Physics question

[Zero]

With some basic assumptions, like the universe is a sphere, and that it's finite and that the atoms are the only 2 objects in that non-expanding or contracting universe, here is a simple Newtonian view of what should happen.

 

[Nords]

Thanks all. I'll have my son read this thread.

Well, heck, if he's going to come up with these physics questions on his own, then he'll need this indispensable scientific resource too:

 

[BigNick]

The question was not homework related; he just thinks up these questions in his spare time to entertain himself.

Cool! You have a future scientist there. Get him some books and encourage the interest!

1. Yes, the posited universe is supposed to be static to avoid the interaction between gravity and the expanding universe we happen to live in.

2. Yes, the universe is supposed to be empty just to simplify the problem.

3. I don't think he knows about quantum stuff (neither do I actually), so I don't think that was part of his question.

5. He maybe also wondering if the very tiny gravitational force (due to tiny masses and great distances) would be "enough" to bring the two atoms together. I think the answer is yes, but obviously, depending on the distance, it could take a really long time.

He would basically be right, as long as he reduced the scale. For example, two hydrogen atoms in a perfect vacuum inside a shoebox in orbit around the earth would eventually gravitate together, but after an amazingly long time. On the scale of the universe, the stochastic events have even more thousands of zeroes in them, on the divisor side.

4. He's been talking about terminal velocity lately, so I think his question was more along the lines of would there be anything else to slow down the two atoms / counteract the acceleration due to gravity like there is with a parachutist entering the atmosphere. I think the answer is no, like most posted here.

Well, on the scale of the universe, you have to take into account dark matter and dark energy. Are you going to remove them to allow the two atoms to see each other ? Part of the problem of doing that is that our current physics doesn't know how to identify them, which is a shame since they represent over 90% of the universe (which I would be pretty embarrassed about, if I were an astrophysicist!)

 

[FIRE'd@51]

Assuming, from what OP has posted, that this is a problem within the framework of Newtonian physics (i.e. neglecting any quantum mechanical or relativistic effects).

First of all, by symmetry, they would collide at a point halfway between the two particles and would each be traveling at the same speed (V), assuming a finite separation as described in post #34 by dpruitt85 and post #30 by ERD50, since the particles have the same mass (M) and are initially at rest. Since the two particles are the only occupants present in the universe, it becomes a conservation of energy problem - the initial gravitational potential energy due to the particles' separation is totally converted into kinetic energy when they collide.

The initial potential energy is the work required to separate the two particles (against the gravitational attraction between them) to a very large distance. This number (to a very close approximation) = GMM / R, where (in the metric system)

G = the gravitational constant = 6.67 x 10^(-11) N(m/kg)^2
M = the mass of a hydrogen atom = 1.674 x 10^(-27) kg
R = the diameter of a hydrogen atom = 10^(-10) m

To find the speed:

2 x ( 0.5 MV^2) = GMM / R

Solving for V (assuming I've done the arithmetic correctly)

V = SQRT ( GM / R) = SQRT ( 6.67 x 1.674 x 10^(-28) ) = 3.3 x 10^(-14) m/s

They ain't going very fast!

 

[rescueme]

But, I'd rather talk about in-laws, politics, finance and sex.

Me too - but in the reverse sequence ...

 

[clifp]

Reading this thread, I think I understand why Quants took over Wall St. Lots of intellectual fun trying to solve problems, plus when you are right you get rich and when you are wrong, you blame somebody else.

 

[Zero]

Here is a discussion on a physics (nerd) forum and it devolves into a discussion of two hydrogen atoms at a distance and the question is what would happen due to their attraction. From reading the discussions it seems that lots of folks interpret the physics associated with the atoms differently.

Inside an Atom [Archive] - Physics Forums

 

[Meadbh]

I think they would come together if they had a sufficient attraction to each other. Whether they would collide or waltz around each other would depend on their conflict management skills.

I got a B+ in physics.

 

[Walt34]

Assuming, from what OP has posted, that this is a problem within the framework of Newtonian physics (i.e. neglecting any quantum mechanical or relativistic effects).

First of all, by symmetry, they would collide at a point halfway between the two particles and would each be traveling at the same speed (V), assuming a finite separation as described in post #34 by dpruitt85 and post #30 by ERD50, since the particles have the same mass (M) and are initially at rest. Since the two particles are the only occupants present in the universe, it becomes a conservation of energy problem - the initial gravitational potential energy due to the particles' separation is totally converted into kinetic energy when they collide.

The initial potential energy is the work required to separate the two particles (against the gravitational attraction between them) to a very large distance. This number (to a very close approximation) = GMM / R, where (in the metric system)

G = the gravitational constant = 6.67 x 10^(-11) N(m/kg)^2
M = the mass of a hydrogen atom = 1.674 x 10^(-27) kg
R = the diameter of a hydrogen atom = 10^(-10) m

To find the speed:

2 x ( 0.5 MV^2) = GMM / R

Solving for V (assuming I've done the arithmetic correctly)

V = SQRT ( GM / R) = SQRT ( 6.67 x 1.674 x 10^(-28) ) = 3.3 x 10^(-14) m/s

Huh?

 

[donheff]

2Cor - terminal velocity would be a factor. And you can forget about dark mater since your son stipulated that the universe is empty except for the two atoms. The determining factor (unspecified) is the size of your son's universe. The atoms will continually accelerate towards each other. If the time available for acceleration (i.e. distance) is sufficient, the atoms will approach the speed of light. As they do time will slow down, mass will increase but the atoms can never exceed the speed of light so there is your terminal velocity.

 

[FIRE'd@51]

donheff - the speed of light is 3 x 10^8 m/s. When the atoms collide, they are traveling at 22 orders of magnitude less than the speed of light (see post #54).

 

[kumquat]

And if they hit head on at near light speed you wouldn't have two H atoms, you'd have 1 He atom and a bunch of superfluous energy.

 

[freebird5825]

I think they would come together if they had a sufficient attraction to each other. Whether they would collide or waltz around each other would depend on their conflict management skills.

I got a B+ in physics.

I majored in Physics for my Bachelor's degree. I earned an A in Atomic and Nuclear Physics. I donated that book to the local library a looooong time ago.
I was intentionally staying out of this thread because it requires higher level thinking and equations, something I gladly gave up when I FIREd.

However, this answer drew me into the vortex. I vote it to be the best answer so far.

 

[FUEGO]

With some basic assumptions, like the universe is a sphere, and that it's finite and that the atoms are the only 2 objects in that non-expanding or contracting universe, here is a simple Newtonian view of what should happen.

What you are saying is it would take 1750 trillion trillion trillion trillion years for these two atoms to collide (using your assumptions). That's pretty close to infinity. Do universes last that long? How did this universe get created and why were the hydrogen atoms so far apart and not moving? Somebody's got some 'splaining to do. I would turn this physics learning moment into a metaphysics learning moment!

 

[Zero]

What you are saying is it would take 1750 trillion trillion trillion trillion years for these two atoms to collide (using your assumptions). That's pretty close to infinity. Do universes last that long? How did this universe get created and why were the hydrogen atoms so far apart and not moving? Somebody's got some 'splaining to do. I would turn this physics learning moment into a metaphysics learning moment!

I had the same question, i.e., "Would the universe exist when the atoms collided?" And if not, where did the atoms go? Did they gradually fade away like Dorian Gray or quickly like the House of Usher?

 

[FUEGO]

I had the same question, i.e., "Would the universe exist when the atoms collided?" And if not, where did the atoms go? Did they gradually fade away like Dorian Gray or quickly like the House of Usher?

Do two hydrogen atoms a universe make?

If a matter-less DW lived in this hypothetical universe, I bet she would always be freezing and trying to turn up the thermostat.

 

[Zero]

Do two hydrogen atoms a universe make?

If a matter-less DW lived in this hypothetical universe, I bet she would always be freezing and trying to turn up the thermostat.

Ut oh, careful how you use that term "matter-less DW" or the universe could get very much colder

 

[dizzy]

Assuming this is strictly a newtonian problem, I see the following errors with the quantitative solutions so far:

- zeros solution contains the error that the radius of separation is a function of time as the particles move together. Thus the force (and therefore acceleration itself) will increase over time.

- Fired@51's solution is more elegant taking the conservation of energy approach. However his solution contains the error that the gravitational potential energy depends on the radius of initial separation of the atoms, not the radius of the atom itself.

 

[FIRE'd@51]

- Fired@51's solution is more elegant taking the conservation of energy approach. However his solution contains the error that the gravitational potential energy depends on the radius of initial separation of the atoms, not the radius of the atom itself.

No, it doesn't. The R in my formula in post #54 is one atomic diameter, i.e. the center-to-center distance between the atoms when they collide (i.e. their surfaces just touch).

 

[Zero]

Assuming this is strictly a newtonian problem, I see the following errors with the quantitative solutions so far:

- zeros solution contains the error that the radius of separation is a function of time as the particles move together. Thus the force (and therefore acceleration itself) will increase over time.

Can we take a look at a detailed solution that you have produced?

 

[dizzy]

No, it doesn't. The R in my formula in post #54 is one atomic diameter, i.e. the center-to-center distance between the atoms when they collide (i.e. their surfaces just touch).

I see. You are looking at the difference in potential energy of the system at collision radius vs. initial radius and making the assumption that the initial radius term is vanishingly small. I understand your thinking now. I didn't see the initial radius in your calculation and jumped to the conclusion that you had made a typo. Actually, this a quantitative version of the escape velocity solution proposed M Paquette in #13.

Can we take a look at a detailed solution that you have produced?

I'm with Fire'd@51. Your solution assumes a constant acceleration, which would imply a constant force independent of position, which is not the case for 2 bodies traveling towards each other.

 

[donheff]

I'm with Fire'd@51. Your solution assumes a constant acceleration, which would imply a constant force independent of position, which is not the case for 2 bodies traveling towards each other.

Why doesn't the force continually increase (inverse to the square of the distance) as the particles approach one another? I am still not clear on why, given a sufficient distance apart at the start) the particles wouldn't accelerate to approaching the speed of light.

 

[FIRE'd@51]

I see. You are looking at the difference in potential energy of the system at collision radius vs. initial radius and making the assumption that the initial radius term is vanishingly small. I understand your thinking now. I didn't see the initial radius in your calculation and jumped to the conclusion that you had made a typo. Actually, this a quantitative version of the escape velocity solution proposed M Paquette in #13.

Yes, that's exactly what I did. And yes, the speed I calculated is the escape velocity.

In a Newtonian framework, in which the atoms are treated as rigid spheres, they would undergo a totally elastic collision and rebound back to their initial separation.

 

[FIRE'd@51]

Why doesn't the force continually increase (inverse to the square of the distance) as the particles approach one another? I am still not clear on why, given a sufficient distance apart at the start) the particles wouldn't accelerate to approaching the speed of light.

The gravitational force does increase inversely with the square of the separation as the atoms approach each other. However, this force is much too small to accelerate the atoms up to the speed of light before they collide.

To prove this to yourself, go back to post #54 and use the equation for the speed I derived. Plug the speed of light in for V and solve for R.

 

[nun]

Two things to think about.

How long would it take the atoms to start moving assuming that gravitons move at the speed of light?

Also as EM force is orders of magnitude stronger than gravity wouldn't that be more important, after all it's the EM force that binds the H2 molecule together and not gravity