- #36
Chronos
Science Advisor
Gold Member
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You can lead a horse to accolades . . . A physicist is a mathematician with a hobby horse.
In summary, the origin of gravity remains elusive and is still a topic of much debate and speculation among physicists. While some theories, such as the Big Bang, attempt to explain the origin of gravity, there is no definitive answer. Gravity is often described as the way matter affects geometry, but this concept raises further questions and puzzles about the nature of gravity and its relationship to the other fundamental forces. Despite our current understanding of gravity through theories like General Relativity, there is still much to be explored and understood about this mysterious force.
- #37
yogi
- 1,525
- 10
pervect said:
try this - consider the gravitational force exerted upon an object of mass M as a deformation of an accelerating spacetime surface in proportion to its inertial reactance M. In other words, there is no gravitational force per se, but only a reactionary force that deforms the acceleration of the spacetime surface - ergo, both the space are affected in proportion to the accelertion-mass product
- #38
Bjarne
- 344
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Chris Hillman
I was not sure if you had understood my point of view: Space seems to play a more important and central role that we usually think:
1.) because of the well know curvature of space
2.) because of space must be the only suspiciously that possible can be responsible for rising the tide.
3.) because of what else as space, - can pull down a stone, straight to the Earth's.
When we think about space, - we accept it curves and also that it can expend. We also off course accept that space somehow seems to be deeply involved in gravity phenomena’s.
But still in our imagination space is for the most of us “a big nothing”. I think that space related to gravity questions doesn’t get the central attention it deserves. Think for instance (a while) of the expression “Space curves”. - In our imagination we can easy imaging that things and physical structures can curve, - but that space “curves” do really sound absurd or at least a bit difficult to accept. – If space is nothing, how can nothing curve?
All what I am saying is just that the only (and poor) expression we have, related to this question seems to me to be too clumsy for our mind really to deal with. Mathematically result are surly very usable, but not always something that meets sympathy for how the ‘real’ world looks or works, - seen from the perspective of how our minds works.
Or we can see the expression “curvature", - in a different way: - It’s a quite mathematically / geometrically (cold) language, not minded for anything else’s like calculations. This would be the end of the road, that means that we on that basis even should not attemp to understand what gravity is.
I am not trying to deny that space really curves, but I think that based on simple observations it’s obviously that space do ‘a lot’ more like ‘curves’. – I mean space seems clearly to be deeply involved in the cause of gravity, its not only a question of curved space. – So the problem seems really to be pretty simple: - Our expression “curvature of space” – is not comprehensive enough to let our mind deal with the phenomena. Curvature of space, - is an expression that only reveals an aspect of the nature of space when it's involved with gravity. Its surly seems that it is this fact that abstain us from a complete coherent understanding of the phenomena.
I think we are force to think more about: what is the true nature of space really? – Is it possible better to understand this? We do not have so many objective options, since we know so little about the nature of space.
One option is: - since we know that space can expand, - it is obvious to ask: can space also have the opposite option: Can space contract, - and could the presence of matter be responsible for the force it requires?
Well, it is correct; - at this point my attempt to look deeper into the nature of space is a bit vague and begins to be philosophic. – But what would happen with dark energy, dark matter and quantum physics when curvature of space is the exactly the same as the opposite of expanded space, - that means: ‘Contracted space’ – Could the big secret code be that simple to crack?
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Bjarne
To be honest I did not know all the reference you was mention, I am not highly educated and can not relate to the same background materiel, - sorry.
I was not sure if you had understood my point of view: Space seems to play a more important and central role that we usually think:
1.) because of the well know curvature of space
2.) because of space must be the only suspiciously that possible can be responsible for rising the tide.
3.) because of what else as space, - can pull down a stone, straight to the Earth's.
When we think about space, - we accept it curves and also that it can expend. We also off course accept that space somehow seems to be deeply involved in gravity phenomena’s.
But still in our imagination space is for the most of us “a big nothing”. I think that space related to gravity questions doesn’t get the central attention it deserves. Think for instance (a while) of the expression “Space curves”. - In our imagination we can easy imaging that things and physical structures can curve, - but that space “curves” do really sound absurd or at least a bit difficult to accept. – If space is nothing, how can nothing curve?
All what I am saying is just that the only (and poor) expression we have, related to this question seems to me to be too clumsy for our mind really to deal with. Mathematically result are surly very usable, but not always something that meets sympathy for how the ‘real’ world looks or works, - seen from the perspective of how our minds works.
Or we can see the expression “curvature", - in a different way: - It’s a quite mathematically / geometrically (cold) language, not minded for anything else’s like calculations. This would be the end of the road, that means that we on that basis even should not attemp to understand what gravity is.
I am not trying to deny that space really curves, but I think that based on simple observations it’s obviously that space do ‘a lot’ more like ‘curves’. – I mean space seems clearly to be deeply involved in the cause of gravity, its not only a question of curved space. – So the problem seems really to be pretty simple: - Our expression “curvature of space” – is not comprehensive enough to let our mind deal with the phenomena. Curvature of space, - is an expression that only reveals an aspect of the nature of space when it's involved with gravity. Its surly seems that it is this fact that abstain us from a complete coherent understanding of the phenomena.
I think we are force to think more about: what is the true nature of space really? – Is it possible better to understand this? We do not have so many objective options, since we know so little about the nature of space.
One option is: - since we know that space can expand, - it is obvious to ask: can space also have the opposite option: Can space contract, - and could the presence of matter be responsible for the force it requires?
Well, it is correct; - at this point my attempt to look deeper into the nature of space is a bit vague and begins to be philosophic. – But what would happen with dark energy, dark matter and quantum physics when curvature of space is the exactly the same as the opposite of expanded space, - that means: ‘Contracted space’ – Could the big secret code be that simple to crack?
-----------
Bjarne
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- #39
Chronos
Science Advisor
Gold Member
- 11,440
- 750
Understanding the forces of nature is not necessary to model their effects. Our models may be unnecessarily complicated, but reasonably accurate approximations [see Ptolemy].
- #40
Bjarne
- 344
- 0
Chronos
I agree, - so far we have good tools to measure, but not to understand what we really really measures.
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Bjarne
I agree, - so far we have good tools to measure, but not to understand what we really really measures.
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Bjarne
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- #41
Chris Hillman
Science Advisor
- 2,355
- 10
I give up!
yogi, you proposed:
Unless I missed something, you didn't define the terms "deformation", "accelerating spacetime surface", "inertial reactance" (of a body? a surface?), and I see no indication that you took the point that the acceleration of a curve (e.g. the world line of an object) is a vector field defined along the curve, with units of reciprocal length, while the Gaussian curvature of a two-dimensional surface (and the sectional curvatures of higher dimensional submanifolds) is a scalar field defined in the surface, with units of reciprocal area. Without meaningful mathematical definitions of your terms, IMO your proposal is too vague to evaluate/discuss.
Bjarne, I am trying to make allowances for English as a second language and for lack of math/physics background, but when you say:
I think the basic problem here is that you have so seriously misunderstood the ideas you want to discuss that it is impossible to hold a meaningful discussion. Your recent posts are mostly incomphrehensible to me, but some things did stand out:
Sure you don't mean spacetime?
An analogy might be helpful: imagine that you walk into a "sports bar" and try to strike up a conversation about the upcoming World Cup, but you keep insisting that you feel that "the Cincinatti Reds" will win this event. I trust you can see why in this situation you would be risk being evicted from the bar if you persisted?
(In case the point is not clear, the Cincinatti Reds is indeed a sports team, but they will not be playing in the World Cup match and they are not even a football/soccer team!)
We can't keep repeating this indefinitely, but as I and others have already noted, part of your confusion may be caused by your insistence on thinking of "space" as something like a material which can "expand" or "contract", perhaps somewhat like a heated/cooled metal bar. In modern cosmology, in an idealized model such as the FRW dust solutions, the thing which "expands", as in "Hubble expansion", is really a "congruence" of certain timelike curves in a spacetime model (a certain four dimensional Lorentizian manifold), namely, the "world lines" of the "dust particles" (highly idealized galaxies).
This kind of query suggests that you have seriously misunderstood the notion of a manifold and the notion of the Gaussian curvature of a two-dimensional manifold (e.g. a "curved surface" in ordinary three-dimensional Euclidean space). If so, you can't possibly have understood the Riemannian notion of curvature in higher dimensional manifolds.
I can only say that comments like this suggest that you have not attempted to understand what mathematical physics is about.
I don't think it will be worthwhile for us to continue this conversation, so I'll bow out here.
yogi, you proposed:
yogi said:
Unless I missed something, you didn't define the terms "deformation", "accelerating spacetime surface", "inertial reactance" (of a body? a surface?), and I see no indication that you took the point that the acceleration of a curve (e.g. the world line of an object) is a vector field defined along the curve, with units of reciprocal length, while the Gaussian curvature of a two-dimensional surface (and the sectional curvatures of higher dimensional submanifolds) is a scalar field defined in the surface, with units of reciprocal area. Without meaningful mathematical definitions of your terms, IMO your proposal is too vague to evaluate/discuss.
Bjarne, I am trying to make allowances for English as a second language and for lack of math/physics background, but when you say:
Bjarne said:
I think the basic problem here is that you have so seriously misunderstood the ideas you want to discuss that it is impossible to hold a meaningful discussion. Your recent posts are mostly incomphrehensible to me, but some things did stand out:
Bjarne said:
Sure you don't mean spacetime?
An analogy might be helpful: imagine that you walk into a "sports bar" and try to strike up a conversation about the upcoming World Cup, but you keep insisting that you feel that "the Cincinatti Reds" will win this event. I trust you can see why in this situation you would be risk being evicted from the bar if you persisted?
(In case the point is not clear, the Cincinatti Reds is indeed a sports team, but they will not be playing in the World Cup match and they are not even a football/soccer team!)
Bjarne said:
We can't keep repeating this indefinitely, but as I and others have already noted, part of your confusion may be caused by your insistence on thinking of "space" as something like a material which can "expand" or "contract", perhaps somewhat like a heated/cooled metal bar. In modern cosmology, in an idealized model such as the FRW dust solutions, the thing which "expands", as in "Hubble expansion", is really a "congruence" of certain timelike curves in a spacetime model (a certain four dimensional Lorentizian manifold), namely, the "world lines" of the "dust particles" (highly idealized galaxies).
Bjarne said:
This kind of query suggests that you have seriously misunderstood the notion of a manifold and the notion of the Gaussian curvature of a two-dimensional manifold (e.g. a "curved surface" in ordinary three-dimensional Euclidean space). If so, you can't possibly have understood the Riemannian notion of curvature in higher dimensional manifolds.
Bjarne said:
I can only say that comments like this suggest that you have not attempted to understand what mathematical physics is about.
I don't think it will be worthwhile for us to continue this conversation, so I'll bow out here.
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- #42
Bjarne
- 344
- 0
To my opinion, it doesn’t matter how complex geometrically or mathematically calculation can be, or how many clever and well-meaning people that have contributed to such knowledge.
What in the end is important is too realize that we are dealing only with fragments of knowledge regarding the origin of gravity.
Concerning the curvature of space we can compare this to: - we know how all the 32 valves works in a 8 cylinders engine, and how these control the flow of air flow running through the engine. We are able precisely to describe this mathematically etc….
BUT - it’s important that we not on this bases limit our understanding, to how the rest of the engine works: - how or why the pistons goes up and down, how and why the crank turns, and what is the cause of the motion of all these parts.
Lets say that we agree to an expression for the phenomena what all the valves is doing, and make a statement; that the engine works because of “Air flow control” – Its not a lie but also not the full truth.
In the same way we have achieved some kind of knowledge / expression of how gravity works, but only a fragment of the gravity phenomena can be described caused by: “Space curves”
In the same way that “Air flow control” not is a expression how or why the engines crank is rotating “curvature of space” is not the correct description to describe how the tide are lifted the opposite direction of that direction we normally see gravity works, neither it can explain / express why a horizontal moving (same size) football and cannonball (moving with the same speed) do not follow the same orbit, that we should expect, - when gravity only was caused by space curvature.
Even though the curvature of space once was a huge discovery 100 years ago, let's not make that naive mistake to believe we now knows nearly everything about “how the gravity engine works” we have only discovered ripples at the surface of the gravity-ocean.
Our understanding how space is involved (or the "shape" of space) - expressed as: “curvature of space”, - is far from completely covering the gravity phenomena, and could very well be a very clumsy and poor expression that instead of leading us to better understanding and solving the total phenomena, it instead prevent us to (at least) reach some kind of a complete coherent acceptable gravity theory..
Even though mathematic is a fantastic tool, - it is still left to our human mind also to interpret the result of it, together with ALL other aspects and facts, - especially also the FORCE that clearly seems to be involved, - and finally reach some kind of coherent complete understanding / theory that can comprehend ALL the mysterious facts that really are involved in that strange phenomena.
Mathematically we have accepted space is nearly like was it a physical structure -, could this be a little too hasty expression ? - that now instead confuse us ?
I mean it is certainly not only what’s comes up that must come down; - caused by the 'shape' of space, - even if this is what we most of the times observes.
Sometimes it is the opposite that happens, - what is down must comes up (the tide).
We shouldn’t underestimate such important facts, - just because we not pay so much attention to that gravity also works in the precise opposite direction.
I am afraid that the expression “space curves” obviously have got an untouchable status, it doesn’t deserve, simply because when all the facts comes together, a such simple expression can not comprehend all that facts what space really also seems to be involved into, and that our poor expression therefore instead very well could contribute to unnecessary confusion, instead of making us wiser.
What if we in reality fail fully to understand the complete range and true nature of what’s really happens to space when it deals with gravity, - mainly because of our expression is too clumsy?.
What in the end is important is too realize that we are dealing only with fragments of knowledge regarding the origin of gravity.
Concerning the curvature of space we can compare this to: - we know how all the 32 valves works in a 8 cylinders engine, and how these control the flow of air flow running through the engine. We are able precisely to describe this mathematically etc….
BUT - it’s important that we not on this bases limit our understanding, to how the rest of the engine works: - how or why the pistons goes up and down, how and why the crank turns, and what is the cause of the motion of all these parts.
Lets say that we agree to an expression for the phenomena what all the valves is doing, and make a statement; that the engine works because of “Air flow control” – Its not a lie but also not the full truth.
In the same way we have achieved some kind of knowledge / expression of how gravity works, but only a fragment of the gravity phenomena can be described caused by: “Space curves”
In the same way that “Air flow control” not is a expression how or why the engines crank is rotating “curvature of space” is not the correct description to describe how the tide are lifted the opposite direction of that direction we normally see gravity works, neither it can explain / express why a horizontal moving (same size) football and cannonball (moving with the same speed) do not follow the same orbit, that we should expect, - when gravity only was caused by space curvature.
Even though the curvature of space once was a huge discovery 100 years ago, let's not make that naive mistake to believe we now knows nearly everything about “how the gravity engine works” we have only discovered ripples at the surface of the gravity-ocean.
Our understanding how space is involved (or the "shape" of space) - expressed as: “curvature of space”, - is far from completely covering the gravity phenomena, and could very well be a very clumsy and poor expression that instead of leading us to better understanding and solving the total phenomena, it instead prevent us to (at least) reach some kind of a complete coherent acceptable gravity theory..
Even though mathematic is a fantastic tool, - it is still left to our human mind also to interpret the result of it, together with ALL other aspects and facts, - especially also the FORCE that clearly seems to be involved, - and finally reach some kind of coherent complete understanding / theory that can comprehend ALL the mysterious facts that really are involved in that strange phenomena.
Mathematically we have accepted space is nearly like was it a physical structure -, could this be a little too hasty expression ? - that now instead confuse us ?
I mean it is certainly not only what’s comes up that must come down; - caused by the 'shape' of space, - even if this is what we most of the times observes.
Sometimes it is the opposite that happens, - what is down must comes up (the tide).
We shouldn’t underestimate such important facts, - just because we not pay so much attention to that gravity also works in the precise opposite direction.
I am afraid that the expression “space curves” obviously have got an untouchable status, it doesn’t deserve, simply because when all the facts comes together, a such simple expression can not comprehend all that facts what space really also seems to be involved into, and that our poor expression therefore instead very well could contribute to unnecessary confusion, instead of making us wiser.
What if we in reality fail fully to understand the complete range and true nature of what’s really happens to space when it deals with gravity, - mainly because of our expression is too clumsy?.
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- #43
yogi
- 1,525
- 10
Chris Hillman said:
I was merely suggesting an alternative to Einstein's static origin of curvature (that is, to suggest that curvature may be the result of some dynamic) where the deformation is created by the interaction of accelerating spacetime (a momentum rate of flow which is equivalent to stress). As we are told, Einstein was happy with Riemannian curvature as a description of spacetime - but at the time gtr was developed he had no knowledge of global expansion, and therefor no reason to suspect that curvature could be consequent to motion rather than static mass
Perhaps he had grave doubts when he referred to the left side of the equation as made of fine marble, and the right side as a house of straw. So my point is, if you consider expanding space as having an intrinsic acceleration, the deformation of such can be equated to stress.
Pervect had commented to the effect that if gravity is simply a force, there could be no time dilation. But if the force is consequent to a dynamic, you can arrive at the left side of the Einsteins equation by a different route.
Not everyone has the same view of space or spacetime.
While it may not be in vogue to think in terms of a spatial medium that can contract and shrink, most persons do not have the ability to deal with these interesting questions from an abstract mathematical perspective
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- #44
Bjarne
- 344
- 0
Yogi
As already mention I can ‘only’ contribute to this conversation with simple thinking, but I think this also very well could be relevant..
Let us try to assume that space not is such mysteries phenomena as we usually think:
We know space can expand. - Can it also contract the precisely opposite way?. - What would now happen to our universe when it all was that simple? – I mean if space NOT bend or curves, but just contracts, - what would be the consequence?
Already we have good reasons to believe that the present of matter must be responsible for ‘pull’ in space. It’s not important at this step to know how matter pulls space; it could be that the elementary particles consume space, etc. etc. etc.
Very – very simple observation shows us that matter must be attached to space; - the only ‘problem’ is that our mind intuitive seems to protest against a such connection, because it seems like space is nothing. - How can matter co-operate with nothing is the way we immediate thinks?.
But it really seems like matter it’s shaking hands with space. This is really not something we have to accept on the level of believes or philosophy, its pretty simple: it’s only space that can be suspected for co-operation with gravity. And this is always the case.
1.) There is nothing between the Earth's and the moon except space – that possible can arrange / pass on the pull on the moon.
2.) There is nothing (suspicious) between a canon ball 1 meter above the earth’s surface, - and the earth, - except space, - what (straight) can pull down the cannonball.
3.) There is nothing between the Earth and the moon except space that possible can be responsible for lifting the tide.
Seen with innocent eyes: matter must be able to pull space. Such ‘handshake’ works off course both ways, - whereby space must also be able to pull matter.
Simply by replacing “curvature” with “contracts” we are force to admit, that now we have at least 2 gravity-mysterious phenomena’s less here on earth. All what we need to find out is then only how can matter pull/contract space.
What about the time deformation? – Well, - it’s no problem, - this part will remain unchanged. Remember that matter is already about 99 % space – (maybe 100% who knows) – If the background for matter changes a bit, its only naturally that time does too.
So, - is variation of gravity simple: variation of ‘space-density’?
Well so far it’s possible that such way of thinking seems to be a bit vague.
But it has be mention that the expression “curvature” is already into a huge headwind.
So far I see it it’s no such huge headwind against the new expression suggested here.
Notice so far I have roughly not changed anything else as an incomprehensive expression.
It’s seems like the gravity mystery now is a lot easier to deal with.
I admit that so far we can’t know if only a simple new expression really should be a solution or a step forward.
I know it sounds a bit naive, but what worse is that a lot of serious people would feel them self stupid if this really was so.
At least it is remarkable - could a simple new expression also open the doors for full understanding of what space is about in a black hole? – and what dark matter and dark energy really are about. – I know if I would continue to these areas I would break the rules for how much is allowed to speculate in this part of the forum, - so I better stop here, and leave it up to other to check the range of the main tread if wished, - if ‘this simple key’ also possible should fit for several other secret doors we so far completely have failed to open.
------
Bjarne
_____________________________
If problems get too complicated we have overlooked something
Albert Einstein.
As already mention I can ‘only’ contribute to this conversation with simple thinking, but I think this also very well could be relevant..
Let us try to assume that space not is such mysteries phenomena as we usually think:
We know space can expand. - Can it also contract the precisely opposite way?. - What would now happen to our universe when it all was that simple? – I mean if space NOT bend or curves, but just contracts, - what would be the consequence?
Already we have good reasons to believe that the present of matter must be responsible for ‘pull’ in space. It’s not important at this step to know how matter pulls space; it could be that the elementary particles consume space, etc. etc. etc.
Very – very simple observation shows us that matter must be attached to space; - the only ‘problem’ is that our mind intuitive seems to protest against a such connection, because it seems like space is nothing. - How can matter co-operate with nothing is the way we immediate thinks?.
But it really seems like matter it’s shaking hands with space. This is really not something we have to accept on the level of believes or philosophy, its pretty simple: it’s only space that can be suspected for co-operation with gravity. And this is always the case.
1.) There is nothing between the Earth's and the moon except space – that possible can arrange / pass on the pull on the moon.
2.) There is nothing (suspicious) between a canon ball 1 meter above the earth’s surface, - and the earth, - except space, - what (straight) can pull down the cannonball.
3.) There is nothing between the Earth and the moon except space that possible can be responsible for lifting the tide.
Seen with innocent eyes: matter must be able to pull space. Such ‘handshake’ works off course both ways, - whereby space must also be able to pull matter.
Simply by replacing “curvature” with “contracts” we are force to admit, that now we have at least 2 gravity-mysterious phenomena’s less here on earth. All what we need to find out is then only how can matter pull/contract space.
What about the time deformation? – Well, - it’s no problem, - this part will remain unchanged. Remember that matter is already about 99 % space – (maybe 100% who knows) – If the background for matter changes a bit, its only naturally that time does too.
So, - is variation of gravity simple: variation of ‘space-density’?
Well so far it’s possible that such way of thinking seems to be a bit vague.
But it has be mention that the expression “curvature” is already into a huge headwind.
So far I see it it’s no such huge headwind against the new expression suggested here.
Notice so far I have roughly not changed anything else as an incomprehensive expression.
It’s seems like the gravity mystery now is a lot easier to deal with.
I admit that so far we can’t know if only a simple new expression really should be a solution or a step forward.
I know it sounds a bit naive, but what worse is that a lot of serious people would feel them self stupid if this really was so.
At least it is remarkable - could a simple new expression also open the doors for full understanding of what space is about in a black hole? – and what dark matter and dark energy really are about. – I know if I would continue to these areas I would break the rules for how much is allowed to speculate in this part of the forum, - so I better stop here, and leave it up to other to check the range of the main tread if wished, - if ‘this simple key’ also possible should fit for several other secret doors we so far completely have failed to open.
------
Bjarne
_____________________________
If problems get too complicated we have overlooked something
Albert Einstein.
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- #45
Chris Hillman
Science Advisor
- 2,355
- 10
Huh?
Hi, yogi,
I don't think this makes any sense. Are you perhaps munging a description you read somewhere?
The Einstein field equation? As usual, context is everything, and I think you've lifted this out of context and in fact have completely misunderstood the meaning. If you put it back in context, I think you'll find it has to do with the issue of what it means to solve the field equation; as I have often pointed out, Einstein's view was more stringent than that of some contemporary physicists, with Lobo representing the opposite extreme of laxity (to the point of absurdity, IMO).
Like Bjarne (whom I've put in my "ignore" list), you appear to have confused "space" with "spacetime", and yo may have misunderstood something you read concerning the kinematic decomposition of a timelike or null congruence (not "space"). If you disagree, can you give a citation to the mainstream literature?
A dynamic? There may an ESL (English as a second language) issue here which might be fostering misunderstanding on my part. Can you give a citation?
Unless stated otherwise, the default assumption is that we are discussing standard gtr. If so, there is no controversy about what we mean by "spacetime". As for "space", you haven't defined what you mean by that, but the obvious guess is that you have in mind some family of hyperperslices. If we think of these as arising as the hyperslices orthgonal to some irrotational timelike congruence, then the kinematic decomposition of this congruence is closely related to quantities defined in terms of the hyperslices (e.g. the expansion of the congruence is closely related to the extrinsic curvature of a hyperslice in the given family). These relations are standard topics in textbooks which discuss for example the ADM formulation, as you may know.
Again, I don't think this makes sense as stated.
As I've already stated, if you carefully define what you mean by "spatial medium", then assuming you are working with gtr I suspect that you can re-express these notions in terms of the kinematic decomposition of a timelike congruence, which has immediate geometric and operational significance.
Hi, yogi,
yogi said:
I don't think this makes any sense. Are you perhaps munging a description you read somewhere?
yogi said:
The Einstein field equation? As usual, context is everything, and I think you've lifted this out of context and in fact have completely misunderstood the meaning. If you put it back in context, I think you'll find it has to do with the issue of what it means to solve the field equation; as I have often pointed out, Einstein's view was more stringent than that of some contemporary physicists, with Lobo representing the opposite extreme of laxity (to the point of absurdity, IMO).
yogi said:
Like Bjarne (whom I've put in my "ignore" list), you appear to have confused "space" with "spacetime", and yo may have misunderstood something you read concerning the kinematic decomposition of a timelike or null congruence (not "space"). If you disagree, can you give a citation to the mainstream literature?
yogi said:
A dynamic? There may an ESL (English as a second language) issue here which might be fostering misunderstanding on my part. Can you give a citation?
yogi said:
Unless stated otherwise, the default assumption is that we are discussing standard gtr. If so, there is no controversy about what we mean by "spacetime". As for "space", you haven't defined what you mean by that, but the obvious guess is that you have in mind some family of hyperperslices. If we think of these as arising as the hyperslices orthgonal to some irrotational timelike congruence, then the kinematic decomposition of this congruence is closely related to quantities defined in terms of the hyperslices (e.g. the expansion of the congruence is closely related to the extrinsic curvature of a hyperslice in the given family). These relations are standard topics in textbooks which discuss for example the ADM formulation, as you may know.
yogi said:
Again, I don't think this makes sense as stated.
As I've already stated, if you carefully define what you mean by "spatial medium", then assuming you are working with gtr I suspect that you can re-express these notions in terms of the kinematic decomposition of a timelike congruence, which has immediate geometric and operational significance.
- #46
yogi
- 1,525
- 10
Chris - thank you for the response - I realize your effort in attempting to clarify erronous notions - but nonetheless have a view that is necessary for me to picture space as substantive (but I don't mean material).
I didn't intend to get into a adversarial discussion - I will simply respond to your post 45 by saying that it is my view that the author of gtr took great effort to express his opinion on space as having physical properties I consider Einstein's words regarding the conditioning of space by matter as definitive as to how we should interpret space in the gtr - Einstein viewed space as something. That may not be the view held by many on these boards - but it was Einstein's view.
Whenever I or anyone else on these forums, cite Einstein’s Leyden address in 1920 or his follow-up embellishments on the subject of how we should look upon the interaction of space and matter, the response is typically to the effect “Einstein didn’t really mean what the words convey”
As far as what I meant by a dynamic, one might find an example in de Sitters spherical universe where both space and time dilate equally. If the de sitter sphere is uniformly expanding (uniform radial dilation c) the spacetime surface(s) [3 space and one time] of the deSitter universe will have normal components of acceleration.
I didn't intend to get into a adversarial discussion - I will simply respond to your post 45 by saying that it is my view that the author of gtr took great effort to express his opinion on space as having physical properties I consider Einstein's words regarding the conditioning of space by matter as definitive as to how we should interpret space in the gtr - Einstein viewed space as something. That may not be the view held by many on these boards - but it was Einstein's view.
Whenever I or anyone else on these forums, cite Einstein’s Leyden address in 1920 or his follow-up embellishments on the subject of how we should look upon the interaction of space and matter, the response is typically to the effect “Einstein didn’t really mean what the words convey”
As far as what I meant by a dynamic, one might find an example in de Sitters spherical universe where both space and time dilate equally. If the de sitter sphere is uniformly expanding (uniform radial dilation c) the spacetime surface(s) [3 space and one time] of the deSitter universe will have normal components of acceleration.
- #47
yogi
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Bjarne said
"Very – very simple observation shows us that matter must be attached to space; - the only ‘problem’ is that our mind intuitive seems to protest against a such connection, because it seems like space is nothing. - How can matter co-operate with nothing is the way we immediate thinks?."
and Bjarne said
"But it really seems like matter it’s shaking hands with space. This is really not something we have to accept on the level of believes or philosophy, its pretty simple: it’s only space that can be suspected for co-operation with gravity. And this is always the case."
It is difficult to comprehend that something non material can interact with matter - but that was the notion Einstein put forth in distinguishing the ether of gtr from Lorentzian ether - in Einstein's view, the ether acted upon matter and conversely matter affected the state of the ether. Einstein called the ether "space" at least he give it the same attributes, but it does not necessarily mean that it behaves as a medium
The usual cop out is to say the properties of the ether (or space) are sui generis -
Interestingly, your comment about matter shaking hands with space. JD Ross wrote a book some years ago where he said "Inertia shows us the hand by which matter grips space and space grips matter."
My opinion is that the connective between space and Newtonian reaction must lie in the fact that somehow local space gets modified a la Mach's idea of distant matter. This conditioning may be the result of expansion so the local affect of the distant matter may exist w/o any time delay since expansion, like the premised big bang, occurs universally at the same timel Expansion, being the result of ongoing motion may be relateable to the properties of space if we knew what they were. I have always had a feeling that spatial stress is created by the G field - and that the energy contained therein is what is required to make the univese flat - Lots to ponder - but not many answers
"Very – very simple observation shows us that matter must be attached to space; - the only ‘problem’ is that our mind intuitive seems to protest against a such connection, because it seems like space is nothing. - How can matter co-operate with nothing is the way we immediate thinks?."
and Bjarne said
"But it really seems like matter it’s shaking hands with space. This is really not something we have to accept on the level of believes or philosophy, its pretty simple: it’s only space that can be suspected for co-operation with gravity. And this is always the case."
It is difficult to comprehend that something non material can interact with matter - but that was the notion Einstein put forth in distinguishing the ether of gtr from Lorentzian ether - in Einstein's view, the ether acted upon matter and conversely matter affected the state of the ether. Einstein called the ether "space" at least he give it the same attributes, but it does not necessarily mean that it behaves as a medium
The usual cop out is to say the properties of the ether (or space) are sui generis -
Interestingly, your comment about matter shaking hands with space. JD Ross wrote a book some years ago where he said "Inertia shows us the hand by which matter grips space and space grips matter."
My opinion is that the connective between space and Newtonian reaction must lie in the fact that somehow local space gets modified a la Mach's idea of distant matter. This conditioning may be the result of expansion so the local affect of the distant matter may exist w/o any time delay since expansion, like the premised big bang, occurs universally at the same timel Expansion, being the result of ongoing motion may be relateable to the properties of space if we knew what they were. I have always had a feeling that spatial stress is created by the G field - and that the energy contained therein is what is required to make the univese flat - Lots to ponder - but not many answers
- #48
Bjarne
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Chris
It’s all right to be sceptical, when someone tries to turn our understang of the world upside down.
But in reality it’s not only me that are doing so. Gravity it self have always done so.
The problem for Chris and a whole world of scientist is that they are dealing with fragmented knowledge, and also puts contradiction gravity phenomena on the “ignore list”, - (a stone fall in one direction,- the tide the other in the opposite).– I can not understand why physicist at least nor tries to understand such huge mysterious phenomena as a whole. There a huge number of broad hints. Unfortunately are all written on the ignore list
Will be back later
-------
Bjarne
_____________________________
If things get too complicated we have overlooked something
Albert Einstein.
It’s all right to be sceptical, when someone tries to turn our understang of the world upside down.
But in reality it’s not only me that are doing so. Gravity it self have always done so.
The problem for Chris and a whole world of scientist is that they are dealing with fragmented knowledge, and also puts contradiction gravity phenomena on the “ignore list”, - (a stone fall in one direction,- the tide the other in the opposite).– I can not understand why physicist at least nor tries to understand such huge mysterious phenomena as a whole. There a huge number of broad hints. Unfortunately are all written on the ignore list
Will be back later
-------
Bjarne
_____________________________
If things get too complicated we have overlooked something
Albert Einstein.
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- #49
Garth
Science Advisor
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What contradiction between the stone's fall and gravitational tides? Who ignores such phenomena? They are basic to understanding the theory of gravitation.Bjarne said:
No wonder people ignore you, you are talking rubbish.
Garth
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- #50
Bjarne
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Yogi
It’s good to read that I am not alone in the world with my point of view.
The biggest problem is to my opinion to relate to what space really is. Our immediate spontaneous impression is that space is nothing. – But how can nothing pass on force, - how can it have extension properties, - and how can it even also curve space?
I know that Einstein too was wondering about what space really was, as well as many before him.
I am not sure I fully got your point; - how you mean the connection between space and matter is.
To my opinion a theory must not have serveral unsolved aspect - All gravity related phenomena’s / mysteries MUST form a synthesis. I am pretty sure that the gravity problem is much larger, like we usually thinks, and that it also certainly includes dark energy and dark matter. – I will later post simple thought concerning this at this forum where it belongs to, and let you know. – In the meantime, try to seriously think of the consequence: what when the presence of matter ‘contracts space’ - witch huge effect would that get?
Garth
A stone fall in one direction, - the tide in the exact opposite.
These phenomena’s is off course not a contradiction, - only our attemp to solve the cause of these often seems to be.
We have no general accepted gravity theory able to comprehend the cause of both these phenomena’s.
It makes no sense to claim that “curvature of space” is the big answer for the cause of gravity, as a whole.
Any such attempt is naturally automatically a contradiction, at least so far. - It can be compared with the the discovery how an engines valves works, but doesn’t give us the right to claim that we now knows how the whole engine basically works.
Many do believe that the cause of gravity is nearly solved by Einstein’s work. - This is certainly rubbish.
We have only reached the foot of the mountain, and have (to my opinion) so fare also achieved to confused us self with a too clumsy (pure mathematically) expression claiming that “space curves”. – I do not deny that this expression mathematically is usable – but it is obviously far from a complete expression for the cause of gravity.
The contradiction could very well be reaching even higher as the highest mountains.
Dark matter and dark energy could very well be part of the problem (I am sure it is).
Regardless my opinion the gravity problem could very well be a lot bigger like only the above mention examples consening the phenomena; cannonball or especially the tide.
We have good reason to believe that dark energy exists, but also good reason to believe it dosen't. What we see is again a strange contradiction, - who can insure us that this not also is part of the same gravity mystery?.
I am sure that it would be very helpful for scientist to be a bit more open minded, and not be too inflexible to what the cause of gravity really is, or how the nature of space really is. Its is certainly not only a question of advanced geometry. - (Sorry for the not perfect english)
--------
Bjarne
It’s good to read that I am not alone in the world with my point of view.
The biggest problem is to my opinion to relate to what space really is. Our immediate spontaneous impression is that space is nothing. – But how can nothing pass on force, - how can it have extension properties, - and how can it even also curve space?
I know that Einstein too was wondering about what space really was, as well as many before him.
I am not sure I fully got your point; - how you mean the connection between space and matter is.
To my opinion a theory must not have serveral unsolved aspect - All gravity related phenomena’s / mysteries MUST form a synthesis. I am pretty sure that the gravity problem is much larger, like we usually thinks, and that it also certainly includes dark energy and dark matter. – I will later post simple thought concerning this at this forum where it belongs to, and let you know. – In the meantime, try to seriously think of the consequence: what when the presence of matter ‘contracts space’ - witch huge effect would that get?
Garth
A stone fall in one direction, - the tide in the exact opposite.
These phenomena’s is off course not a contradiction, - only our attemp to solve the cause of these often seems to be.
We have no general accepted gravity theory able to comprehend the cause of both these phenomena’s.
It makes no sense to claim that “curvature of space” is the big answer for the cause of gravity, as a whole.
Any such attempt is naturally automatically a contradiction, at least so far. - It can be compared with the the discovery how an engines valves works, but doesn’t give us the right to claim that we now knows how the whole engine basically works.
Many do believe that the cause of gravity is nearly solved by Einstein’s work. - This is certainly rubbish.
We have only reached the foot of the mountain, and have (to my opinion) so fare also achieved to confused us self with a too clumsy (pure mathematically) expression claiming that “space curves”. – I do not deny that this expression mathematically is usable – but it is obviously far from a complete expression for the cause of gravity.
The contradiction could very well be reaching even higher as the highest mountains.
Dark matter and dark energy could very well be part of the problem (I am sure it is).
Regardless my opinion the gravity problem could very well be a lot bigger like only the above mention examples consening the phenomena; cannonball or especially the tide.
We have good reason to believe that dark energy exists, but also good reason to believe it dosen't. What we see is again a strange contradiction, - who can insure us that this not also is part of the same gravity mystery?.
I am sure that it would be very helpful for scientist to be a bit more open minded, and not be too inflexible to what the cause of gravity really is, or how the nature of space really is. Its is certainly not only a question of advanced geometry. - (Sorry for the not perfect english)
--------
Bjarne
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- #51
Garth
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If a person is going to criticize a theory, rather than just ask questions about it for enlightenment, then they need to first fully understand that theory; otherwise they demonstrate only their own ignorance.Bjarne said:
The fact that you say "We have no general accepted gravity theory able to comprehend the cause of both these phenomena’s" only illustrates your ignorance.
If you had asked, "What is their explanation", others such as myself would have only been too glad to inform you. Which I will so do now.
The curvature of space-time accurately explains the behaviour of falling bodies. GR explains and predicts the trajectories of freely falling bodies more accurately than the Newtonian gravitational theory, nevertheless Newtonian theory is still used in orbital dynamics in regimes where its accuracy is sufficient because it is simpler.
In a curved space-time bodies such as a free falling stone and the Earth converge because their geodesic paths converge - that is their 'straight-line trajectories upon the curved space-time surface' converge. (Draw a straight line on a flat sheet of paper and then bend/deform the paper).
Now consider the Earth freely falling in the Moon's or the Sun's gravitational field.
Treat the Earth as a sphere of dust. Its centre of gravity is falling directly towards the centre of gravity (CoG) of the Moon (Sun).
All dust particles converge on the Moon/Sun, however those on the side nearer the Moon (Sun) 'fall' at a greater acceleration (- GM/r2) than those on the far side.
The dust particles on the two opposite sides of the Earth also converge onto the CoG of the Moon (Sun), so the two sides close in together.
The spherical dust Earth becomes ellipsoidal, and it is this tidal action that is the local signature or observable evidence that the Earth is freely falling in an external gravitational field.
Relative to the CoG of the Earth the tide on the side closest to the Moon (Sun) appears to be attracted away from the Earth, on the opposite side of the Earth, the Earth appears to be attracted away from the tide, in your own words: "a stone fall in one direction,- the tide the other in the opposite".
At the sides of the Earth there is low tide.
I hope this has made it clear.
Garth
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- #52
Bjarne
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Garth
OK the moons circulation causes the acceleration of the Earth to change a bit and this is the cause of the tide. Well probable nothing wrong with that. I am focused of the variation of force that space passes on between the bodies, and the cause of that. It’s off course the same force that pulls down a stone. We can explain both phenomena’s based on the acceleration of gravity (the expression of a such force) but this is of course only a superficial solution, - and well you are right nothing wrong with that.
Thank you for sharing your knowledge.
-------
Bjarne
OK the moons circulation causes the acceleration of the Earth to change a bit and this is the cause of the tide. Well probable nothing wrong with that. I am focused of the variation of force that space passes on between the bodies, and the cause of that. It’s off course the same force that pulls down a stone. We can explain both phenomena’s based on the acceleration of gravity (the expression of a such force) but this is of course only a superficial solution, - and well you are right nothing wrong with that.
Thank you for sharing your knowledge.
-------
Bjarne
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- #53
Chris Hillman
Science Advisor
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Nature of "space"?
Hi, yogi, I must demur on at least one point:
This sounds like the same fallacy I seem to have been debunking with unusual frequency in recent days here at PF. If so: "length" does not "shorten" and "time" does not "slow down".
Regardless, given that the term "dilation" is seriously misleading but well entrenched, I suggest that everyone here should always take the time to write out more carefully what one really means. Never forget that so-called "time dilation" effects always involves a comparison between two clocks in different states of motion. Thus, it never makes sense to say "time dilates" without the context of what clocks are being compared and how. Similar but even more nuanced remarks hold for "space dilates".
I don't even want to try to guess what you might mean--- particularly if your "c" has something to do with light!
However, I have been mulling the prospect of trying to write some brief expositions of frame fields and "beacon" null geodesic congruences in some simple and often encountered cosmological models including
Hi, yogi, I must demur on at least one point:
yogi said:
- Einstein's views changed so radically and so often that IMO statements of the form "X was Einstein's view" have little meaning.
- Einstein died in 1955, well before the "Golden Age of Relativity" (c. 1960-1975). You might be able to argue that some statement on topic T by Einstein represents his definitive statement of his own most mature view on topic T, but IMO it would be ludicrous to insinuate that physics/mathematics stopped when Einstein died.
yogi said:
This sounds like the same fallacy I seem to have been debunking with unusual frequency in recent days here at PF. If so: "length" does not "shorten" and "time" does not "slow down".
Regardless, given that the term "dilation" is seriously misleading but well entrenched, I suggest that everyone here should always take the time to write out more carefully what one really means. Never forget that so-called "time dilation" effects always involves a comparison between two clocks in different states of motion. Thus, it never makes sense to say "time dilates" without the context of what clocks are being compared and how. Similar but even more nuanced remarks hold for "space dilates".
yogi said:
I don't even want to try to guess what you might mean--- particularly if your "c" has something to do with light!
However, I have been mulling the prospect of trying to write some brief expositions of frame fields and "beacon" null geodesic congruences in some simple and often encountered cosmological models including
- Milne frame in Minkowski vacuum (as a foil for genuine cosmological models),
- expanding inertial frame in deSitter lambdavacuum,
- frame of dust in FRW dust models, plus FRW lambdadust models, plus frame of inertial particles not comoving with dust, plus contracting FRW matched to Schwarzschild as per Oppenheimer-Snyder collapsing dust ball model,
- frame of dust for LTB dusts (spherically collapsing dust clouds),
- ditto, for McVittie dust ("interpolates" between Schwarzschild and FRW),
- for Szekeres dusts (a simple solution with no Killing vector fields at all),
- for planar symmetric Kasner dust (a homogeneous but nonisotropic example),
- for Kantowski-Sach dust (plus matching to Frolov observers in Schwarzschild vacuum future interior)
- for Mixmaster dust (or perhaps its NIL analog, which is simpler)
- for Van Stockum dust (a swirling dust cloud),
- for Godel lambdadust (another swirling dust cloud)
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- #54
yogi
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Chris Hillman said:
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- #55
Garth
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No, "the moons circulation causes the acceleration of the Earth to change a bit and this is the cause of the tide" this is totally wrong, did you not understand the careful illustration I gave you?Bjarne said:
Even if the Moon were not in orbit around the Earth, but the Moon and the Earth were falling directly towards each other, about to collide, the Moon would still raise tides on the Earth.
It is the difference in the Moon's attraction (using the Newtonian paradigm) on different parts of the Earth both in magnitude and direction that causes the tides.
Put a solid sphere inside that sphere of dust. The dust sphere (the sea) deforms and the solid sphere (the rock) does not. Relative to the solid Earth high tides are raised on the side nearest the Moon (the ocean appears to be 'pulled away' from the Earth) and furthest from the Moon (the Earth appears to be 'pulled away' from the ocean) and low tides at the 'sides' of the Earth. (In fact the 'solid' Earth also deforms slightly, but not as much as the fluid ocean).
Draw the dust sphere and the directions and magnitudes of the acceleration vectors of different dust particles towards a nearby Moon and convince yourself the whole sphere deforms into an ellipsoidal shape.
The fact that the Earth and Moon have transverse orbital velocities does not affect the picture, they have an acceleration in the direction connecting their centres of mass and an orbital velocity normal to it, the result being a nearly circular ellipsoidal orbit around each other.
Garth
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yogi
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Chris Hillman said:
I didn't intend to convey that - in the spherical space-time universe of de Sitter, the two sphere surface grid is composed of time and space. As the spherical universe expands, both the time dimension and the space dimension increase in relation to their previous lengths ...its the inflating balloon model except that the surface is composed of one time dimension and one space dimension rather than two space dimensions - so the reference for change is the previous surface itself,
- #57
yogi
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Chris Hillman said:
If you like - with intense effort I will probably to be able to understand about every third word
Regards
Yogi
- #58
Bjarne
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Garth
What confused me was that you was wrote:
” Treat the Earth as a sphere of dust. Its centre of gravity is falling directly towards the centre of gravity (CoG) of the Moon (Sun)”
Well I did already understood it’s mainly the water on Earth's that is effected of the gravity attraction form the sun/moon.
But for some time ago I was wondering if the Earths also follow a weak swaying course, like a drunk man on the road.
Therefore when you also mentioned “acceleration” I was completely confused. - Anyway, illustrations is often good fx > www.clupeid.demon.co.uk/tides/simple.html
If we analyse what happens to the tide: a weak effect of attraction from another body ( sun / moon) pulls the tide which have a bit reducing effect of the Earth's ability to keep it’s grip of its water on the earth. (mostly on that side pointing to the other body off course)
I don’t know if difference gravity phenomena all can be explained from a perspective: that space curves.
If curvature of space can explain both that the moon is kept in its orbit, and that my pencil fall to the floor as well as the tide, - it’s at least anyway a expression not suitable for us too understand / imaging, - but only for a mathematically / calculating part of the brain.
I mean curvature of space does not make much sense to me, when someone claims that space also bends here at my table, and that is the cause to things here falls down to the floor when loosing it? - Is this not a reality / expression beyond the imagination ability ?
I mean is such mathematically / geometrically ‘tools’ not too theoretically for us, unless only for calculation purpose?
Can you agree to that ?
Or can you on this basis also explain why a horisontal moving football reach further like a canonball, when both moves with 100 MPH ?
---------
Bjarne
What confused me was that you was wrote:
” Treat the Earth as a sphere of dust. Its centre of gravity is falling directly towards the centre of gravity (CoG) of the Moon (Sun)”
Well I did already understood it’s mainly the water on Earth's that is effected of the gravity attraction form the sun/moon.
But for some time ago I was wondering if the Earths also follow a weak swaying course, like a drunk man on the road.
Therefore when you also mentioned “acceleration” I was completely confused. - Anyway, illustrations is often good fx > www.clupeid.demon.co.uk/tides/simple.html
If we analyse what happens to the tide: a weak effect of attraction from another body ( sun / moon) pulls the tide which have a bit reducing effect of the Earth's ability to keep it’s grip of its water on the earth. (mostly on that side pointing to the other body off course)
I don’t know if difference gravity phenomena all can be explained from a perspective: that space curves.
If curvature of space can explain both that the moon is kept in its orbit, and that my pencil fall to the floor as well as the tide, - it’s at least anyway a expression not suitable for us too understand / imaging, - but only for a mathematically / calculating part of the brain.
I mean curvature of space does not make much sense to me, when someone claims that space also bends here at my table, and that is the cause to things here falls down to the floor when loosing it? - Is this not a reality / expression beyond the imagination ability ?
I mean is such mathematically / geometrically ‘tools’ not too theoretically for us, unless only for calculation purpose?
Can you agree to that ?
Or can you on this basis also explain why a horisontal moving football reach further like a canonball, when both moves with 100 MPH ?
---------
Bjarne
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- #59
Garth
Science Advisor
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No I cannot agree to that, it is the curvature of space-time that explains, as perfectly as we can experimentally test for, the trajectories of freely falling bodies in a gravitational field.
Consider a ball falling to the floor, or one thrown through a vacuum (ignoring air resistance), both the balls and the centre of the Earth, and indeed a satellite in orbit around the Earth, are 'travelling' through space-time, (actually it is their four-velocity vectors in space-time that are:) on geodesic trajectories.
Geodesics may be thought of as 'straight-lines' through space-time.
The fact that space-time is 'curved' means the 'straight' lines drawn upon that Riemannian manifold ('surface') are curved in some higher dimension so the balls' trajectories converge with the Earth's, whereas the satellite describes a spiral around it.
(As I suggested above, illustrate this by drawing a straight line on a flat sheet of paper and then bend or deform the paper; the line bends with it, but it is still the shortest distance between two points measured along the surface of the paper.)
I use the language of a higher dimension because this is necessary for you to be able to extrinsically visualise the picture. In fact Riemannian geometry does not need this higher dimension, the effects of the curvature can all be described mathematically using tensor calculus intrinsically within the surface itself.
You need to read a basic tutorial on SR and GR if as you say, "it does not make much sense" to you. Try Ned Wright's Relativity Tutorial.
Garth
Consider a ball falling to the floor, or one thrown through a vacuum (ignoring air resistance), both the balls and the centre of the Earth, and indeed a satellite in orbit around the Earth, are 'travelling' through space-time, (actually it is their four-velocity vectors in space-time that are:) on geodesic trajectories.
Geodesics may be thought of as 'straight-lines' through space-time.
The fact that space-time is 'curved' means the 'straight' lines drawn upon that Riemannian manifold ('surface') are curved in some higher dimension so the balls' trajectories converge with the Earth's, whereas the satellite describes a spiral around it.
(As I suggested above, illustrate this by drawing a straight line on a flat sheet of paper and then bend or deform the paper; the line bends with it, but it is still the shortest distance between two points measured along the surface of the paper.)
I use the language of a higher dimension because this is necessary for you to be able to extrinsically visualise the picture. In fact Riemannian geometry does not need this higher dimension, the effects of the curvature can all be described mathematically using tensor calculus intrinsically within the surface itself.
You need to read a basic tutorial on SR and GR if as you say, "it does not make much sense" to you. Try Ned Wright's Relativity Tutorial.
Garth
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- #60
Bjarne
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Garth
Right, - Space-time is a better expression, even though it belongs to a higher dimension.
I mean space can certainly deform whereby time also changes.
But when we want to understand why a horizontal moving cannonballs lose its potential energy (100 MPH) before a football, - we still depend on a Newtonian way of calculation / theory, - right?
--------
Bjarne
Right, - Space-time is a better expression, even though it belongs to a higher dimension.
I mean space can certainly deform whereby time also changes.
But when we want to understand why a horizontal moving cannonballs lose its potential energy (100 MPH) before a football, - we still depend on a Newtonian way of calculation / theory, - right?
--------
Bjarne
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- #61
Garth
Science Advisor
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We certainly can and do use Newtonian theory in regimes where it is accurate enough, such as when NASA sling shot a spacecraft around the solar system with incredible accuracy.Bjarne said:
Newtonian theory is used, if it is accurate enough, because the calculations are much simpler. You just have to be consistent with the paradigm you use.
I don't understand your question of "a horizontal moving cannonballs lose its potential energy (100 MPH) before a football".
In a vacuum the cannonball, a football, and a feather all fall at the same acceleration, this is http://science.nasa.gov/headlines/y2004/06may_lunarranging.htm re-enacted on the Moon by the Apollo 15 astronauts.
Garth
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- #62
Chris Hillman
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Demurral and Request for Clarification
You should say "I think I detect", since others familiar with his writings can and do disagree about what he appears to have meant by various statements.
Huh? As you know there are many coordinate charts we can use on various pieces of the de Sitter lambdavacuum, aka [itex]H^{1,3}[/itex] (a Lorentzian spacetime with uniform negative curvature), including comoving charts adapted to static (non-inertial) observers and to various families of inertial observers. In particular,
[tex]
ds^2 = \frac{-dt^2 + dx^2+dy^2+dz^2}{(t/a)^2}, \;
0 < t < \infty, -\infty < x, \, y, \, z < \infty
[/tex]
is conformal to the upper half space portion of Minkowski spacetime and is comoving with a "collapsing" family of inertial observers whose world lines form a vorticity-free timelike geodesic congruence, whose orthogonal hyperslices are all isometric to euclidean three-space. Here, intervals of t do not correspond to intervals of proper time as measured by ideal clocks carried by our observers, but we can change to a comoving chart
[tex]
ds^2 = -d\tau^2 + \exp(-2 \, \tau/a) \; \left( dx^2 + dy^2 + dz^2 \right),
\; -\infty < \tau, \, x, \, y, \, z < \infty, \;
[/tex]
There is a very similar chart for a family of expanding inertial observers, who also have orthogonal hyperslices isometric to euclidean three-space. But there are also families of inertial observers whose world lines form a vorticity free timelike geodesic congruence, whose orthogonal hyperslices are each isometric to [itex]H^3[/itex], e.g.
[tex]
ds^2 = -dT^2 + a^2 \, \sinh(T/a)^2 \; \left( \frac{dx^2+dy^2+dz^2}{z^2} \right), \;
0 < T, \, z < \infty, \; -\infty < x, \, y < \infty
[/tex]
And there are observers who have constant acceleration directed radially inward in a suitable polar spherical chart, such as this one (analgous to Eddington chart):
[tex]
ds^2 = -(1-(r/a)^2) \, dv^2 + 2 dv \, dr + r^2 \; \left( d\theta^2 + \sin(\theta)^2 \, d\phi^2 \right), \;
-\infty < v < \infty, \; 0 < r < \infty, \; 0 < \theta < \pi, \; -\pi < \phi < \pi
[/tex]
The world lines of these observers again form a vorticity-free timelike congruence whose orthogonal hyperslices are each isometric to [itex]S^3[/itex]. Many other charts can be found in Hawking and Ellis and in the literature, e.g. "static" version of the previous chart (analgous to Schwarzschild chart), Brill chart, Penrose chart, etc. I stress again that there are both expanding and contracting observers in this spacetime who can be used to define "negligible density" cosmological models (better say "toy models").
So what is your "two-sphere grid"?
This makes no sense as written. Can you explain what you are trying to say in terms of the line element in some coordinate chart? Any "increase" or other physical change will probably be seen to refer to some family of observers whose motion can be characterized geometrically, independently of coordinate description.
That's not very encouraging! Yogi, may I ask: what is your comprehension rate when you read Hawking and Ellis? If you don't understand timelike congruences and their kinematic decomposition (acceleration, expansion scalar, shear tensor, vorticity vector) and null geodesic congruences and their optical scalars, you really can't hold any meaningful discussion of cosmological models! Remember, this ideas were imported/introduced more than forty years ago and immediately became standard core topics due to their great utility. These techniques are perfectly suited to studying the geometry (i.e. the physics) without getting confused by "features" ("bugs"?) which merely characterize a particular aspect of a given coordinate representation.
yogi said:
You should say "I think I detect", since others familiar with his writings can and do disagree about what he appears to have meant by various statements.
yogi said:
Huh? As you know there are many coordinate charts we can use on various pieces of the de Sitter lambdavacuum, aka [itex]H^{1,3}[/itex] (a Lorentzian spacetime with uniform negative curvature), including comoving charts adapted to static (non-inertial) observers and to various families of inertial observers. In particular,
[tex]
ds^2 = \frac{-dt^2 + dx^2+dy^2+dz^2}{(t/a)^2}, \;
0 < t < \infty, -\infty < x, \, y, \, z < \infty
[/tex]
is conformal to the upper half space portion of Minkowski spacetime and is comoving with a "collapsing" family of inertial observers whose world lines form a vorticity-free timelike geodesic congruence, whose orthogonal hyperslices are all isometric to euclidean three-space. Here, intervals of t do not correspond to intervals of proper time as measured by ideal clocks carried by our observers, but we can change to a comoving chart
[tex]
ds^2 = -d\tau^2 + \exp(-2 \, \tau/a) \; \left( dx^2 + dy^2 + dz^2 \right),
\; -\infty < \tau, \, x, \, y, \, z < \infty, \;
[/tex]
There is a very similar chart for a family of expanding inertial observers, who also have orthogonal hyperslices isometric to euclidean three-space. But there are also families of inertial observers whose world lines form a vorticity free timelike geodesic congruence, whose orthogonal hyperslices are each isometric to [itex]H^3[/itex], e.g.
[tex]
ds^2 = -dT^2 + a^2 \, \sinh(T/a)^2 \; \left( \frac{dx^2+dy^2+dz^2}{z^2} \right), \;
0 < T, \, z < \infty, \; -\infty < x, \, y < \infty
[/tex]
And there are observers who have constant acceleration directed radially inward in a suitable polar spherical chart, such as this one (analgous to Eddington chart):
[tex]
ds^2 = -(1-(r/a)^2) \, dv^2 + 2 dv \, dr + r^2 \; \left( d\theta^2 + \sin(\theta)^2 \, d\phi^2 \right), \;
-\infty < v < \infty, \; 0 < r < \infty, \; 0 < \theta < \pi, \; -\pi < \phi < \pi
[/tex]
The world lines of these observers again form a vorticity-free timelike congruence whose orthogonal hyperslices are each isometric to [itex]S^3[/itex]. Many other charts can be found in Hawking and Ellis and in the literature, e.g. "static" version of the previous chart (analgous to Schwarzschild chart), Brill chart, Penrose chart, etc. I stress again that there are both expanding and contracting observers in this spacetime who can be used to define "negligible density" cosmological models (better say "toy models").
So what is your "two-sphere grid"?
yogi said:
This makes no sense as written. Can you explain what you are trying to say in terms of the line element in some coordinate chart? Any "increase" or other physical change will probably be seen to refer to some family of observers whose motion can be characterized geometrically, independently of coordinate description.
yogi said:
That's not very encouraging!
Yogi, may I ask: what is your comprehension rate when you read Hawking and Ellis? If you don't understand timelike congruences and their kinematic decomposition (acceleration, expansion scalar, shear tensor, vorticity vector) and null geodesic congruences and their optical scalars, you really can't hold any meaningful discussion of cosmological models! Remember, this ideas were imported/introduced more than forty years ago and immediately became standard core topics due to their great utility. These techniques are perfectly suited to studying the geometry (i.e. the physics) without getting confused by "features" ("bugs"?) which merely characterize a particular aspect of a given coordinate representation.
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- #63
Bjarne
- 344
- 0
Garth
Imaging you is an artillerist. If you have a same size football and cannonball, and use the same amount of gun power, the football will reach furthest. (Lets say the wind resistance is the same for both objects)
My point is that it can’t only be ‘curved space’ that determinate how fare an objects travel. – But on the other hand I am not highly educated and don’t know how advanced this science is.
I think it is difficult to understand how ‘curved space’ should possible could explain the different gravity ‘pull’ effecting different masses / objects. I mean what have ‘space-geometry’ with a force / pull to do? – I can not unite these two factors based on the today available knowledge. I also can’t see that Einstein had reason to triumphant over Isaac Newton. – To my opinion why should it not be possible that both Newton and Einstein both was right? - A (invisible) Newtonian force (though space) could very well pull space until it ‘curves’.
We still don’t’ know the cause of the gravity; is it a force? – How can matter be the origin? - How can space pass on such pull / force, - or what is ‘curved space’ really for a strange kind of nature, - and a lot more why?
My underlying point is that I simply can not imaging me that space really (just) ‘curves’, like was it a roulet. – Its fine that such model can be used mathematically, - but its not all right that our imagination not is allowed to understand it..
Maybe space is not such complex and hard to imagine curved nature. - Already it is complicated enough that space is able to expand, - why make it even more unnecessary mysterious?
What when the nature of space really only is so simple like; - space can expand and therefore (off course) also contract –and that’s it.?.
Einstein didn’t know (belived) that space really had the ability to expand, even though matematically result was showing this as well as space could contract.
I think as a starting point we naturally at least should allow us self to finish simple thinking; - what if space only is a ‘flexible’ simply kind nature? - Before we begins to complicate the phenomena further.
Well this seems immediate to be a vague argument to explain the underlying cause of gravity, - but why make the properties of space even more complex and thereby making space a lot more mysterious, when everything seems to point to that it really is not necessary, - for achieving a coherent complete understanding of gravity.?
Imaging that matter (somehow) contracts space around it self. Such simple starting point really would from a synthesis between Einstein, Newton and all our formula’s without violating anything.
The winner would be our imagination that suddenly was allowed to enter into the gravity secret, - doesn’t matter where the mean tread would lead us. – I mean black holes, dark matter, dark energy, the cause of galaxy- solar system – heavenly body formation, and much more.
So why not first try to keep ‘space’ so simple as possible, and see where this leads us? - What if space only is is stupid flexible nature, - nothing more likes that.
---------
Bjarne
Imaging you is an artillerist. If you have a same size football and cannonball, and use the same amount of gun power, the football will reach furthest. (Lets say the wind resistance is the same for both objects)
My point is that it can’t only be ‘curved space’ that determinate how fare an objects travel. – But on the other hand I am not highly educated and don’t know how advanced this science is.
I think it is difficult to understand how ‘curved space’ should possible could explain the different gravity ‘pull’ effecting different masses / objects. I mean what have ‘space-geometry’ with a force / pull to do? – I can not unite these two factors based on the today available knowledge. I also can’t see that Einstein had reason to triumphant over Isaac Newton. – To my opinion why should it not be possible that both Newton and Einstein both was right? - A (invisible) Newtonian force (though space) could very well pull space until it ‘curves’.
We still don’t’ know the cause of the gravity; is it a force? – How can matter be the origin? - How can space pass on such pull / force, - or what is ‘curved space’ really for a strange kind of nature, - and a lot more why?
My underlying point is that I simply can not imaging me that space really (just) ‘curves’, like was it a roulet. – Its fine that such model can be used mathematically, - but its not all right that our imagination not is allowed to understand it..
Maybe space is not such complex and hard to imagine curved nature. - Already it is complicated enough that space is able to expand, - why make it even more unnecessary mysterious?
What when the nature of space really only is so simple like; - space can expand and therefore (off course) also contract –and that’s it.?.
Einstein didn’t know (belived) that space really had the ability to expand, even though matematically result was showing this as well as space could contract.
I think as a starting point we naturally at least should allow us self to finish simple thinking; - what if space only is a ‘flexible’ simply kind nature? - Before we begins to complicate the phenomena further.
Well this seems immediate to be a vague argument to explain the underlying cause of gravity, - but why make the properties of space even more complex and thereby making space a lot more mysterious, when everything seems to point to that it really is not necessary, - for achieving a coherent complete understanding of gravity.?
Imaging that matter (somehow) contracts space around it self. Such simple starting point really would from a synthesis between Einstein, Newton and all our formula’s without violating anything.
The winner would be our imagination that suddenly was allowed to enter into the gravity secret, - doesn’t matter where the mean tread would lead us. – I mean black holes, dark matter, dark energy, the cause of galaxy- solar system – heavenly body formation, and much more.
So why not first try to keep ‘space’ so simple as possible, and see where this leads us? - What if space only is is stupid flexible nature, - nothing more likes that.
---------
Bjarne
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- #64
Garth
Science Advisor
Gold Member
- 3,581
- 107
In order to criticize a theory a person has to understand it first, otherwise they only demonstrate their own ignorance.
From your post above it is obvious you don't actually understand GR, try reading one of the excellent introductions to relativity theory recommended elsewhere on these Forums or on the web you can begin by reading Ned Wright's Tutorial.
In the football and cannon ball case the same amount of gunpowder would accelerate the football to a higher velocity than the cannon ball because it was lighter, this is the law of momentum.
Air resistance would affect the football more because it had less mass, it would have a higher deceleration, this is fluid dynamics and not either Newtonian nor Einsteinian gravity.
Ignoring air resistance the trajectories of both balls is accurately described by GR. and nearly as accurately by Newtonian theory.
Garth
From your post above it is obvious you don't actually understand GR, try reading one of the excellent introductions to relativity theory recommended elsewhere on these Forums or on the web you can begin by reading Ned Wright's Tutorial.
In the football and cannon ball case the same amount of gunpowder would accelerate the football to a higher velocity than the cannon ball because it was lighter, this is the law of momentum.
Air resistance would affect the football more because it had less mass, it would have a higher deceleration, this is fluid dynamics and not either Newtonian nor Einsteinian gravity.
Ignoring air resistance the trajectories of both balls is accurately described by GR. and nearly as accurately by Newtonian theory.
With the correction that we are talking about curved 'space-time' and not just 'space', yes space-time curvature as defined in GR can accurately determine free falling trajectories, that is the point.
because observations have been made, such as the light deflection by the Sun or time delays of spacecraft whose radio pulses pass close to the Sun en route to Earth, that are accurately predicted by GR but not Newton. It is called doing science, theories stand or fall on empirical testing and falsification.
Garth
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- #65
Bjarne
- 344
- 0
Garth
You are right,- just 5 minutes simple reflecting over ‘fluid dynamics’ and a ‘mystery' is gone. - Thank you.
You are also right that it would be very helpful to read more about known knowledge of gravity / relativity.
Well this is 'mainly' correct, - the point here is that it wouldn’t bring anyone closer to a coherent complete understanding of the origin of gravity or why a huge number of very related questions remains unanswered.
Notice I am not criticize any prevailing theories, but only that it seems that something very simple very well could be overlooked.
What I mean 'curved space' could very well be the exactly same as 'contracted space' - It is not necessary (no reason) to think a such understanding involves any kind of conflict , - but could be only a little different way of perception of the same phenomena..
As I wrote I haven’t fully explained the full range of this simple claim, I will do this in a couple of weeks, and post it to the relevant part of this forum its belong.
----------
Bjarne
You are right,- just 5 minutes simple reflecting over ‘fluid dynamics’ and a ‘mystery' is gone. - Thank you.
You are also right that it would be very helpful to read more about known knowledge of gravity / relativity.
Well this is 'mainly' correct, - the point here is that it wouldn’t bring anyone closer to a coherent complete understanding of the origin of gravity or why a huge number of very related questions remains unanswered.
Notice I am not criticize any prevailing theories, but only that it seems that something very simple very well could be overlooked.
What I mean 'curved space' could very well be the exactly same as 'contracted space' - It is not necessary (no reason) to think a such understanding involves any kind of conflict , - but could be only a little different way of perception of the same phenomena..
As I wrote I haven’t fully explained the full range of this simple claim, I will do this in a couple of weeks, and post it to the relevant part of this forum its belong.
----------
Bjarne
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- #66
andrewj
- 33
- 0
is gravity stronger than we think possibly due to Planck sized dimensionsmarcus said:
- #67
andrewj
- 33
- 0
gravity can be repulsive ?
- #68
Bjarne
- 344
- 0
Andrewj
A none philosophic answer to that question is; we don’t know.
We also don’t know if dark energy exists, there is good reason to believe it does and good reason to believe it doesn’t.
If dark energy exists it is reason to believe that it is could be part of the gravity mystery (as well as dark matter possible could be).
Gravity could very well have a repulsive property. But again fully understanding the nature of ‘space’ is necessary.
You questions can only be answered philosophic. Assuming that gravity / curved space is variation of ‘space density’ would mean that gravity at the same time both can have attraction as well as repulsion properties / forces, even though it immediate seems to be a self-contradiction.
------
Bjarne
A none philosophic answer to that question is; we don’t know.
We also don’t know if dark energy exists, there is good reason to believe it does and good reason to believe it doesn’t.
If dark energy exists it is reason to believe that it is could be part of the gravity mystery (as well as dark matter possible could be).
Gravity could very well have a repulsive property. But again fully understanding the nature of ‘space’ is necessary.
You questions can only be answered philosophic. Assuming that gravity / curved space is variation of ‘space density’ would mean that gravity at the same time both can have attraction as well as repulsion properties / forces, even though it immediate seems to be a self-contradiction.
------
Bjarne
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- #69
Chris Hillman
Science Advisor
- 2,355
- 10
Come again?
Not sure why you ask (possibly because Bjarne is in my Ignore list), but let me ask you a question of my own: are you familiar with the Raychaudhuri formula, a fundamental theorem in gtr? If not, I highly recommend that you read about this in a standard textbook, such as the very clear undergraduate textbook by D'Inverno, Understanding Einstein's Relativity.
andrewj said:
Not sure why you ask (possibly because Bjarne is in my Ignore list), but let me ask you a question of my own: are you familiar with the Raychaudhuri formula, a fundamental theorem in gtr? If not, I highly recommend that you read about this in a standard textbook, such as the very clear undergraduate textbook by D'Inverno, Understanding Einstein's Relativity.
- #70
Bjarne
- 344
- 0
Chris?
Einstein’s relativity does not answer the question.
Einstein didn’t even not know that the universe was expanding - Dark energy was also not know at that time.
Why should someone ask a gravity related question because ‘Bjarne’ is on you ignore list?
Do you think it is fair to post such kind of repeated negative ‘attention’ - Chris?
---------
Bjarne
Einstein’s relativity does not answer the question.
Einstein didn’t even not know that the universe was expanding - Dark energy was also not know at that time.
Why should someone ask a gravity related question because ‘Bjarne’ is on you ignore list?
Do you think it is fair to post such kind of repeated negative ‘attention’ - Chris?
---------
Bjarne
Last edited:
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