Gravity and The Curvature of Space Question

[mjc (Mark)]

Here's something I can't get my mind around.

Take a black hole. There is no path from any point within the event horizon to any point outside of the event horizon - no outward path. Space is curved back onto itself and any path for a photon that is within the event horizon leads to the singularity.

So - if I've got this correctly. Get a wire frame to represent the three spatial axes and place it within the event horizon. Now as we we migrate along any of the axes we find ourselves at the singularity.

But we have have an inward direction that allows for material to cross over the event horizon from the outside to the inside. This could possibly (or possibly not) be rephrased as there is a direction - independent from the three spatial dimensions - that allows a vector to be constructed that gravitationally binds an object outside of the event horizon and the singularity - and possibly any object that has crossed the event horizon but has not yet reached the singularity.

So in how many "directions" is gravity operating - the three internal (within the event horizon) spatial 3D plus radially outwards (what ever that means) in an external 3D frame of reference - is that effectively six - and how would that effect any test of the inverse square law?

Its a brain teaser for me.

I'm not trying to be provocative - its a genuine Winnie the Pooh type of experience - you know - "I'm a bear of little brain and big words bother me".

If I got a nudge or a clue I'd be happy.

Mark C.

[CraigS]

G'Day Mark !

Welcome back !!

I'm not a very good answerer of these kinds of questions (other folk are more qualified) but it seems to me that the force due to gravity around a black hole (or any other matter dense body) is directed inwards, towards the centre.

If the hole is rotating, then I would think that the net resultant direction, due to gravity would be along curved lines, as this kind of BH drags spacetime with it, (outside of the event horizon).

I don't see the need for extra dimensions in all of this.

Also, the Event Horizon is unnoticeable to a falling body. It is only noticed by an observer. I think a photon is theorised to move in curved world lines inside the Event Horizon … (but this can still be envisaged within the normal three dimensions).

Over to others.
Good to have you back.

Cheers

[Robh (Rob)]

Mark,

Does anyone really know what happens inside the event horizon?
I can't comment about the internal physics but this is my opinion of the picture outside it.
Consider objects with different mass traveling at the same velocity towards a common centre in a plane, each object initially at equal distance from this centre. Now move the plane near a black hole (non-rotating) so that a radial line from the centre of the black hole is normal to this circle at its centre. The path of the objects will lie on a surface which was the plane but is now symmetrically distorted towards the black hole relative to the normal. This is the picture of a sink hole given for the black hole or equivalently a representation of the curvature of space around the black hole. To a distant observer the path of each object is essentially similar and two dimensional and distances covered will diminish with time as the objects approach the event horizon. At the event horizon, the objects appear to stop.
The visual representation of a sink hole around a black hole is not entirely accurate and is for impression only. There are an infinite number of such planes that will form their own sink holes relative to the black hole. A picture of this cannot be drawn in three dimensions.
However, for a single object, the path is essentially two dimensional with a relativistic time component.

Regards, Rob.

[mswhin63 (Malcolm)]

Black holes are contraversial for a lot of people and a very difficult thing to actaually prove due to sperical bulb of light surrounding the location suspected on being the black hole.
Determining if an location in space is a Black Hole is determined by XRay ejection. Is it possible the Potons or something are all sucked in are converted the XRay emmisions and able to escape. Who know what kinds of physics occur at such great speed. I believe Neutrino espcape as these travel faster than light.

Black Holes are essentially rotating Star of emmence proportions both small mass and large gravity, but they don't spin in a 3D rotation so it should look like a double ended whirlpool. I would also FEEL the sucking energy on both axis would be the same as the repelling energy around the equator of the spinning mass in the centre. So what happens on the edge I am not sure at the moment still learning.

I am long way off learning about black holes and whether they are real or not or even how they operate. What is real is that a high mass object is spinning at a great velocity and it is capable of sucking in mass. Photons are I think are pure energy so how is mass able to spin as fast than pure energy I do not know and find this hard to get my head around.

Disclaimer: I am not qualified to make a comment so dont beat me up please. I also have feelings. I am considering seriously about going back to school. Maybe I am too old.

[CraigS]

Originally Posted by mswhin63

Disclaimer: I am not qualified to make a comment so dont beat me up please. I also have feelings. I am considering seriously about going back to school. Maybe I am too old.

Hey Malcolm … that's cool .. we all have 'em (feelings) .. I've been beaten up heaps around here, too


Come to think of it, I got beaten up at school, also !
I don't think you can escape at school, regardless of age !!

(Just kidding around).

Cheers

[CraigS]

Whilst its a bit sneaky of me, Steven once said (in another thread which got onto black holes and gravitons):

Originally Posted by sjastro

In GR photons travel along what are known as null geodesics or the shortest pathway that can be taken in a gravitational field.

For black holes, this null geodesic wraps itself around the black hole inside the horizon. The photon isn't held there due to gravity but is constrained by the extreme space time curvature.

Don't you hate it when someone digs up stuff from the past ?


I never did quite get to the bottom of this one, though (which is kind of why I dug this up).
I presume this is fairly speculative and I hope he doesn't mind.

Cheers

[xelasnave]

I find it difficult to understand how whatever boson one may select to convey the message of gravity can get off or move away from the extremely curved grid of space time.... How can our graviton move away from the constricted path dictated by the extreme space time curvature such that it can tell the space outside the event horizon that within there be a black hole...it would seem that whatever particle one selects to construct a gravity field it will be incapable of escape and bound to follow the extreme curvature suggested to exist at and past the vent horizon.
alex

[mjc (Mark)]

Originally Posted by Robh

Mark,

Does anyone really know what happens inside the event horizon?
I can't comment about the internal physics but this is my opinion of the picture outside it.
Consider objects with different mass traveling at the same velocity towards a common centre in a plane, each object initially at equal distance from this centre. Now move the plane near a black hole (non-rotating) so that a radial line from the centre of the black hole is normal to this circle at its centre. The path of the objects will lie on a surface which was the plane but is now symmetrically distorted towards the black hole relative to the normal. This is the picture of a sink hole given for the black hole or equivalently a representation of the curvature of space around the black hole. To a distant observer the path of each object is essentially similar and two dimensional and distances covered will diminish with time as the objects approach the event horizon. At the event horizon, the objects appear to stop.
The visual representation of a sink hole around a black hole is not entirely accurate and is for impression only. There are an infinite number of such planes that will form their own sink holes relative to the black hole. A picture of this cannot be drawn in three dimensions.
However, for a single object, the path is essentially two dimensional with a relativistic time component.

Regards, Rob.

Rob - very well expressed.

Alex actually captured my conundrum - though I wouldn't use the language expressed. However - I'd like to leverage of Alex's reply - as it was more succinct. Basic problem is how can space-time be curved in on itself and information still be exchanged between the singularity and a mass outside of the event horizon.

That implies that there is a path from within the event horizon to out side - as outside knows what mass lies within the event horizon.

My line of enquiry doesn't seek to challenge existing theory - merely to inch towards a better understanding of what current theory says. But I have a suspicion that General Theory of Relativity is such that one probably needs to have a mathematical appreciation as qualitative explanations are just going to be an oversimplification to the point of being useless.

I appreciate Alex's comment - as it is so succinct.

Rob, your comment regarding knowing what happens at the other side of the event horizon is also thought provoking. From what I read - nothing changes other than all paths lead to the singularity and hence no particle can move from the inside to the out side. If the black hole were sufficiently massive then the gravitational gradient may not be that great across a short distance that crosses the event horizon and an observer crossing the event horizon wouldn't really experience any change to his environment when he crossed it - physics is still predictable. But an observer outside would not see this - but can predict it. Again, from the perspective of an outside observer timings of events as they approached the event horizon would slow down. But what we see is increasingly red-shifted to the point where we can't see them any more. Now - at some point (post event horizon) closer to the singularity our laws of physics may break down for the observer that is falling in - and at the singularity - I would expect this as I'm sure there are many equations that have the radius - or distance from centre - as a denominator and when you get zero we have stuff that can't be computed. I'm of the understanding that it is the division by zero is what mathematicians call a singularity.

I can buy a lot of this but its the conundrum of how information is shared (re gravity) between inside and outside of the event horizon that I can't visualise.

Mark C.

[xelasnave]

Hi Mark your comment....

But I have a suspicion that General Theory of Relativity is such that one probably needs to have a mathematical appreciation as qualitative explanations are just going to be an oversimplification to the point of being useless.

is absolutely correct. Usless in the context that the math becomes the delight of discovery rather than grappling with the major problems our original premise has left us with...blach hole equales nothing can escape...even gravitons??? we can not happily rush past such an anomoly.

The point is GR is in effect an attempt to provide humans with some understanding of something perhaps that will forever remain beyond our comprehension.

Notwithstanding the complexity of the maths (try getting your head around the 11 field equations) GR is geometry where we use x y and z axis and then incorporate a negative "time" line..to descibe to measure to quantify ...space...whatever space is.. understanding the math and focusing upon its value without additional regard to the difficulties we are left with if we rely upon the extrapolations GR suggests.

I find it interesting that Dr Einstein found great difficulty in excepting the black hole idea and given he is the man who gave us general relativity I for one take such as reasonable support to question the likelyhood of their very existence.

However irrespective of how complex one may wish to call the math of GR if one follows it we come to difficulties when considering "extremes" ..in my view.

One such extreme is the difficulty of working out a path for messenger particles (the standard model of particle physics suggest and endorses such concept..bosons I think...certainly outside the event horizon we can easily speculate to a point where we can move stuff about but once inside we must content with the logic and conscequence of the null geodesics which tells us clearly... whatever be on this path will remain on that path forever or until the laws of GR collapse or are modified to overcome what would seem a mecahism which prevents all and any activity at any level ....

The complexity one wishes to place upon the math or perhaps more correctly the geometry we work in GR should not be enlisted to dump such relevant questions you raise.. In seeking an answer something perhaps will need adjustment be it the math or indeed the very premise of a balck hole.

AND I know when one questions the existence of black holes all will laugh at the apparent ignorance of the proposer to all the "black hole discoveries" now cataloged. THey are fact not speculation we are told ..and yet I say this..until the problem of how messages pass between a balck hole and the rest of the universe is satifactorily addressed we have a grave problem which can not be dismissed merely by reference to a lack of understanding of the math... the math is there to make ideas managable by a human mind not to exclude logical thought on perplexing matters one could suggest.

Prof Hawking spent much time considering the memory problem for matter within a black hole... or once matter has been crushed or smashed or experienced whatever condition we can speculate may occur within a balck hole the question is raised ..what if this matter gets free can it remember what it "was" and "go back" so we can enjoy managing all sorts of problems within our black hole .... however it would be wise to remember we possibly speculate upon conditions within a body that may be very different to what we mathmatically have determined in the absence of specific observation.

alex

[CraigS]

Originally Posted by mjc

If the black hole were sufficiently massive then the gravitational gradient may not be that great across a short distance that crosses the event horizon and an observer crossing the event horizon wouldn't really experience any change to his environment when he crossed it - physics is still predictable.
But an observer outside would not see this - but can predict it. Again, from the perspective of an outside observer timings of events as they approached the event horizon would slow down. But what we see is increasingly red-shifted to the point where we can't see them any more.

Mark;

From what I’ve read, the perspective of what the observer outside the Event Horizon sees, is directly related to which model one chooses to employ, to envisage what might happen. Quantum Field theory for instance, says that objects appear to break down into progressively smaller objects – ever smaller. But as the parts of it become as small as Planck length, a new pattern somewhat akin to Russian Dolls appears. Things inside things. They move, and the smaller they are, the faster they move. More and more structure appears.

String theory however shows that they occupy an increasing amount of space, so that the entire structure falling into the EH, grows. The strings vibrate in a special, predetermined way and eventually become so big, they spread over the entire horizon of the Black Hole.

The story continues to be different as we move into strings attached to D-Branes, for example, (which obey the same rules as Quantum Chromodynamics).

So, if there are differences between what each theory says about what an observer sees, the information conveyed to that observer, is clearly different. The means of that conveyance is related to the definitions of each theory's respective, fundamental constituents.

This problem is at the cutting edge of theoretical development and physicists all over the world have not yet resolved it. You are not alone in your conundrum. I suggest you take a more detailed look at what each theory says happens, as a next step. There are no easy answers to this, and most answers from this point onwards are directly related to the knowledge of the answerer. They are partly theoretical, and increasingly speculative, as one goes further into them.

Cheers & Rgds.

[Robh (Rob)]

Originally Posted by xelasnave

AND I know when one questions the existence of black holes all will laugh at the apparent ignorance of the proposer to all the "black hole discoveries" now cataloged. THey are fact not speculation we are told ..and yet I say this..until the problem of how messages pass between a balck hole and the rest of the universe is satifactorily addressed we have a grave problem which can not be dismissed merely by reference to a lack of understanding of the math... the math is there to make ideas managable by a human mind not to exclude logical thought on perplexing matters one could suggest.

alex

Alex,

You are assuming there has to be a messenger particle like a theorised graviton. But what if mass simply bends space so that objects follow geodesics on this space curvature in travelling from A to B? Consider a river whose path is guided by the contours of the landscape. The river is the flow (geodesic) and the landscape is the analogy to the mass which shapes the geodesic. A boat simply follows the course of the river. It does not need to communicate with the landscape itself. Even an electromagnetic field, which directs the path of an electron, can be considered a river with essentially no necessity for a messenger particle. General relativity basically treats gravity as a field theory and so far has worked pretty well.

Regards, Rob

[xelasnave]

Hi Robh
Yes indeed my view is formed no doubt from my desire to have a "mechanical" explanation and so particles speculated upon such as a graviton are of interest.... however it was not I that came up with the graviton or the boson and the fact that others greater than I have arrived at such hypothesis does not make my thoughts out of bounds.

The premise of general relativity is very much as you suggest things may be..it just is.... if asked for a simple explanation of general relativity one could answer that it is a concept that attributes space with certain properties "that just are" particularly that space is "bent" by mass.

The geometry lets us then look at gravity as little more than the shortest path between two objects with mass and this "shortest" distance is in effect the result of the bending of space.

However at the risk of over simplification what we deal with is a geometric construct with no reference to how space does what we attribute to its working.

I simply contend that there must be more at work than geometry. We use geometry to plan a house and such plan is invaluable during construction...but the plan is not the house..the house finally will be constructed with real things each capable of classification and measurement.

In the case of the flow of a river it is clear rivers flow to the sea... that is simlar to saying mass bends space and time but further consideration enables us to propose that it is the difference in height at either end of the river and what we observe is water flowing to the lowest point..again similar to the space time bend approach..but there is something happening at a particle level one could expect that enables particles in the river to chose which way they must travel...


In any event if we stick doggedly to the notion that space bends and that is the end of it we simply dabble with geometry and avoid adding any reason as to why the geometry dictates what we observe.. we can draw the house plans but then offer no candidates for the materials to be used in its construction....as I understand it physisits are happy to stop at the geometry point and that is fair but I think we will miss a grander story..and the grander story does not have to conflict with GR in fact one reasoning should and must compliment the other.

I think to offer nothing more than geometry misses the point and folk are so happily indulging the math they fail to recognise that probably things dont happen as if by magic but there is possibly a particle conection and interaction...

Also I ask..how can folk happily indulge speculation upon what happens in a black hole if nothing can escape...even presumably any possibilty of an observation that will support any of the speculations presented.

I think my consideration that a feild must be made up of some particle flow is far from unreasonable in terms of speculation when one considers the speculation other indulge when it comes to black holes.

Frankly I think its like arguing about what Hobbits have for their second breakfasts
Have to go will edit this later it was a rush..
alex

[CraigS]

Ahh Alex;

Good to see you back.

I have been thinking about you and our many discussions.

as I understand it physisits are happy to stop at the geometry point and that is fair but I think we will miss a grander story..and the grander story does not have to conflict with GR in fact one reasoning should and must compliment the other.

But someone has invented a graviton. Quantum Field theory and Quantum Chromodynamic theories have been created as has String and M-theories. Someone has spent billions of dollars building particle accelerators and observatories looking for gravity waves. Doesn't this show that someone is pursuing the grander story ?

I think my consideration that a feild must be made up of some particle flow is far from unreasonable in terms of speculation

Bu this is someone else's theory .. are you claiming it as your own ??….

however it was not I that came up with the graviton or the boson

???

Cheers & welcome back !

[xelasnave]

Good to see you back.

I have been thinking about you and our many discussions.

Thank you Craig.


But someone has invented a graviton. Quantum Field theory and Quantum Chromodynamic theories have been created as has String and M-theories. Someone has spent billions of dollars building particle accelerators and observatories looking for gravity waves. Doesn't this show that someone is pursuing the grander story ?

Yes it does... I feel better ..there was a time where I felt I was the only one who cared

Bu this is someone else's theory .. are you claiming it as your own ??….

Not for a moment. My point is simply this..the aspect of messenger particles is within the current cold dark matter theory of particle physics and given this it would seem relevant to fit that in ... where who knows but you have my view at least...It is my suggestion that fields rely upon a flow of particles and gravity fields may work this way.
Perhaps my extreme humility on all matters make it difficult to understand my points
Craig if there is one thing my many orbits around our star has show to me is this..the are very few original ideas... folk around here think I think outside the box but in truth most things I mention have been published before.

For years I developed the push universe only to find that as early as 1745 Le Sage had been working along similar lines... but this was wonderful because it released me from the duty of working it all out in detail.. to that point I saw my duty to humanity as showing folk how gravity may work..mmm also my TOE I felt could help... and now there seems to be many folk working along the lines that fit my approach...not from my influence but simply developing their ideas on the workings of everything. AND so I say that I claim nothing from this world by way of recognition or wealth because I have come up with anything useful.

Mind you I am working on a sailing vessel to take the world record and so far the design seems original.... but once I invented a boat paddle which I built and used only to find the same on an old Chinese wood print. In fact all of my inventions seem to have been done before.... no I claim nothing other than the right to be here and live out my final years in peace.



???
I merely used the little I read on same to try and fit it in someplace.
Cheers & welcome back !

Thank you Craig. I do read here a lot but given my travels can not post and compliment you upon the many interesting threads you start. I do feel that many folk get some love of physics through the interesting subjects you raise.

alex

[CraigS]

Thanks for your compliments, Alex, (although many might argue about my choice of topics).

[Robh (Rob)]

Originally Posted by xelasnave

Yes indeed my view is formed no doubt from my desire to have a "mechanical" explanation and so particles speculated upon such as a graviton are of interest.... however it was not I that came up with the graviton or the boson and the fact that others greater than I have arrived at such hypothesis does not make my thoughts out of bounds.

The premise of general relativity is very much as you suggest things may be..it just is.... if asked for a simple explanation of general relativity one could answer that it is a concept that attributes space with certain properties "that just are" particularly that space is "bent" by mass.

The geometry lets us then look at gravity as little more than the shortest path between two objects with mass and this "shortest" distance is in effect the result of the bending of space.

However at the risk of over simplification what we deal with is a geometric construct with no reference to how space does what we attribute to its working.

I

Alex,

I think your attributing too much importance to the existence of a particle in considering gravitational forces. The effects of these forces can quite happily be described without knowing the properties of any supposed carrier particle.

Consider the boat in the river. Studying the composition of a water molecule alone will tell you nothing about the river's speed and course. The speed and course of a river varies primarily according to external factors (e.g. incline and contour of the valley).
Consider another analogy. A tornado whisks a car up and throws it some 100 m away. Is the idea of a messenger particle relevant to this action? Not really. Sure, the air is composed of molecules but these molecules exist even when the tornado doesn't. The molecules constitute the air flow but the air flow is a result of extraneous factors (e.g. heat of the Sun on land and water). Studying the composition of an air molecule (and there are many different types of molecule) won't tell you why the car landed over their. Studying the holistic behaviour of a mass of air molecules and the forces it produces is relevant. This behaviour largely depends on differences in air temperature and pressure around regions and patterns are studied over time to make predictions.

If there is a graviton then how important will it be to a description of the forces due to gravity? Like a single air molecule, a description about the graviton itself will not lead to a description of the path of a moving body. The gravitons in a field, like air molecules, might exert a force (if that is what they do) but the movement of gravitons will be governed by the dynamics created by surrounding bodies of mass. It is essentially a study of gravitational field theory that describes the motion. Although the existence of a graviton would be highly interesting as a component of the particle physics of the Universe, it is still mass that governs motion. The bigger the mass, the bigger the influence.
Is the graviton a messenger particle? Not any more than than a molecule caught up in a flow of air.

So, incline and contours determine the river flow, temperature and pressure determine the air flow and mass determines the gravitational "flow". General Relativity describes this flow. The particles of the flow (if they exist) are a different matter and that's an unintended pun.

Regards, Rob

[CraigS]

Yeah Rob;

Nicely put.

Not that I’m into Alex’s quest, but I think we all know the search for the source of gravity, really is the search to understand the nature and the origins of the universe.

The inclusion of all the fundamental forces under the one descriptive framework is clearly, the Holy Grail of Science.

Alex’s quest to understand what causes gravity is an extremely interesting one, (despite my teasing him about it on occasions).

The types of Einstein, Bohr, et al knew this, which is why they spent time wrangling about Quantum Mechanics vs General Relativity. This continues today.

Somehow though, I don’t think this is going to be sorted out by pure thought experiments. I’d put my money on the LHC at CERN, although there is so much riding on the outcomes that this beastie may produce, it is difficult to imagine if anyone could admit that it may actually tell us nothing.

Nice “field” analogies though.

It is interesting that people seem to enjoy creating their own theories about them … there are so many of them, I’ve almost lost count ! Empirical data is the only way I can see to reduce the theory count, (as disappointing as that may be for the ‘speculative scientists’ amongst us).

Science is about asking questions eh ?
My feeling is that there may be no answers for a long while on this one.

Cheers & Rgds.

[Robh (Rob)]

Originally Posted by CraigS

The inclusion of all the fundamental forces under the one descriptive framework is clearly, the Holy Grail of Science.

Alex’s quest to understand what causes gravity is an extremely interesting one, (despite my teasing him about it on occasions).

Hi Craig,

Here is a "clarification" of what a magnetic field is (from wikipedia: Magnetism) ...
"The phenomenon of magnetism is "mediated" by the magnetic field. An electric current or magnetic dipole creates a magnetic field, and that field, in turn, imparts magnetic forces on other particles that are in the fields."
Now does anyone really know what a magnetic field is? We have a cause and we have a field model to explain the effects.

Curiously, I can re-word the statement as follows ...
"The phenomenon of gravity is "mediated" by the gravitational field. A body of mass creates a gravitational field, and that field, in turn, imparts gravitational forces on other bodies that are in the fields."
Like magnetism, we have a cause and we have a field model to explain the effects.

Regards, Rob

[sjastro]

Originally Posted by mjc

Here's something I can't get my mind around.

Take a black hole. There is no path from any point within the event horizon to any point outside of the event horizon - no outward path. Space is curved back onto itself and any path for a photon that is within the event horizon leads to the singularity.

So - if I've got this correctly. Get a wire frame to represent the three spatial axes and place it within the event horizon. Now as we we migrate along any of the axes we find ourselves at the singularity.

But we have have an inward direction that allows for material to cross over the event horizon from the outside to the inside. This could possibly (or possibly not) be rephrased as there is a direction - independent from the three spatial dimensions - that allows a vector to be constructed that gravitationally binds an object outside of the event horizon and the singularity - and possibly any object that has crossed the event horizon but has not yet reached the singularity.

So in how many "directions" is gravity operating - the three internal (within the event horizon) spatial 3D plus radially outwards (what ever that means) in an external 3D frame of reference - is that effectively six - and how would that effect any test of the inverse square law?

Its a brain teaser for me.

I'm not trying to be provocative - its a genuine Winnie the Pooh type of experience - you know - "I'm a bear of little brain and big words bother me".

If I got a nudge or a clue I'd be happy.

Mark C.

Mark,

In GR gravity is a fictitious force that acts only along the radial component. The forces acting on a particle moving along any of the 3D axes are not gravitational but are inertial forces such as tidal forces, centrifugal forces, corolis forces etc.

Regards

Steven

[sjastro]

The premise of general relativity is very much as you suggest things may be..it just is.... if asked for a simple explanation of general relativity one could answer that it is a concept that attributes space with certain properties "that just are" particularly that space is "bent" by mass.

Alex,

That's news to me.
Try thinking of space-time instead of space.

Here are some fundamental differences between space time and space.

(1) An object that is stationary in space moves in space time.
(2) An object that moves at a constant velocity in a straight line in space moves in a straight line in space time.
(3) An object that accelerates in a straight line in space moves in a curve in space time.
(4) An object in free fall in gravitational field moves in a straight line in space but in a curve in space time.
(5) The Earth's orbit is nearly circular in space has a helical orbit in space time.

The question as to why mass bends space-time is totally meaningless if
you notice that (3) and (4) are the same statements. This is the equivalence principle of GR at work.

Regards

Steven