# Gravity (over extremely long distances)

1. Aug 30, 2010

### jspstorm

This question may be a little vague or difficult to answer definatively.

Take an empty universe, completely bereft of all energy and matter, with the exception of two neutrons. These two neutrons are placed a trillion light years apart from eachother and each have no velocity with respect to the other.

My question is: Will gravity eventually pull them together?

2. Aug 30, 2010

### fatra2

Yes.

3. Aug 30, 2010

### mathman

Yes and no. Neutrons are radioactive with a half life of about 15 minutes. As a result, they will be long gone before they can come together. However the resultant protons and electrons will eventually come close enough that quantum effects will come into play.

4. Aug 30, 2010

### DLuckyE

Isn't that assuming that there's no lower limit to the strength of gravity? Doens't everything have a lower limit in QM?

That's even besides the fact it'd take a trillion years before they'd even notice the gravity from eachother (if it can reach that far)

5. Aug 30, 2010

### Lsos

Yeah and then there's that whole dark energy thing which is supposed to make up most of the universe.

I think it's safe to assume that in this case, we don't know.

6. Aug 30, 2010

### DaveC426913

Without complicating the question beyond the intent of the OP, fatra2 is correct.

As far as we know, gravity has an infinite reach.

7. Aug 30, 2010

### pallidin

Just a thought:
In this case as described by the OP, I think the gravity over that distance would be so extraordinarily weak as to unable to break the inertia of the non-moving neutrons to initiate attractive motion.
Could be wrong, of course, but I tend to agree that there should be some lower limit.

8. Aug 30, 2010

### JDługosz

Inertia is not like static friction.

9. Aug 30, 2010

### pallidin

Understood, but can a stationary bowling ball(for example) move from a stationary position in space if a light feather impacts it slowly?
There is simply not enough force to break inertia.
At least in my thoughts. Could be wrong!

10. Aug 30, 2010

### pallidin

To my understanding, an object at rest tends to stay at rest unless acted upon by outside forces.
Fine, but surely there must be some lower limit which defines at what "force level" the object will start to move.
After all, could I responsibly say that a force of .000000000000000000000000000001 grams will even slightly move a bowling ball in space?

11. Aug 30, 2010

### diazona

Yes. Absolutely.

Inertia is not something that can be "broken". There is no predicted or observed lower limit for the amount of net force that it takes to make an object move. So as far as we can tell, any force, no matter how tiny, applied to any mass, no matter how large, will induce some acceleration.

12. Aug 30, 2010

### pallidin

Ok. Interesting. Thanks.

13. Aug 31, 2010

### Mentallic

Just our of curiosity, could anyone calculate the magnitude with what kind of Newton force we are dealing with between these 2 neutrons? Remember, 2 neutrons and a trillion light years apart

I'd do it myself but I don't know what equations to use.

14. Aug 31, 2010

### betel

The equation would be
$$F = \frac{G m_n^2}{r^2}$$
Now we have
$$m_n = 1.67 \cdot 10{-27}kg$$
$$G = 6.67\cdot 10^{-11}N\frac{m^2}{kg^2}$$
$$r= 10^{12}ly = 10^{12}\cdot 9.46 \cdot 10^{15}m=9.46\cdot 10^{27}m$$
Together
$$F \approx 2\cdot 10^{-120}N$$

15. Aug 31, 2010

### Mentallic

That's one hell of a force!

Assuming the force stays constant on both neutrons attracting each other, then it would take approx 1053 years for them to collide. At the time of their collision, they'll be slamming into each other at a whopping 200 Planck lengths per second.

But what bothers me is that I've used a simplified version of events with my assumption. Of course the attractive force will increase as they get closer to each other. Anyone know how this could be calculated?

16. Aug 31, 2010

### DaveC426913

Why would you assume this? It's like assuming a jumper will reach the ground at the same velocity with which they left the top of the building.

17. Aug 31, 2010

### .physics

I was just astonished to find out how you guys get such brilliant ideas. jspstorm, I liked your query.

Going by the law of physics and usual calculation , the attraction surely look possible though very negligible.But what I feel is that the gravitons responsible for creating gravity that too emitted by a neutron for attracting another neutron even 1 cm away is impossible. Gravitational force has always been used to calculate the force between bodies with large mass.The value of G by definition is found wrt object with huge masses. I don't think this thing practically exists at atomic level though we can prove it theoretically

And one more thing that I strongly believe is that the laws of physics though seem to be applicable in earth and in nearby galaxies, it might just be a coincidence and different law of physics exists there. Let's take example of an atom - though we can't exactly tell or see if the atomic model is correct, it has been working fairly good for required calculations and reactions. Might be there's some more complex part that has been abstracted to justify a simple model by the atom itself. We are still debating on it aren't we- quantum theory , string theory etc...

So I strongly believe that universe got itself different kind of laws and and it doesn't follow the earthly law of physics. We can't argue that astrophysics is the most mysterious and interesting field of science.

So, the answer for me - NO!! if earthly knowledge is applied.

Yes , if there exists any other universal surprise.

18. Aug 31, 2010

### Mentallic

Because I couldn't calculate it properly otherwise

19. Aug 31, 2010

### betel

To calculate it properly you would have to use the equations of motion
$$2m \ddot r = -G\frac{m^2}{r^2}$$
Or use the easier way of energy conservation
$$E = 2m \dot r^2 - G\frac{m ^2}{r}=E_0=-G\frac{m^2}{r_0}$$
Integrating this for r from $$r_0$$ to 0 gives
$$T=\sqrt{\frac{4}{\pi}}\Gamma\left(\frac{3}{4}\right)^2\frac{1}{\sqrt{G m}} \sqrt{r_0}^3$$
For $$r_0=10^{12}ly$$ this is $$T = 5 10^{60}s \approx 10^{53} y$$

Of course this calculation is only using Newtonian Gravity and neglecting any effects from Quantum processes or General Relativity. The last has to be taken into account for the last few seconds.

20. Aug 31, 2010

### KingNothing

I am guessing that you haven't taken calculus 2. Essentially an integral is a way of adding up little bits of an equation evaluated at different points.

In this case, it'd be a matter of finding the time it takes to travel some small distance x based on the radius (distance between the two neutrons), and integrating that over the entire distance.

On a side note, our definition of time is completely invalid in this case, as "earth time" is not the same as "universe time", and if there is no earth, then any measurement of time is invalid.