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Old 05-13-2011, 08:49 AM   #21
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If there is nothing else in the universe except the two atoms and conventional gravity, there is gravitational attraction between them which would eventually bring them together. The problem is that at extreme distances the gravitational force would be infinitesimally small, so the acceleration towards each other would be infinitessimally small. Also, the "universe" as we know it is not a fixed size, so there is a problem with the formulation of the problem "at opposite ends of a static universe" since we do not know what size the "universe" has been fixed at, nor how it is made static.
This post made me think (I don't know how right the thought is): if the universe is expanding faster than the very weak gravitational attraction, they'd continually move towards each other, and continually get further apart.

For the most part I agreed with Gumby in this thread.
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Old 05-13-2011, 09:04 AM   #22
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I don't want to seem argumentative, but the solutions proposed other than mine do not take account of the two atoms being at opposite ends of a universe. What sort of universe has opposite ends?
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Old 05-13-2011, 09:12 AM   #23
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I don't want to seem argumentative, but the solutions proposed other than mine do not take account of the two atoms being at opposite ends of a universe. What sort of universe has opposite ends?
By matter of definition, a universe contained all matters and forms. Therefore, no wrong answer what so ever to questions being asked about only 2H on the opposite ends. I wished I had questions like that where there are no wrong answers when I went to school.
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Old 05-13-2011, 09:16 AM   #24
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I don't want to seem argumentative, but the solutions proposed other than mine do not take account of the two atoms being at opposite ends of a universe. What sort of universe has opposite ends?
I would assume that to mean equally distant from each other in every direction.

EDIT: which I guess still makes your solution have some sense.
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Old 05-13-2011, 09:26 AM   #25
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I would suggest that hydrogen fuel cells would be the most efficient and most readily available source of energy in this universe.
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Old 05-13-2011, 09:52 AM   #26
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This is a special case of the two body problem. As the initial velocities are both zero the "orbit" will be a straight line between the two atoms. This "orbit" will pass through the center of mass of the system and so they will collide.
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Old 05-13-2011, 11:54 AM   #27
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OK now that have have solved that one, what about that 14 trillion $ deficit?

(It is these types of theoretical questions that turned me off school. I quit right after the Masters degree. My buddy who went on to get his PhD in Theoretical Physics eventually was gainfully employed through the delivery of the Charlottesville telephone directories!)
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Old 05-13-2011, 12:25 PM   #28
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OK now that have have solved that one, what about that 14 trillion $ deficit?
"First, we assume a spherical cow..."

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Old 05-13-2011, 12:43 PM   #29
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These are the kinds of things my kids come up with:

Assuming two hydrogen atoms starting out motionless at opposite ends of a static universe, with nothing else in the universe and standard gravity. Would they eventually hit each other, and if so, what speed would they hit each other at, and would they still be accelerating when they hit?

(I've no idea; I got a C in physics!)

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If I am reading correctly, you say "standard gravity", and if that is the case then someone has to provide information on what populates the "static universe". If there are other masses, as in planets or stars, then there are many gravitional fields and there is certainly no way to answer the question. If it is an empty universe then the only gravity would be the gravity associated with the mass of the atoms. In that case the atoms would begin to accelerate towards each other and collide.

The interesting thing about a question from a child is that they expect there to be "some" answer. Any protestation on your part that there is "no" answer will be interpreted as "dad/mom doesn't know the answer."
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Old 05-13-2011, 03:20 PM   #30
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The interesting thing about a question from a child is that they expect there to be "some" answer. Any protestation on your part that there is "no" answer will be interpreted as "dad/mom doesn't know the answer."
I bet the kids really didn't mean to complicate the question with the "opposite ends of a static universe" line. I think they really meant to simplify it, something like - 'really, really, really far apart, in a big ol' universe with nothin' else in it, but the conventional formulas for gravity still apply in this universe'.

So, unless some quantum levels need to be exceeded for these very small forces to react, or other forces are stronger, I guess the standard formula applies:

Newton's law of universal gravitation - Wikipedia, the free encyclopedia

Quote:
F = G*(m1*m2)/r^2
where:
F is the force between the masses,
G is the gravitational constant,
m1 is the first mass,
m2 is the second mass, and
r is the distance between the masses.

Assuming SI units, F is measured in newtons (N), m1 and m2 in kilograms (kg), r in meters (m), and the constant G is approximately equal to 6.674×10^−11 N(m/kg)^2.
So some tiny force that pulls them together, and the force keeps increasing pulling them harder and harder as they get closer and closer. With even a constant force, they would keep accelerating.

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Old 05-13-2011, 04:22 PM   #31
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Don't know if there is a 'correct' answer. Interesting subject though.

I posed the question to a person that I consider somewhat 'abnormal' in thought. The reply:

"If they don't miss and orbit each other, then they accelerate continuously since gravity is inversely proportional to the square of the distance between them. Oh, wait. Tricky since supposedly stuff can't go faster than speed of light. Don't know. Light speed shan't limit these atoms."
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Old 05-13-2011, 04:35 PM   #32
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I don't know why anyone would expect them not to come together in the scenario posited. Two atoms, gravity exists, universe is static - gravity would serve to pull the atoms together with no other forces to screw with them. In a classical universe they would accelerate constantly with the final speed depending on the initial distance up to, presumably, the speed of light. But with quantum effects, Katie bar the door. They could jump together instantly or never - but there would be a high probability of collision, at least in most of the universes.
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Old 05-13-2011, 04:39 PM   #33
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I don't want to seem argumentative, but the solutions proposed other than mine do not take account of the two atoms being at opposite ends of a universe. What sort of universe has opposite ends?

Something like this was my first thought..... if you have only two atoms, then the universe is only as 'big' as the distanct between the atoms...

IOW, what else is beyond these atoms? What is an edge to a universe?

But, here is the formula to get the force of gravity...



Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them:[3], where:
  • F is the force between the masses,
  • G is the gravitational constant,
  • m1 is the first mass,
  • m2 is the second mass, and
  • r is the distance between the masses.
Edit to add:
OK... I was not the first with the formula... OH WELL....
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Old 05-13-2011, 04:57 PM   #34
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If the atoms are infinitely far apart (as assumed in the universe) then the gravitational force is 0. In the gravitational force equation with 'r' being infinity and r^2 being infinity, anything divided by infinity is zero. If the force is zero and force equals mass*acceleration, then the acceleration must be zero.

In essence, you must define the distance.

EDIT: However, even if you defined an extremely large distance, say 5 quadrillion light years, the theoretical upper limit for velocity is the speed of light, regardless of acceleration.
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Old 05-13-2011, 04:57 PM   #35
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So, TP, by your formula there will be a force no matter how far apart they are. As it draws them together the force will increase. So they will increasingly accelerate as they approach. The farther apart they start, the greater their speed at collision (in a classical universe). Who cares about the edge of the universe. We all know that beyond that "there be dragons."
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Old 05-13-2011, 05:07 PM   #36
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So, TP, by your formula there will be a force no matter how far apart they are. As it draws them together the force will increase. So they will increasingly accelerate as they approach. The farther apart they start, the greater their speed at collision (in a classical universe). Who cares about the edge of the universe. We all know that beyond that "there be dragons."
Except if the universe is expanding at a faster rate than they move together (which seems very likely, as the distance between them would be so great as to make the attraction between them so small). See my post at the top of page 2.
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Old 05-13-2011, 05:11 PM   #37
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Except if the universe is expanding at a faster rate than they move together. See my post at the top of page 2.
I believe the OP said "static" universe for this question. But you are correct.
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Old 05-13-2011, 07:49 PM   #38
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OK now that have have solved that one, what about that 14 trillion $ deficit?
Congress will solve it the way they always do - by printing more money.
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Old 05-13-2011, 08:47 PM   #39
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Murphy's law says the atoms will only collide if they are trying their best to avoid collision.

A.
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Old 05-13-2011, 10:44 PM   #40
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zzzzzzzzzzzzzzz...........

No idea, I flunked Physics because I didn't really care if, where or when "Plane A" would meet "Plane B". Your kids have too much time on their hands...shouldn't they be on Facebook or something?
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