Can someone explain equivalence of gravity and inertia?

In summary, the conversation discusses the equivalence of gravity and inertia, with a focus on Mach's Principle. It is mentioned that gravity acts over long distances and its effects weaken the further away you are from the source. The conversation also touches upon the idea of an edge of the universe and the role of gravity in this concept. Overall, the conversation explores the relationship between gravity and inertia and how they are related to the distribution of mass in the universe. The analogy of a ball on an elastic surface is used to explain this concept.
  • #1
Crazy Tosser
182
0
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
 
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  • #2
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.
 
  • #3
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.
 
  • #4
Can someone explain equivalence of gravity and inertia?

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

--------------------------------------------------------------------------------

..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...
 
  • #5
atyy said:
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
 
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  • #6
Crazy Tosser said:
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
 
  • #7
atyy said:
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.
 
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  • #8
Crazy Tosser said:
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".
 
  • #9
Pippo said:
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 :)
 
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  • #10
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.
 
  • #11
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...
 
  • #12
Crazy Tosser said:
............
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.
 
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1. What is the equivalence of gravity and inertia?

The equivalence of gravity and inertia is a concept in physics that states that the effects of gravity and acceleration are indistinguishable. This means that an observer in a gravitational field would experience the same effects as an observer in an accelerating reference frame.

2. How was the equivalence of gravity and inertia discovered?

The concept was first proposed by Albert Einstein in his theory of general relativity, which was published in 1915. Einstein realized that the acceleration caused by gravity is not a force, but rather a result of the curvature of spacetime caused by massive objects.

3. Can you explain how the equivalence of gravity and inertia works?

The equivalence of gravity and inertia can be explained by the principle of equivalence, which states that the laws of physics are the same for all observers in uniform motion, regardless of their reference frame. This means that the effects of gravity and acceleration are indistinguishable because they are both manifestations of the same spacetime curvature.

4. What are some real-life examples of the equivalence of gravity and inertia?

One example is the experience of weightlessness in an orbiting spacecraft. The astronauts inside the spacecraft are in a state of constant free-fall, experiencing the same effects as if they were in an accelerating reference frame on Earth. Another example is the bending of light by massive objects, such as stars, which can be explained by the curvature of spacetime.

5. Why is the equivalence of gravity and inertia important?

Understanding the equivalence of gravity and inertia is crucial for our understanding of the fundamental laws of the universe. It also plays a key role in modern technologies, such as GPS systems, which rely on precise measurements of both gravity and acceleration. Additionally, the concept has significant implications for the study of black holes and the search for a unified theory of physics.

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