Gravity and the shape of Universe

[rpmath]

Except for distances too close to the Schwarzschild radius, the Newton inverse square law is supposed to be very accurate for Gravity...<br />but what happens if the universe is curve?<br />I think gravity must be a little stronger than supposed for a flat universe.<br /><br />If the Universe is the 3D surface of a 4D hypersphere, y can represent it as the attached picture.<br />Lets say the Universe radius is R, I have a mass at point A and I want to test the gravity field at some point B whose distance to A is d.<br /><br />By Newton:<br />a = -GM / r²<br /><br />but if the universe is round, the real radius of the sphere centered in A where the gravity is distributed when it reaches B is not the same distance d between A and B, but a smaller value r, that I can calculate as:<br /> r = R sin(d / R)<br />and: <br /> a = -GM / (R sin(d / R))²<br /><br />if d is much smaller than the universe:<br /> a = -GM / d² -GM /(3 R²) -GM d² /(15 R⁴) - ...<br /><br /> a = -GM / d² * ( 1 + 1/3 (d/R)² + 1/15 (d/R)⁴ + ... )<br /><br />Is seems as a good way to get the size of the universe... but may be “d / R” is too small to measure the “1/3 (d/R)²” factor...<br /><br />If average Universe expansion speed is near light speed, R will be near 14 * 10⁹ light years the earth orbit radius is near 8 light minutes, so d/R will be near 8 min / ( 14 * 10⁹ * 365.25 * 24 * 60 min) = 10^-15<br /><br />can a error in the acceleration of 10^-30 be measured?<br />

 

[jmilsom]

I cannot respond to your technical post. But I was just reading in New Scientist about the Allais pendulum effect and Pioneer 10 and 11 anomaly - which may (but there are more skeptics than adherents) demonstrate flaws in our understanding of gravity! I see that there are scientists vigorously testing for the former, but so far nothing other than some unexplainable periodic effects. <br /><br />Any bearing on what you are saying here or completely unrelated? <div class="Discussion_UserSignature"> </div>

 

[frobozz]

Hmm, I was wondering if you could clarify a couple things in this. (1) Accepting general relativity, we accept that the universe has some intrinsic curvature as gravity is essentially a "bending" of space-time if you will excuse the metaphor. Thus, the universe already is not flat in that sense. This being the case, assuming that the universe is a bounded 4-manifold of some sort, why should we expect it's boundary to smooth like that of a sphere?<br /><br />(2)If it's not infact smooth (in the sense that it has no bumbs) , as your method seems to require, do you think that it might be possible to extend your idea slightly so that it still yields the size of the universe? <br />

 

[emperor_of_localgroup]

Interesting try to find radius of the universe. First your are using 'g' of a mass not force 'F'. That's OK. But the actual distance between the mass and point B when the univ is curved shouldn't be 'd', not 'r'? <br /><br />In that case d=R(theta). and the 'a' becomes<br /><br />a=GM/(theta*R)^2. <br /><br />Which is basically what you found for small angle. In either case, we have two very undeterminable unknowns, the angle and the R.<br /><br />Just my 2 cents. Nice idea tho.<br /> <div class="Discussion_UserSignature"> <font size="2" color="#ff0000"><strong>Earth is Boring</strong></font> </div>

 

[rpmath]

<font color="yellow">I cannot respond to your technical post. But I was just reading in New Scientist about the Allais pendulum effect and Pioneer 10 and 11 anomaly - which may (but there are more skeptics than adherents) demonstrate flaws in our understanding of gravity! I see that there are scientists vigorously testing for the former, but so far nothing other than some unexplainable periodic effects. <br /><br />Any bearing on what you are saying here or completely unrelated?<br /></font><br />I was thinking in “Pioneer anomaly” when I started to calculate this...<br />but the correction term I got was so small that using Pioneer distance and accumulating the acceleration over decades it still wouldn't be noticed...<br />so... I didn't find the answer <img src="/images/icons/frown.gif" />

 

[rpmath]

<font color="yellow">Hmm, I was wondering if you could clarify a couple things in this. (1) Accepting general relativity, we accept that the universe has some intrinsic curvature as gravity is essentially a "bending" of space-time if you will excuse the metaphor. Thus, the universe already is not flat in that sense. This being the case, assuming that the universe is a bounded 4-manifold of some sort, why should we expect it's boundary to smooth like that of a sphere?<br /></font><br />Well... I just jumped to the easiest solution: assuming after the big bang everything expanded at the same speed in a 4D space, so it wold be located in the 3D surface of an hyper-sphere... <br />but it may be different. <br /><br /><font color="yellow">(2)If it's not infact smooth (in the sense that it has no bumbs) , as your method seems to require, do you think that it might be possible to extend your idea slightly so that it still yields the size of the universe?</font><br />It would be much harder...<br />The test would give the curvature radius of the closer bumb... <br />then repeat the test at different locations and you can get the real shape of that and some differences than can be associated with the curvature of the universe... <br />or just another bigger bumb!!!

 

[rpmath]

<font color="yellow">Interesting try to find radius of the universe. First your are using 'g' of a mass not force 'F'. That's OK. But the actual distance between the mass and point B when the univ is curved shouldn't be 'd', not 'r'?<br /></font><br />I was looking gravity as a flow.<br />If it is flowing from a source, the flow itself must be constant through surfaces enclosing the source.<br /><br />flow = a * 4 pi r² = (GM / r²) * 4 pi r² = 4 pi GM<br /><br />If the surface of the enclosing sphere at a distance d is 4 pi r² instead of 4 pi d², the acceleration must be related to r instead of d... <br /><br />Other problem with my idea is that if you go to the other half of the universe, the gravity keeps growing as you go farther, and at the opposite point of the universe it will look like you have a repulsive equivalent of this mass...<br /><br />Opposite to each mass you would have a void region with repulsive gravity...<br />This sounds very strange, but there are galaxies alternated with void regions without something inside we can look to see if there is repulsive gravity... so it still cannot be discarded.

 

[tex_1224]

what if inside your 4D grid, was 6 outer planes that make up the solid. 10 total. yes you are right. the reason its too small to count is that this effect goes on infinitely in all directions by multiples of 6. But by using a cube shape, we can see 10 total dimensions, which in fact is a 3 dimensional object. Gravity is indeed much more powerful than we think. Gavity combined with the force of electro-magnetism will show us the power of a super nova. caught in a reactor and tapped for energy. I have a model of an Electro-magnetic jet engine, that is nowhere near being a jet, but a very powerful magnet.

 

[frobozz]

>Well... I just jumped to the easiest solution: assuming >after the big bang everything expanded at the same >speed in a 4D space, so it wold be located in the 3D >surface of an hyper-sphere... <br /> />but it may be different. <br /><br />Here my physics runs completely into a hole and dies horribly, but could one, starting with some reasonable assumptions how the universe began, perhaps prove that the universe expanded evenly within some error term (reasonably small one).<br />