Gravity's Influence on 2 Isolated Hydrogen Atoms

[The_Cuckoo]

Hi all,

I hope this isn't a stupid question, but I was wondering this. If the universe only consisted of two hydrogen atoms, and those atoms were billions of light years apart. Would their weight bend space enough for them to be attracted to each other? Or does their influence have a point where it no longer has an effect? If so, does this mean the universe isn't entirely frictionless? Or that there is (I suppose you'd call it) cushioning in the fabric of space? I know that gravity is very weak compared to other forces, but would this make a difference?

I am nothing more than an layman enthusiast, but I'd be interested to hear about this works.

 

[jerromyjon]

Hi and welcome to PF!

Gravity is infinite, and gradual in my opinion, in contrast to electromagnetic force which is also infinite... but it peaks sharply in close range.

Infinite just means there is no conceivable distance for which the effect is zero.

 

[Simon Bridge]

In a universe with only two masses, those masses would gravitate together at any finite separation. Yes.
Note... a limiting range to a force of interaction does not imply friction. The concept of friction does not apply here.

 

[The_Cuckoo]

Thank you both, that's very interesting. So conceivably, given enough eons, those two hydrogen atoms would eventually be drawn together and (I presume) form a hydrogen molecule?

 

[Nugatory]

Gravity is infinite, and gradual in my opinion, in contrast to electromagnetic force which is also infinite... but it peaks sharply in close range.

That is not right. Both gravity and electromagnetic forces obey the same $1/r^2$ law for their strength at a distance.

The impression that electromagnetic forces "peak sharply in close range" is created because we have much more experience with large gradients for electromagnetic force. Measure the force of gravity at the surface of the Earth and one kilometer up; measure the electrostatic force from a charged object on the bench under your nose and then on the far side of the room; and you might conclude that the electromagnetic force peaks much more at short range. But what's really going on is that in one case you're looking at the difference between $1/6371^2$ and $1/6372^2$ and in the other case you're looking at the difference between $1/.1^2$ squared and $1/5^2$ (radius of Earth is 6371 km, and I'm assuming the lab bench is something like .1m away and the room is about 5m across).

 

[Nugatory]

Infinite just means there is no conceivable distance for which the effect is zero.

Yes, and an easy way to see this is to look at the classical equation for gravitational force: $F=Gm_1m_2/r^2$. No matter how large $r$ is, $F$ never falls to zero - the there is always some teeny force.

It's worth noting that this question could just as easily have been asked in the classical physics subforum instead of the relativity forum. That's not surprising, because we expect that GR and classical physics give the same results except when dealing with very strong gravitational fields and very fast-moving bodies - and two atoms drifting light-years apart is not that.

 

[Simon Bridge]

Thank you both, that's very interesting. So conceivably, given enough eons, those two hydrogen atoms would eventually be drawn together and (I presume) form a hydrogen molecule?

Yes... though the bond is not all that can happen.
It would be a nice exercize for you to work out the ballpark speeds the atoms would be moving wrt each other after falling together over very long distances.

 

[DaveC426913]

Yes... though the bond is not all that can happen.
It would be a nice exercize for you to work out the ballpark speeds the atoms would be moving wrt each other after falling together over very long distances.

If we assume no initial translational motion, then they make heap big collision.

 

[Simon Bridge]

People often underestimate the results of a small effect accumulation over a long time/distance.
This is why it is good to get the student to work it out.. did you have a go ? ;)

 

[The_Cuckoo]

Thank you all, I suspected it was the case that they would still be attracted over any finite distance, but I couldn't be sure. As I said, I'm a layman. I'd love to be able to sit down and do the maths, but my physics knowledge is also so inconceivably small, that I wouldn't even know where to start. :)

This question just occurred to me when I was watching the latest BBC Horizon about the cosmic dawn. I had no idea that the first hydrogen atoms were spaced so far apart in the early stages (about half a meter I think they suggested). That got me thinking about the OP question.

Fascinating stuff, thanks again. :)