General Relativity.

Great question Time to introduce the light-cone. I'm busy so read this very short overview: Light cone - WikipediaIn SR, you can change inertial frame and the insides of the cone will slew around, i.e. that vertical time-line will tilt anywhere within the cone. BUT, the cone remains fixed. There is a light-cone at every point in space-time an they are all perfectly aligned.In GR, curvature of space-time causes the light-cones to tilt, so that they are no longer aligned. Your world-line, if you do not accelerate, will simply follow a winding path of sequential light-cones, tracking their tilt as you move through time. So what we call gravitational attraction is simply following your light-cones... or more simply, just following time To not follow your light-cone, you must accelerate. But of course the best you can do is to accelerate towards c, i.e. the edge of your light-cone. You cannot tip beyond the edge of the cone...You are now effectively moving wrt your light-cone. You have also accelerated to get there, and if you think about this in SR-terms, you are going to experience a real time-dilation. It is quite possible that you are not now moving wrt a distance observer. But you are still moving wrt to your light-cone. E.g. stood on the earth, where you light-cone is pointing inwards towards the centre of the earth (actually, slighlty to the side becasue of the rotation) Thus you would expect to see a real time-dilation wrt someone who isn't fighting their light-cone so hard.Now imagine where your light-cone is tipped through 45 degrees, so that one edge is pointing in the time-direction. Unless you can move at c, you are going to be herded in the direction of the light-cone... no choice! The interior of the upper half of your light-cone is your future. If all of the light-cones on a sphere are tipped at 45 degrees inwards, you have a potential event horizon. This is what happens around a black-hole and is why you cannot escape. Your future lies within the event horizon. Inside the horizon, it gets worse. Now the light-cones are all pointing inwards towards the singularity. The singularity no longer exists in a spatial direction, but in your future!!! This is why you cannot avoid the singularity. Can you avoid tomorrow?Back to the event horizon. Remember I said that the light cones are tipped at 45 degrees. So their vertical edges make up the surface of the horizon. But the edge of a light-cone is a light-ray by definition. So the horizon is actually a surface of light rays, and therefore must be moving at the speed of light... wrt the light cone. We call it a null surface, in the same way we call a light-ray a null-path. If you hang just outside a black hole, you are effectively travelling at c. You would expect to see massive time dilation when you move back away from the black hole, and this is exactly what happens.Around a rotating object, the light cones don't just tip inwards, but sideways as well. This is what we call frame-dragging, but it is just your time-line being spiralled around the object (planet, star, black hole). Of course, your light-cone can tip so far sideways that you cannot prevent yourself from spinning without exceeding c. This generates a static-limit and marks the boundary of the ergosphere.How's that for now? Wish you hadn't asked?

Nothing feeble here. Some very astute points and some very deep questions. Good stuff! I will get back to this as time allows... or maybe SG will show up and actually put some work in

Exactly. The axis of the light cone is the path you will follow as long as you don't accelerate. By accelerating, you can move your path so that it points anywhere within the forward cone.

Yes there is a distinction, otherwise all of this would be meaningless. But all you ever know is what you are doing, not what someone else is doing. You know if you are experiencing force, or if you are "weight-less". If you are weight-less, you are following your light-cone, following your geodesic through space-time. If you feel a force, you are accelerating, fighting your light-cone, deviating from your geodesic.It is as simple as that. This is what gave rise to GR in the first place. Einstein considered a person in an elevator. He asked if the preson could tell the difference between the elevator being sat on the ground, or it being accelerated at 1g through free-space. He realised that in both cases, you are simply accalerating against your light-cone.

Phew, that's a lot of thoughts Rather than talk to your points, which can get confusing, I will give a brief overview to explain both your ideas and your confusion.There is no gravitational field... there is no gravity. To simplify things, I will take your view and talk about space rather than space-time.Objects move along straight lines in space, just like good old Newton I: an object will remain in a state of constant velocity unless acted upon by an external force.If space is curved, objects will appear to be deflected from straight lines, but in reality they are just following the "straighest" line on a curved surface, like a plane following a "great circle" as it transits the world. An orbit is actually a straight line!For space to be curved, there must be something that describes how curved it is at each point in space. We call this the "metric" or metric-field. The metric is sometime described as the gravitational field, but this is confusing and incorrect. It is best not to think of gravity at all when looking at this. You are bang-on when you talk about a density of space, becasue this is what the metric measures. It gives the distance between two infinitesimally close points, and from this distance-element, you can construct a volume-element which is your density.Considering the distance-element to be based on the planck length is racing beyond General Relativity into Qunatum Gravity, so I will simply ask you to slow down a bit! But you are talking about precisely the right things if you wish to pursue that avenue once you have mastered your GR...Mass curves space. Matter has mass, so matter curves space. Curved space itself has mass. So curved space can curve space... how cool is that! But what is matter? Well, the clue is in this paragraph. What do we know that already curves space? Curved space! So matter is actually curved space... very tightly woven, highly curved space!I wish it were that simple, but this cannot be true in basic General Relatvity. However, when we expand to something like supergravity or string theory, we regain this wonderful picture that space and matter are the same thing.Now, we have been talking about all of this while ignoing time. Just add time back in to your space, so you now have space-time. It's exactly the same, only now your density is a 4d density.Digest the above and come back with your next set of musings and questions

I'm sure you meant to say "a bit slower" Likewise, I'm sure you meant to say that a 3rd person would never perceive you reaching the event horizon, but to you, you would simply fall in.

Hi, sorry to not get back to your previous message(s). I don't get a lot of time to post... mostly I just read when I can.There are a number of problems here as you can imagine:Don't forget that your dog cannot make his path from A to B in the presence of the mass without accelerating: A to B is no longer a geodesic. You would be able to detect the acceleration/force applied. Similarly when you attempt to walk the path.You won't ever see 50 feet and measure 60 feet. It's the other way round. Your movement will shrink the distance and the time, so that your distance will measure as shorter.

The link doesn't work, but anyway, critical density does not necessarily imply an infinte universe. One of the major points of inflation is that it produces a critical universe from a non-critical universe. After inflation, both a closed and an open FRW will look flat and critical. It's a nice answer to an otherwise problematic fine-tuning question.

Yes It depends. It could be either, depending on the nature and extent of the curavture. Same as above. Yes, it can.If you make your mass a cosmic string, aligned normal to your AOB plane, then you have a situation where all of space is flat apart from at the string. The effect of the string is to introduce an angle deficit, such that there are less than 360 degrees around the string. Thus you can still have A and B appearing at 90 degrees and at the declared distances, but the line AB will certainly not be the pythagorean distance, nor the angles OAB and OBA the expected trignometric values.This message has been edited by cavediver, 10-12-2005 01:03 PM

You will measure the real distance. You can measue the distance to A from O and B from O. But travel to A and measure AB, you will find it not equal to sqrt(OA^2 + OB^2). By taking enough measurements like this, you can build up a picture of the local curvature.

You would just see them accelerate (in direction as well as speed), then decelerate but would not discern any force exerted.

A bit too busy at the moment to address this, but I will come back to it. Good "question" though, and it does have an important connection to GR so it is not too out of place here. A quick point though... it's not just photon exchange but also graviton exchange. The others we can effectively ignore for your discussion.

Here's as good a place as any...RAZD made the following remarks over in Biological Evolution: Peppered Moths and Natural Selection. I naturally blew my top at this, and RAZD came back with this My first remark is that there is confusion here between GR and cosmology. Our theory of gravity is General Relativity. There is no "theory\on theory\on theory". GR is not tailored by empirical data apart from the value of G. The interplay of "space warping, gravity waves" is all contained and explained within GR. Gravitons are going beyond into quantum gravity and theories of everything, but are not in any way contradictory with General Relativity.Perhaps RAZD would like explain away all of the theoretical predictions of GR that have been observationally measured: equivalence principle, grav time-dilation, grav red-shift, bending of light, lensing of light, binary pulsar energy loss, corrections to planetary motions (perihelion of mercury as the original), frame dragging, and of course the entire world of special relativity. That is off the top of my head. This message has been edited by cavediver, 11-26-2005 11:41 AM

No time at the moment, but just to say that your post does not explain your use of the phrase "scanty at best".Even if I accept your description of the "anomalies" (which I do not), how does that enable you to describe the evidence for our theory of gravity (General Relativity) as scanty?You are correct, we have gone over this before and I have explained why the PA is not worth considering as it stands. You are misrepresenting my science and I find that highly objectionable. You have a little knowledge of the subject but you are presenting yourself as an expert to a gullible audience and making claims that are simply false. You have much to learn...This message has been edited by cavediver, 11-27-2005 04:18 PM

Although Newtonian spacetime can be described as curved, it would be more appropriate to describe the bundle structure of spatial hypersurface fibres on the time base-space as having non-trivial connection. BUT I do not see how this can possibily give rise to Newtonian "gravitational force". Can you explain?