What is the elusive origin of gravity?

[Garth]

What contradiction between the stone's fall and gravitational tides?

A stone fall in one direction, - the tide in the exact opposite.
These phenomena’s is off course not a contradiction, - only our attemp to solve the cause of these often seems to be.
We have no general accepted gravity theory able to comprehend the cause of both these phenomena’s.

If a person is going to criticize a theory, rather than just ask questions about it for enlightenment, then they need to first fully understand that theory; otherwise they demonstrate only their own ignorance.

The fact that you say "We have no general accepted gravity theory able to comprehend the cause of both these phenomena’s" only illustrates your ignorance.

If you had asked, "What is their explanation", others such as myself would have only been too glad to inform you. Which I will so do now.

The curvature of space-time accurately explains the behaviour of falling bodies. GR explains and predicts the trajectories of freely falling bodies more accurately than the Newtonian gravitational theory, nevertheless Newtonian theory is still used in orbital dynamics in regimes where its accuracy is sufficient because it is simpler.

In a curved space-time bodies such as a free falling stone and the Earth converge because their geodesic paths converge - that is their 'straight-line trajectories upon the curved space-time surface' converge. (Draw a straight line on a flat sheet of paper and then bend/deform the paper).

Now consider the Earth freely falling in the Moon's or the Sun's gravitational field.

Treat the Earth as a sphere of dust. Its centre of gravity is falling directly towards the centre of gravity (CoG) of the Moon (Sun).

All dust particles converge on the Moon/Sun, however those on the side nearer the Moon (Sun) 'fall' at a greater acceleration (- GM/r²) than those on the far side.

The dust particles on the two opposite sides of the Earth also converge onto the CoG of the Moon (Sun), so the two sides close in together.

The spherical dust Earth becomes ellipsoidal, and it is this tidal action that is the local signature or observable evidence that the Earth is freely falling in an external gravitational field.

Relative to the CoG of the Earth the tide on the side closest to the Moon (Sun) appears to be attracted away from the Earth, on the opposite side of the Earth, the Earth appears to be attracted away from the tide, in your own words: "a stone fall in one direction,- the tide the other in the opposite".

At the sides of the Earth there is low tide.

I hope this has made it clear.

Garth

 

[Bjarne]

Garth

OK the moons circulation causes the acceleration of the Earth to change a bit and this is the cause of the tide. Well probable nothing wrong with that. I am focused of the variation of force that space passes on between the bodies, and the cause of that. It’s off course the same force that pulls down a stone. We can explain both phenomena’s based on the acceleration of gravity (the expression of a such force) but this is of course only a superficial solution, - and well you are right nothing wrong with that.

Thank you for sharing your knowledge.

-------
Bjarne

 

[Chris Hillman]

Nature of "space"?

Hi, yogi, I must demur on at least one point:

I consider Einstein's words regarding the conditioning of space by matter as definitive as to how we should interpret space in the gtr...Einstein viewed space as something. That may not be the view held by many on these boards - but it was Einstein's view.

• Einstein's views changed so radically and so often that IMO statements of the form "X was Einstein's view" have little meaning.
• Einstein died in 1955, well before the "Golden Age of Relativity" (c. 1960-1975). You might be able to argue that some statement on topic T by Einstein represents his definitive statement of his own most mature view on topic T, but IMO it would be ludicrous to insinuate that physics/mathematics stopped when Einstein died.

in de Sitters spherical universe where both space and time dilate equally.

This sounds like the same fallacy I seem to have been debunking with unusual frequency in recent days here at PF. If so: "length" does not "shorten" and "time" does not "slow down".

Regardless, given that the term "dilation" is seriously misleading but well entrenched, I suggest that everyone here should always take the time to write out more carefully what one really means. Never forget that so-called "time dilation" effects always involves a comparison between two clocks in different states of motion. Thus, it never makes sense to say "time dilates" without the context of what clocks are being compared and how. Similar but even more nuanced remarks hold for "space dilates".

If the de sitter sphere is uniformly expanding (uniform radial dilation c) the spacetime surface(s) [3 space and one time] of the deSitter universe will have normal components of acceleration.

I don't even want to try to guess what you might mean--- particularly if your "c" has something to do with light!

However, I have been mulling the prospect of trying to write some brief expositions of frame fields and "beacon" null geodesic congruences in some simple and often encountered cosmological models including

• Milne frame in Minkowski vacuum (as a foil for genuine cosmological models),
• expanding inertial frame in deSitter lambdavacuum,
• frame of dust in FRW dust models, plus FRW lambdadust models, plus frame of inertial particles not comoving with dust, plus contracting FRW matched to Schwarzschild as per Oppenheimer-Snyder collapsing dust ball model,
• frame of dust for LTB dusts (spherically collapsing dust clouds),
• ditto, for McVittie dust ("interpolates" between Schwarzschild and FRW),
• for Szekeres dusts (a simple solution with no Killing vector fields at all),
• for planar symmetric Kasner dust (a homogeneous but nonisotropic example),
• for Kantowski-Sach dust (plus matching to Frolov observers in Schwarzschild vacuum future interior)
• for Mixmaster dust (or perhaps its NIL analog, which is simpler)
• for Van Stockum dust (a swirling dust cloud),
• for Godel lambdadust (another swirling dust cloud)

So we should postpone further discussion until this material appears.

 

[yogi]

Hi, yogi, I must demur on at least one point:

• Einstein's views changed so radically and so often that IMO statements of the form "X was Einstein's view" have little meaning.
• Einstein died in 1955, well before the "Golden Age of Relativity" (c. 1960-1975). You might be able to argue that some statement on topic T by Einstein represents his definitive statement of his own most mature view on topic T, but IMO it would be ludicrous to insinuate that physics/mathematics stopped when Einstein died.
  
  

True - his views did change - what I detect was a shift in the direction of attempting to explain physics in terms of space as a substantive

 

[Garth]

Garth

OK the moons circulation causes the acceleration of the Earth to change a bit and this is the cause of the tide. Well probable nothing wrong with that. I am focused of the variation of force that space passes on between the bodies, and the cause of that. It’s off course the same force that pulls down a stone. We can explain both phenomena’s based on the acceleration of gravity (the expression of a such force) but this is of course only a superficial solution, - and well you are right nothing wrong with that.

Thank you for sharing your knowledge.

-------
Bjarne

No, "the moons circulation causes the acceleration of the Earth to change a bit and this is the cause of the tide" this is totally wrong, did you not understand the careful illustration I gave you?

Even if the Moon were not in orbit around the Earth, but the Moon and the Earth were falling directly towards each other, about to collide, the Moon would still raise tides on the Earth.

It is the difference in the Moon's attraction (using the Newtonian paradigm) on different parts of the Earth both in magnitude and direction that causes the tides.

Put a solid sphere inside that sphere of dust. The dust sphere (the sea) deforms and the solid sphere (the rock) does not. Relative to the solid Earth high tides are raised on the side nearest the Moon (the ocean appears to be 'pulled away' from the Earth) and furthest from the Moon (the Earth appears to be 'pulled away' from the ocean) and low tides at the 'sides' of the Earth. (In fact the 'solid' Earth also deforms slightly, but not as much as the fluid ocean).

Draw the dust sphere and the directions and magnitudes of the acceleration vectors of different dust particles towards a nearby Moon and convince yourself the whole sphere deforms into an ellipsoidal shape.

The fact that the Earth and Moon have transverse orbital velocities does not affect the picture, they have an acceleration in the direction connecting their centres of mass and an orbital velocity normal to it, the result being a nearly circular ellipsoidal orbit around each other.

Garth

 

[yogi]

This sounds like the same fallacy I seem to have been debunking with unusual frequency in recent days here at PF. If so: "length" does not "shorten" and "time" does not "slow down".

Regardless, given that the term "dilation" is seriously misleading but well entrenched, I suggest that everyone here should always take the time to write out more carefully what one really means. Never forget that so-called "time dilation" effects always involves a comparison between two clocks in different states of motion. Thus, it never makes sense to say "time dilates" without the context of what clocks are being compared and how. Similar but even more nuanced remarks hold for "space dilates".

I didn't intend to convey that - in the spherical space-time universe of de Sitter, the two sphere surface grid is composed of time and space. As the spherical universe expands, both the time dimension and the space dimension increase in relation to their previous lengths ...its the inflating balloon model except that the surface is composed of one time dimension and one space dimension rather than two space dimensions - so the reference for change is the previous surface itself,

 

[yogi]

However, I have been mulling the prospect of trying to write some brief expositions of frame fields and "beacon" null geodesic congruences in some simple and often encountered cosmological models including

• Milne frame in Minkowski vacuum (as a foil for genuine cosmological models),
• expanding inertial frame in deSitter lambdavacuum,
• frame of dust in FRW dust models, plus FRW lambdadust models, plus frame of inertial particles not comoving with dust, plus contracting FRW matched to Schwarzschild as per Oppenheimer-Snyder collapsing dust ball model,
• frame of dust for LTB dusts (spherically collapsing dust clouds),
• ditto, for McVittie dust ("interpolates" between Schwarzschild and FRW),
• for Szekeres dusts (a simple solution with no Killing vector fields at all),
• for planar symmetric Kasner dust (a homogeneous but nonisotropic example),
• for Kantowski-Sach dust (plus matching to Frolov observers in Schwarzschild vacuum future interior)
• for Mixmaster dust (or perhaps its NIL analog, which is simpler)
• for Van Stockum dust (a swirling dust cloud),
• for Godel lambdadust (another swirling dust cloud)

So we should postpone further discussion until this material appears.

If you like - with intense effort I will probably to be able to understand about every third word

Regards

Yogi

 

[Bjarne]

Garth

What confused me was that you was wrote:
” Treat the Earth as a sphere of dust. Its centre of gravity is falling directly towards the centre of gravity (CoG) of the Moon (Sun)”

Well I did already understood it’s mainly the water on Earth's that is effected of the gravity attraction form the sun/moon.
But for some time ago I was wondering if the Earths also follow a weak swaying course, like a drunk man on the road.
Therefore when you also mentioned “acceleration” I was completely confused. - Anyway, illustrations is often good fx > www.clupeid.demon.co.uk/tides/simple.html

If we analyse what happens to the tide: a weak effect of attraction from another body ( sun / moon) pulls the tide which have a bit reducing effect of the Earth's ability to keep it’s grip of its water on the earth. (mostly on that side pointing to the other body off course)

I don’t know if difference gravity phenomena all can be explained from a perspective: that space curves.
If curvature of space can explain both that the moon is kept in its orbit, and that my pencil fall to the floor as well as the tide, - it’s at least anyway a expression not suitable for us too understand / imaging, - but only for a mathematically / calculating part of the brain.

I mean curvature of space does not make much sense to me, when someone claims that space also bends here at my table, and that is the cause to things here falls down to the floor when loosing it? - Is this not a reality / expression beyond the imagination ability ?
I mean is such mathematically / geometrically ‘tools’ not too theoretically for us, unless only for calculation purpose?
Can you agree to that ?

Or can you on this basis also explain why a horisontal moving football reach further like a canonball, when both moves with 100 MPH ?

---------
Bjarne

 

[Garth]

No I cannot agree to that, it is the curvature of space-time that explains, as perfectly as we can experimentally test for, the trajectories of freely falling bodies in a gravitational field.

Consider a ball falling to the floor, or one thrown through a vacuum (ignoring air resistance), both the balls and the centre of the Earth, and indeed a satellite in orbit around the Earth, are 'travelling' through space-time, (actually it is their four-velocity vectors in space-time that are:) on geodesic trajectories.

Geodesics may be thought of as 'straight-lines' through space-time.

The fact that space-time is 'curved' means the 'straight' lines drawn upon that Riemannian manifold ('surface') are curved in some higher dimension so the balls' trajectories converge with the Earth's, whereas the satellite describes a spiral around it.

(As I suggested above, illustrate this by drawing a straight line on a flat sheet of paper and then bend or deform the paper; the line bends with it, but it is still the shortest distance between two points measured along the surface of the paper.)

I use the language of a higher dimension because this is necessary for you to be able to extrinsically visualise the picture. In fact Riemannian geometry does not need this higher dimension, the effects of the curvature can all be described mathematically using tensor calculus intrinsically within the surface itself.

You need to read a basic tutorial on SR and GR if as you say, "it does not make much sense" to you. Try Ned Wright's Relativity Tutorial.

Garth

 

[Bjarne]

Garth

Right, - Space-time is a better expression, even though it belongs to a higher dimension.
I mean space can certainly deform whereby time also changes.

But when we want to understand why a horizontal moving cannonballs lose its potential energy (100 MPH) before a football, - we still depend on a Newtonian way of calculation / theory, - right?

--------
Bjarne

 

[Garth]

Garth

Right, - Space-time is a better expression, even though it belongs to a higher dimension.
I mean space can certainly deform whereby time also changes.

But when we want to understand why a horizontal moving cannonballs lose its potential energy (100 MPH) before a football, - we still depend on a Newtonian way of calculation / theory, - right?

--------
Bjarne

We certainly can and do use Newtonian theory in regimes where it is accurate enough, such as when NASA sling shot a spacecraft around the solar system with incredible accuracy.

Newtonian theory is used, if it is accurate enough, because the calculations are much simpler. You just have to be consistent with the paradigm you use.

I don't understand your question of "a horizontal moving cannonballs lose its potential energy (100 MPH) before a football".

In a vacuum the cannonball, a football, and a feather all fall at the same acceleration, this is http://science.nasa.gov/headlines/y2004/06may_lunarranging.htm re-enacted on the Moon by the Apollo 15 astronauts.

Garth

 

[Chris Hillman]

Demurral and Request for Clarification

what I detect was a shift in the direction of attempting to explain physics in terms of space as a substantive

You should say "I think I detect", since others familiar with his writings can and do disagree about what he appears to have meant by various statements.

in the spherical space-time universe of de Sitter, the two sphere surface grid is composed of time and space.

Huh? As you know there are many coordinate charts we can use on various pieces of the de Sitter lambdavacuum, aka H^{1,3} (a Lorentzian spacetime with uniform negative curvature), including comoving charts adapted to static (non-inertial) observers and to various families of inertial observers. In particular,
<br /> ds^2 = \frac{-dt^2 + dx^2+dy^2+dz^2}{(t/a)^2}, \;<br /> 0 &lt; t &lt; \infty, -\infty &lt; x, \, y, \, z &lt; \infty<br />
is conformal to the upper half space portion of Minkowski spacetime and is comoving with a "collapsing" family of inertial observers whose world lines form a vorticity-free timelike geodesic congruence, whose orthogonal hyperslices are all isometric to euclidean three-space. Here, intervals of t do not correspond to intervals of proper time as measured by ideal clocks carried by our observers, but we can change to a comoving chart
<br /> ds^2 = -d\tau^2 + \exp(-2 \, \tau/a) \; \left( dx^2 + dy^2 + dz^2 \right),<br /> \; -\infty &lt; \tau, \, x, \, y, \, z &lt; \infty, \;<br />
There is a very similar chart for a family of expanding inertial observers, who also have orthogonal hyperslices isometric to euclidean three-space. But there are also families of inertial observers whose world lines form a vorticity free timelike geodesic congruence, whose orthogonal hyperslices are each isometric to H^3, e.g.
<br /> ds^2 = -dT^2 + a^2 \, \sinh(T/a)^2 \; \left( \frac{dx^2+dy^2+dz^2}{z^2} \right), \;<br /> 0 &lt; T, \, z &lt; \infty, \; -\infty &lt; x, \, y &lt; \infty<br />
And there are observers who have constant acceleration directed radially inward in a suitable polar spherical chart, such as this one (analgous to Eddington chart):
<br /> ds^2 = -(1-(r/a)^2) \, dv^2 + 2 dv \, dr + r^2 \; \left( d\theta^2 + \sin(\theta)^2 \, d\phi^2 \right), \;<br /> -\infty &lt; v &lt; \infty, \; 0 &lt; r &lt; \infty, \; 0 &lt; \theta &lt; \pi, \; -\pi &lt; \phi &lt; \pi<br />
The world lines of these observers again form a vorticity-free timelike congruence whose orthogonal hyperslices are each isometric to S^3. Many other charts can be found in Hawking and Ellis and in the literature, e.g. "static" version of the previous chart (analgous to Schwarzschild chart), Brill chart, Penrose chart, etc. I stress again that there are both expanding and contracting observers in this spacetime who can be used to define "negligible density" cosmological models (better say "toy models").

So what is your "two-sphere grid"?

As the spherical universe expands, both the time dimension and the space dimension increase in relation to their previous lengths ...its the inflating balloon model except that the surface is composed of one time dimension and one space dimension rather than two space dimensions - so the reference for change is the previous surface itself

This makes no sense as written. Can you explain what you are trying to say in terms of the line element in some coordinate chart? Any "increase" or other physical change will probably be seen to refer to some family of observers whose motion can be characterized geometrically, independently of coordinate description.

If you like - with intense effort I will probably to be able to understand about every third word

That's not very encouraging! Yogi, may I ask: what is your comprehension rate when you read Hawking and Ellis? If you don't understand timelike congruences and their kinematic decomposition (acceleration, expansion scalar, shear tensor, vorticity vector) and null geodesic congruences and their optical scalars, you really can't hold any meaningful discussion of cosmological models! Remember, this ideas were imported/introduced more than forty years ago and immediately became standard core topics due to their great utility. These techniques are perfectly suited to studying the geometry (i.e. the physics) without getting confused by "features" ("bugs"?) which merely characterize a particular aspect of a given coordinate representation.

 

[Bjarne]

Garth

I don't understand your question of "a horizontal moving cannonballs lose its potential energy (100 MPH) before a football".

Imaging you is an artillerist. If you have a same size football and cannonball, and use the same amount of gun power, the football will reach furthest. (Lets say the wind resistance is the same for both objects)

My point is that it can’t only be ‘curved space’ that determinate how fare an objects travel. – But on the other hand I am not highly educated and don’t know how advanced this science is.

I think it is difficult to understand how ‘curved space’ should possible could explain the different gravity ‘pull’ effecting different masses / objects. I mean what have ‘space-geometry’ with a force / pull to do? – I can not unite these two factors based on the today available knowledge. I also can’t see that Einstein had reason to triumphant over Isaac Newton. – To my opinion why should it not be possible that both Newton and Einstein both was right? - A (invisible) Newtonian force (though space) could very well pull space until it ‘curves’.

We still don’t’ know the cause of the gravity; is it a force? – How can matter be the origin? - How can space pass on such pull / force, - or what is ‘curved space’ really for a strange kind of nature, - and a lot more why?

My underlying point is that I simply can not imaging me that space really (just) ‘curves’, like was it a roulet. – Its fine that such model can be used mathematically, - but its not all right that our imagination not is allowed to understand it..

Maybe space is not such complex and hard to imagine curved nature. - Already it is complicated enough that space is able to expand, - why make it even more unnecessary mysterious?
What when the nature of space really only is so simple like; - space can expand and therefore (off course) also contract –and that’s it.?.

Einstein didn’t know (belived) that space really had the ability to expand, even though matematically result was showing this as well as space could contract.
I think as a starting point we naturally at least should allow us self to finish simple thinking; - what if space only is a ‘flexible’ simply kind nature? - Before we begins to complicate the phenomena further.

Well this seems immediate to be a vague argument to explain the underlying cause of gravity, - but why make the properties of space even more complex and thereby making space a lot more mysterious, when everything seems to point to that it really is not necessary, - for achieving a coherent complete understanding of gravity.?

Imaging that matter (somehow) contracts space around it self. Such simple starting point really would from a synthesis between Einstein, Newton and all our formula’s without violating anything.

The winner would be our imagination that suddenly was allowed to enter into the gravity secret, - doesn’t matter where the mean tread would lead us. – I mean black holes, dark matter, dark energy, the cause of galaxy- solar system – heavenly body formation, and much more.

So why not first try to keep ‘space’ so simple as possible, and see where this leads us? - What if space only is is stupid flexible nature, - nothing more likes that.
---------
Bjarne

 

[Garth]

In order to criticize a theory a person has to understand it first, otherwise they only demonstrate their own ignorance.

From your post above it is obvious you don't actually understand GR, try reading one of the excellent introductions to relativity theory recommended elsewhere on these Forums or on the web you can begin by reading Ned Wright's Tutorial.

In the football and cannon ball case the same amount of gunpowder would accelerate the football to a higher velocity than the cannon ball because it was lighter, this is the law of momentum.
Air resistance would affect the football more because it had less mass, it would have a higher deceleration, this is fluid dynamics and not either Newtonian nor Einsteinian gravity.

Ignoring air resistance the trajectories of both balls is accurately described by GR. and nearly as accurately by Newtonian theory.

My point is that it can’t only be ‘curved space’ that determinate how fare an objects travel

With the correction that we are talking about curved 'space-time' and not just 'space', yes space-time curvature as defined in GR can accurately determine free falling trajectories, that is the point.

To my opinion why should it not be possible that both Newton and Einstein both was right?

because observations have been made, such as the light deflection by the Sun or time delays of spacecraft whose radio pulses pass close to the Sun en route to Earth, that are accurately predicted by GR but not Newton. It is called doing science, theories stand or fall on empirical testing and falsification.

Garth

 

[Bjarne]

Garth

You are right,- just 5 minutes simple reflecting over ‘fluid dynamics’ and a ‘mystery' is gone. - Thank you.
You are also right that it would be very helpful to read more about known knowledge of gravity / relativity.
Well this is 'mainly' correct, - the point here is that it wouldn’t bring anyone closer to a coherent complete understanding of the origin of gravity or why a huge number of very related questions remains unanswered.
Notice I am not criticize any prevailing theories, but only that it seems that something very simple very well could be overlooked.
What I mean 'curved space' could very well be the exactly same as 'contracted space' - It is not necessary (no reason) to think a such understanding involves any kind of conflict , - but could be only a little different way of perception of the same phenomena..
As I wrote I haven’t fully explained the full range of this simple claim, I will do this in a couple of weeks, and post it to the relevant part of this forum its belong.

----------
Bjarne

 

[andrewj]

the most accurate theory of gravity, currently, represents it as the way matter affects geometry. I think this remains mysterious. How can matter affect geometry?

and there is the puzzle about inertia. why should stuff follow geodesics? and why should a thing's inertia ("inertial mass") be the same as the ("gravitational mass") strength with which it bends geometry? this does seem elusive, to use your word.

I've just been reading a 2001 book by Smolin called *Three Roads to Quantum Gravity* and I'm amazed at how good it is. Didn't expect such clarity and depth in a popular-written book. The last chapter has a prospective on how these very same problems might eventually (over next 10 years say) be addressed and solved. nice thing is that he doesn't just trivialize the problems---he takes a serious look into them. Great book.

is gravity stronger than we think possibly due to Planck sized dimensions

 

[andrewj]

gravity can be repulsive ?

 

[Bjarne]

Andrewj

gravity can be repulsive ?

A none philosophic answer to that question is; we don’t know.
We also don’t know if dark energy exists, there is good reason to believe it does and good reason to believe it doesn’t.
If dark energy exists it is reason to believe that it is could be part of the gravity mystery (as well as dark matter possible could be).
Gravity could very well have a repulsive property. But again fully understanding the nature of ‘space’ is necessary.
You questions can only be answered philosophic. Assuming that gravity / curved space is variation of ‘space density’ would mean that gravity at the same time both can have attraction as well as repulsion properties / forces, even though it immediate seems to be a self-contradiction.

------
Bjarne

 

[Chris Hillman]

Come again?

gravity can be repulsive ?

Not sure why you ask (possibly because Bjarne is in my Ignore list), but let me ask you a question of my own: are you familiar with the Raychaudhuri formula, a fundamental theorem in gtr? If not, I highly recommend that you read about this in a standard textbook, such as the very clear undergraduate textbook by D'Inverno, Understanding Einstein's Relativity.

 

[Bjarne]

Chris?
Einstein’s relativity does not answer the question.
Einstein didn’t even not know that the universe was expanding - Dark energy was also not know at that time.
Why should someone ask a gravity related question because ‘Bjarne’ is on you ignore list?
Do you think it is fair to post such kind of repeated negative ‘attention’ - Chris?

---------
Bjarne

 

[zankaon]

robust manifold

Because it's right under our noses.

That is, the robust manifold (continuum) i.e. pseudo-Riemannian spacetime, is right under (and part of) our nose etc.