At Rest with our Hubble view

[Undefined]

In Schwarzschild space-time, "coordinate speed" is not even defined at the event horizon !

Forgive my naive question: What is the implication of such an assertion in the reality of motion through space (as distinct from 'through a spaceTIME' model/graph construct/theory) at that location in space with respect to the massive body 'source' of the space conditioning leading to an 'event horizon' of motion/speed through space outside, at and below that 'horizon' associated with the massive body involved?

 

[Undefined]

...If, however, we place a massive body somewhere in the vicinity of our particles ( let's imagine it to be point-like ), that parallelism will be disturbed, and the geodesics will deviate. In standard GR this is an almost trivially simple problem, since the geodesics follow the curvature of space-time; if the separation between the two particles' geodesics is denoted by the 4-vector v, the resulting deviation is

$$\displaystyle{\frac{D^2v}{d\lambda ^2}=-R(u,v,u)}$$

wherein R is the Riemann curvature tensor, and the capital D denotes the covariant derivative as opposed to the ordinary partial derivative. That's it. No assumptions about speeds of light, wave nature of matter etc etc needed. We are in fact not at all interested in any speeds, we only want to look at the separation between their trajectories, and separation ceases to be constant simply because space-time is no longer flat if we place a massive body in it. This is just a very simple model of gravitational attraction.

So now, how would that very simple scenario play out in your little world where space-time is flat, and only the speed of light varies ? What happens to the particles' trajectories, and why?...

Hello Markus Hanke. Sorry I have been busy and can only stay a few minutes again today. So please forgive my brevity in posing this respectful and naive observations/questions to what you posted above to Farsight. I have bolded those three sections of your post which I particularly want to have your further clarification on (which I will catch up with tomorrow if I can). Anyhow, ...

In the first bolded section, you restate what the observation is in fact, but without any explanation of what causes the deviation. Yes?

In the second bolded section, you restate the very question yet to be answered by actual explanation (as distinct from a 'modeling of observation' bvy using a math spaceTIME construct) of what is happening in the space (not spacetime). Yes?

In the third bolded section, the obvious naive compound question again arises in my mind: what and how and why, exactly, does a 'spaceTIME' construct have to do with the behaviour of a particle through space OR spaceTIME whether conditioned/inhomogenous or homogenous/flat, respectively?

Seems to me so far in your discussion with Farsight that it's going round in circles because the actual question of WHY and WHAT MECHANISM is not yet resolved between you two. Can you two come to a consensus at to what you two are talking about? Is it space and MOTION in it, or is it GRAPH 'space' and PLOTTED TIMES of motions involved in real space which that 'graph' MODELS as you say?

I mean, irrespective of the 'maths', there must still be some REALITY of spatial extent and MOTION within same that any complete discussion must address and resolve non-circuitously on a common basis as to the 'arena' where all the observed/modeled phenomena occurs, evolves and devolves as we scientists have discovered so far?

Again, I look forward to uour polite discussion with Farsight, as it has been most interesting and stimulating to my naive mind and its naive understandings so far in this area of the universal physics. Keep it up, both of you, and I trust you two will meet at some common understandings down the line of your robust discussion! Until tomorrow.

 

[Markus Hanke]

On a different topic, when you said something like "GR is deterministic", a question came to mind. Are you refering to the philosophical meaning of determinism? Can you elaborate on the difference between a static determined cosmology and a philosophical determinism?

GR is deterministic in the sense that, given a set of initial conditions, one can in principle calculate the dynamics of a given system ( involving only gravity ) into all eternity. This would not, for example, be possible in quantum mechanics.

 

[Markus Hanke]

(double post)

 

[Markus Hanke]

Forgive my naive question: What is the implication of such an assertion in the reality of motion through space (as distinct from 'through a spaceTIME' model/graph construct/theory) at that location in space with respect to the massive body 'source' of the space conditioning leading to an 'event horizon' of motion/speed through space outside, at and below that 'horizon' associated with the massive body involved?

I don't really understand what you are trying to ask, but the situation is that a far away observer sees the infalling object slow down and fade away as it approaches the event horizon ( and never reaches it ), whereas the infalling object itself notices nothing special as it crosses the horizon in a finite, well defined time. This disagreement is simply because the observers "operate" in different coordinate systems.

In the first bolded section, you restate what the observation is in fact, but without any explanation of what causes the deviation. Yes?

The explanation is in the next sentence. The geodesics follow the curvature of space-time, and hence cease to be parallel.

In the second bolded section, you restate the very question yet to be answered by actual explanation (as distinct from a 'modeling of observation' bvy using a math spaceTIME construct) of what is happening in the space (not spacetime). Yes?

No, it is a simple question to be answered within the axioms of GR, i.e. with space-time physics.

In the third bolded section, the obvious naive compound question again arises in my mind: what and how and why, exactly, does a 'spaceTIME' construct have to do with the behaviour of a particle through space OR spaceTIME whether conditioned/inhomogenous or homogenous/flat, respectively?

The point is that I want to see how Farsights treats this simple scenario by employing only a variable speed of light, without any reference to space-time curvature.

Can you two come to a consensus at to what you two are talking about?

No, because Farsight's assertions are wrong, plain and simple. GR is about space-time curvature, not some nonsense about inhomogeneous space. There is no "consensus" here.

I mean, irrespective of the 'maths', there must still be some REALITY of spatial extent and MOTION within same that any complete discussion must address and resolve non-circuitously on a common basis as to the 'arena' where all the observed/modeled phenomena occurs, evolves and devolves as we scientists have discovered so far?

Everything that has been discovered thus far is consistent with 4-dimensional space-time, and GR. The same can not be said for Farsight's inhomogeneous space, as has been repeatedly demonstrated. Farsight will never admit the error of his ways, because he has been at it far too long.

Spatial extent was never doubted, and motion is real if one "foliates" space-time into individual slices of space indexed by a time coordinate, as I have explained. The underlying space-time itself, however, is static. Newtonian gravity considers ( for example ) the moon as describing a circular orbit in space, indexed by a time coordinate to tell exactly where on the orbit it is to be found. It's a dynamic system. GR on the other hand does not separate time and space; the moon orbiting the earth now becomes a static helix in 4-dimensional space-time. Thus far these are only two different ways to look at the same thing; however, the differences now arise in that GR now longer requires space and time to be flat, quite unlike Newtonian gravity. And because space and time in GR are two aspects of the same underlying "thing", curvature will always effect both.

Take as another example the so often quoted scenario of a ray of light crossing right down the center between two massive bodies; in space that ray looks straight and flat, but in space-time it is curved, and the curvature is along the time direction. This manifests as a delay in receiving the light ray on the other side, a phenomenon called the Shapiro delay. Again, this does not require any changes in light speed.
In general, curvature along the space dimensions manifests as changes in trajectories in space, whereas curvature components along the time dimension manifest as time dilation. In GR both are combined into changes in the 4-dimensional world line of particles in space-time, and in general curvature will be present along all dimensions. None of this requires any changes in the speed of light, which remains the same for all observers in all regions of space-time, and all the problematic issues ( like frequency-dependent refractions etc ) never even arise. There is, in fact, not even one gravitational phenomenon which cannot be understood in terms of space-time, but there are plenty of issues with the notion of a varying light speeds in purely flat space.

Seems to me so far in your discussion with Farsight that it's going round in circles

Yes, that's for sure. Discussions with Farsight always end up going in circles, because he never addresses the issues at stake, but simply repeats the same stuff over and over again. He has been stuck for years on a handful of textual quotes while steadfastedly refusing to consider the overall context and meaning of GR, as given to us by Einstein, and elaborated upon by many brilliant physicists in the past 100 years. He dismisses all of it, largely based on a single sentence which Einstein once said in an address to a lay audience ( which no one denies he did ). Farsight considers this conclusive evidence that everyone in the physics and maths community is wrong. Go figure.

 

[quantum_wave]

GR is deterministic in the sense that, given a set of initial conditions, one can in principle calculate the dynamics of a given system ( involving only gravity ) into all eternity. This would not, for example, be possible in quantum mechanics.

In regard to the dynamics of a given system, does that refer to any given space, meaning that any particular volume of space can have its individual curvature. Where I'm going with that is I'm still working on my layman characterization of GR vs. classical descriptions of gravity.

Classical equations focused on matter density (the mass), mass being the quantity of matter in a body.

In GR matter and energy are equivalent, and both matter and space have energy density. Thus the EFEs focus on energy density of space which can contain energy density in the form of both matter and space.

Motion of an object through any volume of space depends on the dynamics or geometry of that space as defined via the EFEs. Thus the curvature of space-time in a given system is relative to the energy density in that particular volume.

Simply, the geometry of space-time determines the world lines or geodesics of objects moving through the particular space in question, i.e. objects move along world lines?

 

[Undefined]

Thanks Markus Hanke for your, again, considered and courteous response to my naive questions and observations on the very interesting and stimulating points Farsight and you are discussing here. I am still very busy so I will again have to beg your forgiveness for my haste in answering your points.

I don't really understand what you are trying to ask, but the situation is that a far away observer sees the infalling object slow down and fade away as it approaches the event horizon ( and never reaches it ), whereas the infalling object itself notices nothing special as it crosses the horizon in a finite, well defined time. This disagreement is simply because the observers "operate" in different coordinate systems.

When you state that (my bolding) that the object is "seen" to slow down", does this "apparent slowing" also apply to the light itself as 'an object' in the sense that a photon is "apparently slowed" to look like the "coordinate speed" of that photon-object is slowed as "measured/seen" from the remote observer coordinate/position/state relative to the event horizon? If so, that would imply that Farsight's assertion about changing coordinate speed of light is not altogether illogical given his arguments so far, yes?

The explanation is in the next sentence. The geodesics follow the curvature of space-time, and hence cease to be parallel.

My naive mind reads that as abstract mathematical "modeling of observed effects", as distinct from "explanation as to cause" of said observed effects abstractly modeled. In my mind there is a gulf of difference between the two as to their explanatory power regarding the reality physics as distinct from the abstract modeling of same, yes?

No, it is a simple question to be answered within the axioms of GR, i.e. with space-time physics.

Your use of the phrase "Axioms of GR" is the most honest and straightforward thing I have read from mainstream mathematical-physicists in a long time on the forums. It says to my naive mind that you recognize the fact of the axiomatic nature of all the 'definitions' accordingly ascribed to the EFE's, including "spaceTIME" definition/construct. It tacitly recognizes the further fact that these EFE's may "define axiomatically", but do not actually "determine physically" the reality of cause and effect mechanisms/phenomena which so far as my naive mind can grasp involves only space and MOTION within same 'for real' as distinct from "abstractly Axioimatically defined construction", yes? Thank you for your integrity in acknowledging the fundamental difference between the respective bases from which you and Farsight come to this discussion so far. I hope that you two will soon come to be 'on the same page' as to the origins of your 'understandings' so that a common consensus can be reached between you two. Kudos to both of you for persisting despite your different 'takes' so far!

The point is that I want to see how Farsights treats this simple scenario by employing only a variable speed of light, without any reference to space-time curvature.

But your "challenge" there is a non-sequitur impossible to address and answer unless you first stipulate WHY the speed of light MAY change; which immediately brings the discussion back to the question of space inhomogeneity as the "reason" why; which further brings us back to the question of why does the presence of mass-energy concentrations affect local space "conditions" to produce varying degrees of inhomogeneity of space conditions affecting motions within that conditioned space? If the space is not affected by any associated mass-energy concentration, then your "challenge" is impossible to treat because there is no "question" to answer at all, since motions will BE "straight" and unaffected by definition as per such a "incomplete challenge" as put, yes?

No, because Farsight's assertions are wrong, plain and simple. GR is about space-time curvature, not some nonsense about inhomogeneous space. There is no "consensus" here.

That essentially is the problem of "apples and oranges" cross-purpose misunderstandings which keep arising between you two on this. You are talking abstract models (spacetime defined by EFEs) and Farsight is talking space and motion as observed concretely, which occurs for real irrespective of humans/mathematics modeling of same, yes? So my naive suggestion is that you two first set the basis for discussion on one or the other basis (spacetime model or space and motion reality). Perhaps it might be best at this juncture for you two to first review/windback your discussion to a common ground for both, and then treat the points according to first ONE and then the OTHER context? It would save a lot of cross-purpose exchanges which I keep seeing again and again in all such discussions all over.

Everything that has been discovered thus far is consistent with 4-dimensional space-time, and GR. The same can not be said for Farsight's inhomogeneous space, as has been repeatedly demonstrated. Farsight will never admit the error of his ways, because he has been at it far too long.

You already acknowledged that it is an "Axiomatic" consistency, not necessarily a "real cause" explanation. That is the gap between the perspective you are arguing from and the perspective which Farsight is coming from. Until you two settle this so that you two get oin the same page, misunderstandings (and tempers, no doubt) will rise; and such will help nothing and no-one except the 'troll population' who enjoys that more than the science discussion itself (as we have seen all too often from certain quarters, yes)?

Spatial extent was never doubted, and motion is real if one "foliates" space-time into individual slices of space indexed by a time coordinate, as I have explained. The underlying space-time itself, however, is static. Newtonian gravity considers ( for example ) the moon as describing a circular orbit in space, indexed by a time coordinate to tell exactly where on the orbit it is to be found. It's a dynamic system. GR on the other hand does not separate time and space; the moon orbiting the earth now becomes a static helix in 4-dimensional space-time. Thus far these are only two different ways to look at the same thing; however, the differences now arise in that GR now longer requires space and time to be flat, quite unlike Newtonian gravity. And because space and time in GR are two aspects of the same underlying "thing", curvature will always effect both.

Yes, motions in space are what they are 'for real', irrespective of how we model or think upon same. That is already naively agreed by all concerned I trust, and is the common starting point for all discussion that has occurred so far between you two, yes? It is the causes rather than the thin king and modeling that Farsight seems to be talking about, as distinct from the modeling and thinking about the effects observed from such causes, yes? Which is why naively I don't see your discussion as 'disagreement' so much as continuing cross-purpose 'apples and oranges' misunderstandings.

Take as another example the so often quoted scenario of a ray of light crossing right down the center between two massive bodies; in space that ray looks straight and flat, but in space-time it is curved, and the curvature is along the time direction. This manifests as a delay in receiving the light ray on the other side, a phenomenon called the Shapiro delay. Again, this does not require any changes in light speed.

But given all the recent reappraisal of the "time" aspect having its "dimensionality" status as an abstraction from the modeling of "motion", then that "curvature in the time direction" is just another way of saying the object is "moving through space and doing so in a straight line", yes? So which is the "real" thing, the motion or the time aspect? If the 'motion', then I humbly submit that motion's abstraction as 'time' is merely an Axiomatic 'term', and not necessarily determinant of the physics itself in any way other than giving it a 'mathematical label' in lieu of identifying the 'physical cause' of it?

In general, curvature along the space dimensions manifests as changes in trajectories in space, whereas curvature components along the time dimension manifest as time dilation. In GR both are combined into changes in the 4-dimensional world line of particles in space-time, and in general curvature will be present along all dimensions. None of this requires any changes in the speed of light, which remains the same for all observers in all regions of space-time, and all the problematic issues ( like frequency-dependent refractions etc ) never even arise. There is, in fact, not even one gravitational phenomenon which cannot be understood in terms of space-time, but there are plenty of issues with the notion of a varying light speeds in purely flat space.

Following on from the previous item, I again humbly suggest that "time dilation" is just another "math label" in lieu of the actual "slowing motion" effect from whatever causes. The periodic motion of a clock mechanism may change, so the "time label" must change with it, or else the "time term" values have no basis as a standard/logical abstraction of such variable motions as we observe. Like Farsight says, we do not 'see time varying' in a clock, we see its inherent 'clock process motions' varying according to location in space and state of overall motion of the overall containing structure of the clock 'body' as a whole through varying space 'conditioning' by mass-energy concentrations nearby. How one models all that is "axiomatic', but it in no way explains it unless the real causes are identified as more than just 'abstract unknowns'. The models are useful, but so far not actually explanatory as to 'unknown physical causes', since the 'Axiomatic theories' and models are not yet 'complete enough', yes?

Yes, that's for sure. Discussions with Farsight always end up going in circles, because he never addresses the issues at stake, but simply repeats the same stuff over and over again. He has been stuck for years on a handful of textual quotes while steadfastedly refusing to consider the overall context and meaning of GR, as given to us by Einstein, and elaborated upon by many brilliant physicists in the past 100 years. He dismisses all of it, largely based on a single sentence which Einstein once said in an address to a lay audience ( which no one denies he did ). Farsight considers this conclusive evidence that everyone in the physics and maths community is wrong. Go figure.

Once again, my naive observation here is that you two are at cross-purpose misunderstandings due to 'baggage' and repeated crossings which lead to the 'repetition' which you mention. Until you two are on the same page before you discuss further, then the discussions will be doomed to repetition from both sides and fraying tempers because of those very same misunderstandings which my naive observations tell me is happening. I humbly suggest you two 'reset' your discussion from scratch based on what it is exactly that you wish to argue about. I mean, do you two wish to argue 'Axiomatic modeling abstractions' of space and motions in that space; or about the real causes of motions in space as observed, irrespective of modeling?

Sorry Markus Hanke, but I have to go again. Back another day. Please forgive me if my naive approach to the discussion between you two has led to any unintended offense against either you or Farsight. None intended at all. Thanks again for your and Farsight's stimulating in-depth discussions to date. Bye for now!

 

[Undefined]

In regard to the dynamics of a given system, does that refer to any given space, meaning that any particular volume of space can have its individual curvature. Where I'm going with that is I'm still working on my layman characterization of GR vs. classical descriptions of gravity.

Classical equations focused on matter density (the mass), mass being the quantity of matter in a body.

In GR matter and energy are equivalent, and both matter and space have energy density. Thus the EFEs focus on energy density of space which can contain energy density in the form of both matter and space.

Motion of an object through any volume of space depends on the dynamics or geometry of that space as defined via the EFEs. Thus the curvature of space-time in a given system is relative to the energy density in that particular volume.

Simply, the geometry of space-time determines the world lines or geodesics of objects moving through the particular space in question, i.e. objects move along world lines?

Just to say 'hello', q-w! And to direct you to my post to Markus Hanke above, where I pointed out that while the EFEs 'define axiomatically', they in no way 'determine physically' what is happening 'for real'. Hence why the causes for the effects are still two very important and distinct aspect which so far no theory has been 'complete' enough to make clear in their own contexts (axiomatic models and identifiable causes)? I thought I should point this out again because of your own comment about EFEs etc in your response to Markus Hanke above. Still reading you and everyone. See you round, q-w!

 

[quantum_wave]

Just to say 'hello', q-w! And to direct you to my post to Markus Hanke above, where I pointed out that while the EFEs 'define axiomatically', they in no way 'determine physically' what is happening 'for real'. Hence why the causes for the effects are still two very important and distinct aspect which so far no theory has been 'complete' enough to make clear in their own contexts (axiomatic models and identifiable causes)? I thought I should point this out again because of your own comment about EFEs etc in your response to Markus Hanke above. Still reading you and everyone. See you round, q-w!

Thank you for the acknowledgement and for the efforts to help draw out a clear understanding of the nature of the universe from the perspective of consensus theories as well as by drawing attention to the desire all of us must have to determine physically what is happening.

 

[Farsight]

Yes. Just like digital clocks. And atomic clocks. And mechanical clocks. And lifetimes of particles. All clocks show the same "tick rates" at the same region of the gravitational field; gravitational time dilation is independent of the clock mechanism.

Wrong! The grandfather clock isn't like other clocks. Now go and check it out. If you have quartz wristwatch and a grandfather clock synchronised at sea level, then when you take them to a high altitude, the quartz wristwatch ticks faster in line with gravitational potential. However the grandfather clock ticks slower because the force of gravity is lower.

I have no problem admitting when I am wrong, and have done so on a number of occasions.

You have a BIG problem admitting when you're wrong.

Now, let physics speak - present us with some experimental evidence that gravitational time dilation is dependent on the type of clock used, and its mechanism. Mainstream science says there is no such dependency, you say otherwise, so the onus is on you to provide the appropriate evidence.

You are wrong again, mainstream science says the grandfather clock is affected in a different fashion to other clocks. Again, do your own research. You will find papers such as this: http://arxiv.org/ftp/physics/papers/0701/0701109.pdf

"Let us see how this definition works. The period of a pendulum clock is equal to T = 2Π √(l / g) , where l is the pendulum length, g is the free fall acceleration. Hence placed
in a valley, such a clock will run faster than on the top of a high mountain because the free fall acceleration gets greater when you are going down".

I don't accuse, I am merely stating facts.

Yes, I thought you were going to say something along these very lines. You have played the "censorship" card before, just as you have the "abuse" and "insult" cards. Not very successfully, I might add.

Just stick to the physics. No insults, no abuse, no throwing around words like "crackpot" and "doesn't belong in the physics section". Then we can all enjoy the discussion.

What you said is that "objects fall down" because of "the wave nature of matter". Since GR is a model of gravitational interactions, you are thus implying that GR deals with the "wave nature of matter" in some form or another. If that is not the case, then we are clearly off in the direction of a personal theory of yours. So which one is it?

Neither. It isn't GR and it isn't my personal theory. I first came across the general idea in an article by an aether-theory guy called Reg Norgan, and I've seen the same general idea described by people like Albrecht Giese. I don't concur with everything these guys say, but GR is beyond doubt as is the wave nature of matter, and gravity cannot be action-at-a-distance magic.

No, you are merely and intentionally misrepresenting them.

Einstein said what he said. You are clinging to an interpretation of GR that pretends he didn't.

No, I am thinking that space-time around Earth and on Earth and inside Earth is curved. Hence gravitational attraction. Hence frame dragging. Hence Thomas precession. Hence light deflection. Hence gravitational time dilation. And so on.

Then you're wrong. Because the Earth is not surrounded by static spacetime where motion is merely some illusion, it is surrounded by space through which things move.

What trick ? A simple Google search yields the appropriate translations :

http://en.wikisource.org/wiki/The_Field_Equations_of_Gravitation

Note the use of the term "space-time" throughout, and the complete absence of any mention of variable speeds of light, just as I have told you previously.

My references to Einstein trumps your reference to Wikipedia.

This isn't really the point at stake, now is it. What we are discussing is your assertion that GR does not deal with space-time curvature, but instead only with flat spaces and variable speeds of light.

I didn't assert that. I asserted that spacetime is not the same thing as space, which you agreed with, and that inhomogeneous space is the physical reality underlying curved spacetime.

Your assertion is that all gravitational interactions, of which GR is a model, can be explained via variable speeds of light in flat space. You are in essence saying that Einstein redefined the meanings of the tensors in his equations to take the "curvature" element out, i.e. he redefined the entire maths of differential geometry. Now try and back that up from Einstein's publications !

I didn't assert that. I said Einstein presented GR using a local viewpoint wherein you always measure the local speed of light to be the same even though you know that the coordinate speed of light varies in a gravitational field.

 

[Farsight]

I have a very simple scenario for you, which should be quite instructive, and should illuminate things a little.

I presume you mean me.

Imagine a particle travelling along some geodesic which crosses through a given event;

Take care with this, the particle travels through space, not through spacetime. We represent the motion through space with a worldline in spacetime, but the particle doesn't travel along it. There is no motion in spacetime, none whatsoever.

this shall be our reference. Now we imagine a second particle, and say that it initially travels parallel to the reference particle with some 4-velocity u through empty space.

Again, take care, a particle travels with a velocity through space, not with a four-velocity. The magnitude of its four-velocity is always c because "four-velocity is the rate of change of both time and space coordinates with respect to the proper time of the object". I hope you can see already that confusion is creeping in because you conflate space and spacetime.

We assume for simplicity's sake that the particles are uncharged, and don't interact except through gravitation; let's further assume they are massive particles.

OK. I rather thought you were going to refer to the wave nature of matter, but nevermind.

Now, so long as they are travelling through empty space their geodesics will remain parallel, no surprises here. If, however, we place a massive body somewhere in the vicinity of our particles ( let's imagine it to be point-like ), that parallelism will be disturbed, and the geodesics will deviate. In standard GR this is an almost trivially simple problem, since the geodesics follow the curvature of space-time; if the separation between the two particles' geodesics is denoted by the 4-vector v, the resulting deviation is

$$\displaystyle{\frac{D^2v}{d\lambda ^2}=-R(u,v,u)}$$

wherein R is the Riemann curvature tensor, and the capital D denotes the covariant derivative as opposed to the ordinary partial derivative. That's it. No assumptions about speeds of light, wave nature of matter etc etc needed. We are in fact not at all interested in any speeds, we only want to look at the separation between their trajectories, and separation ceases to be constant simply because space-time is no longer flat if we place a massive body in it. This is just a very simple model of gravitational attraction.

OK. But it lacks explanatory power because those particles are moving through space rather than spacetime. In spacetime they are represented by lines.

So now, how would that very simple scenario play out in your little world where space-time is flat, and only the speed of light varies?

Spare me the "little world" jibe Markus. I have said repeatedly that inhomogeneous space underlies curved spacetime. I never said space-time is flat. I explained the relationship in post #158 in another thread. You derive Weyl/Riemann curvature from the equatorial-plane light-clocks. They run at different rates, not because your plot is curved, but because space at one location is different to space at another. Because space is inhomogeneous. Again, remember the Baez article which stressed the distinction between curved space and curved spacetime.

What happens to the particles' trajectories, and why ? Remember also that we are not assuming photons here, these could be any type of particle, we place no constraints on it.

Exactly what you expect.

And don't even think about bringing out the "hiding behind the maths" argument - this is a simple, perfectly reasonable question about a perfectly simple scenario, to which we can expect an answer from you. This should be interesting

Yes, it is interesting. It demonstrates again that your confusion between space and spacetime is the source of your misunderstanding.

 

[Farsight]

Quite right according to everything I have read. Even though GR is portrayed as being unchanging and firmly established by Einstein, BBT is the current cosmological consensus, and it has evolved as I have pointed out throughout this thread.

Noted. IMHO when you read the original material by Einstein his "greatest blunder" involving a static universe is all the more surprising.

I stand corrected, but as you can tell, getting the particulars straight is like shooting at a moving target. Time delay can cause a miss, but of course there is no time delay in GR, right, lol.

It's the Shapiro delay, but people like Markus insist that it's because of "space-time curvature", when such is merely employed to model motion through space. Einstein gave the equations of motion, not the equations of curved space-time. When you contrive a Shapiro-like delay wherein light passes between two nearby stars, it goes dead straight. If you strung light-clocks along its path you could plot a curvature in their readings, but it's your plot that's curved, not space, and not the light path.

I agree that the light clocks show the inhomogeneity, and I agree that any path other than perpendicular to the center of gravity will be curved. So I agree, if you plot any such path then the plot is curved.

Pay special attention to that perpendicular direction when it comes to black holes. People say the light can't get out because spacetime is curved, but again you've got a dead-straight line and space isn't curved.

The "natural geometric cause" was meant to be a reference to the strict mainstream consensus that there is no mechanism, it is "geometry". I agree that the cause is a concentration of energy, whether tied up as the matter of a star, or in the gravitational energy that the so called "mechanism" governs. We share the view that it is not a curvature of an abstract mathematical space that is absolutely static. We agree that space is not spacetime, and I recognize that is an alternative view right now.

Good stuff. Amazingly, many people who are taught the mainstream view seem to be incapable of thinking for themselves about the discrepancies between it and what Einstein said along with quite patent scientific evidence and scenarios.

That is fine between us, but I was just pointing it out. GR is what it is, although the further away you get from the EFE's and into the greater standard cosmological model of BBT with Inflation, the more room there for disagreement.

No problem. If we all agreed about everything we'd have nothing to talk about.

As far as it goes, that is perfectly consistent with my evolving view. Now if it was just the two of us talking, the issue between us would not be the inhomogeneity which we agree on, it is the cause of the homogeneity. We both say it is gravity, but the cause of gravity has a mechanism that orchestrates it, while GR and spacetime do not require any mechanism unless you call the geometry of spacetime a mechanism, and they don't. Maybe they don't because they cannot point to any physical nature of it, just math.

There's maybe some confusion here? I said the cause of the inhomogeneity is the concentration of energy, and pointed out the shear stress and gave an elastic-space analogy. Your plot of light-clock measurements gives you a space-time "metric" which is curved, and motion through space is curved. But it isn't curved because your plot of light-clocks is curved.

You and I differ there. Einstein lived a long and controversial life during a period in history where science as advancing in leaps and bounds. He said a lot of things, but he left us the EFE's. Anything beyond the EFEs can certainly be an honest portrayal of what Einstein said or thought at any time, so disputing GR on the basis of "but he said this or that" is a no win situation, IMHO.

We'll have to agree to differ on that.

Undefined: your posts noted. You sir, are not naïve.

 

[Markus Hanke]

I hope you can see already that confusion is creeping in because you conflate space and spacetime.

I don't see any confusion at all. What is given are geodesics in space-time, with a 4-velocity defined at each event. It's really not hard.

OK. But it lacks explanatory power because those particles are moving through space rather than spacetime. In spacetime they are represented by lines.

That's exactly what the relation means; it gives the separation between the geodesics at each point. That separation changes along the geodesics, because the Riemann curvature tensor no longer vanishes since we are now in a curved space-time. In other words - the geodesics either diverge or converge, depending on the initial conditions.
This doesn't lack explanatory power - it gives an exact prediction on how the particles behave, and why.

have said repeatedly that inhomogeneous space underlies curved spacetime.

It doesn't. Curved space-time is what it is, and does not need any such nonsense as "inhomogeneous space". This was one of the points of the exercise, namely to demonstrate that space-time curvature alone is perfectly capable of explaining gravitational interactions; variable speeds of light and such are not needed. That is what GR is about. If you take the reference geodesic to be, for example, a planet, and the other geodesic to be something like an asteroid or similar, you see why the asteroid will be deflected towards the planet as it approaches. It is simply geodesic deviation.

So now you are acknowledging that GR is indeed about space-time curvature, or how are we to understand the above statement ?

You derive Weyl/Riemann curvature from the equatorial-plane light-clocks.

No you don't. Both of them are defined via geodesic deviation, in a coordinate independent way. This is basic differential geometry, and doesn't even have anything to do with physics or GR !

Yes, it is interesting. It demonstrates again that your confusion between space and spacetime is the source of your misunderstanding.

What is interesting here is that you failed to answer the question. How do you model the particles' behaviour with only "inhomogeneous space" ? Can we expect an answer from you on this or not ?

 

[Markus Hanke]

You have a BIG problem admitting when you're wrong.

No I don't. I will readily admit that I am wrong when doing so is warranted. Which it isn't in this case.

Just stick to the physics.

I first came across the general idea in an article by an aether-theory guy called Reg Norgan, and I've seen the same general idea described by people like Albrecht Giese.

Man, are you serious ?? You are telling me to stick to physics, but then try to proliferate the ideas of an aether theory guy ?

Then you're wrong. Because the Earth is not surrounded by static spacetime where motion is merely some illusion, it is surrounded by space through which things move.

Earth is space-time just like vacuum is. There is no distinction except in the way the curvature is influenced. And it is space-time.

My references to Einstein trumps your reference to Wikipedia.

You asked me for an English translation of Einstein's publication. I gave it to you. Now you are denying that it actually is Einstein's publication ? Talk again about intellectual dishonesty !
The link I gave is a word-by-word translation into English of Einstein's original publication, which I referenced earlier. How Farsight's references trump Einstein's very own publication remains yet to be explained.

I asserted that spacetime is not the same thing as space, which you agreed with, and that inhomogeneous space is the physical reality underlying curved spacetime.

If this is what you assert then we have clearly left the realm of General Relativity, and are far gone into the region of your personal theories. Thanks for finally admitting this.
General Relativity deals with space-time curvature which manifests itself as gravitation. Period. Above and beyond that you are free to dream up any personal theory you want, just don't try to sell those as Einstein's ideas, because they aren't.

I didn't assert that. I said Einstein presented GR using a local viewpoint wherein you always measure the local speed of light to be the same even though you know that the coordinate speed of light varies in a gravitational field.

Einstein did not present any "viewpoints", whether global or local. That is the whole point of using covariant tensors, because they are defined quite independently of any specific coordinate system and frame of reference.

 

[Farsight]

I don't see any confusion at all. What is given are geodesics in space-time, with a 4-velocity defined at each event.

You said "imagine a second particle, and say that it initially travels parallel to the reference particle with some 4-velocity u through empty space". A particle sitting motionless in space has a four-velocity of c or 1 in natural units. It isn't its velocity through space, which is zero. Its velocity through space is a three-velocity. And it has no velocity through space-time because the latter is static. The motionless particle has a vertical worldline, the uniformly-moving particle has an angled worldline. Use a "particle" in the form of a parallel-mirror light clock to understand four-velocity aand the Lorentz interval. Look at the zigzag light-path length.

It's really not hard.

No it isn't. There's no problem with geodesics and four-velocities provided you don't mix up space and space-time.

That's exactly what the relation means; it gives the separation between the geodesics at each point. That separation changes along the geodesics, because the Riemann curvature tensor no longer vanishes since we are now in a curved space-time. In other words - the geodesics either diverge or converge, depending on the initial conditions. This doesn't lack explanatory power - it gives an exact prediction on how the particles behave, and why.

It predicts, but it doesn't explain why at all. If you think it does, try explaining why an electron falls down.

It doesn't. Curved space-time is what it is, and does not need any such nonsense as "inhomogeneous space". This was one of the points of the exercise, namely to demonstrate that space-time curvature alone is perfectly capable of explaining gravitational interactions; variable speeds of light and such are not needed. That is what GR is about. If you take the reference geodesic to be, for example, a planet, and the other geodesic to be something like an asteroid or similar, you see why the asteroid will be deflected towards the planet as it approaches. It is simply geodesic deviation.

You made two mistakes concerning geodesics and four-velocity and treated spacetime and space as if they were the same thing, and you've made a further mistake in confusing a prediction with an explanation. The model provides the prediction, but the map is not the territory. Please read Undefined's latest post.

So now you are acknowledging that GR is indeed about space-time curvature, or how are we to understand the above statement?

I've never said it wasn't. What I've said repeatedly is that space-time is not space, and the space around a planet is inhomogeneous rather than curved.

No you don't. Both of them are defined via geodesic deviation, in a coordinate independent way. This is basic differential geometry, and doesn't even have anything to do with physics or GR!

Oh yes you do. Note that I said derived, not defined. Your equatorial-plane light clocks go slower when they're lower. They do not do that because of some geodesic derivation or because of differential geometry. They don't go slower when they're lower because your plot of light-clock measurements is curved.

What is interesting here is that you failed to answer the question. How do you model the particles' behaviour with only "inhomogeneous space" ? Can we expect an answer from you on this or not ?

I told you, Einstein modelled it the way he did, from the local point of view wherein the measured speed of light is always c even though the coordinate speed of light varies in a gravitational field. I can't give you an alternative model. Remember I'm not saying GR is wrong, I'm saying your understanding of it is wrong.

No comment on the grandfather clock Markus? I thought you said I have no problem admitting when I am wrong, and have done so on a number of occasions. This is another such occasion. Or could it be that you do have a problem admitting you're wrong when it means you have to admit that I'm right?

 

[Farsight]

No I don't. I will readily admit that I am wrong when doing so is warranted. Which it isn't in this case.

You were wrong about the grandfather clock, and your evasion will be noted.

Man, are you serious ?? You are telling me to stick to physics, but then try to proliferate the ideas of an aether theory guy?

What, you mean a guy like Einstein? Have you ever even read Einstein's 1920 Leyden Address? Its title is Ether and the Theory of Relativity. Now I suggest you look at arXiv. Aether is only a dirty word for popscience physicists.

Earth is space-time just like vacuum is. There is no distinction except in the way the curvature is influenced. And it is space-time.

No Markus, space is not spacetime. Things move through space. They don't move through spacetime. It's a static mathematical space. Motion is real, it is not some "illusion".

You asked me for an English translation of Einstein's publication. I gave it to you. Now you are denying that it actually is Einstein's publication ? Talk again about intellectual dishonesty! The link I gave is a word-by-word translation into English of Einstein's original publication, which I referenced earlier. How Farsight's references trump Einstein's very own publication remains yet to be explained.

Sorry, my mistake. I didn't follow the link, and thought it was just some random wikipedia article.

If this is what you assert then we have clearly left the realm of General Relativity, and are far gone into the region of your personal theories. Thanks for finally admitting this.

Sigh. It isn't my personal theory, it's Einstein's theory. It's a curvature of light can only occur when the speed of light varies with position. Not a curvature of light can only occur when light curves.

General Relativity deals with space-time curvature which manifests itself as gravitation. Period. Above and beyond that you are free to dream up any personal theory you want, just don't try to sell those as Einstein's ideas, because they aren't.

General relativity models gravity using space-time curvature. Space-time is not space, the space around the Earth is not curved, instead as Einstein said, it is inhomogeneous.

Einstein did not present any "viewpoints", whether global or local. That is the whole point of using covariant tensors, because they are defined quite independently of any specific coordinate system and frame of reference.

Yes he did, and we've been through all this before Markus. There's a c in the expression below. That's the constant locally measured speed of light, not the "big picture" coordinate speed of light varying in a gravitational field.

$$R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}$$

 

[Markus Hanke]

Ok, I think the last few posts were indeed instructive. So this is where we stand now :

1. Farsight was asked about an actual quantitive relation for the ( varying ) speed of light in the presence of massive bodies. He has failed to do so.
2. Farsight was presented with a simple scenario, and asked to explain how "inhomogeneous space" could model such an interaction. He has failed to do so.
3. It was pointed out that a varying speed of light would lead to frequency dependent refraction effects. Farsight has failed to address this point. Instead he asserts, it would seem, that Snell's law is invalid, and that refraction really should not occur at all in any medium. Again, no clear answers were forthcoming when pressed for details.
4. Farsight has now admitted that his personal theories are inspired by aether models
5. Farsight has thus far failed to reply to, or even acknowledge, most of the references given to him which show that his ideas are not part of GR

Where does this leave us ? Well, first of all it can be formally shown that gravitational light deflection due to a varying speed of light ( refraction ), and deflection due to space-time curvature are not equivalent. In fact, refraction gets it wrong by a factor of two :

http://mathpages.com/rr/s8-04/8-04.htm

I quote the relevant passage :

"This implies our calculation above for the deflection of the refractive model is too large by a factor of two. (...) It’s also worth noting that physical refraction is ordinarily dependent on the frequency of the light, whereas gravitational deflection is not, so even a formal match between the two relies on the physically implausible assumption of refractive index that is independent of frequency. Furthermore, even if we postulated a suitable non-isotropic index of refraction, and suppose it to be independent of frequency, this postulated field would be entirely ad hoc, derived solely from the requirement to match the null paths predicted by the Schwarzschild solution, which has its basis in the field equations of general relativity. Any such refractive theory is at best incomplete without some rationale or justification for why the index of refraction (and presumably the underlying properties of the medium) would have this particular form. It does not even remotely approximate the behavior of, for example, a simple gaseous atmosphere surrounding a gravitating body. (This is one reason it was possible to rule out a coronal atmosphere surrounding the sun as an explanation of the deflection of light grazing the sun.) Thus some completely different, and probably non-mechanistic, rationale would have to be provided. Lastly, it isn't self-evident that a refractive model can correctly account for the motions of time-like objects, whereas the curved-spacetime interpretation handles all these motions in a unified and self-consistent manner."

Secondly, I cannot but find the general carry-on by Farsight to be disingenuous at best. He presents his ideas as being self-evident physical facts, and, worse, attempts to imply that his ideas are in fact Einstein's ideas, which is very clearly not the case. His ideas are just that - his own ideas. They have little if anything to do with Einstein's GR, which is a model of curved space-time, and the resulting manifestation as gravity. That's it. His persistent failure to acknowledge that this is the case does not change the facts. Regardless of whether or not one likes the notion of space-time curvature, GR has nothing in it about "inhomogeneous space" and varying speeds of light, and trying to assert otherwise based merely on a single sentence uttered by Einstein in a verbal address to an assembly of lay people is quite simply wrong. Furthermore, the reader of this thread will have noticed that Farsight consistently fails to answer any questions concerning quantification of his notions - when asked about values of "variable speeds of light" he doesn't answer. When asked about a demonstration how "inhomogeneous space" effects particle trajectories, he doesn't answer. It is just a long string of repetitions of the same old and tired phrases.

Lastly, Farsight's admission that his ideas are based on aether theory are the final nail in the coffin. This is meant to be a discussion about physics, as Farsight himself demanded from me, not flights of fancy about a notion which has been abandoned a century ago, and for good reason. Farsight is of course entitled to pursue his own ideas, as are we all, but this certainly does not include an entitlement to sell our ideas as physical facts. Drawing animated GIFs and pretending they are an accurate description of the real world, while at the same time refusing to give quantitive answers to the hard question just doesn't cut it, not even on an Internet forum such as this.

So far as I am concerned I see no point in wasting any more time on this thread. Whether or not this is allowed to continue in the mainstream sections of this board isn't up to me ( "censorship", ha ); what is up to me though is how I spend my time. And I can think of better things to do then arguing with someone who is a) not prepared to do any maths or quantify his ideas, b) refuses to acknowledge even basic physics, such as Snell's law, and c) tries to intentionally mislead people by asserting his own ideas as Einstein's. Better things like further studying the maths and physics of the real GR. I have made my points in the cause of this thread; there isn't really anything else to add, and I would urge all casual readers to at least skim through the article I referenced above. It is quite good, and addresses most of Farsight's fringe ideas. It is not like he is the first none spouting such nonsense !

Yes he did, and we've been through all this before Markus. There's a c in the expression below. That's the constant locally measured speed of light, not the "big picture" coordinate speed of light varying in a gravitational field.

So then, where is the "variable speed of light" you so fiercely preach to be found in the EFEs, considering that this is a covariant coordinate-independent tensor equation ?
Nowhere to be found. Unsurprising, since it doesn't exist.

And with that, I wish you all the best. Going in circles must be fun !

 

[Markus Hanke]

Oh I forgot to add - I'll be back once real answers are given to the points raised throughout this discussion, or if anyone has any genuine questions regarding GR. Always happy to help out, but I will not go around in circles with crackpots and their personal aether theories.

 

[Farsight]

And still no admission that you were wrong about the grandfather clock. And no sincere responses to my winning points concerning Einstein and arXiv and aether, and four-velocity and motion through space v static spacetime, and the coordinate speed of light varying in a gravitational field.

Yes, cut and run Markus. Throw out some "crackpot" abuse to cover your retreat. Squeal for censorship too. Your smokescreen does not however conceal your insincerity. That lies bare.

All: beware of responses from pompous quacks who pretend to be experts, but in truth do not understand the subject, and who brook no challenge from somebody who does. When a response is unsatisfactory and a non-answer is presented as an answer, do not be afraid to press your point.

 

[Tach]

I first came across the general idea in an article by an aether-theory guy called Reg Norgan,

...a well known crackpot.

and I've seen the same general idea described by people like Albrecht Giese.

This is another well known crackpot pushing the theory of variable speed of light.

I don't concur with everything these guys say, but GR is beyond doubt as is the wave nature of matter, and gravity cannot be action-at-a-distance magic.

Then you should cease and desist from pushing your own crackpot theory of "variable light speed".