Gravitational Attraction of Motionless Masses

[killshot]

Assuming a universe with only space and two motionless masses, would the two masses start to move toward each other?

 

[Pengwuino]

Yes, they will, they both create gravitational fields.

 

[chrisphd]

No, because without time, no motion can occur.

 

[Hootenanny]

No, because without time, no motion can occur.

I don't think that the OP meant "space" to mean only the spatial dimensions. I rather think that they meant "nothing but empty space and two masses".

 

[chrisphd]

I see. In that case we have a more tricky question on our hands.

So firstly i'll assume the particles are "point" particles. Then there exists only 1 "ruler", if you like, in space in which distance can be measured with. That is, the distance between these two particles is the only possible measuring device.

This to me implies that describing the particle's as moving towards one another is meaningless, because there is no concievable way to infact identify that the distance between the particles is decreasing.

What analogy can I use to make my picture clear. Immagine that tommorrow, everything in the universe is exactly half the size it was today. That is, I am now half my height, and the ruler I use to measure my height is also half the height of what it was today, and the expectation value of the radius of an electron around the universe is halved. Clearly in this situation, because everything in the universe has halved, there is absolutely no way to tell at all that anything has changed.

In fact, because in the previous paragraph, the consequences of everything in the universe halving in size, is identical to the theory that nothing in the universe changed at all, we would use occam's razor to say that in fact nothing in the universe changed at all.

Similarly in your example of a two particle universe. Whether the distance between the particles is decreasing or staying the same, because the only distance unit in your scenario is the distance between the two particles, these scenarios would be equivalent.

Therefore, it is reasonable to suggest that no motion occurs.

 

[Born2bwire]

There would still be means of denoting the motion. First, since the force is dependent upon the separation of the masses, the force will increase as the masses attract each other. So the observers on the either mass will not only experience an extra acceleration, but a changing acceleration which should be measurable. In addition, one could make measurements of the other mass and derive it's motion in the same way that we have deduced the expansion of the universe despite being part of it. In your analogy, the universe is changing in size which is what is happening currently in the real Universe but despite not being able to observe the Universe outside of it (disregarding the physical implications of whether this is a possible supposition) we are still able to take the appropriate measurements to observe this.

 

[Hootenanny]

I see. In that case we have a more tricky question on our hands.

So firstly i'll assume the particles are "point" particles. Then there exists only 1 "ruler", if you like, in space in which distance can be measured with. That is, the distance between these two particles is the only possible measuring device.

This to me implies that describing the particle's as moving towards one another is meaningless, because there is no concievable way to infact identify that the distance between the particles is decreasing.

What analogy can I use to make my picture clear. Immagine that tommorrow, everything in the universe is exactly half the size it was today. That is, I am now half my height, and the ruler I use to measure my height is also half the height of what it was today, and the expectation value of the radius of an electron around the universe is halved. Clearly in this situation, because everything in the universe has halved, there is absolutely no way to tell at all that anything has changed.

In fact, because in the previous paragraph, the consequences of everything in the universe halving in size, is identical to the theory that nothing in the universe changed at all, we would use occam's razor to say that in fact nothing in the universe changed at all.

Similarly in your example of a two particle universe. Whether the distance between the particles is decreasing or staying the same, because the only distance unit in your scenario is the distance between the two particles, these scenarios would be equivalent.

Therefore, it is reasonable to suggest that no motion occurs.

Nonsense. There are several measurements that observers on either mass could make that would show that the masses were not only accelerating, but accelerating at an increasing rate.

Edit: I seem to be following Born2bwire around today

 

[chrisphd]

A body in free fall cannot detect that it is in free fall.
An analogy is that when you stand in an elevator that is free falling, the laws of physics are such that the elevator is approximately an inertial reference frame.

 

[Born2bwire]

A body in free fall cannot detect that it is in free fall.
An analogy is that when you stand in an elevator that is free falling, the laws of physics are such that the elevator is approximately an inertial reference frame.

Yes, but we have the caveat here that the force applied is not constant. If the force was constant, then the acceleration would be constant and one could argue this. But with the change of the force as a function of distance, we cannot make the same argument. If I am in an elevator that is going up, while it is in motion between two floors it just feels like I have consumed one too many Krispy Kremes that morning, but during the moments that elevator starts up and stops at a floor I can detect the changing acceleration.

 

[Hootenanny]

A body in free fall cannot detect that it is in free fall.
An analogy is that when you stand in an elevator that is free falling, the laws of physics are such that the elevator is approximately an inertial reference frame.

Free fall (or more precisely the equivalence principle) only applies when the acceleration is constant, which is not the case here.

Edit: dammit Born2bwire!

 

[chrisphd]

In fact, the force acting on the free falling elevator is also not constant because as the elevator gets closer to the Earth, the acceleration will increase. There is no way to determine the change in acceleration, because the elevator does not exert a force on your body. This is because your body is subject to the same external acceleration the elevator is subjected to.

 

[Hootenanny]

In fact, the force acting on the free falling elevator is also not constant because as the elevator gets closer to the Earth, the acceleration will increase.

So technically, the equivalence principle doesn't apply here. However, the gravitational field can be approximated as uniform near the Earth's surface. The correction is so small that the elevator can be approximated as free-falling. Once once again, the equivalence principle only applies in a uniform field.

 

[chrisphd]

Ok, so you seem to be implying that there is something special about changing acceleration that can be detected.

Let's consider a person in a spaceship (At the present, the person is hovering in the middle of the spaceship). Assume there is no gravity between the person and the spaceship. Now let the spaceship be attracted by gravity to a planet in space, and thus as the spaceship approaches the planet, the acceleration will also increase.

Now because the acceleration of the person inside the spaceship will always be the same as the acceleration of the spaceship itself, the velocity of the spaceship will always be the same as the man within the spaceship at any time and therefore there will be no force or interaction between the spaceship and the person within the spaceship. The man will always remain where he is, in the centre of the spaceship.

This implies that the man cannot detect his changing acceleration based on his physical interaction with the spaceship.

So by what mechanism can the man detect his changing acceleration?

 

[Born2bwire]

Again, take the example of a real elevator. When the elevator starts up and when it slows down, you can physically feel it, the change in acceleration. When it is moving between floors at a more or less constant speed, we are experiencing a constant accleration (due to the net force from gravity and the movement of the elevator propagated through our contact with it on the floor). At this point, everything else is just a question of figuring out how to quantify this measurement, the change of acceleration (called "jerk" I believe) using a device. Whether this device is our own body or some black box is now irrelevant.

EDIT: If you want an example of a device, a simple one would be a submerged ball in a graduated cylinder. The cylinder would be filled with a fluid that has a gradient density. Let's say various oils of different densities. The oils will form layers of constant densities, the highest at the bottom, the lowest at the top. The acceleration of the float in the liquid will give it a weight and cause it to seek out one of the oil layers. As the acceleration changes, the float's weight changes and it will move to a different oil layer. I guess to make sure that the oils are not affected by the changing accleration we would need to stipulate that they are incompressible.

 

[chrisphd]

Please read my previous post. It explains why your intuitive view is flawed. The "jerk" you feel in an elevator is due to the additional force between the elevator and the human. The "jerk" is not experienced when it is an external force that is causing the changing acceleration. Do read my previous post.

 

[Hootenanny]

Any object of non-zero dimensions in a non-uniform gravitational field would experience a tidal force, which is most certainly detectable. In fact these so-called tidal forces appear as components of the Riemann tensor.

 

[Born2bwire]

Please read my previous post. It explains why your intuitive view is flawed. The "jerk" you feel in an elevator is due to the additional force between the elevator and the human. The "jerk" is not experienced when it is an external force that is causing the changing acceleration. Do read my previous post.

No, we can always sense an additional force. When the elevator is moving up, there is an additional force and we sense that as an overall increase in our body weight. However, we detect the jerk by the fact that we can sense a time dependent change in our body weight. If I have a mass on a spring, the amount of deflection of the spring is a measurement of the weight of the mass. A jerk would cause this deflection to change over time. It doesn't matter whether this jerk is transmitted at a subset of points on the mass or our body (like the surface of our feet in contact with the elevator floor) or if it is spread out through our body (like due to a gravitational force). The end result is that there will be change in weight which is detectable because if we have weight then there is still a net force acting on us and our bodies, or devices, can detect a change in this force even if we cannot detect the force when constant if we are in free fall.

 

[chrisphd]

Any object of non-zero dimensions in a non-uniform gravitational field would experience a tidal force, which is most certainly detectable.

My previous thought experiment in the spaceship however was showing that there is no interaction between the human and the spaceship even if their accelerations were changing, to show why born2bwire's intuitive argument was wrong. I did neglect the subtleties of tidal effects.

None the less, if this is the measurement you are going to use, it will not apply to the "point" particles i was referring to in my original post.

 

[chrisphd]

end result is that there will be change in weight which is detectable

Read the following carefully born2bwire, because i'll not exlpain this part again.

Actually in my spaceship thought experiment, the human in the spaceship at all times will appear to be weightless. This is because his velocity will always be equal to the velocity of the spaceship at any time, since they are both being accelerated at the same rate at any time. Therefore there is no interaction between the spaceship and the human. We can therefore neglect the spaceship from the picture.

We now have a picture of just a human moving towards this planet. Now the human is comprised of atoms. Each atom in the human is also accelerating at the same rate as any other atom at any time, and thus will all have the same velocities as each other at any time. This means there will be no "intra-body" forces, if you like, to detect the changing acceleration. The picture can then be further simplified, because there is no interaction between the atoms, we can remove all atoms from the picture except for one atom.

We can continue simplifying the picture indefnitely, and there will be no way to determine the changing acceleration.

Of course this neglects tidal effects, as ultimately the discussion should converge to the point particles mentioned in my earliest post.

 

[Born2bwire]

Then you simply apply a constant force to an object along the direction of the jerk, the resultant net force would be time dependent.

Edit: To clarify, you could do something as simple as toss a ball and measure it's path, the jerk would result in a path different from that of a constant force. This would be compounded even more by the fact that the force on the ball after being tossed is spatially dependent and time dependent in this context.

 

[Buckleymanor]

I see. In that case we have a more tricky question on our hands.

So firstly i'll assume the particles are "point" particles. Then there exists only 1 "ruler", if you like, in space in which distance can be measured with. That is, the distance between these two particles is the only possible measuring device.

This to me implies that describing the particle's as moving towards one another is meaningless, because there is no concievable way to infact identify that the distance between the particles is decreasing.

What analogy can I use to make my picture clear. Immagine that tommorrow, everything in the universe is exactly half the size it was today. That is, I am now half my height, and the ruler I use to measure my height is also half the height of what it was today, and the expectation value of the radius of an electron around the universe is halved. Clearly in this situation, because everything in the universe has halved, there is absolutely no way to tell at all that anything has changed.

In fact, because in the previous paragraph, the consequences of everything in the universe halving in size, is identical to the theory that nothing in the universe changed at all, we would use occam's razor to say that in fact nothing in the universe changed at all.

Similarly in your example of a two particle universe. Whether the distance between the particles is decreasing or staying the same, because the only distance unit in your scenario is the distance between the two particles, these scenarios would be equivalent.

Therefore, it is reasonable to suggest that no motion occurs.

Why would you expect the particles to act like Zeno's Paradox.
Time exists so why would'nt the particles or masses eventualy touch or collide.

 

[chrisphd]

That was in the back of my mind too. I was wondering when someone would finally say it. that

 

[D H]

All of the above assumes a universe with only two masses will have the same physical laws as does our universe. While don't really know what time or space are, they appear to be intimately entangled with our huge and expanding universe. We don't know what mass is or why the equivalence principle holds. If Mach's Principle has any validity, a universe with only two masses will be nothing like our universe.

In other words, the answer to the question is "who knows?"

 

[killshot]

Although very interesting, the thread on detecting motion was based on the assumption that G is like an attractive force field (which MAY be the case if CERN detects gravitons). I was looking for some thoughts on the motion or lack of motion for the masses if G is only manifest as SpaceTime warping. ?

 

[Kaimyn]

Actually in my spaceship thought experiment, the human in the spaceship at all times will appear to be weightless. This is because his velocity will always be equal to the velocity of the spaceship at any time, since they are both being accelerated at the same rate at any time. Therefore there is no interaction between the spaceship and the human. We can therefore neglect the spaceship from the picture.

In essence, what you are saying is that there are no practical application of seatbelts? If this is true, why to balls with another ball inside make a rattling sound when you shake them? How come I go flying forward on the bus when it slows down?

You are neglecting simple Newtonian physics. Unless the human is fixed in position, which is not so in your example, he will move around while the spaceship speeds up. There is nothing to push against him (until he reaches the end of the spaceship and is fixed in place). What is your evidence to say he won't move at all?

And this applies to acceleration, let alone jerk. Sure enough, acceleration is indistinguishable from gravity, but that is not to say no force is exterted. As has been said before, should the planets be moving towards each other with increasing acceleration, then, as force is proportional to acceleration, there is the force of gravity on the planet, combined with the INCREASING force of the bodies accelerating. As we feel weight, not mass, this means that there will be a change in weight (as acceleration is indistingishable from gravity) and we will notice it.

It has the bonus effect of getting heavier when you are facing the planet, and get lighter on the other side. Wouldn't that be cool?

 

[James Leighe]

*'Point' particles are not infinitely small, they are roughly the 'size' of their wavelength.

*You can't have a universe with two particles, as they interact with particles and virtual particles. Without those we are not talking about reality as we experience it.

*You would have no trouble defining units by which to measure distance even if there were only two 'real' particles in the thought experiment. A second could be defined as a number of oscillations of the wave of the particle, a light-second would be how far the gravitational force travels that many oscillations etc.

*The particles would be coming together at greater and greater velocities as they became closer due to gravity. This accelerating force would increase as the distance decreases, by which I mean you could feel the jerk increase as you got closer.

I think...

It seems the confusion is coming from the idea that particles are infinitely small and that our measurements would have no meaning. I think they would, for example, a second is defined as some number of oscillations of a specific frequency of light emitted from a cesium atom. Even if there are no cesium atoms in the thought experiment the time is still valid (as long as we are talking about a universe in which cesium can exist, even in theory) Distance is defined similarly (how far some light goes in a vacuum in that many oscillations)

 

[Evolver]

Assuming a universe with only space and two motionless masses, would the two masses start to move toward each other?

Matter attracts matter with a gravitational fall off rate of the inverse of r2 or 1/r2.

"The gravitation attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation distance. The force is always attractive and acts along the line joining them."

The only things that affect gravitation are mass and distance. Since two objects in space would fit those prerequisites... they would experience gravitation and would attract towards each other based on their distance to one another. This is also assuming that this hypothetical "space" we are talking about would not some how interfere with the masses via quantum fluctuations or virtual particles.

Since our understanding of what causes gravity is limited, it very much may have to do with quantum interactions of this sort, and this "space" you have deemed the medium for these interactions of mass may very well be a moot hypothetical argument.

The problem with this question is that is attempts to harness our limited understanding of gravity (they have never even seen proof of the theorized graviton force carrying particle). So to say what causes gravity itself is unknown at this point. Your question of putting two objects of mass in space with nothing else may very well defy some law of gravitation that we are currently unaware of.

But to the best of my knowledge, with our modern view of gravity... yes, as long as they have mass they will affect one another proportianally to the distance between them.

 

[killshot]

Matter attracts matter with a gravitational fall off rate of the inverse of r2 or 1/r2.

"The gravitation attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation distance. The force is always attractive and acts along the line joining them."

The only things that affect gravitation are mass and distance. Since two objects in space would fit those prerequisites... they would experience gravitation and would attract towards each other based on their distance to one another. This is also assuming that this hypothetical "space" we are talking about would not some how interfere with the masses via quantum fluctuations or virtual particles.

Since our understanding of what causes gravity is limited, it very much may have to do with quantum interactions of this sort, and this "space" you have deemed the medium for these interactions of mass may very well be a moot hypothetical argument.

The problem with this question is that is attempts to harness our limited understanding of gravity (they have never even seen proof of the theorized graviton force carrying particle). So to say what causes gravity itself is unknown at this point. Your question of putting two objects of mass in space with nothing else may very well defy some law of gravitation that we are currently unaware of.

But to the best of my knowledge, with our modern view of gravity... yes, as long as they have mass they will affect one another proportianally to the distance between them.

Concurring that this all hypothetical;

Assuming the masses can feel(?) the curvature of the space.

Could G be a potential energy when they are motionless and therefore the masses remain motionless? Then if one mass is set in motion in any direction would the two masses eventually come together?

Could motion some how be part of the gravitation mystery?

I know this begs the question about G as a constant (but that maybe a matter of scale).

 

[Evolver]

Concurring that this all hypothetical;

Assuming the masses can feel(?) the curvature of the space.

Could G be a potential energy when they are motionless and therefore the masses remain motionless? Then if one mass is set in motion in any direction would the two masses eventually come together?

Could motion some how be part of the gravitation mystery?

I know this begs the question about G as a constant (but that maybe a matter of scale).

Well considering the inverse r2 law, that implies that the attraction can never actually reach 0, so it implicitly will have some small amount of attraction... I guess if the masses were the only things in the "universe" then they would eventually attract each other no matter how far apart.

As for motion being part of what causes gravity, it's hard to tell. Because as we do not know exactly what causes it, motion could be a contributing factor or could simply be a byproduct. This is where we get into sticky territory because motion is relative.

It's an interesting theory, but would be sufficiently hard to test considering most things are in motion relative to something else.

 

[Dadface]

The OP described a universe with only space and two masses but it seems that people have been adding to this universe.Where, for example, did the observers come from?

 

[Buckleymanor]

The OP described a universe with only space and two masses but it seems that people have been adding to this universe.Where, for example, did the observers come from?

He did not mention any commentators either.
Maybe I should shut up.

 

[Evolver]

The OP described a universe with only space and two masses but it seems that people have been adding to this universe.Where, for example, did the observers come from?

Maybe the two masses are those of the observer...

He did not mention any commentators either.
Maybe I should shut up.

And the commentator... ;)

 

[pep_i]

hello everyone i am new to this website and forum.But i have been really good at physics this topic gravity has become quite appaling sometime now.However i believe Einstein theory to be wrong and i will keep reading the posts here and joined in where i see it fit.

 

[pep_i]

Assuming a universe with only space and two motionless masses, would the two masses start to move toward each other?

Good question man