put another second ball on the same surface, you may see that the two balls move toward each other, this effect is the same as the gravity.
Now remove the term "elastic surface" and replace it with "space".

I believe that the analogy of space-time with a stretching sheet of rubber is not a very good one, because we all know how that works - gravity pulls on the ball, the rubber stretches, the ball stays in place because of it's inertia, or, without inertia, because it tends to take the path of least energy, but once you take away the concepts of gravity and inertia from the ball on the elastic surface, the analogy doesn't work anymore...

But anyway, now I understand that what it says is: how much an object resist changes in motion and how much it attracts other objects is, in the lamest terms, the same thing :)

 

[russ_watters]

Note that we do have more stars in our galaxy on one side of the sky than the other. We orbit the galactic center near the edge of one of the spiral arms. This does not affect the way we perceive gravity because we are in orbit around the common center of gravity of all those stars.

 

[Naty1]

In rereading my own post:

(a) the Earth's gravitational field will overpower the effects of the entire universe(that's why you don't fly off Earth and into space and

I don't really like the analogy I made...its ok, maybe, for illustrative purpose, but if there was a strong gravitational attraction,say nearby, the Earth and you and I would all accelerate in unison towards that source...in other words, we'd all be yanked out of our normal orbit with the sun...and in fact the sun would also be yanked along by the gravitational source...

and russ waters makes an interesting point...it's the center of gravity rather than the number of stars that matters...

 

[Pippo]

............
But anyway, now I understand that what it says is: how much an object resist changes in motion and how much it attracts other objects is, in the lamest terms, the same thing :)

It's exactly what I've tried to say, thanks.