A way to calculate the practical range of gravity

[pkcyll]

Theoretically, the range of gravity is infinite. OK. But the nature of the fabric of space has "building blocks" (Planck volume?)
So while a localized body of mass/energy distorts space-time, the distortion decreases away from the body. I would think this has a practical limit. Just as energy has to have a minimum of h to exist "permanently" in our universe, any space distortion less than a Planck area should have no effect of the local geometry - I would think.

Does anyone has a back of the envelope method of calculating what that distance ought to be for a particular mass?

Thanks,

 

[torquil]

First of all, the established facts about space and time is that it is continuous and obeys general relativity on a large range of scales. Nothing about quantum gravity has been confirmed, so we do not really know if anything special happens with spacetime at the Plancklengths/times or not. Nothing about discreteness or non-commutativity.

However, I think I understand what you are getting at. But e.g. in quantum field theory, there is no lower limit > 0 on the weakness of a particular interaction. And the energy/momentum of a freely moving object can change by an arbitrarily small amount, at least as long as the size of the universe is infinite. This would also be true for an object's interaction with a graviton, if quantum gravity exists. By the same token, there is no "practical upper limit" on the range of the interaction in QED.

Torquil

 

[torquil]

One more thing. In a quantum gravity, space itself would have vacuum fluctuations. When you go far enough away, the gravitational field from the source will be so small that it is similar in value to these fluctuations. Despite this, I'm not sure it would be correct to say that this defines an upper limit for the gravitation from a given localized object. In any case, you need the size of these space-time fluctuations in order to complete the estimate.

Torquil

 

[pkcyll]

Hi Torquil,

Thanks for the clarifications. I was under the impression that the space-time fluctuations are found below the Planck length (10^-35 m)

 

[Naty1]

I was under the impression that the space-time fluctuations are found below the Planck length (10^-35 m)

thats correct...

When you go far enough away, the gravitational field from the source will be so small that it is similar in value to these fluctuations.

so's that...

and that's the answer I would have given. these vacuum fluctuatons are essentially zero and that's the value of the gravitational field near infinite distance...

I'd be amazed if anyone has a "back of the envelope" approximation...

 

[torquil]

thats correct...
so's that...

and that's the answer I would have given. these vacuum fluctuatons are essentially zero and that's the value of the gravitational field near infinite distance...

I'd be amazed if anyone has a "back of the envelope" approximation...

Get ready to be amazed!

Consider a source mass m at a distance r. Also, consider that an experiment is made over the time space t. I would say that if the test mass has moved more than a few Planck lengths towards the source, it would be an indication that the distant gravity field from the source is still dominant. However, if it only moves one Planck length, then it is comparable. So I try to find this point to define this limiting distance.

So, using Galilei's s = 0.5*a*t^2 (Lp is Planck length)

$$\frac1{2} * a * t^2 = L_p$$

where a is the acceleration caused by the distant mass m in the weak Newtonian limit (with G:=1):

$$a = m/r^2$$

Thus

$$r = \sqrt(\frac{m}{2L_p})*t$$

So this depends on how long a time you want to wait for the measurement.

Putting in the mass of the sun, the Planck length, and a time of measurement of one year, I get:

$$r \approx 10^{40}m$$

or around $$10^{24}$$ light-years.

Of course, this could all be complete nonsense, but I was kinda motivated by the above statement :-) Feel free to shoot it down...

Torquil

 

[pkcyll]

Hi Torquil,
Thanks for the approach! I wonder why you normalized G to be 1. Using the usual 6.63 10^-34m lowers r if we keep in the mks system. Also why a year? Why not a second? For that matter (no pun intended), at those scales, 1 second is pretty close to eternity (the smallest time scale being used for the Universe to emerge from the Plank Era being 10^-43 second.) [I am not implying that time has a quantum pulse - I am just wondering if 1 year wait for something to move 10^-34 m is a bit much.]

 

[torquil]

Hi Torquil,
Thanks for the approach! I wonder why you normalized G to be 1. Using the usual 6.63 10^-34m lowers r if we keep in the mks system. Also why a year? Why not a second? For that matter (no pun intended), at those scales, 1 second is pretty close to eternity (the smallest time scale being used for the Universe to emerge from the Plank Era being 10^-43 second.) [I am not implying that time has a quantum pulse - I am just wondering if 1 year wait for something to move 10^-34 m is a bit much.]

Your quite right. No particular reason for any of the choices. And I may have done something incorrect with the units, it all went by so quickly! Actually, I just wanted to not have to write G a few times, and the other choices were quite arbitrary. I actually think that I used the 10^-34m value for the Planck length when I plugged into my formula. So something may be wrong, but now it is 3AM here, so I think I'll get some sleep instead of checking the calculation...

Torquil