Steve...that's a little dangerous. Vis: the old tale, a Physicist is looking to get some dry-cleaning done, and sees a sign "dry-cleaning" in a shop front.
Goes inside, and is greeted by the store owner who and as it turns is a mathematician.
"I need this shirt dry-cleaned" says the Physicist.
"Sorry..I can't help you" replies the owner.
"Why not??"
"We just make signs!"
In short, without the physics, the math can be a little meaningless.
The sign writer is obviously a pure mathematician instead of an applied mathematician.
Then you would get a dry cleaned sign pressed onto the shirt.
Seriously modern day physics has such a voracious appetite for pure mathematics, it has actually become difficult to categorize whether for example String Theory is a branch of theoretical physics or pure mathematics.
It's all a bit symbiotic isn't it? Observation leads us to theories and the theories point us in different directions for observation. These either confirm or refute the theories. Which then get modified and sent back for observation...so both happen together. However, I am always amazed at how intricately mathematics is a part of how things work. And how well it predicts what is later observed.
I think the main thing with any body of knowledge is to keep an open mind. Use what tools we have, but always be open to other possibilities.
Steven said....That's a conspiracy theory Alex. Science papers are peer reviewed which minimizes the chances of such nefarious activities.
I've mentioned the concept of renormalization earlier in the thread as an example to indicate that the science community will react to any perceived tampering with mathematics...
Sorry Steven I can see why you responded so...the manipulative hands I was hinting at were mine making a subdivision spread sheet say what I wanted it to say....
Still a lot of bad stuff happens but I never see one scientist fudging the books as representative of the profession..in fact as with most things if humans follow the rules we wont have problems.. and liars usually get found out one would like to think.
alex.
Before you can ask the question "What is Gravity", might I suggest a healthy understanding of curvature first...real curvature.
Next, understand the definitions and the similarities (the links) between the two;
In geometry, curvature may be defined as the mathematical obstruction within a curvilinear coordinate system, so that it cannot be transformed into a flat coordinate system. In the general theory of relativity, gravitation may be defined as the obstruction of tidal forces within a gravitational field, so that it cannot be transformed into a field of flat spacetime.
Then the 'Connection' (The Christoffel symbols), between energy and negative divergence.
ie. Curvature Tensor = Energy Momentum
roughly speaking; The metric must equal the E=mc^2 of all the mass within a given space (3D) and over a given time.
Before you can ask the question "What is Gravity", might I suggest a healthy understanding of curvature first...real curvature.
Next, understand the definitions and the similarities (the links) between the two;
In geometry, curvature may be defined as the mathematical obstruction within a curvilinear coordinate system, so that it cannot be transformed into a flat coordinate system. In the general theory of relativity, gravitation may be defined as the obstruction of tidal forces within a gravitational field, so that it cannot be transformed into a field of flat spacetime.
Then the 'Connection' (The Christoffel symbols), between energy and negative divergence.
ie. Curvature Tensor = Energy Momentum
roughly speaking; The metric must equal the E=mc^2 of all the mass within a given space (3D) and over a given time.
Some Pics for the Geeks are attached
Valiant effort. Why bring real science into this pathetic discussion. Most people get lost with integrals let alone matrices. They would far more prefer to argue from a totally nebulous basis. It makes hand waving almost acceptable.
Gravity could be the 'connections' that are a result of the effect of quantum entanglement.
It is is very suspicious that all galaxies tend to keep their matter to themselves.
Interacting galaxies could be the 'mad uncles'.
Bert
I do think that coalescence of matter and an inflatory universe are to blame for the aloofness of galaxy matter, the clicky groups of stars, but now that you mention it, I could easily imagine the Cosmological Constant being a reluctance (impedance) across space…but that would be non-local…unless there’s a law behind it.
What I find really interesting about gravity, it that Gravity Waves are not included within the Einstein Equation, in that on the left side we have the Einstein Tensor (consisting of the Ricci Tensor, the Metric, and then the Scalar Curvature), then on the right side we have the Energy Momentum (consisting of the 8xPi, the Gravitational Constant, and the Energy Density).
But gravity waves are separate, they run only within the metric tensor, and as such energy within a gravitational field cannot be conserved, unlike electric and magnetic fields.
SO, this means that gravity waves slip underneath the gravitational field (geodesics) without being affected…we see this in Black Holes, where nothing can escape them, not even light, but the mass of a black hole creates gravity waves which can and do escape.
This is totally bizarre, and in some part, conflicts with special relativity. Remember the forces are carried within the geodesic, within the Christoffel symbols. So how can you detect gravity waves when these quadrapole waves radiate out the metric, underneath the field??? You just can’t because light bends within the geodesic, which again, is governed by the Einstein Tensor, so I don't feel they will be found.
I've said it before, gravity (GR) is a fictitious force, it is mediated by “slippery-trickery mathematics” and is nothing like the other forces.
It’s as though gravity waves operate through the [dare I say] 'Ether'…
I have given you a HW answer about gravity. If you think of all particles that have interacted in the past and they are now 'smeared' across some finite space but still linked by entanglement. I find it hard to put into words but what is going on? I do not understand quantum mechanics. Anyone who claims to is a fool! But I think that human if not all brains work at the QM level. Indeterminism leading to insight!
The only 'proof' for this is the bewildering complexity shown by our abilities for reason and deduction and yes inspiration from 'nowhere'.
I have given you a HW answer about gravity. If you think of all particles that have interacted in the past and they are now 'smeared' across some finite space but still linked by entanglement. I find it hard to put into words but what is going on? I do not understand quantum mechanics. Anyone who claims to is a fool! But I think that human if not all brains work at the QM level. Indeterminism leading to insight!
The only 'proof' for this is the bewildering complexity shown by our abilities for reason and deduction and yes inspiration from 'nowhere'.
Bert
Assume I don't know what HW means...now, don't assume...???
You wrote, "that have interacted in the past and they are now 'smeared' across some finite space but still linked by entanglement"...I really, really want to reply to this statement...but cannot. I PM'd you a request.
You wrote, "I find it hard to put into words but what is going on?"...yes, the itch you cannot scratch...I believe that there is a connection...but not the quantum direction, the relativity path is still not closed.
What I find really interesting about gravity, it that Gravity Waves are not included within the Einstein Equation, in that on the left side we have the Einstein Tensor (consisting of the Ricci Tensor, the Metric, and then the Scalar Curvature), then on the right side we have the Energy Momentum (consisting of the 8xPi, the Gravitational Constant, and the Energy Density).
The matter energy tensor (the right hand term) is not relevant if one wants to use black holes in the argument. This term is only applied when one is interested in external gravitational and/or electromagnetic fields acting on the field in question. It also applies to extended objects where matter is found in the field.
Gravitational waves are formed by variations of the field itself.
In other words you only need to consider the extension of the field into empty space and the propagation of gravitational waves into empty space.
The Einstein equation simply becomes Ricci Tensor=0.
Gravitational waves are derived mathematically by applying perturbation to the metric components of the Lorentzian metric. The components are time dependent indicating the field varies with time.
This is a solution to the equation.
Quote:
But gravity waves are separate, they run only within the metric tensor, and as such energy within a gravitational field cannot be conserved, unlike electric and magnetic fields.
You have lost me. If a gravitational field varies, the energy in the field is conserved by the radiation of gravity waves. That's the basis behind the existence of gravitational waves.
Quote:
SO, this means that gravity waves slip underneath the gravitational field (geodesics) without being affected…we see this in Black Holes, where nothing can escape them, not even light, but the mass of a black hole creates gravity waves which can and do escape.
The mass alone (density) does not create gravitational waves. A static (Schwarzchild metric) black hole doesn't generate gravitational waves. A rotating (Kerr metrc) black hole can be a different matter. Since it rotates, there is centripetal force (with a non vanishing Christoffel) that adds to the field strength. By slowing down the rotation, the loss in rotational energy is taken up by the frequency of the emitted gravitational waves.
Quote:
I've said it before, gravity (GR) is a fictitious force, it is mediated by “slippery-trickery mathematics” and is nothing like the other forces.
There is nothing devious about the maths unlike the manipulations that occur in Quantum Field Theory.
Regards
Steven
Last edited by sjastro; 12-10-2009 at 08:28 AM.
Reason: More info
The matter energy tensor (the right hand term) is not relevant if one wants to use black holes in the argument. This term is only applied when one is interested in external gravitational and/or electromagnetic fields acting on the field in question. It also applies to extended objects where matter is found in the field.
Gravitational waves are formed by variations of the field itself.
In other words you only need to consider the extension of the field into empty space and the propagation of gravitational waves into empty space.
The Einstein equation simply becomes Ricci Tensor=0.
Gravitational waves are derived mathematically by applying perturbation to the metric components of the Lorentzian metric. The components are time dependent indicating the field varies with time.
This is a solution to the equation.
You have lost me. If a gravitational field varies, the energy in the field is conserved by the radiation of gravity waves. That's the basis behind the existence of gravitational waves.
The mass alone (density) does not create gravitational waves. A static (Schwarzchild metric) black hole doesn't generate gravitational waves. A rotating (Kerr metrc) black hole can be a different matter. Since it rotates, there is centripetal force (with a non vanishing Christoffel) that adds to the field strength. By slowing down the rotation, the loss in rotational energy is taken up by the frequency of the emitted gravitational waves.
There is nothing devious about the maths unlike the manipulations that occur in Quantum Field Theory.
Regards
Steven
Hi Steven,
The mass energy tensor is as it says, it can be either energy as energy, or energy in the guise of mass, which is moving through a given spatial region over a temporal period. A black hole still has energy moving through given regions over a given periods, even if the mass energy tensor and [mathematical] dimensions breaks down in this environment. And this is one of my main points; hat breaks down here isn't reality at all, it’s still there, it's our mathematics and our understanding which does. The universe is doing what it has always done and doesn't need the math. This relates to the thread about Math Lingo, where math is manipulated to suit the observation (not necessarily the reality) and thus it is merely a descriptive language, NOT the be-all and end-all. But why do so many people tout it to be an absolute. This really needs to be understood by everyone; Newton was hailed as being correct, now not so correct, Einstein could well be next. My point here is simple; there are mathematical principles which merely describe reality, and there is reality. The two can and do conflict all, the time. The key difference is really simple; reality is what it is, reality. Mathematics is equally simple; it’s a visualization tool, a language, and nothing more!
My tutor spent his entire life working for NASA as an astrophysicist and lecturing at Cambridge, understanding how light is created within stars and logic in mathematics, and you should hear what he has to say about this topic. He was the one who showed me that there is a separation between math and reality that needs to be clearly understood. In one of my scanned notes, I wrote his words, “people these days run around talking about what light is, I’ve spent my entire life trying to understand what is light, and I haven’t a clue”.
Back to gravity: Gravitational waves are linked to the field, I agree, but they behave only in accordance with the [symmetric] metric tensor, and the Ricci and Scalar must be dropped in order to describe these waves (convenience of mathematics again). It takes all three to describe the gravitational field, therefore, gravity waves do not operate through the gravitational field, they have their own and they set-up the gravitational field (probably why we now need a Higgs field). We need to now drop mathematics entirely and look at gravitation as a physical form, two structures are present, a field which spreads out at the speed of light and for all we know, may well set-up of define the metric in some ether of energy, and a field which hold the interplay between energy and curved geodesics (Not curved space and time at all!) brought about from the negative divergence.
Without transferring understanding of gravitation from mathematics across to a physical mental picture, we are forever lost within the “tool”, the “language”.
"you only need to consider the extension of the field into empty space and the propagation of gravitational waves into empty space...the Einstein equation simply becomes Ricci Tensor=0."...yes, exactly!
There can be no conservation in a gravitational field since gravitational waves are radiating [sending out of the system] energy from the massed [energy dense] region where our star, or whatever, is. Again, my point is that gravity waves are a separate structure to the gravitational field, but there are linked. Einstein knew this and accounted for it. This is why he said that there is no background structure with which to measure against; even his evolution equations for quantum measurements hold an “all of universe” solution, “without a fixed background structure”. Ergo the importance of clocks (synchronicity).
I know what you're saying about black holes, and I agree, but there is a separation between the gravitational field and how the field is setup, a separation between math and the reality.
"There is nothing devious about the maths unlike the manipulations that occur in Quantum Field Theory."...yes there is. For example, every mathematician (Gauss, Riemann, Ricci, Minkowski, Christoffel, Einstein, all of them) played around with the math, creating variations in the chain rule for instance, until "hey presto", "that seems to match the observations or what we need". When we get to a black hole, all of a sudden we say that a new type of math needs to be derived in order to describe this region. Yet another variation in the language, yet reality chugs along in the background.
Again, mathematics is merely an aid in understanding what is happening in reality and not the contrary; reality is not the aid to understanding mathematics.
Anyway, I’ve said enough on this topic and I’m sure you get my point.
I dont know but it seems all are at the end of a dead end laneway as a result of following incorrect directions and instead of accepting such as the inescapable conclusion those in that dead end lane are content to count the bricks in the wall preventing further progress rather than to back up and seek a lanr way that actually takes one someplace. AND even standing looking at those bricks no one is concerned of their make up or composition... I find that strange.
We have a hypothethic object (a black hole) from which nothing can escape and yet somehow it can advise the rest of the Universe it is there presumably by magic, as any particle via which one could think may be required to form a field is prevented from escape and thereby communicate whatever message it is to communicate..gravity in particular.
I dont care what the math says that does not add up.
We have clear observational evidence that attraction is not the force that holds galaxies together unless we add matter (dark matter) which is only able to be observered by an inference that it has to be there to make any hypothisis based upon attraction work.
What maths predicted the Pioneer would not slow and what maths will be put forward to say we are still in the right lane way. I think Steven offerred the most reasonable explaination some time ago which still seeks to accomodate the rule subject to an exception.
Folk decry my non acceptance of the math and ignorance of the meat of the matter yet I work upon observation of what I see and a reasonable expalination of why it may be so... why that is a problem I do not know.
I predicted that the Pioneer would slow ( as a sticky space must suggest) and yet am told it was a lucky guess because I provide no math for the right answer so I find it frustrating that NASA using the correct math got it wrong are still somehow right on that matter...
I find it frustrating that those who have all the answers are unable to answer the question posted here...what is gravity... I really do not think that question has been answered herein.
Not that such a problem confinded those who read or contribute to this thread for as much as we say we have the answers it is clear we do not ... I am sorry Bert to upset you by saying we no nothing about gravity when you can on behalf of science take pride in the various wonderful things humans have achieved using what we know to date... I am truely no trying to be disrespectful to you or anyone but the fact remains we no nothing about gravity other than how many bricks it takes to make a wall..
Humans have simple sences, sight hearing taste etc and it would be best to recognise that and work within those limits as then we would not be so determined to entertain notions of things we can not see or observe directly to be realities but matters that we still do not understand.
AND why when we have something we do not understand do we insist on calling it black or dark ... I came across "a dark accelorator" and you guessed it ...we dont understand so its dark.
The items one reads about dark matter and black holes leaves me wondering if we are no less superstitious than any other group of humans before us.
Blame the science jounalists if you like but when someone comes up with "black holes may hold the key to time travel" why is there no scientist jumping forward to point out the fanciful nature of such a statement.
Now Bert, Steven and Mark as this is too limited a region to publish all the math supporting current science I say that the answer to the original question has not been answered and the number of bricks in the wall preventing us moving forward are really not going to answer the question presented here.
If the String hypothisis goes anywhere it seeks to find a graviton..which as I understand is the force carrying particle engineered to suit that hypothisis and one would think that no matter what hypothisis we subscibe to we will finally need a particle to carry "the message" so I find it hard to accept a black hole can happily let them (gravitons or whatever thing finally selected for the job) escape and yet the same black hole will grab a photon and never let it go.
I find it hard to imagine how a black hole can have a gravity field (at all given its properties) and that a gravity wave (if they exist) can be seperate..the math may support this approach but I ask you does that really sound reasonable.
Thank you for reading the above now please ignore all of it and move on as if I had not posted and enjoy your day for I am only having a grizzle on this subject when in truth it is other matters that cause my frustration and grumpiness today. If only all my problems were as simple as solving the gravity question I would be happy.
alex
alex
When maths is manipulated to suit the observation that's simply the Scientific Method in process and represents one end of the spectrum.
The other end of the spectrum is when observation verifies the theory.
For example many of the subatomic and carrier particles in particle physics are mathematical inventions which have been subsequently proven to exist in nature.
Does that put mathematics in conflict with reality? No it doesn't.
Mathematics is part of the reality.
On the subject of gravitational waves we will have to agree to disagree.
The driving force behind behind gravitational waves are the time dependent metric components. Not the metric itself but the components.
The metric components are analogous to gravitational potential in Newtonian theory. To move from one gravitational potential in the field to another requires an expenditure or release of energy.
If the field changes in strength (without a gain or loss of the generating mass) then the field is conserved through the emission of gravitational waves.
Astronomers are looking for this phenomena to occur, such as the rotation of 2 massive bodies (black holes) around a centre of mass. The bodies lose energy in the field and gravitational waves are emitted in the process equal to the lost energy.
The driving force behind behind gravitational waves are the time dependent metric components.
Yes, interesting indeed.
I said metric as a general comparison between all components within the Einstein Tensor...but if I must be specific, I would say that it is not the "components" either, I believe it would all come down to variations of the derivative values (1st and 2nd derivatives) held within the metric components. Of course the numbers of values vary depending upon how many dimensions we are talking about. 256 for a spacetime metric.
The "components" of the metric, are the mathematical operators, not the values themselves, true?
...I feel that we still don't have an answer to the question, "What is Gravity?" (causally), we haven't as yet discussed a reason why it exists either...I raise that question with trepidation.
I can suggest a cause...a reason...but I don't think that anyone will like it.
I said metric as a general comparison between all components within the Einstein Tensor...but if I must be specific, I would say that it is not the "components" either, I believe it would all come down to variations of the derivative values (1st and 2nd derivatives) held within the metric components. Of course the numbers of values vary depending upon how many dimensions we are talking about. 256 for a spacetime metric.
The "components" of the metric, are the mathematical operators, not the values themselves, true?
Cheers
Mark
The number of components is based on the rank of the curvature tensor. For example the Riemann curvature tensor which has a rank of 4 has 4^4=256 components for 4 dimensional space.
The Ricci tensor which is a contracted version of the Riemann tensor has 2^4=16 components in 4 dimensional space. Taking into account symmetry the total number of components is 10.
Thus GR is a gravitational theory for 10 potentials (Newtonian theory has only 1 potential).
The Christoffel symbols in the Ricci or Einstein field equations result in the partial differentiation (1st and second order) of the each metric component. The metric component is the potential.
If the metric components are constant, the Christoffel symbols vanish and the metric is simply a geodesic or straight line in flat space.
Non vanishing Christoffel symbols (metric components are not constant) indicates curved geodesics.
You just can’t because light bends within the geodesic, which again, is governed by the Einstein Tensor, so I don't feel they will be found.
and is nothing like the other forces.
. I havent got a clue what you guys are on about in the last few posts, so maybe in a way an average dummy can understand ? 
