Markus Hanke
Registered Senior Member
Precisely. That is a very accurate assessment of the situation. It's that, and Farsight's complete lack of willingness and/or ability to actually learn something from what is pointed out to him.
Why two mass attracts each other?
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Precisely. That is a very accurate assessment of the situation. It's that, and Farsight's complete lack of willingness and/or ability to actually learn something from what is pointed out to him.
I have checked the dimensions. You also can cross-check to see, whether the dimensions are correct or not.
What about "frame-dragging", "gravitational lensing", "red-shift", "blue-shift", "expansion of our universe"? Isnt space-time "stretched" or "compressed" in these cases?
I think Lorentz Transformations, SR, GR are all related. These are all relativistic phenomena.
This example you also gave earlier to explain that GR is geometry(differential) and not force. But then you could not explain orbital motion of "the Earth" around "the Sun" in terms of GR.
Markus Hanke
Registered Senior Member
No, it is just curved in non-trivial ways. There is no compression or stretching.
SR is a special case of GR for purely inertial reference frames, i.e. for frames where acceleration/gravity is absent. Lorentz transformation then are transformations which bring you from one inertial frame to another; this relies specifically on the fact that space-time is flat, i.e. it is not applicable to GR except perhaps locally as an approximation.
Why would I not be able to explain that ? Just pick a different analogy, and think of space-time as a frictionless sheet with an indentation in the middle, the center of that indentation being the sun. The earth then corresponds to a small marble or similar just "rolling" along the contours of the indentation. That's all. Again, this is just a very much simplified analogy, but it does illustrate the principle once again, namely that the marble stays in an elliptical orbit because it follows the curvature of the indentation, not because there is any force present. Mathematically, in GR the orbit of the earth is just a solution of the so-called geodesic equation. This is quite simply the GR equivalent of the two-body problem, which can be solved exactly. See here for example :
Essential Relativistic Celestial Mechanics by Victor A. Brumberg (Adam Hilger, London, 1991) ISBN 0-7503-0062-0.
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Mass-attracts? O><O
What is this space-time as presented via "embedded in space-time"?
If mass-attraction is attributed to something called gravity ergo gravitational space-time/spacetime then we have to go beyond relatively simple ideas of a complex math, that causes mass-attraction i.e. there has to be inter-mediating force--- gravitonic boson presumed --or there is physical or quasi-physical-- because ultra-micro ---somethingness membrane/fabric/web/substance/medium, that is curves in response to mass.
1) one hemi-sphere of the brain, we can attribute Universe existence--- ergo mass-attraction ---to being only a mathematical illusion. See Jacob Bekenstiens holographic-like ideas, derived from his black hole mathematics and his subsequent conclusion, that, "we appear to be 2D creatures, having and illusion of 3D".;
2) the other hemi-sphere of the brain, responses to the incoming sensorial phenomena and concludes, the illusion has a intermediating somethingness, substance/fabric/membrane that surrounds-- if not composes ---every quantum fermionic or bosonic particle of Universe to connect all as one finite, interrelated whole integrity.
3) we have no other hemi-spheres, so, ethier of two above-- or both --coincide, or we have to leave our hemi-spheres of the brain out of the mix/equation and only consider other parts of the brain, mid-brain etc....
There still so many weird oddities of Universe, that we do not have and answer for, so we all are left to speculate.
r6
What is this space-time as presented via "embedded in space-time"?
If mass-attraction is attributed to something called gravity ergo gravitational space-time/spacetime then we have to go beyond relatively simple ideas of a complex math, that causes mass-attraction i.e. there has to be inter-mediating force--- gravitonic boson presumed --or there is physical or quasi-physical-- because ultra-micro ---somethingness membrane/fabric/web/substance/medium, that is curves in response to mass.
1) one hemi-sphere of the brain, we can attribute Universe existence--- ergo mass-attraction ---to being only a mathematical illusion. See Jacob Bekenstiens holographic-like ideas, derived from his black hole mathematics and his subsequent conclusion, that, "we appear to be 2D creatures, having and illusion of 3D".;
2) the other hemi-sphere of the brain, responses to the incoming sensorial phenomena and concludes, the illusion has a intermediating somethingness, substance/fabric/membrane that surrounds-- if not composes ---every quantum fermionic or bosonic particle of Universe to connect all as one finite, interrelated whole integrity.
3) we have no other hemi-spheres, so, ethier of two above-- or both --coincide, or we have to leave our hemi-spheres of the brain out of the mix/equation and only consider other parts of the brain, mid-brain etc....
There still so many weird oddities of Universe, that we do not have and answer for, so we all are left to speculate.
r6
Has anyone ever considered that when there are two atoms separated by a distance,
those atoms disappear and then reappear closer to each other.
That way gravity would be a matter of probability rather than a force.
those atoms disappear and then reappear closer to each other.
That way gravity would be a matter of probability rather than a force.
LOL — So in other words, it can all be reduced to a roll of the dice?
You have heard of, "An object at rest will remain at rest unless acted on by an unbalanced force. An object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force.?
The object has momentum which, without an interaction from an outside force would continue in a straight line. In an orbit, that straight line momentum, is constantly altered by an outside force.., gravity. Spacetime, is a geometric description of that interaction. It is not a explanation of how gravity or what gravity is. If it were there would be no need to search for a functional model of quantum gravity.
Most of the time what is being talked about when gravitation is discussed is how two objects interact, separated in spae over time. However, when, you begin to look at frame dragging, what is being looked at is how an object interacts with space, over time. A gravitationally significant object dynamically interacts with the space around it, in the case of frame dragging.., by "dragging" it along with the object's motion, in a weakly defined manner. This is part of the geometric description of spacetime in GR. But once again, the mechanism that generates the interaction has not been described, only the dynamic relationship.., which is the geometry of spacetime.
In school you learned how to ploy points on a piece of paper, in two dimensions, an x a y coordinate system. You later learned how to expand that coordinate sytem by adding a third axis for depth, to understand 3D space. Spacetime adds a forth "dimension" time, so you have a 3D+1 or 4D representation of space over some period of time. Spacetime is not grabity. It is a picture of what the dynamic affect of gravity looks like, over time.
GR has from it early days described spacetime as dynamic. Which means that the interaction of space (a 3D geography) with the objects in it changes.., over time (time being the plus 1 and completing spacetime as a 4D geography). No one has yet been able to come up with a convicting description of the "substance" of space. (I use the word substance, because "we" have difficulty imagining things other that those with some substance as being dynamically kinetic in any way and space within the context of spacetime and GR is kinetically dynamic.)
So, spacetime itself is a geometry. A geometric construct that successfully describes the interaction of both objects in space with eachother and objects in space with space..., over time. When people say that objects or light etc. follow the curvature of spacetime, they are just saying that the object or light follows the geometric predictions of GR associated with gravitation. They are not saying that the geometry itself represents any force, or even in a classical sense any physical mechanism, influencing object's within it.
Well said, but Marcus has said that there is no missing mechanism, and that spacetime curvature is the mechanism. I say that if people are OK with that concept, they are fine because the math works very well, but if you are not OK with geometry and math being able to curve spacetime, then you are interested in the search for quantum gravity, as I am.
I said it equates to it. Everybody can google this to check that I was correct. You know I'm correct.
It's you showing the unwillingness to learn. I've explained inhomogeneous space and curved spacetime to you here and elsewhere, and you refuse to accept it or enter into discussion of it.
If I might chime in, gravity is not a force in the Energy = Force x Distance sense. When you drop a brick, it hits the ground with considerable kinetic energy, but gravity didn't do any work on it. Instead you did the work when you raised the brick. You exerted a force for a distance, and you added energy to the brick. This is stored as potential energy in the brick. Gravity merely releases it, converting it into kinetic energy. Note that the mass of the motionless brick at altitude is higher than that of the same brick motionless on the ground.
Don't forget that Heaviside developed gravitomagnetism before any geometric description of spacetime in GR.
Quite right. That's why it's wrong to say "light curves because spacetime is curved". That's assigning cause to a model of the effect, and is at odds with what Einstein said.
Sounds good to me.
I'm not fond of the word substance in this context either. And yes, I'd say convincing descriptions are lacking. But I'd say the important point to appreciate is that space is not nothing. It is the "medium" through which light waves propagate, and when it's in some "condition", what we have is a "field".
This is good stuff. However I would say when you read more widely you will come to appreciate that it's all in the geometry. What's the simplest thing you can think of? A light wave. What's that? A wave in space. That's hard to imagine, so go stand on a gedanken cliff, and look out over the flat calm ocean. Wait a minute or two, and here comes a wave. You notice that the wave's path is curved. This equates to curved spacetime. But note that the wave doesn't follow that curved path because the sea is curved. It does so because the sea is inhomogeneous, like it's saltier over there than it is over here. And get this: where the wave is, the sea is curved.
Geometry cannot move objects, but I have come to the point where I understand gravity as an influence, a pervasive wave energy influence that expands out equally in all directions from matter. Matter not only sends out its influence, i.e. all the information about its mass and motion, but it reacts to the pervasive presence of net gravitational influences in the space through which it passes, driven in fact by those influences.
That thought is what lead to my question about the Lagrangian, and its influence in the mathematics of dynamic systems where kinetic and potential energy are playing out during every instant of motion in my Gnats analogy thread.
Markus Hanke
Registered Senior Member
This is true only on a flat space-time without curvature or torsion. It is not generally true on a pseudo-Riemannian manifold; on such a manifold objects which are not subject to an external force trace out geodesics through space-time, which possess intrinsic curvature, torsion or both. This is why I mentioned the geodesic equation, which quantifies this relationship, in conjunction with the Raychaudhuri equation. These differential equations do not contain any forces, they are written purely in terms of the metric tensor and its derivatives; plugging in numbers and applying the correct boundary conditions immediately yield the correct orbits, from purely geometric principles.
May I ask how familiar you are with the differential geometry behind this ? Have you ever done any calculations for various scenarios using the geodesic equation ? That just out of interest.
I did not say that it was. What I said is that gravity is a geometric property of aforementioned space-time.
GR is a purely classical model of space-time geometrodynamics; it determines the geometry of the space-time manifold, and describes the geometric properties of the world lines of particles and bodies in the presence of energy. In doing so GR does away with the notion of forces and gravitational fields; these concepts are simply no longer needed. This is in contrast to QFT, which relies on the concept of the fundamental interactions being due to the exchange of virtual vector bosons, which mediate forces. This way of describing gravity makes no predictions as to the geometry and topology of the underlying space-time on which the quantum fields exist; this leads to infinities which cannot be renormalised. Therefore, both of these approaches are limited in their domains of applicability, and fundamentally incompatible. The search for a self-consistent model of QG is the search for a model which either reduces to QFT and GR in the high and low energy limits, or does away with both and supersedes them with an entirely new paradigm. Ultimately the aim is not to explain just gravity, but to describe all fundamental interactions as facets of just one common mechanism.
Yes, that is right. There are no forces, and hence no mechanisms needed here.
Markus Hanke
Registered Senior Member
You are not correct. What is true is that the Riemann tensor contains information about tidal forces ( duh ! ), but the only object in GR which actually equates to tidal forces is the Weyl tensor. The Riemann tensor contains much more information than just tidal forces, for example how the shape and geometry of bodies change when they move along geodesics, and what happens when you parallel-transport vectors; it does not equate to a force - unsurprisingly, since it is a rank 4 tensor ! It does, however, serve as the base from which all other curvatures are calculated, because it is the only object which contains all relevant information. I had already said that much in my previous post. The Weyl tensor, on the other hand, contains only the effects of tidal forces, and thus more or less equates to such forces.
If you wish to rely on Google, then go ahead and google "Weyl tensor" or "Weyl curvature". You will find the necessary information as to the distinction between Weyl curvature and Riemann curvature. Like I said, they are not the same thing.
Outside force( vector boson ) O><O fields( vector boson )
Mass-attracts?...O><O....field?.....Vector Boson?.....
Is there a spacetime/"space-time" "field" called quantum gravity ergo a vector boson quantity/quantum called a graviton?
and/or
Is there a spacetime/"space-time" called a vector boson graviton? Is it a field, a force, a substance, a membrane, a fabric, medium etc........
We know there is the associated geo-metrics and what ever other metrics, but IF spacetime/space-time is a "field" then it is a somethingness that exists in complement to the metaphysically abstract concepts of mathematical metrics( quantify ), that is waiting to be quantized metric, and not just geo-mathematical metrics.
r6
Mass-attracts?...O><O....field?.....Vector Boson?.....
Is there a spacetime/"space-time" "field" called quantum gravity ergo a vector boson quantity/quantum called a graviton?
and/or
Is there a spacetime/"space-time" called a vector boson graviton? Is it a field, a force, a substance, a membrane, a fabric, medium etc........
We know there is the associated geo-metrics and what ever other metrics, but IF spacetime/space-time is a "field" then it is a somethingness that exists in complement to the metaphysically abstract concepts of mathematical metrics( quantify ), that is waiting to be quantized metric, and not just geo-mathematical metrics.
r6
What is this space-time as presented via "embedded in space-time"?
If mass-attraction is attributed to something called gravity ergo gravitational space-time/spacetime then we have to go beyond relatively simple ideas of a complex math, that causes mass-attraction i.e. there has to be inter-mediating force--- gravitonic boson presumed --or there is physical or quasi-physical-- because ultra-micro ---somethingness membrane/fabric/web/substance/medium, that is curves in response to mass.
1) one hemi-sphere of the brain, we can attribute Universe existence--- ergo mass-attraction ---to being only a mathematical illusion. See Jacob Bekenstiens holographic-like ideas, derived from his black hole mathematics and his subsequent conclusion, that, "we appear to be 2D creatures, having and illusion of 3D".;
2) the other hemi-sphere of the brain, responses to the incoming sensorial phenomena and concludes, the illusion has a intermediating somethingness, substance/fabric/membrane that surrounds-- if not composes ---every quantum fermionic or bosonic particle of Universe to connect all as one finite, interrelated whole integrity.
3) we have no other hemi-spheres, so, ethier of two above-- or both --coincide, or we have to leave our hemi-spheres of the brain out of the mix/equation and only consider other parts of the brain, mid-brain etc....
There still so many weird oddities of Universe, that we do not have and answer for, so we all are left to speculate.
r6
Note what he said. He said it does not directly equate to it. If you actually knew how to do any GR you'd know that you can construct the tidal tensor from the Riemann curvature tensor but that doesn't mean it is the tidal tensor, which is what you said when you said "I said it equates to it".
The tidal tensor is obtained from certain components and geodesic tangent vectors. More specifically it is the 'electrogravitic tensor' obtained by the Bel decomposition of the curvature tensor.
Once about you show you don't understand the subtle issues, you just parrot what Google can explain in layperson terms to you.
Hardly. You and I have already been over the FRW metric's relevance to cosmology and variations in matter distribution and now here's another example of you don't getting the specifics right.
As for unwillingness to learn you know zero working details of GR. You talk about inhomogeneous space, Riemann curvature and FRW metrics but you cannot do anything with them. You don't even know calculus, something EVERY engineering, physics and maths student knows in some way. Hell, it's A Level stuff! And yet you pretend to understand Riemann curvature? If you were honest in how you represent your 'knowledge' you'd only present yourself as believing you have a qualitative grasp of qualitative explanations others have provided you as you have zero quantitative understanding. Despite the years and years you've been going around claiming to have explained or understood this stuff you still cannot do anything of any quantitative substance with any of it.
The fact the Riemann curvature tensor has rank 4 and thus cannot be equal to an acceleration or force is something completely beyond Farsight's ability to grasp but neither of us are surprised by that.
Farsight, since you don't know what a tensor's rank means I'll give an analogy, since that seems to be the only way you can think about or understand anything; in the same way it is nonsense to say 3 metres = 5 seconds + 2 kilograms equating tensors of different rank is nonsense. Acceleration is a vector, a rank 1 tensor. The tidal tensor is rank 2. The Riemann curvature tensor is rank 4. The tidal tensor is formed from the Riemann tensor by contracting it with particular other tensors, namely those associated to geodesic tangents. Not all of the components of the curvature tensor contribute to the tidal tensor, as shown by the Bel decomposition (the Weyl tensor is identified by this decomposition). But hey, you've never done any of this and because you're so unwilling to learn about such stuff before shooting your mouth off in regards to it you get things wrong.
Speaking of being unwilling to learn, any rational person with your track record of making uninformed assertions about quantitative aspects of physics would have realised they should stop making uninformed assertions about quantitative aspects of physics. But then it would seem your approach to science isn't rational. It certainly isn't informed.
No problem. An electromagnetic wave is a dynamical system which moves itself, and "the geometry of spacetime" describes how that motion is curved in a gravitational field. But what is an electromagnetic wave? Have a read of this and you can see Einstein saying this:
"It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds, and it is natural to suspect that this only appears to be so because the structure of the physical continuum is not completely described by the Riemannian metric."
If Einstein was still around, I reckon he'd be telling you that the electromagnetic wave is just a bit "dynamical geometry" propagating through space, and that it's all in the geometry.
I didn't say they were. Now please address my post #158 instead of clutching at you don't understand differential geometry straws. It is important that you learn the distinction between space and spacetime. Light does not move through spacetime, because spacetime models space at all times. Therefore light does not curve because spacetime is curved. Take the differential of your curved spacetime and what have you got? Inhomogeneous space. That's what light moves through. And as I said, you know what die Ausbreitungs-geschwindigkeit des Lichtes mit dem Orte variiert means. Do not dismiss it because it is not in accord with the general relativity you've been taught.
I didn't say directly and I didn't say is. Would you care to address my post #158 instead of boring us all with your customary carping whining ad-hominems?
Your [POST=3066616]post #158[/POST] doesn't contain any new arguments. You've posted them on this forum before, and they've been rebutted before many times now. Yet you're posting them again essentially unmodified. So it rather looks more like you aren't learning anything and you're just looking for a different audience.
Personally I'm getting tired of explaining why you're wrong about something only to see you repeat the same argument a few months later as if nothing had happened. So let's try it differently this time. One of the expectations of scientific discourse is intellectual honesty. In particular, if you advance an argument, you are expected to be honest about any possible weaknesses in your argument or any reasons your conclusions might be wrong. In many ways you are expected to be your own harshest critic.
Here's a few select arguments you make in post #158:
1) "There is no motion in spacetime".
2) General relativity is, or can be interpreted as, a theory about flat but inhomogeneous space.
3) Albert Einstein was personally a proponent of point #2.
I could explain what's wrong with those arguments, but by now you should already know what I'm going to say.
So what do you think my main criticisms would be, and what specific responses have you come up with since the first time I made them?
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