Gravity (over extremely long distances)

[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 each other and each have no velocity with respect to the other.

My question is: Will gravity eventually pull them together?

 

[fatra2]

Yes.

 

[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.

 

[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 each other (if it can reach that far)

 

[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.

 

[DaveC426913]

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

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

 

[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.

 

[JDługosz]

Inertia is not like static friction.

 

[pallidin]

Inertia is not like static friction.

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!

 

[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?

 

[diazona]

Understood, but can a stationary bowling ball(for example) move from a stationary position in space if a light feather impacts it slowly?

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.

 

[pallidin]

Ok. Interesting. Thanks.

 

[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.

 

[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

 

[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?

 

[DaveC426913]

Assuming the force stays constant on both neutrons attracting each other,

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.

 

[.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.

 

[Mentallic]

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.

Because I couldn't calculate it properly otherwise

 

[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
<br /> 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.

 

[KingNothing]

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?

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.

 

[QuantumPion]

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.

Could you elaborate your reasoning of this?

 

[Mentallic]

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.

I've studied integration, I couldn't wrap my head around the required equation.

Why is Earth required to measure time? So if we lived on Mars then the measurement of time would be invalid? Nonsense...

 

[Mentallic]

To calculate it properly...
T = 5 10^{60}s \approx 10^{53} y

That doesn't seem right, since I already calculated the time to be exactly that, but with the assumption that the gravitational attraction between them increases as they get closer. I'm expecting it to be orders of magnitude faster than that value.

 

[DaveC426913]

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.

Yeah, that is kind of strange.

So, do you claim that these two neutrons do not have a decay rate if there is no Earth? The lack of an Earth somehere in the universe means that these neutrons behave by different laws of physics?

 

[rcgldr]

Prior threads that show the math for this (without using energy conservation method). Credit to Arildno for figuring how to solve one of the integrals:

point masses:
https://www.physicsforums.com/showthread.php?t=360987

masses of fixed size:
https://www.physicsforums.com/showthread.php?t=306442[/QUOTE]

 

[Janus]

That doesn't seem right, since I already calculated the time to be exactly that, but with the assumption that the gravitational attraction between them increases as they get closer. I'm expecting it to be orders of magnitude faster than that value.

I got 6.9e52 years.

Here's how:

Two objects sitting at rest at a given distance from each can be treated like two objects in orbit around each other but in extremely eccentric orbits, with a semi-major axis equal to half the distance between them with each at the periapsis of its orbit.

The period of the orbits of such bodies is found by:

P^2 = 4 \pi^2\frac{a^3}{G(M_1+M_2)}

Since falling in from periapsis to collision represents 1/2 of an orbit,

The time will be half that of the period of a whole orbit.

 

[DaveC426913]

I got 6.9e52 years.

Here's how:

Two objects sitting at rest at a given distance from each can be treated like two objects in orbit around each other but in extremely eccentric orbits, with a semi-major axis equal to half the distance between them with each at the periapsis of its orbit.

The period of the orbits of such bodies is found by:

P^2 = 4 \pi^2\frac{a^3}{G(M_1+M_2)}

Since falling in from periapsis to collision represents 1/2 of an orbit,

The time will be half that of the period of a whole orbit.

And what is their speed at perigee?

 

[betel]

I recheck my calc. I got the integral wrong but this will only change the numerical factor.
T= \sqrt{r_0}^3\frac{1}{\sqrt{Gm}}\frac{\pi}{\sqrt{2}}=1.9e53y
My formula is the same as Janus' but I get a different numerical result.

 

[Mentallic]

Is T in years or seconds?

 

[betel]

This is in years

 

[Janus]

And what is their speed at perigee?

Assuming it is when the neutrons are about two neutron radii apart, I get about 0.1 Angstrom/sec

 

[DaveC426913]

Assuming it is when the neutrons are about two neutron radii apart, I get about 0.1 Angstrom/sec

That's pretty slow for 1 trillion years of acceleration..

 

[.physics]

Assuming it is when the neutrons are about two neutron radii apart, I get about 0.1 Angstrom/sec

I recheck my calc. I got the integral wrong but this will only change the numerical factor.
T= \sqrt{r_0}^3\frac{1}{\sqrt{Gm}}\frac{\pi}{\sqrt{2}}=1.9e53y
My formula is the same as Janus' but I get a different numerical result.

That doesn't seem right, since I already calculated the time to be exactly that, but with the assumption that the gravitational attraction between them increases as they get closer. I'm expecting it to be orders of magnitude faster than that value.

You guys seem to be genius trying to crack this riddle. In fact you are doing it the way it should be done. Don't take it otherwise but I have second thoughts over the matter.

It might be easy to prove theoretically that any phenomena abiding by the contemporary law of physics can happen and the numbers can also be calculated accordingly. We also know that many of the laws of physics were proven wrong or modified through time for some specific conditons and were tagged limited for certain attributes.For eg E=mv² is not always applicable until v=c i.e. speed of light(I don't think that has been proven yet as well)

I surely don't think that the numbers obtained here would actually occur in practical scenario.
Talking pragmatically, we should better try to challenge the existing laws and modify them if required because every law should necessarily have some limitations and it would be better if we could find them and fix the bugs.

We are the same who made the formula and they obviously contain some errands. So I think it would be more rational to revise the laws of physics and modify it and get a more applicable and acceptable law , especially for the cases like this rather than blindly insisting on the theoretical possibilities generated by existing law.

So from my side there's a straight NO for the answer.
My proof: No one can prove it right practically and no one can prove me wrong.
I don't think the gravitational field created by a mere neutron would extend so long distance. We need to somehow embed this limitation into formula and modify it.

 

[DaveC426913]

I don't think the gravitational field created by a mere neutron would extend so long distance.

OK, based on what evidence? Is there precedent for thinking that gravity would not extend this far?

If not, why would you even invent such a limitation? And what is preventing me from inventing, like you, a hypothesis that, say the scenario spontaneously generates a unicorn?

The scientific method is not about some sort of 'knowing what really happens'; it is about rationality - observing and developing rational rules that seem to describe how the universe works.

 

[diazona]

For eg E=mv² is not always applicable until v=c i.e. speed of light(I don't think that has been proven yet as well)

There is no such equation as E=mv². The equation is E = mc². Energy = mass × (a constant). It just happens that the constant has the numerical value and units of the speed of light squared. The equation applies only to objects at rest, i.e. v=0, and it has been well verified by experiments. See e.g. this thread for more information.

 

[jspstorm]

So how does gravity function according to the most recent standard model? Is there particle interaction? I remember reading about gravitons years ago, but it seems unlikely to me that any particle could be involved, I mean try to imagine a mass emitting so many particles that the universe could be sufficiently saturated as to constantly affect every other mass in existence, even masses a trillion light years distant. Also, this particle would have to have a constant velocity of infinity in order to operate in accordance with our observations on gravity.

I also read that gravity is the distortion of space-time, maybe this is the more likely answer?

 

[DaveC426913]

So how does gravity function according to the most recent standard model? Is there particle interaction?

This is quantum gravity. They're working on it, but it has mixed success so far.

this particle would have to have a constant velocity of infinity in order to operate in accordance with our observations on gravity.

Gravity changes do not travel at infinity; they travel at c.

I also read that gravity is the distortion of space-time, maybe this is the more likely answer?

That is the GR model, yes.

The $64,000 problem is reconciling GR and QG.

 

[jspstorm]

Gravity changes do not travel at infinity; they travel at c.

So if the Earth's sun spontaneously collapsed into a black hole, then gravitational tides would reach us immediately after the last photon emitted by the sun?

 

[DLuckyE]

OK, based on what evidence? Is there precedent for thinking that gravity would not extend this far?

If not, why would you even invent such a limitation? And what is preventing me from inventing, like you, a hypothesis that, say the scenario spontaneously generates a unicorn?

The scientific method is not about some sort of 'knowing what really happens'; it is about rationality - observing and developing rational rules that seem to describe how the universe works.

If gravity is actually caused by a something like a graviton, wouldn't you also have to conclude that at a far enough distance the gravitons are going to be to spread out to hit your other little particle?

 

[jspstorm]

What about conservation of angular momentum? If gravitons take time to reach their "targets" wouldn't planetary orbits become seriously messed up?

Also, doesn't the minimum level of illumination caused by a solar eclipse lag several seconds behind the gravitational effects?

 

[DaveC426913]

So if the Earth's sun spontaneously collapsed into a black hole, then gravitational tides would reach us immediately after the last photon emitted by the sun?

Correct. We would not know what happened to the Sun for 8 minutes after it happened. The grav effects would show up simultaneously with the visuals.

 

[DaveC426913]

If gravity is actually caused by a something like a graviton, wouldn't you also have to conclude that at a far enough distance the gravitons are going to be to spread out to hit your other little particle?

Why? Individual photons can travel a trillion light years.

 

[JDługosz]

OK, based on what evidence? Is there precedent for thinking that gravity would not extend this far?

Existing "correct" theories tend to break when pushed far beyond observed ranges of operation, with the old theory being a limiting approximation in that regime. E.g. SR replaces Newton's laws, when speeds get high.

Nobody has studied very small accelerations or weak gravity. If current theory were to be wrong, this is an area where it might show up. Meanwhile, QM + Gravity is a major unsolved problem. So, the behavior of gravity outside of its known regime is a point of, at the very least, humility in our confidence.

 

[JDługosz]

So if the Earth's sun spontaneously collapsed into a black hole, then gravitational tides would reach us immediately after the last photon emitted by the sun?

What "tides"?
If the sun collapsed into a black hole, it would weight the same and its gravity would not change.

 

[Mentallic]

If gravity is actually caused by a something like a graviton, wouldn't you also have to conclude that at a far enough distance the gravitons are going to be to spread out to hit your other little particle?

Why? Individual photons can travel a trillion light years.

He didn't say individual particles can't reach that far, but rather since they are individual gravitons and there are a certain finite number of them when they are ejected from the neutron, the gravitons would be too spread apart by the time they reach the other neutron to hit it. The likelihood of a graviton reaching the other neutron would be very low, so maybe gravity works differently in extreme cases like this?

What "tides"?
If the sun collapsed into a black hole, it would weight the same and its gravity would not change.

I read it the same as DaveC did. He was just trying to explain some way that the sun would suddenly disappear as if it were never there. A black hole wouldn't work like that, but it was close enough

 

[diazona]

He didn't say individual particles can't reach that far, but rather since they are individual gravitons and there are a certain finite number of them when they are ejected from the neutron, the gravitons would be too spread apart by the time they reach the other neutron to hit it. The likelihood of a graviton reaching the other neutron would be very low, so maybe gravity works differently in extreme cases like this?

Well technically a graviton is a quantum of the gravitational field, in the same sense that a photon is a quantum of the electromagnetic field. It's sort of, but not exactly, like a classical particle. You could think of it like this: when the first neutron's gravity actually interacts with the other neutron, it acts like a particle (the graviton), but when it's traveling between the neutrons it's more like a wave, and a wave would never get spread out enough that it would "miss" its target.

 

[Mentallic]

I see.. I knew there would be a catch to it being called a particle

 

[DaveC426913]

What "tides"?
If the sun collapsed into a black hole, it would weight the same and its gravity would not change.

Heh. You are, of course, right. And I never tire of pointing that out usually. Missed it this time.

Well technically a graviton is a quantum of the gravitational field, in the same sense that a photon is a quantum of the electromagnetic field. It's sort of, but not exactly, like a classical particle. You could think of it like this: when the first neutron's gravity actually interacts with the other neutron, it acts like a particle (the graviton), but when it's traveling between the neutrons it's more like a wave, and a wave would never get spread out enough that it would "miss" its target.

What he said.

 

[cjameshuff]

Something worth noting is that there's nothing special gravitationally speaking about two bits of mass being lumped together to form a larger object...the gravitational field of the whole is simply the sum of the fields of each of the parts. (aside from details like binding energy...)

The force holding you onto Earth's surface is the sum of that of each subatomic particle comprising each atom of the planet, most of them being thousands of km away from you. The same goes for the force holding the Earth in orbit around the sun, and the solar system in orbit through the galaxy. Galaxy clusters are held together by the gravitational fields of electrons and protons acting across millions of light years of distance. The gravitational field of a single subatomic particle may be unmeasurably small, but it adds up.

 

[DaveC426913]

Something worth noting is that there's nothing special gravitationally speaking about two bits of mass being lumped together to form a larger object...the gravitational field of the whole is simply the sum of the fields of each of the parts. (aside from details like binding energy...)

The force holding you onto Earth's surface is the sum of that of each subatomic particle comprising each atom of the planet, most of them being thousands of km away from you. The same goes for the force holding the Earth in orbit around the sun, and the solar system in orbit through the galaxy. Galaxy clusters are held together by the gravitational fields of electrons and protons acting across millions of light years of distance. The gravitational field of a single subatomic particle may be unmeasurably small, but it adds up.

You know ... you're right.

It isn't always obvious that a single proton a hundred million light years distant has a gravitational effect on us here on Earth, but it is indeed true and quite easily observable. If it were not true, then galaxy clusters would not be bound gravitationally.

The only thing binding galaxy clusters across hundreds of millions of light years is the gravity between the individual bits of matter.