The real question is: why are so many PF threads posted in the wrong forums?
Shouldn't this thread be in "Astrophysics", or even "Beyond the Standard Model"?
wolram said:
why is the origin of gravity so elusive?
You're surprised that the "origins" of gravity/inertia are elusive? I'm surprised that you are surprised!
marcus said:
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.
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/Articles/lrr-2004-3/index.html
marcus said:
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?
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.
dilletante said:
I guess I don't even understand if there is a consensus on whether gravity is a force or not. While apparently GR does not consider it a force, what about QG or string theory? If they postulate a graviton as a carrier, do they consider gravity a force, in opposition to GR?
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!]
Bjarne said:
Could it be that force that 'pulls' space until it bend / curves
So that both Einstein and Newton both was right?
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!
jonmtkisco said:
I think it's fair to say that most, but certainly not all, physicists agree that gravity curves the geometry of space. Some say that "gravity acts on space" while others more conservatively say that "gravity acts on matter."
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.
jonmtkisco said:
Since the effects of gravity perfectly mimic a curvature of space, as far as I know there's no (known) way to be sure whether space is actually being curved, or instead whether instead the "force" of gravity just adheres to a geometrically-based algorithm.
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.
jonmtkisco said:
but it is very sane to question whether the geometry of space is actually capable of curvature.
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.
jonmtkisco said:
I think that in GR there is no functional distinction between a "force" and "pseudo-force".
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.
jonmtkisco said:
Einstein appears to personally have favored the notion that gravity is a "real" force, and therefore that, for example, the coriolis effect is also a "real force". But most GR specialists after Einstein seem to believe that both are mere "pseudo-forces."
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!
Bjarne said:
We know that space expands. Can space also become contracted?
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.)
Bjarne said:
I think the biggest problem in physics 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 Earth's 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)
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 O(m/r^3), 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 O(1/r). (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 O(1/r^2).)
Jorrie said:
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?
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!
Jorrie said:
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 (?)
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.
Jorrie said:
Is an electromagnetic field a real or pseudo-force?
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).
jonmtkisco said:
Does an electromagnetic field cause geometric curvature of space?
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!
Jorrie said:
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).
Exactly.
Jorrie said:
As I understand it, the acceleration will differ over the length of the rocket, because the rocket approximates Born-rigid acceleration.
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.
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