Origin or source of gravity?

Bjarne

Hi Joinmtkisco
Yes, - you are right, - what Einstein or Newton said and thought doesn’t take us very far.
It’s important to keep in mind that space is a ‘connecting link’. It’s no doubt that space must somehow be involved in the ‘phenomena’ - Simply because if we should agree that space is nothing, how can NOTHING arrange exchange of gravity and pull down a stone to earth.

But exactly how is space involve, - do space really curves, - or just gets ‘thinner’ - or what happens to space between? – Its a pretty good question.
We know that space expands. Can space also become contracted?
I think the biggest problem in physic in our time, is that we haven’t understood the connection and nature of space and matter and how these two are connected. This is already clearly emphasized of other related huge understanding problems we have, fx dark matter, dark energy black holes, or think of a simply daily event: the moon, on the one hand it is attracted of the earth, and the (tide) water on earth is attracted of the moon. The earths and the moon are reaching out of each other, we surly can agree. – But what is the role of the space between? - In this case it doesn’t make sense to claim that the ‘contact’ between the moon and the tide is caused of “curvature” of space. How is space ‘linked’ to matter is probably a bit more complex and will certainly be a big question, - in this century? (Sorry for the bad English)
Bjarne

Chronos

Perspective is a key issue. To any 'fixed' observer, the metric of spacetime appears to be curved. Is that 'reality'? Hard to say. Devising a non-fixed observer is difficult.

Jorrie

Wouldn't a rocket provide a 'real' force on its payload, even in a GR environment? Isn't that different to the 'pseudo-force' of gravity?

jonmtkisco

Hi Jorrie,

Good question. To an outside observer who knows that the rocket is the source of acceleration, it seems reasonable to consider this a "real" force. But to an observer who is unaware that she's in a rocket, how does she know whether it's a real or pseudo-force? I guess that the uninformed observer could tell the difference by measuring tidal effects (?) (Can you measure the tidal effect if you're inside the accelerating frame?) As I understand it, an accelerating rocket would not create tidal forces because the acceleration force is completely "uniform", i.e. not a field.

Maybe the answer is that things are "real" TO US only if we can observe and identify the underlying cause of movement. By that test, we are currently unable to judge whether gravity is a real or pseudo-force.

One can say that we are able to stand outside of the coriolis effect and more or less identify its cause. That is, we can identify its "first order cause" as the rotation of earth's sphere. But below that there remains a "second order cause", gravity, the cause of which we currently are unable to fully comprehend. So one might reluctantly conclude that we can't yet decide whether coriolis is real or pseudo-.

I think it's going too far to say that if we can't determine whether a particular force is real or pseudo-, that we must automatically consider it to be pseudo-. In my view, the answer is that "the jury is still out."

Another example occurs to me: Is an electromagnetic field a real or pseudo-force? Compared to gravity, we are much more confident about how electromagnetism works (i.e., the force is mediated by exchanges of virtual photons). But there are so many similarities between the fields of electromagnetism and gravity that I would be reluctant to put them in different "reality categories" unless I was absolutely convinced.

Jon

jonmtkisco

Does an electromagnetic field cause geometric curvature of space?

Bjarne

Jon
http://answers.google.com/answers/threadview?id=430345
Bjarne

Jorrie

Hi Jon.

No she can't, but the force is not gravity in either case. IMO, it is in both cases simply the 'floor' pushing at her body. In a gravitational field one can view the force as pushing her out of her free-fall spacetime geodesic, where her geodesic movement would have been force-free (except for tidal forces, of course).

As I understand it, the acceleration will differ over the length of the rocket, because the rocket approximates Born-rigid acceleration. (http://www.mathpages.com/home/kmath422/kmath422.htm) Shouldn't there then be 'pseudo-tidal forces' over the length of the rocket in the radial direction?

Jorrie

jonmtkisco

Hi Jorrie and Bjarne,

1. It sounds right to me that a comoving observer could measure tidal effects.

2. Bjarne, I didn't formulate my question clearly enough. I should have asked, "Does an electromagnetic field cause geometric curvature of space with respect to a charged particle moving through the field?" In that respect, I note the following from the Wikipedia article on "Maxwell's equations in curved space:"

"In physics, Maxwell's equations in curved spacetime govern the dynamics of the electromagnetic field in curved spacetime (or more generally, spacetime with a non-Euclidean metric). They can be viewed as a generalisation of the vacuum Maxwell's equations as they are normally formulated in the local coordinates of flat spacetime, but general relativity dictates that the presence of electromagnetic fields themselves induce curvature in spacetime, so Maxwell's equations in flat spacetime should be viewed as a convenient approximation."

It sure is interesting to contemplate the idea that an electromagnetic field actually curves spacetime, but in a way that is "apparent" only to charged particles. If it's true, then it reinforces the question of how "real" the curvature of space by gravity is.

Jon

Chris Hillman

Shouldn't this thread be in "Astrophysics", or even "Beyond the Standard Model"?

You're surprised that the "origins" of gravity/inertia are elusive? I'm surprised that you are surprised!

As you probably know, there have been many speculations about what physical principles might underlie those enshrined in theories of gravitation such as gtr (for example, the equivalence principle). You might be interested in this review of one perenially popular line of speculation:
http://relativity.livingreviews.org/...4-3/index.html

I would be astonished if you were not talking about gtr, but for the record: I assume that you were talking about gtr!

I suppose you can say that it is a mystery why the presence of matter (or other mass-energy) affects the geometry of spacetime. But is this really more mysterious than saying that the motion of charges in a wire creates something we call a magnetic field? What the heck is a magnetic field "really"? What is "electrical charge"? And why should magnetism care a jot about charge? I dunno, but I know that according to Maxwell's theory, it does, and I know that this has been a highly successful theory which predicts/explains a lot of useful stuff, like radio waves.

I dare say that most physicists asked such questions when they were young. But at some point, one learns to focus on questions which can be attacked via the scientific method. Specificially, wolram should be encouraged to try to formulate a theoretical speculation which might someday admit an experimental test.

It's difficult to explain how physicists use these terms without getting more deeply into the relevant theories than we can do at PF. I'll just offer a few vague pointers regarding gtr:

The best short answer to the question "how does gtr treat gravitational interactions?" is that gtr treats "the gravitational field" as (part of) the curvature of spacetime itself, i.e. as a geometrical effect which affects how objects move, how clocks behave, and so on. In addition, energy and momentum act as the "source" of the gravitational field, i.e. when they are present in some region of spacetime, that region is curved in a certain way. This circle of ideas is very well summarized in the famous slogan of John Archibald Wheeler: "[the geometry of] spacetime determines how matter moves, and matter tells spacetime how to curve [which changes its geometry]".

However, in some contexts it is convenient to elaborate on this slogan. In gtr, a special case of Wheeler's slogan shows that the world line of a small freely-falling object in a vacuum region is a timelike geodesic in the Lorentzian manifold which we use to define the geometry of the "setting" for physics, spacetime. But in Newtonian gravitation--- or rather, the non-relativistic "Newtonian" field theory in which the Poisson equation plays a role analogous to the EFE in gtr-- offers a very different description of gravitation in this situation. Namely, the gravitational acceleration of a small object in a vacuum region of space is given by the gradient of the gravitational potential, which is determined by solving the Laplace equation, the analogue in this theory of the vacuum EFE. Now Newtonian gravitation works very well in many situations, so one of the the first tasks facing the physicist who constructed gtr[*] was to verify that in an appropriate limit it gives the same predictions as Newtonian gravitation. To do this, one studies a slow motion weak-field limit and re-expresses the gtr law in an operational but less geometric way (one looks at the connection), and one verifies that in this limit, gtr does indeed give the same predictions as Newtonian gravitation. My point is that you shouldn't be surprised that this "correspondence" between slow motion weak-field gtr and Newtonian gravitation is somewhat roundabout, given that these two theories are based on such different conceptual principles!

[*Yes, of course I mean Albert Einstein!]

Your question is pretty vague, so it is hard to be sure, but you might be groping toward the details of the program I outlined just above, where we compare Newtonian gravitation with slow motion weak-field gtr.

It might also be useful to state that in gtr, there is a very simple and beautiful geometric concept which corresponds quite precisely to acceleration (the kind measured by accelerometers): small objects (or more generally, bits of matter inside big objects) have world lines which are timelike curves. Such curves have path curvatures defined at each event on the curve. The path curvature at any event on the curve is a spacelike vector which is in fact orthogonal to the tangent vector. Its length gives the magnitude of acceleration experienced by the object at this event, and it's direction gives the direction of acceleration. (More precisely, one should smoothly assign a frame field along the curve, and then any vector orthogonal to the tangent vector, which is the timelike unit vector in the frame, is a linear combination of the three spacelike unit vectors in the frame. Thus, it makes sense to regard the path curvature as a three dimensional vector which lives in the "spatial hyperplane element" orthogonal to the curve at a given event.)

In contrast, in gtr the gravitational field is treated as (part of) the curvature of spacetime itself. Spacetime curvature is tensorial and the components of the Riemann (or Weyl, or Ricci, or Einstein, or tidal) curvature tensors have the units of reciprocal area. Path curvature is vectorial and its components have the units of reciprocal length. So once you know the math, there is little chance of confusing them!

Assuming you are talking about our gold standard theory of gravitation, gtr, there is no controversy! I suspect you have been misled by a discussion you read or heard which actually concerned something like the (quite unambiguous!) geometrical distinction between spacetime curvature and path curvature and the very different physical interpretations assigned to these quantities in gtr.

This remark seems to be a somewhat murky reference to the fundamental distinction between local and global structure in the theory of manifolds, which enforces such a distinction in metric theories of gravitation, such as gtr. That is, in any sufficiently small local neighborhood one can choose to regard curvature as a mathematical fiction, albeit one which is undeniably conceptually convenient in order to take maximum advantage of the simple geometric structure on the tangent spaces of our Lorentzian manifold models of spacetime. However, at the level of global structure such an "effective field theory" is quite unambiguously a distinct theory from gtr. That is, one can describe scenarios in which an observer would report physical experiences which might contradict gtr but not its local mimic, or contradict the local mimic but not gtr, or which contradicts both theories.

Curious readers may wish to depart the thread at this point and study Box 7.1 and 17.2 in MTW, then related discussion in the textbook by Weinberg.

Good physics tends to employ mathematical reasoning rather than philosophical disputation, so I prefer to stick to the realm of mathematical reasoning. In this realm, depending upon your mathematical definition of "geometry", this may be more or less sane. You might be interested for example in teleparallel gravity. In some styles of developing a teleparallel theory, instead of modeling the gravitational field as the curvature of a torsion-free connection, one models it as the torsion of a curvature-free connection.

No, path curvature as discussed above is quite clearly distinct mathematically and conceptually from something like the Coriolis force. Tidal accelerations are quite distinct from these, as are spin-spin accelerations.

Tidal accelerations are modeled in gtr by the electrogravitic tensor, or tidal tensor, which is one piece of the Bel decomposition of the Riemann tensor, and spin-spin accelerations are modeled by the magnetogravitic tensor. The Bel decomposition splits the Riemann tensor into three-dimensional tensor fields, wrt some timelike congruence. It is fully analgous to the decomposition of the "EM field tensor" into electric and magnetic fields (vector fields), with respect to some timelike congruence.

This thread is already far too cluttered to discuss historical viewpoints, but I assure you that "gravitational force" is usually taken to mean the same thing in gtr as it means in Newtonian physics. In both theories, a free falling observer feels no force. But an object sitting on the floor of a room on the surface of the Earth feels a radially outward force. This force is physically due to EM interaction betwen the object and the floor of the room, but it is usually called the gravitational force. This makes perfect sense in the context of discussing the hydrostatic equilibrium of a ball of perfect fluid held up against its gravitational self-attraction by the pressure of the fluid!

You are venturing into dangerous territory here! If you are very careful to define mathematically what you mean by "space expands" or "contraction of space", you can make sense of this, but if you try to do this, I think you will find that that you are really talking about the expansion or contraction of a congruence; that is, a family of non-interesecting curves which fill up a region of spacetime. (More precisely, they are the integral curves of some vector field; timelike and null congruences are particularly important in gtr.)

This mostly strikes me as too philosophical for this forum, but it might be worthwhile to remark that in another useful decomposition of the Riemann tensor, the Ricci decomposition into the completely tracefree piece (the Weyl or conformal curvature tensor) plus a piece built from the tracefree Ricci curvature tensor, plus a piece built from the Ricci curvature scalar, the last two pieces contain exactly the same information as the Einstein tensor. Then we can say: Ricci curvature, or equivalently Einstein curvature, represents that part of the spacetime curvature which is due to the immediate presence at a given event of some energy and momentum, via the EFE. Weyl curvature represents that part of the spacetime curvature which can propagate across a vacuum region as gravitational radiation. The two types are connected via a differential equation which arises from the contracted Bianchi identities. This equation says that Ricci curvature HERE can create Weyl curvature nearby, which can then create more Weyl curvature a little further away, and so on.

In this way, when one forms a star by gradually concentrating matter in a compact region, the surrounding vacuum region is slowly curved up. In the end we have a region filled with matter, in which the geometry is dominated by Ricci curvature (in fact, in the simplest model of an isolated object, Schwarzschild's stellar model, the only curvature inside the star is Ricci curvature), surrounded by a vacuum region, in which the geometry is controlled by Weyl curvature. In the case of an isolated object, the curvature in the vacuum region falls off like [itex]O(m/r^3)[/itex], the same way that tidal accelerations of test particles scale in Newtonian gravitation. To forestall possible confusion, I should emphasize that Weyl curvature includes both such "Coulomb curvature" and the curvature typical of gravitational radiation, which typically oscillates in time but which decays with distance much more slowly, like [itex]O(1/r)[/itex]. (The respective buzzwords in the trade are "Petrov type D" and "Petrov type N" Weyl curvature; there is also Petrov type III Weyl curvature which decays like [itex]O(1/r^2)[/itex].)

Yes, exactly--- that is what I was talking about above. In a rocket, idealized as a pointlike object, the acceleration corresponds to the path curvature of the world line of the rocket. This is quite distinct mathematically, geometrically, and physically from something like Coriolis "force". Just try analyzing a block sliding on a turntable!

No, he can tell, without looking out the window of his spaceship, that he is accelerating by employing an accelerometer. OTH, if he is in free-fall, he feels no forces to O(dx). At order O(dx^2) he can measure small tensions and compressions of his spaceship, from which he can conclude (according to Newtonian gravitation, or gtr, or any reasonable theory of gravitation) that he is falling freely near some massive object and that the axis of maximal tension points approximately in the direction of this object--- but he can't tell "down" from "up" by measuring the tidal forces, at least not at O(dx^2). Over time he may find that the maximal tension is increasing, in which case he is probably getting closer. Or he may eventually conclude (still without looking out the window) that he is in orbit around the object. In this case, with even more sensitive equipment, he can in principle test gtr vs. Newtonian gravitation by looking for evidence of precession of the spin axis of gyroscopes which he carries inside his spaceship. See Cuifolini and Wheeler, Gravitation and Inertia for further discussion of such experiments.

There is generally a pretty clear distinction in classical physics between field and a force. I have already mentioned a pair of mathematically analogous observer dependent decompositions of fields (of the EM field tensor into electric and magnetic vector fields, and of the Riemann curvature tensor into tidal tensor and some others).

In Maxwell's theory of gravitation, an EM field is associated with energy and momentum which is represented in the "electromagnetic stress tensor". In gtr, this contributes directly to the right hand side of the Einstein field equation, so it is the direct cause of some Ricci curvature, which turns out to cause some Weyl curvature.

Incidently, it is possible to write down exact solutions of the EFE which represent an EM plane wave accompanied by a comoving gravitational plane wave. This is a very direct way of appreciating what we mean by saying the EM radiation and gravitational radiation propagate at the same speed!

Exactly.

Much needless ink has been spilled on this subject, and alas this topic has proven to be a crank-magnet at PF (and Wikipedia) in the recent past, so I wish to avoid it. Suffice it to say that the Rindler congruence consists of hyperbolas which are nested in a manner analogous to to nested circles. The trailing edge of the rocket has a smaller radius of curvature, so a larger path curvature, so surprisingly enough the trailing edge has to accelerate harder than the leading edge in order to maintain the "rigidity" of the rocket. More precisely, by "rigid" we mean that the expansion tensor of the timelike congruence consisting of the world lines of bits of matter in the rocket must vanish. There is another congruence, the Bell congruence, in which the magnitude of acceleration in constant along the length of the rocket, but this forces the expansion tensor to be nonzero. In fact, the rocket would slowly elongate until it breaks apart! (A real rocket would of course elongate or compress slightly depending on the details of where and how forces are applied along the length of the rocket, until it reaches some equilibrium--- or until some vibration sets in, but it would either behave on average over time like a Rindler congruence, or else it would break up.

Chris Hillman

Caution: Wikipedia articles are unfortunately neither stable nor reliable, since, you know, anyone can edit them There is a new Wikiproject Relativity founded by M. Patel http://en.wikipedia.org/wiki/Wikiped...ect_Relativity, which derives from previous work (2005-2006) by MP, myself http://en.wikipedia.org/wiki/User:Hillman/Archive, and EMS, and you can probably trust anything any of us three write about mainstream physics. But I caution that there are numerous cranks active in the physics/math pages at Wikipedia, far too many for MP and EMS or even a dozen project members to revert/argue-with/bring-before-ArbCom, particularly if they are trying to create new content. In late 2006, I reluctantly concluded that it is impractical to try to follow the Wikipedia model of deciding disagreements by consensus, since it is impossible to argue with a crank, so I Ieft the Wikipedia community. I wish them well, but I am not optimistic about the future of Wikipedia (or Web 2.0). 'Nuff said.

You misunderstood. In principal, an EM field affects the curvature of spacetime in ways which will in general affect the motion even of neutral particles. (As I already said, these effects are too small to hope to measure with forseeable technology.)

Bjarne

Chris Hillman

The question of this tread is: Why is the origin of gravity so elusive?
No doubt that the origin of gravity is elusive, - we even don’t know if gravity is caused by a force or not.

Imaging a football flying through the air side by side with a canon ball, (with same speed) Some kind of a FORCE pulls the canon ball faster down to the earth like it pull down a football. If gravity only was a property of space, the canon ball would fly the same distance like the football, - right?

So is gravity caused by a FORCE? - Or caused by curvature of space? – Or both?

Was Einstein right or do we (still) have more or some faith to Newton, - or was both right? Are these confusions not elusive?

It is inevitable; - we are force to ask the question: Is gravity in reality a force that not only pulls down the canon ball, but that also pulls space until it curves. – And yes immediate we are forced into philosophy behinds gravity, and still ‘on the thinner ice’ we do not find a coherent answer, - to why is the origin of gravity so elusive.

I am not highly educated, - but it would surprise me a lot if space not should curves proportional with the acceleration of gravity.

I weak remember a quotation of Einstein, - he was wondering what space really was. But I can’t find that piece of text again, maybe someone have seen it and remember it.

Bjarne Lorenzen

jonmtkisco

Bjarne, if you remember your Newtonian physics, if a football and a football-shaped cannonball are simultaneously dropped from the same height, they will strike the ground at the same time, regardless of the difference in their respective masses.

However, before they can fall, they each must be projected upwards, against gravity, by the application of force. More force is required to raise the heavier object to the highest point in its arc than to raise the lighter object to the same height. More force is also required to impart any given horizontal speed to the heavier object.

The difference in the two objects' total flight time depends on how high the highest point in their respective flight arcs are, not on their respective masses.

Air friction and wind introduce additional forces that can cause variations in the outcome, of course.

Jon

Chronos

There is no harm in conceding you might be in over your head, Jon. Chris is a world class phycisist who donates his time here to explain the difference between science and superstition.

Bjarne

Joinmtkisco

Right. - Bodies accelerate and fall towards a gravity field (vacuum) with the same speed..
This happens even though the pull of gravity affects the canon ball with much greater attraction than it effect the football.
The cause of this factum is it self really a mystery, - we have no idea of why this is so.
Intuitive we would expect that the canon ball would fall faster, - but it’s not what happens.

Imaging a football and a canon ball falling down to earth from let say only 1 meters height.
Its not “space enough” for believing that the cause of these bodies both fall with the same speed, (on that short distance) is due to curvature of space.
Both bodies follow a straight line and are not affected of the curvature of space. – So how can the curvature of space in this particular example be the cause of gravity? - It’s simple make no sense.

What we do know is that it requires more force to lift a canon ball to 1 meter height as it require to lift a football to same height.
The canon ball will in this position have greater potential energy. If we accelerate the football and the canon ball up to both 100 MPH (1 meter above the surface of earth) the canon ball still will have greater potential energy.

Let’s say that that the size of the canon ball and the football is the same, wind resistance is therefore also the same.
If we should be able to explain gravity based on curvature of space, - the football as well as the canon ball (moving with 100 MPH) would hit the earth’s surface simultaneously, - but this is not what happens.
The explanation is of course, - the canon balls have greater potential energy proportion to the earth. – It is this FORCE involved that pull down the canon ball first.

So based on simple everyday’s observation gravity seems to be a FORCE. – On the other hand we can not close our eyes for the fact that the curvature of space ALSO seems parts of the gravity phenomena.
But attempt to implement this aspect in a complete and coherent way is: 'the end of the known road'; - from here we are forced into philosophically considerations.

So far we have not been able to archive any kind of coherent understanding to why we can say we have two independent (and both pretty good) theories for the same gravity phenomena. Common for these 2 theories is that we do not understand on the one hand why space curves, and on the other hand from where does the 'well known' FORCE come from, and how does it occour.

Well, - it seems to be a broad hint build in, - matter must be responsible / the origin for this force, - Could this force also be responsible for space to curve? – Or why do space curve? - What does 'curvature of space' really mean? - I mean think about a game-roulet, - it is something physical we know - but this is not the way space is? - What is space? - What's its nature?

Bjarne

gdpudasaini

Although the search for gravity began before 500 years but we don't yet have a complete picture about how gravity works. So we come across this sort of many times. What you have to note is "what we see and feel in everyday life in not nature"So spacetime curvature can't be felt in everyday life.To feel it you have to go extreme.

<< post edited by PF Mentor berkeman >>

Bjarne

We do not need to involve time, even though its ‘deformation’ together with space is a consequence. It will only contribute to unnecessary confusion. We can feel and measure gravity. The force is a reality.

Chris Hillman

You addressed me, but your comments suggest that you did not bother to read my long and thoughtful post #26-27! This is dismaying, as are comments by several posters in this thread which appear to me to verge on personal attacks

(Before anyone cites Jn8:7, I am aware that in the past I have myself sometimes expressed frustration stemming from the apparent obtuseness of some PF poster.)

PF is a public forum which welcomes participants with a very broad range of interests and backgrounds. I have no expection that everyone here should have a formal background in mathematics and physics, although quite frankly I often wish that were the case. But while I am all too well aware that many laypersons who participate in PF have little appreciation of what mathematical physics is all about, or even what the scientific method is all about, I do think I have the right to demand that you at least try to read my posts before "replying" to them. Please note that I was trying to raise the level of discourse by taking the time to try to clear up multiple misconceptions and to convey some sense of why the beliefs, achievements, shortcomings, and controversies of contemporary (mainstream) physics/cosmology are quite different from and far more subtle and interesting than most laypersons and self-described "critics" appreciate.