Gravity is proportional to mass, why?

[alpha2cen]

Some difficult question.

Mass.

When two objects collide, the momentum equation is like this.

m1v1 + m1v1 = 2m1v1

 

Gravity.

F= c(m1* m2)/r^2

Why is gravity proportional to mass?

mass factor ~= gravity factor in the particular system??

Any good opinion?

[ajb]

Why is gravity proportional to mass?

Any good opinion?

 

The only partial answer I can think of is to think about general relativity, or any very similar theory.

 

The Einstein tensor is quite a general thing, we require a tensor that is at most quardartic in derivaties of the metric. I think the Einstein tensor is just about the most general thing you can think of, given the symmetries of the indices and maybe some other things. (I should think more about this really).

 

It has two indices and we then need to couple this to matter. The easiest thing with all the right is the energy-momentum tensor. The field equations are loosley

 

G = T

 

Now we need to take limits of the metric being Minkowski, assume the matter is an isolated (bosonic) particle etc... and you will see that you get back to Newtonian gravity. In particulat the tt-component of the energy-momentum tensor is proportinal to the mass of the particle.

 

We should look at this more carefully. However, it is about the best I can offer as to why mass is important. To recap: metric theory of gravity, quadratic in derivatives, couple to matter by the energy-momentum tensor, take limits of flat space-time.

[D H]

It starts with Galileo. He demonstrated that acceleration of an object subject to Earth's gravity is independent of the object's mass. Since force is mass times acceleration, we can write F=mg for an object near the surface of the Earth, where g is this common acceleration. To be compatible with Newton's third law, this object must exert an equal but opposite force on the Earth. Newton's third law also says that these equal but opposite forces are the same type of force. The third law counterpart to the gravitational force exerted by the Earth on a falling apple, the gravitational force exerted by the apple on the Earth, must be proportional to the mass of the Earth. This says that the gravitational force between the apple and the Earth is proportional to the product of their masses. Finally, the r² term in the denominator arises from the geometry of space. Put it all together and you get that gravitational force is proportional to the product of the masses and inversely proportional to the square of the distance, or =Gm₁m₂/r².

 

 

 

Einstein recognized that this equivalence of gravitational mass and inertial mass was an implicit assumption in Newtonian mechanics. That inertial mass and gravitational mass are one and the same is still axiomatic in general relativity. Einstein made the assumption explicit in his equivalence principle.

[alpha2cen]

I mean why the attraction force(gravity) between two objects are proportional to mass.

Not electron number or neutron number , .....

[D H]

Did you ever play the "why" game with your parents? Eventually you get to the point where they are 'fess up and say they don't know, or they get mad and say "because I said so."

 

The immediate answer to your question is "because that is what the equivalence principle says." I gave this as the answer in post #3. Anticipating your next "why?" question, the answer is either "Because I said so" or "I don't know." Pick or choose; there is no other answer. The equivalence principle is axiomatic.

 

Every theory in science and every theorem in mathematics has some set of axioms. Those axioms are true because we said so. That is as deep as our knowledge goes (right now). That is the way it is. The same goes for the speed of light being the same in all frames. It is axiomatic.

 

There is no particular need for justifying the axioms of some mathematical theorem. This is one place where science and math differ. The axioms that form the basis of some scientific theory do need justification, very much so. The justification is not through more theory, because then they wouldn't be axioms. They justification is that those axioms are consistent with observation. Above all else, science has to faithfully describe some aspect of the universe.

 

The equivalence principle and the constancy of the speed of light are central to much of modern physics. We physicists don't just make stuff up and then take that made-up stuff for a joy ride. We test and retest and re-re-test those axioms. The equivalence principle and the constancy of the speed of light are two of the most accurately tested of all of the propositions of modern physics.

Edited December 16, 2010 by D H

[alpha2cen]

 

There is no particular need for justifying the axioms of some mathematical theorem.

 

We did not say it's wrong.

What we want to know is the detail mechanism.

How mass is related to the attraction force- such as gravity?

We know gravity comes from mass or acceleration.

The relation between gravity and acceleration is not difficult to understand.

But the connection between gravity and mass is not easy to understand.

Why mass give same effect as acceleration?

Not volume.

The one which pushes out the space is volume.

[D H]

We did not say it's wrong.

What we want to know is the detail mechanism.

We don't know, we don't know, we don't know.

 

How many times do you need me to repeat that? You can demand an answer all you want. That will not change the fact that the answer is "We don't know." Some crackpot might give you a completely crackpot answer. That most certainly will turn out to not be the answer.

 

See this thread, http://www.scienceforums.net/topic/52948-why-does-mass-curve-space-time/.

[swansont]

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Moderator Note

Owing to the overlap, I have moved subsequent posts to the thread D H has linked to above.