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Lv 6

# Two Bubbles?

This is a rather advanced problem, so either skim it or dig in!

If all space were empty except for two nearby masses, say two drops of water, the drops would, according to Newton's Law of gravity, be attracted together. Now suppose all space were full of water except for two bubbles. How would the bubbles move?

a) They would move apart

b) They would not move at all

c) They would attract each other

Update:

The answer is: c. What is the pont of this question? There are at least two points. The first is to show how easily a simple situation, which we think we thoroughly understand, can be transformed (by turning it inside out) into a baffling situation. The second point will come later.

Why do the bubbles move together? If all space were completely full of water there would be no net gravity at a point midway between the two bubbles (let's call it point 'P") because if we draw both bubbles and designate the bubble on the left as "R" and the bubble on the right as "Q" any attraction due to water at Q would be cancelled by the attraction of the water at R. But if the water at R is removed to make a bubble, the balance at P is upset and there is a net attraction to the water at Q. So now there is gravity at P--the attraction is towards Q or away from R. It is as if R repelled things.

But what is meant by "thing"? By things we mean particles, pebbles, and rocks and the like.

Update 2:

A rock at P wold move away from R. But what about bubbles? How does gravity affect bubbles? Gravity makes rocks and bubbles move in opposite directions--rocks down, bubbles up. So if a rock at P would move away from R then another bubble at P would move towards R. The bubbles would attarct each other.

Now for the second promised point of this question. We started with the idea that mass attracts mass and from that reasoned that bubble must attract bubble or empty space attracts empty space. But we could have just as well started with the idea that empty space attracts empty space and from that reasoned that mass must attract mass. Our universe is mostly empty space with a little mass in it so we get one view of things, but if our universe were mostly mass with a little empty space in it we would get a different view of things. Or, on the other hand, we might just interchange our idea of what was mass and what was empty space.

Update 3:

In physics you are always close to the deep water. take two steps off the beaten path and you may be into it. And it's not make believe.

Update 4:

In honor of Remo's poetical contribution...

Miss Farad was pretty and sensual

And charged to a reckless potential;

But a rascal named Ohm

Conducted her home -

Her decline was, alas, exponential.

O.K., I can't resist a joke also...

There was this physicist who was in the habit of getting home quite

late. One time, he came home at 2:30 a.m. with a torn shirt, lipstick

on his collar, hair messed up, and generally looking like hell. His

wife caught him coming in the door and demanded to know why he came

home so late.

His story:

"Well, after I quit work for the day, a few friends and I went out to

the bar for a few drinks. We met up with some rather good-looking

young women, and started to drink to excess; things just kept

happening, as you can well see. I sobered up enough to note how late

it was, so I rushed home."

She said, "YOU LIAR!! YOU WERE IN THE LAB AGAIN, WEREN'T YOU???!!!"

Relevance

C's the answer. [Edit: Actually A, B or C, depending on the density of each of the bubbles and the media. See below]

They would move towards each other, but they would not attract each other int the usual sense. The bubble would create gravitational/mass lows. The water molecules around the bubbles would find themselves attracted in a direction opposite the bubbles The psuedo repulsive force of the bubbles on the Water molecules would cause the molecules to move out of the path between the bubbles. The bubbles would 'float' towards each other as a result of the displacement of water heading to areas of lower potential gravity away from the bubbles.

Good gedanken problem

.............................................................

I am having trouble 'fathoming' a universe completely filled with water. I feel like I am over my head.

Needs to be a uniformily dense universe, either infinite or finite but unbounded (without edges) so that there is no center of gravity. Since uniform density implies that it is static, I guess we are going to have to throw in a cosmological constant. There also must be some pressure otherwise the bubble would blow up and the water boil away. But from where does this pressure come from? No up, No down. Oh well, it is just a hypothetical.

But the truth is in the real world the attraction would be small between the two bubbles. Just apply Newton's law of Gravitation and substitute for the two Ms the amount of water displaced -- and make both the Ms negative since they are negative to the surrounding media. The force of gravity between the bubbles pops out. (Note, the two 'negative' masses cancel to make a positive force -- cool). The force between the two bubbles will be identical (sans the air in the bubbles) to the world with just two drops of water if the drops and the bubbles are the same size. (very cool).

But the bubbles probably wouldn't do much at all. They would be small enough such that local forces such as currents would overpower any gravitational force. And if there weren't any currents, then Brownian motion caused by the water molecules would almost certainly overpower the force of gravity. So in the real hypothetical world, while finding each other attractive, the two bubbles would be doomed to drift aimless.

>>>>>>>>>>>>>>>>>>>>>>>

Combine Archemides' Principle with Newton's Law of Gravitation. Let's call it the Universal Law of Bubble Attraction. It is pretty simple:

Fa=G* [(1- ρfluid/ρbub1) *Mbub1]*[(1- ρfluid/ρbub2)*Mbub2]/r^2

Where ρ is the density and M is the mass.

**You should also note that you will get negative numbers for the 'mass' component of a bubble less dense than the media. Don't worry, you'll get the right answer.

***The true fromula for the 'mass' component should be (Mbub- Volumebubble*ρfluid) which combines the gravitational force of the mass of the bulb less the fluid it displaces. Makes sense. But for non-vaccum bubbles, i.e., bubbles with mass, Archemedes formula is a dervivation and works just fine.

You don't need a special universe to calculate it. It happens on Earth everyday. It is just it is so small in ordinary situations that it is 'swamped' by, in rough order, gravity of the earth (causing flotation or sinking), the motion of the media, drag, and brownian motion.

This presents several solutions. The bubbles would:

a) Repel each other if one of the bubbles is denser than the media (e.g., Mercury) and the other is less dense than the media (e.g. Air).

*Note: This is actually a psuedo force. They bubbles would attract each other, but the net forces would be repulsive because of the affect of the media.

b) Not affect each other if one of the bubbles had the same density as the media (e.g., a balloon filled with water), the other bulb can have any density.

c) Attract each other if both the bubbles were either denser or less dense than the media (e.g. two bubbles of Mercury or two bubbles of Air)

All right, lets do a hypothetical. 2 balloons, each one cubic meter in volume, are tethered in water exactly 2 meters away from each other. For a first order approximation, assume the balloons and their content have no mass. Applying the formula above in the case of zero mass, we get:

F=G (0-Vρ)(0-Vρ)/r^2

=6.67 × 10^−11 N m2 kg^−2*(-1m^3*1000kg/m^3)^2/2m^2

=1.67 x 10^-5 Newtons

The attraction would hardly be noticable here on earth since the bouyant force on each of these balloons would be 9,810 Newtons! And if you were in some water universe with no center of gravity, it would take a long, long time before the bubbles covered even that short distance.

*If you run the same example, but use Mercury for one of the bubbles, the Force = -2.26x10^-4 Newton (the negative sign indicates that it is repulsive).

"Falling in love is not at all the most stupid thing that people do — but gravitation cannot be held responsible for it."

--Albert Einstein

• Edward
Lv 7

Do these two bubbles of empty space know each other?

Probably not. How would empty space know anything? Or be attracted to anything? Nay!

If they are not empty space but say gas bubbles they have bigger masses to deal with before they 'notice' each other.

And

The universe made of water with two lonely bubbles ... Hmm..

The bubbles probably will be forced toward the center of the universe where they would joint each other and live happily after.

When do you dream up these wonderful things?

OMG my learned friends are really serious. Okay let me put my thinking hat on. (Where is that silly thing? ...searching everywhere.)

Okay here it is (Wearing a thinking heat)

1. Yes if it is empty space it would not stay empty for long and that is the end. (that was said earlier)

2. If it is real physics as we know it then this body of water would collapse into a super-super massive black hole and that would be the end of Newtonian mechanics.

3. So now we have a problem similar to Newton’s Enigma for bubbles inside a sphere. Since we are in this funny physics world I wonder if the Gas Law, Archimedes and Bernoulli’s Principles also apply.

The problem is a simplified version of the one that faces scientist who are investigating dynamics in stars.

A. Archimedes principle – the bubbles rise. The higher they get the less is the probability of them to join (or attract). These bubbles are closer to the surface

B. Bernoulli’s Principles – the bubbles are deep inside the sphere and get squeezed to a tiny space and become liquefied and get dissolved in that universe of water.

C. The bubbles are close to the center of the water universe. What bliss? Now they are getting closer and closer as the forces of the universe are balanced upon them and they “joint each other and live happily after”.

Sorry (subbing) I do not belive in happy fairy tale ending. The C never happened. If it deed the Earth could have had a ‘bubble’ core.

I rest my case.

The bubbles probably will be forced toward the center of the universe where they would joint each other and live happily after.

When do you dream up these wonderful things?

• Anonymous
5 years ago

Well they have mass so they are subject to gravitational attraction but it is a very small effect and only if they are at he same size would it make sense to try and calculate it,this is because the large bubble will rise faster than the other and will leave it behind with the gravitational effect shrinking all the time.Question; if you hung two lead balls on thread close to each other how close together do you think you would be able to move them before they started to make a noticeable move towards each other? (You'd have to make certain that the two balls were at the same electric potential )There are equations to calculate the force but measuring the force is tricky but has been carried out to find the value of 'G'the universal gravitational constant.Good thinking,good question.

It's basically buoyancy at work. Buoyancy works in the opposite direction to gravitational acceleration. In energy terms, the lowest energy state has the denser materials at the bottom and less dense materials on top. (Bottom and top are defined by the direction of gravitational acceleration.) In fluids and suspensions, this state of stable equilibrium is easily attained. So anthropomorphizing a little, the bullying denser material forces the wimpy less dense one to get out of the way by moving upwards. ("King of the hill" in this case means being on the bottom.)

So answer A would seem to be the choice. However, there has to be acceleration. Is there? In an infinite universe, is there a CG? Is there a net gravitational acceleration toward it? Which way is that? It depends on the details of the "infinite universe" definition. My conception is that each bubble (say bubble 1) is at the center of its U, which extends infinitely far from it, so it resides inside an infinite series of shells, which, as the shell theorem tells us, should have no effect on it. However, there's an exception: one shell contains bubble 2. OK, let's replace bubble 2 with an equal volume of water taken from the opposite side of the shell and compensate by putting a small ball of lead in place of the displaced water on the opposite side. We have the same mass imbalance as before. Since bubble 1 has some mass, it's attracted toward the lead (i.e., away from where bubble 2 was). But the water in the all-water shell immediately surrounding bubble 1 is also attracted by the lead. So bubble 1, the wimp, is driven away from the lead and toward bubble 2's ex-location. This leads to answer C; they move toward each other.

Summarizing, in an infinite U with a CG, answer A. In one with an undefined CG, answer C, which is what I'm voting for.

Goodness, Dr H, you do tend to encourage the ramblers, train-of-thoughters and ratiocinators hiding inside each of us! More power to you!

• Mike
Lv 5

The answer depends on the nature of the bubbles.

If the bubbles are bubbles of empty space then they would move towards each other and collapse.

If the bubbles are bubbles of gas then they would move apart in the same way as bubble move upwards in fizzy drinks(moving away from the centre of gravity).

Now this was all assuming that your water universe is in the liquid state. If it was frozen water then the bubble would not move (or would move very slowly unless it was at absolute zero).

• 5 years ago

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