Gravity

[Vindhya]

Why gravity is always atractive. Why there is no repulsion?

[ajb]

Well, one simple answer is because general relativity says it is. I believe you can use the equivalence principle to show this, but I am not really sure.

[swansont]

Short answer: No negative mass

[Pete]

Why gravity is always atractive. Why there is no repulsion?

Actually that's wrong. There is gravitational repulsion. Dark energy is one example. It is responsible for the inflationary model of the universe as well as the observed accelerating expantion of the universe. This only becomes apparent in Einstein's general theory of relativity where the cosmological constant is used to provide an equivalent negative gravitational mass density. In cosmology there is an object called a vacuum domain wall. Objects placed near the wall are gravitationally repelled by the wall.

 

Pete

[Klaynos]

Dark energy might not be a gravitational effect.

[ajb]

Anything that look like negative gravity would (presumably) violate the weak energy conditions (?), which are used to "prove" things like positive mass and positive energy-momentum etc. I will look into it a little.

 

A far as I know, such conditions are violated quantum mechanically and (maybe?) even classically. So, maybe it is not "obvious" that repulsive gravity does not exists.

[Pete]

Dark energy might not be a gravitational effect.

"might not"? I guess so. But the same could be said of the inflationary universe model. As it is currently explained and understood it is very much a gravitational effect. Its description is postulated in two ways (1) by the presents of tension (negatgive pressure) or (2) by a positive cosmological constant.

 

Alan Guth has this to say about it. From http://www.edge.org/documents/day/day_guth.html

Our current picture of the universe has a new twist, however, which was discovered two or three years ago. To make things fit, to match the observations, which are now getting very clear, we have to assume that there's a new component of energy in the universe that we didn't know existed before. This new component is usually referred to as "dark energy." As the name clearly suggests, we still don't know exactly what this new component is. It's a component of energy which in fact is very much like the repulsive gravity matter I talked about earlier — the material that drives the inflation in the early universe. It appears that, in fact, today the universe is filled with a similar kind of matter. The antigravity effect is much weaker than the effect that I was talking about in the early universe, but the universe today appears very definitely to be starting to accelerate again under the influence of this so-called dark energy.

If it wasn't gravitational in nature then what other possibilities exist? It is gravity that drives the expansion of the universe is it not? After all the acceleration of matter which is independant of its mass is basically the definition of gravity itself. And the accelerating expansion of the galaxies apart from each other is clearly indendant of the mass of the galaxies.

Anything that look like negative gravity would (presumably) violate the weak energy conditions

I disagree. That is a postulate based on the assumption that negative energy density. However mass density is what determines whether there is a gravitational repulsion and the two are not proportional. In the case of negative pressure scenrio its the negative pressure can overcome the positive energy density. That would lead to gravitational repulsion. I recall that the same arguement holds for a positive cosmological constant.

(?), which are used to "prove" things like positive mass and positive energy-momentum etc. I will look into it a little.

I disagree here too for the reason stated above.

A far as I know, such conditions are violated quantum mechanically ...

What are you basing that on?

 

Pete

Edited July 13, 2008 by Pete
multiple post merged

[ajb]

I will need to think about this a little more.

 

Now, negative mass does not imply repulsive gravity.

 

The energy conditions can be used to "prove" positive mass etc. It is a case of what conditions you use exactly and if you think the conditions are the "correct ones".

 

It is well established that the weak-energy conditions are violated in semi-classical gravity.

 

I suspect (but I don't really know) that using the equivalence principle and some (classical) energy conditions you could start to make some statement about repulsive gravity. But again, this could well depend on the exact energy condition you use.

 

I will ask some experts on this. These sort of things are near my research work, but not quite close enough for me to know "off the top of my head" what has been done.

Edited July 13, 2008 by ajb

[Pete]

I will need to think about this a little more.

 

Now, negative mass does not imply repulsive gravity.

On the contrary. Negative gravitational mass most definitely implies gravitational repulsion.

The energy conditions can be used to "prove" positive mass etc. It is a case of what conditions you use exactly and if you think the conditions are the "correct ones".

The weak energy condition does not contradict negative mass. The energy density could be positive and yet leave the mass density as negative. In the weak field limit (which applies to our accelerating universe) the following relation holds

 

del^2 Phi = rho_{gravitational mass} = 4pi(u + 3p)/c²

 

where u = energy density and p = pressure. When the pressure has the value p = -u then rho_{gravitational mass} < 0 which results in gravitational repulsion. One version of the equivalence principle states that all matter accelerates at a rate which is independant of its mass. This still holds for gravitational repulsion.

 

Pete

[ajb]

I won't do it all for you, but consider Newtonian gravity. It is quite straight forward to show that if one of the masses becomes negative that the acceleration does not change in direction. That is gravity is still attractive. Negative mass, at least by itself does not imply repulsive gravity.

 

The hint I will give you is to consider [math]F = - G\frac{ m_{1}m_{2}}{r^{2}}[/math] and [math]F = ma[/math] and then set one of the masses to minus.

[Pete]

I won't do it all for you, ..

Not necessary anyway since I already know basics physics.

..but consider Newtonian gravity. It is quite straight forward to show that if one of the masses becomes negative that the acceleration does not change in direction.

 

That is gravity is still attractive. Negative mass, at least by itself does not imply repulsive gravity.

I have to say that this is wrong. Its not like I haven't studied this before.

The hint I will give you is to consider [math]F = - G\frac{ m_{1}m_{2}}{r^{2}}[/math] and [math]F = ma[/math] and then set one of the masses to minus.

 

Okay. Let us define some terms and solve the problem. Let m₁ = -M where M is the absolute value of the active gravitational mass of body 1 (e.g. a planet). Let m₂ = m where m is the passive gravitational mass of body 2 which we will assume equals the inertial mass of body 2. Then

 

[math]F = - G\frac{ Mm}{r^{2}} = ma[/math]

 

Therefore

 

[math]a = G\frac{M}{r^{2}}[/math]

 

Which shows that this results in gravitational repulsion. I don't understand why you disagree with this result, can you elaborate more please? Thank you.

 

There are more ways to do this when you keep in mind that there are three kinds of mass (1) active gravitational mass (i.e. the source of gravity) (2) passive gravitational mass (what gravity acts on) and (3) inertial mass (i.e. the quantity defined by m = p/v). The equivalence principle only requires that these quantities be proportional, not equal.

 

Pete

[ajb]

What about working out the force (and in particular the acceleration) on a negative mass in the field of a positive mass. I will show that these are attracted.

 

[math]F = -G\frac{ m_{1} m_{2}}{r^{2}}[/math]

 

Now

 

[math] a = \frac{F}{m_{1}}[/math] for the mass [math]m_{1}[/math].

 

Now let [math]m_{1}\rightarrow - m_{1}[/math]

 

where hense

 

[math]a \rightarrow -a [/math], so in particular

 

[math]a = - \frac{G m_{2}}{r^{2}}[/math].

 

So they are attracted. Unless like you say, gravitational mass and inertial mass are only proportional and not equal.

[swansont]

What about working out the force (and in particular the acceleration) on a negative mass in the field of a positive mass. I will show that these are attracted.

 

[math]F = -G\frac{ m_{1} m_{2}}{r^{2}}[/math]

 

Now

 

[math] a = \frac{F}{m_{1}}[/math] for the mass [math]m_{1}[/math].

 

Now let [math]m_{1}\rightarrow - m_{1}[/math]

 

where hense

 

[math]a \rightarrow -a [/math], so in particular

 

[math]a = - \frac{G m_{2}}{r^{2}}[/math].

 

So they are attracted. Unless like you say, gravitational mass and inertial mass are only proportional and not equal.

 

m₁ cancels, so its sign is irrelevant. But what if you change the sign of m₂?

[Pete]

What about working out the force (and in particular the acceleration) on a negative mass in the field of a positive mass. I will show that these are attracted.

 

[math]F = -G\frac{ m_{1} m_{2}}{r^{2}}[/math]

 

Now

 

[math] a = \frac{F}{m_{1}}[/math] for the mass [math]m_{1}[/math].

 

Now let [math]m_{1}\rightarrow - m_{1}[/math]

 

where hense

 

[math]a \rightarrow -a [/math], so in particular

 

[math]a = - \frac{G m_{2}}{r^{2}}[/math].

 

So they are attracted. Unless like you say, gravitational mass and inertial mass are only proportional and not equal.

Classically this would be described as a particle subjected to an relusive gravitational force but the inertial mass is negative and thus the force is in the opposite direction of the particle's acceleration. There is an interesting article on this subject that you might enjoy readind. The article I speak of is

 

Negative Mass in General Relativity, Herman Bondi, Rev. Mod. Phys, 29(3), July 1957

 

I have a copy if you'd like to read it.

m₁ cancels' date=' so its sign is irrelevant.

[/quote']

To be precise one doesn't always cancel the minus sign. Its the magnitude that is canceled. When the signs are the same they cancel. In ajb's example he chose to alter not only the inertial mass (i.e. he gave the particle a negative inertial mass) but the gravitational mass as well. This in this case the signs canceled. This means that particle's with negative inertial mass and negative passive gravitational mass will fall down and particles with positive inertial mass and negative passive gravitational mass will fall up. Particles with normal mass will fall down too. In the example that I gave above I took the simplest root and considered only the acctive gravitational mass of the source, such as a planet. Normal matter will be repulsed. While I know of examples in GR where there is repulsive gravitational fields I've never heard of particles with negative inertial mass. But that doesn't mean that they don't exit of course.

 

Pete

[ajb]

Ok, I have gone through it carefully and I now stand corrected and that negative mass does have some weird properties.

 

Positive mass is attracted to positive mass.

 

A negative mass is attracted to a positive mass. (Thus, here on Earth I think it would be hard to decide if we did have an isolated lump of negative mass.) The interesting thing here is that the positive mass is repulsed by the negative mass. Something I was not really expecting, but that appears to be the case. They both move off in the same direction. I don't think this violates energy conservation or anything.

 

Negative mass repulses negative mass (and positive mass as stated earlier).

 

The question now is why we don't have negative mass. From what I have read on the subject space-times with negative mass are inconstant and negative mass violates some energy condition. I don't know the references, but when I get time I will hunt them down,

Edited July 15, 2008 by ajb
multiple post merged

[Pete]

The question now is why we don't have negative mass. From what I have read on the subject space-times with negative mass are inconstant and negative mass violates some energy condition. I don't know the references, but when I get time I will hunt them down,

In general relativity it seems possible to have a negative inertial mass. Since stress contributes to mass then it follows that when the tension of a body is greater in magnitude that the energy density of the body then the inertial mass will become negative. E.g. if you had a long very strong rod which has two charges on the ends and it is placed in a very strong electric field then, when the stress in the rod is great enough, its inertial mass will become negative.

 

The meaning of a negative inertial mass is that the momentum is in a direction opposite to that of velocity.

 

Pete

Edited July 15, 2008 by Pete

[Brian O'Donnell]

If normal mass is seen as a dent in space-time then -ve mass can be seen as a bump. From here there are 2 options. With Option 1, all test masses roll 'downhill'. For Option 2, +ve masses go 'downhill' and -ve masses go 'uphill'.

In terms of F=ma, the inertial mass 'm' is the same sign and magnitude as the gravitational mass under Option 1. If you pull at a -ve mass it accelerates in the opposite direction. For Option 2, 'm' is always +ve, ie. |m|, and all masses accelerate in the direction of the force. Both options obey the laws of physics if you make consistent assumptions for each case.

Option 1 follows Bondi's assumptions and has the advantage of inertial and gravitational mass being identical.

Under Option 2, like masses attract and unlike masses repel with an inverse square of distance law, offering a kind of symmetry with electrical charges. Negative mass would end up in the spaces between the +ve mass galaxies, a possible explanation for at least some of the observed expansion of the universe.

[north]

Why gravity is always attractive. Why there is no repulsion?

 

because gravity is about the order of space

 

and this order of space is based on the spin or rotation energy of the object

[Klaynos]

because gravity is about the order of space

 

and this order of space is based on the spin or rotation energy of the object

 

Can you please explain what this "order of space is"?

 

And how gravity has anything to do with the "spin or rotation energy of the object"?

[north]

Can you please explain what this "order of space is"?

 

And how gravity has anything to do with the "spin or rotation energy of the object"?

 

space without order is non-directional

 

what gives order to space is the rate of spin or rotation

 

plus the density of matter within this said space within the objects rotational influence

 

the thinner the density of matter per cubic meter of space the less influence the rotation has or " gravity "

[Klaynos]

I still don't really understand what you mean here....

 

If the sun stopped spinning tomorrow the earths orbit would not change.

[Obba]

Hummm, not sure about that Klaynos. What about drag. Space isn't a perfect vacume. or am i being super picky

[north]

Hummm, not sure about that Klaynos. What about drag. Space isn't a perfect vacume. or am i being super picky

 

just a very good question

[Klaynos]

There is drag in space it's about cancelled by the solar wind pressure from the sun...

 

Neither of which are greaty effected by the suns rotation...