Obelix

Whether gravity "gravitates" (i.e. whether it interracts with another gravitational field) is a capital question. Black Holes (at least the objects that have been observed as such) do gravitate, to be sure. Yet there is a difficulty in many people (myself included) to conceive the compatibility (which MUST be there!) between a geometrical theory of gravity (gravity as spacetime geometry = "Geometrodynamics") and another theory where gravity shows up as an inrerraction by a field throughout spacetime. If that compatibility had been conceived we would have the Theory of Everything! In the case we are discussing here: Whatever gravitons are (provided they do not follow spacelike trajectories, i.e. they do not travel faster than light) THEY WOULD NOT BE ABLE TO ESCAPE AN EVENT HORIZON. This is a property of spacetime GEOMETRY. It is not a matter of "how strong is the gravitational pull of gravitons on gravitons". A technical question: Is anyone familiar with Feynman's Integrals? If they were to work for gravitons, how would they be extended from the inside of a black hole to its outside, via its event horizon? (I'm a relativist, not quite familiar with Quantum Field Theory, so I may be asking stupid questions here...Sorry if that's so!) Once again: I'm not adequately familiar with QFT: If gravitons were spacelike, wouldn't gravity propagate faster than light? Besides it's not only gravity and gravitons. There also are charged black holes (at least in theory). Electromagnetism is a well studied interraction with a very successfull QF theory of its own. How do charged black holes excert electromagnetic interraction on the rest of the universe? Do you know any texts where the question is posed?

Aw, c'mon! I LOVE this font! Is it so horrible to you? That was precisely what I wrote in the last paragraph above. Read a bit more carefully: I wonder IF all the above mean that a Quantum Gravity is, after all, IMPOSSIBLE! As to whether "gravity influences gravitons" ("does gravity gravitate?") this is a very much open question indeed. It is connected with the so called "Very Strong Equivalence Principle" which asserts that ALL laws of Physics (gravitational ones included) can be expressed in a Special Relativistic form, in a local freely falling frame of reference.

"Weird question!" you are likely to say. Kindly follow me for a moment: Suppose a Quantum Theory of Gravity does hold. Then, gravitational influence of a body (call it B1) on another (call it B2) would be excerted by means of a shower of gravitons (virtual partices) B1 would emit, which would transfer momentum and energy to B2. And vice versa. Those gravitons (if they trully exist) are supposed to be emitted by the MASS of B1...Any objections so far? Suppose however that B1 undergoes gravitational collapse (e.g., if it is a red supergiant after the supernova phase) causing its mass to shrienk within its Schwarzschild Radius, i.e. confine itself within an "event horizon", thus becoming a Black Hole. From that point on, if the mass of B1 (now enveloped by an "event horizon") emitted any gravitons, THEY WOULD NOT BE ABLE TO MOVE OUTSIDE THAT "EVENT HORIZON" OF THAT BLACK HOLE. How would then that Black Hole excert any gravitational influence on stars, etc. outside its "event horizon"??? It is obvious that Black Holes (at least the ones supposed to have been observed - if they ARE indeed Black Holes!) DO excert gravitational influence on other bodies, resulting in the formation of "accretion disks" and "jets". What are we to conclude? That Gravity HAS to be described in terms of a Geometry of Spacetime ("Geometrodynamics") whereas a Quantum Theory of Gravity is impossible? Would Hawking radiation suffice for the gravitational interraction? Anything else?... C'mon, make suggestions!!!

This seems a very interesting idea and worths formulating mathematically! Yet I can readily think of one objection: Einstein started from Mach's assumption that the inertia of any specific mass is a result of the total gravitational interraction of ALL the masses in the universe with that mass. Hence, it is INERTIA that results from GRAVITATION. You, on the other hand say that it is the other way round. Maybe the idea is the same in the overall.

Using the term "force" can be seriously misleading. It was used by Newton in a rather loose way, in the absence of a better term, and it has been long given up in Physics. Do you mean to say that the instinct of self preservation is what identifies a "living" entity as such? If so, it must be still existing. How does it appear in what is called "non - living" matter (stones, water, etc)? What known properties are there in such matter, which, if extrapolated, can lead to an instinct of self preservasion in living matter? Is it the very old idea of a vis vitalis you have in mind? But this used to be, by definition, the very thing that was absent from non - living matter, distinguishing it from the living one...

I would say that, according to Einstein's field equations, space and time are interrelated dynamically. They both evolve, and whatever happens to one of them influences the other. This is unlike Newtonian space and time, which are static, non - evolving, and independent from each other. In G.R., as time moves on, that has an impact on space, causing objects to gravitate and move, even if they are initially at rest. Hey, iNow, what's wrong with this font? I find it attractive and definetely easier to read. And why on earth did it feel I was "yelling at...YOU"??? I didn't even quote you!

Oooops!...I'm a bit hopeless when it comes to pictorial or intuitional description of Physics. I remember, when I was in Imperial College / London (1993) attending the class of Chris Isham (anybody knows him?) he had made a distinction between those people who prefer description in terms of Analysis, and those who choose Geometry and / or pictures in general. He had said that the latter ones are those who typically will live up a party, dance, talk with people of the opposite sex, and generally have a good time, whereas the former ones are what he called "party poopers" (I'm not sure those were his exact words - English is not my mother tongue). That is, people who prefer Analysis are the ones who will just simply sit isolated in a party and do nothing... When I heard all that I was astonished - I was hearing an EXACT description of myself! (In fact I had had a recent experience of a party where I had felt very isolated and very dissapointed, whereas Analysis had always been my favourite way, and it still is...) So when Isham asked us to tell him frankly if any of us was a "party pooper", I immediately raised - no, actually launched my hand, nearly under his nose (I was sitting on a front desk). It was obvioys he didn't expect anything like that. The class rolled down with laughter... Seriously now: I understand there are threads for people who want rigor and threads "for the layman". How can I tell which is which? Besides, how could I tell that Riogho was not asking for a mathematical answer? It was definetely in "Back to the future". I wasn't sure it was John Lithgow, but he looked like him. What movie was "3rd rock from the Sun"? Is there a relative web site?

I'm afraid "you are not thinking 4 dimensionally", as John Lithgow often said in "Back to the future". 1) It is not Space that is curved, it is SPACETIME (4 dimensions). 2) If at rest in a three dimensional space, be it curved as, e.g., the sides of a pit, one needs a force to get him/her rolling downwards. 3) In 4 dimensional SPACETIME, on the other hand, it s a principle of its GEOMETRY that paricles/bodies not influenced by anything except the gravitational field, move along TIMELIKE GEODESIC CURVES. This is a GEOMETRIC PROPERTY, as particles/bodies are themselves GEOMETRIC FEATURES of Spacetime, according to Einstein's Gravitational Field Equations. In other words: The geometric features of spacetime called material particles satisfy the equations of timelike geodesics: [math]\frac{d^2x^\alpha}{ds^2} + \Gamma^{\alpha}_{\beta\gamma}\frac{dx^\beta}{ds}\frac{dx^\gamma}{ds}=0 \Leftrightarrow \frac{d^2x^\alpha}{ds^2} = - \Gamma^{\alpha}_{\beta\gamma}\frac{dx^\beta}{ds}\frac{dx^\gamma}{ds}[/math] the indices running over the values: [math]0[/math] (time coordinate) and [math]1, 2, 3[/math] (spatial coordinates) whereas summation is understood over repeated indices ("dummy indices"). The second half of this relation gives the acceleration ([math]\frac{d^2x^\alpha}{ds^2}[/math]) of the material particle. 4) Nowthen: Suppose Spacetime is curved, i.e. the quantities [math]\Gamma^{\alpha}_{\beta\gamma}[/math] (Levi - Civita connection coefficients) are not all zero. In that case, even if the spatial velocity is initially zero ([math]\frac{dx^\alpha}{ds} = 0, \alpha = 1, 2, 3[/math]) , this is NOT the case with the temporal velocity ([math]\frac{dx^0}{ds} \neq 0[/math] - no material particles can stand still in time!) Hence, from our equation above: [math]\frac{d^2x^\alpha}{ds^2} = -\Gamma^{\alpha}_{00}\frac{dx^0}{ds}\frac{dx^0}{ds} \neq 0[/math] for [math]\alpha = 1, 2, 3,[/math] i.e., even if, initially, the particle is at rest (in space) it will accelerate, in general (that is, if [math]\Gamma^{\alpha}_{00}[/math] are NOT zero for all spatial values [math]\alpha = 1, 2, 3[/math]) as a result of the GEOMETRY of spacetime. 5) Motion along geodesic curves manifests itself in 3 dimensions by falling down the gravitatonal field. I hope this has helped you out!