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General relativity derives non-Euclidean geometry from changes in motion...Special relativity derives Euclidean geometry from changes in length/distance...
Accomplished by including non-Euclidean geometry, via the equivalence of inertial and gravitational mass, Changes in motion result from acceleration or gravity or both.
General Relativity deals with gravitational fields and according to this theory the velocity of light appears to vary with the intensity of the gravitational field.
So my question is - when the tests of GR set out in the 'tests of general relativity' link provided above are calculated, are the deviations from Euclidean geometry being calculated as spatial additions to the geometric distance between objects?
But light rays are moving at a constant speed, aren't they? So how is the geometry of spacetime distinguishing the constant speed of light?
That's light in free fall, considered equivalent to inertial motion and a straight line in Euclidean space.. In freefall you do not sense any acceleration....where I'll add that deceleration is no different to being at rest but with a gravitational field turned on
The light rays being bent towards a star are being bent because time in the 'space' near the star is running faster than the time in the 'space' between the background object emitting the light rays and the star that these light rays are being bent towards
Time is not bending the rays, gravity is
:Lee SmolinLet us start with the cosmological constant, thought to represent the dark energy accelerating the universe's expansion. As discussed in chapter 10, this energy was not anticipated by string theory, nor by most theories, and we have no idea what sets its value. Many people have thought hard about this for years, and we are more or less nowhere. I don't have an answer either, but I have a proposal for how we might find one. Let's stop trying to account for the cosmological constant's value in terms of known physics. If there is no way to account for the phenomenon on the basis of what we know, then maybe this is a sign that we need to look for something new. Perhaps the cosmological constant is a symptom of something else, in which case it might have other manifestations. How are we to look for them, or recognize them?The answer will be simple. because universal phenomenon are ultimately simple. Forces in physics are characterized by just a few numbers - for example, the distance over which a force travels and a charge to tell us how strong it is. What characterizes the cosmological constant is a scale, which is the distance scale over which it curves the universe. We can call this scale R. It is about 10 billion light years, or 10power27 centimeters. What is weird about the cosmological constant is that its scale is huge compared with other scales in physics. Scale R is 10power40 times the size of an atomic nucleus and 10power60 times the Planck scale (which is about 10power-27 times the size of a proton). So it's logical to wonder whether scale R might reflect some totally new physics. A good approach would be to look for phenomenon that happen on the same vast scale.Does anything else happen on the the scale of the cosmological constant? Let's start with cosmology itself. The most precise cosmological observations we have are the measurements of the 'cosmic microwave background'. This is the radiation left over from the Big Bang, which comes to us from all directions of the sky. The radiation is purely thermal - that is, random. It has been cooling as the universe expands, and it is now at the temperature of 2.7 degrees Kelvin. The temperature is uniform across the sky to a high degree of precision, but at the level of a few parts in 100 000 there are fluctuations in it. The patterns in these fluctuations gives us important clues to the physics of the early universe.Over the last decades, the temperature fluctuations of the microwave background have been mapped by satellites, balloon-borne detectors, and ground based detectors. One way to understand what these experiments measure is to think of the fluctuations as if they were sound waves in the early universe. It is then useful to ask how loud the fluctuations are at different wavelengths. The results give us a picture, which tells us how much energy there is at various wavelengths.The picture is dominated by a large peak, followed by several smaller peaks. The discovery of these peaks is one of the triumphs of contemporary science. They are interpreted by cosmologists to indicate that matter filling the early universe was resonant, much like the head of a drum of the body of a flute. The wavelength at which a musical instrument vibrates is proportional to its size, and the same is true of the universe. The wavelengths of the resonant modes tell us how big the universe was when it first became transparent: that is, when the initial hot plasma developed, or 'de-coupled'. into separate realms of matter and energy some three hundred thousand years after the Big Bang, at which time the microwave background became visible. These observations are extremely helpful in tying down the parameters of our cosmological models.Another feature we see in the data is that there is very little energy in the largest wavelength. This may be just a statistical fluctuation, because it involves a small number of pieces of data. But if it is not a statistical fluke, it can be interpreted as indicating a cut-off, above which the modes are much less excited. It is interesting that this cutoff is at the scale of R, associated with the cosmological constant.The existence of such a cutoff would be puzzling from the point of view of the most widely accepted theory of the very early universe, which is 'inflation'. According to the theory of inflation, the universe expanded exponentially fast during one extremely early period. Inflation accounts for the observation that the cosmic background radiation is so nearly uniform. It does this by ensuring that all parts of the universe we see now could have been in causal contact when the universe was still a plasma..The theory also predicts the fluctuations in the cosmic microwave background, which are hypothesized to be remnants of quantum effects during the period of inflation. The uncertainty principle implies that the fields dominating the energy of the universe during inflation fluctuate, and these fluctuations become imprinted on the geometry of space. As the universe expand exponentially, they persist, causing fluctuations in the temperature of the radiation produced when the universe becomes transparent.Inflation is believed to have produced a huge region of the universe with relatively uniform properties. This region of the universe is thought to be many orders of magnitude larger than the observable region, because of a simple argument about scales. If inflation had stopped just at the point where it created a region as large as we now observe, there must have been some parameter in the physics of inflation that selected a special time to stop, which just happens to be our era. But this seems improbable, because inflation took place when the universe had a temperature ten to twenty orders of magnitude greater than the center of the hottest star today; thus the laws governing it must have been different laws, which dominate physics only in those extreme conditions. There are many hypotheses about the laws that govern inflation, and none of them say anything about a time scale of 10 billion years. Another way to put this is that there seems no way for the present value of the cosmological constant to have anything to do with the physics that caused inflation.Thus if inflation produced a uniform universe on the scale that we observe, it likely produced a universe that is uniform on much larger scales. This in turn implies that the pattern of fluctuations produced by inflation should go on and on, no matter how far you look. If you could see beyond the present size of the observable universe, you should continue to see small fluctuations in the cosmic microwave background. Instead, the data hint that the fluctuations may cease above the scale of R.Indeed, as cosmologists have examined the large-scale modes in the microwave background, they have found more mysteries. It's an item of faith among cosmologists that at the largest scales the universe should be symmetric - that is, any one direction should be like any other. This is not what is seen. The radiation in these large-scale modes is not symmetric; there is a preferred direction. (It has been called "axis of evil" by the cosmologists Kate Land and Joao Magueijo). No one has any rational explanation for this effect.These observations are controversial because they disagree profoundly with what we would expect on the basis of inflation. Since inflation explains so much of cosmology, many prudent scientists suspect that there is something wrong with the microwave data. Indeed , it is always possible that the measurements are just wrong. A lot of delicate analysis is applied to the data before they're presented. One thing that's done is to subtract the radiation known to come from the galaxy that we live in. This may have been done incorrectly, but few experts familiar with the details of how the data are analyzed believe that to be the case. Another possibility, as noted, is that our observations are just statistical anomalies. An oscillation at a wavelength of the scale R takes up a huge part of the sky - about 60 degrees; consequently we see only a few wavelengths, and there are only a few pieces of data, so what we are seeing may just be a random statistical fluctuation. The chances of the evidence for a preferred direction being a statistical anomaly have been estimated at less than 1 part in 1000. But is may be easier to believe in this unlikely bad luck than to believe that the predictions of inflation are breaking down.These issues are currently unresolved. For the time being, it is enough to say that we went looking for strange physics on the scale of R and found it.
The physics books do not give any description as to 'how' a clock changes it's rate (as per GR) in the differing potentials of space, they only describe that a clock's rate of time will change.
Clearly, from the nature of the question, you are assuming that the rate of time for a clock in the differing potentials of space is changing because the rate of time in the differing potentials of space changes.
the clock "in' the gravity potential is ticking at a rate that is independent and differing from the rate of time in the space of that position of gravity potential,
(But by who's rate of time are we holding the speed of light relative to?)
(This renders the theory of special relativity as background dependent, in that it requires that the gravitational field be ignored, i.e. it requires a fixed, non-dynamic Euclidean background. So in a universe where gravity is mostly weak, physicists can feel justified in ignoring the gravity field.)
Einstein had developed another theory called General Relativity that deals with gravitational fields and according to this theory the velocity of light appears to vary with the intensity of the gravitational field.
SR time dilation can be described as losing, or gaining potential energy due to motion relative to the gravitational field.
I repeat again... that if a body is in motion in a field that has progressively changing rates of time, that bodies motion will be accelerated where seconds become shorter,
I can equate your 'changing rates of time' to 'changing field strength.'
SR time dilation works without g-fields!
Time dilation results from light chasing a moving target, in constant or changing speeds.
Quote Lee Smolin"We are not accustomed to thinking of space as an entity with properties of it's own, but it certainly is".If you can discover how a structured space, any type field, stores energy, and the process of releasing it to an object passing through it, you will answer many questions.
Lee Smolin"We are not accustomed to thinking of space as an entity with properties of it's own, but it certainly is".If you can discover how a structured space, any type field, stores energy, and the process of releasing it to an object passing through it, you will answer many questions.
I would question your current understanding of conventional physics.
Relativity is successful. This shows we don't need a complete understanding of all elements of a theory.
:Lee SmolinBut at some point during that afternoon, we hit on a key factor that had evaded us for months, having to do with trading momenta for positions. When we were done, we had invented a second version of DSR, much simpler than the one developed by Giovanni Amelino-Camelia. Now it is known to experts as DSR 2.This was what Joao had wanted. In our version, photons that have more energy travel faster. Thus, in the very early universe when the temperature was very high, the speed of light was, on average, faster than it is now. As you go back further in time and the temperature approaches the Planck energy, the speed of light becomes infinite. It took somewhat longer to show that this led to a version of a variable-speed-of-light theory that was also consistent with the principles of general relativity, but we eventually got there, too. We call this theory "Gravity's Rainbow" after Thomas Pynchon's novel."Doubly special relativity' is a stupid name, but it has stuck. The idea is an elegant one, by now much studied and discussed. We don't know if it describes nature, but we know enough about it to know that it could.
In our version, photons that have more energy travel faster.
Thus, in the very early universe when the temperature was very high, the speed of light was, on average, faster than it is now. As you go back further in time and the temperature approaches the Planck energy, the speed of light becomes infinite.
:Lee SmolinWhile there is today an exciting sense of progress among quantum-gravity theorists, there is also a strong expectation that the road ahead will bring at least a few surprises. Unlike string theorists in the exhilarating says of the two super-string revolutions, few of the people working on quantum-gravity believe they have their hands on a final theory. We recognize that the accomplishments of background-independent approaches to quantum gravity are a necessary step to finishing Einstein's revolution. They show that there can be a consistent mathematical and conceptual language that unifies quantum theory and general relativity. This gives us something that string theory does not, which is a possible framework in which to formulate the theory that solves all five of the problems I listed in chapter 1. But we are also fairly sure that we do not yet have all the pieces. Even with the recent successes, no idea has that absolute ring of truth.When you look back at the history of physics, one thing sticks out: When the right theory is finally proposed, it triumphs quickly. The few really good ideas about unification appear in a form that is compelling, simple, and unique; they do not come with a list of options or adjustable features. Newtonian mechanics is defined by three simple laws, Newtonian gravity by a simple formula with one constant. Special relativity was complete on arrival. It may have taken twenty five years to fully formulate quantum mechanics, but from the beginning it was developed in concert with experiment. Many of the key papers in the subject from 1900 on either explained a recent experimental result or made definite prediction for an experiment that was shortly done. The same was true of general relativity.Thus, all the theories that triumphed had consequences for experiment that were simple to work out and could be tested within a few years. This does not mean that the theories could be solved exactly - most theories never are. But it does mean that physical insight led immediately to a prediction of a new physical effect.Whatever else one says about string theory, loop quantum gravity, and other approaches, they have not delivered on that front. The standard excuse has been that experiments on this scale are impossible to perform - but, as we've seen, such is not the case. So there must be another reason. I believe that there is something basic that we are all missing, some wrong assumption we are all making. If this is so, then we need to isolate the wrong assumption and replace it with the new idea.What could that wrong assumption be? My guess is that it involves two things: the foundations of quantum mechanics and the nature of time. We have already discussed the first. I find it hopeful that new ideas about quantum mechanics have been proposed recently, motivated by studies of quantum gravity. But I strongly suspect that the key is time. More and more, I have the feeling that quantum theory and general relativity are both deeply wrong about the nature of time. It is not enough to combine them. There is a deeper problem, perhaps going back to the origin of physics.Around the beginning of the seventeenth century, Descartes and Galileo both made a wonderful discovery: You could draw a graph, with one axis being in space and the other being in time. A motion through space then becomes a curve on the graph. In this way, time is represented as if it were another dimension of space. Motion is frozen, and a whole history of constant motion and change is presented to us as something static and unchanging. If I had to guess (and guessing is what I do for a living), this is the scene of the crime.We have to find a way to unfreeze time - to represent time without turning it into space. I have no idea how to do this. I can't conceive of mathematics that doesn't represent a world as if it where frozen into eternity. It's terribly hard to represent time, and that's why there is aa good chance that this representation is the missing piece.
:linkBy combining quantum physics with general relativity, however, Ashtekar and colleagues report they have been able to develop a model that describes a transition from a previous universe, through the Big Bang to an expanding universe that exhibits physics similar to the one that exists today.Reporting in the current issue of Physical Review Letters, the team said their calculations reveal that prior to the Big Bang, there was a contracting universe with space-time geometry otherwise similar to the current expanding universe.As gravitational forces pulled this previous universe inward, it reached a point at which the quantum properties of space-time cause gravity to become repulsive, rather than attractive.
: FeynmanThis is an example of the 'uncertainty principle': there is a kind of "complementary" between knowledge of where the light goes between the blocks and where it goes afterwards - precise knowledge of both is impossible.I would like to put the uncertainty principle in its historical place: When the revolutionary ideas of quantum physics were first coming out, people still tried to understand them in terms of old-fashioned ideas (such as, light goes in straight lines). But at a certain point the old-fashioned ideas would begin to fail, so a warning was developed that said, in effect, "Your old-fashioned ideas are no damn good when..." If you get rid of all the old-fashioned ideas and instead use the ideas that I'm explaining in these lectures - adding arrows for all the ways an event can happen - there is no need for an uncertainty principle!
Then on the other hand - there is the school of thought that a person will age in keeping with their time dilated clock as described in the NIST link above, and the link below.
http://www.spacedaily.com/reports/Model_Suggests_Pre_Big_Bang_Physics.htmlQuote :linkBy combining quantum physics with general relativity, however, Ashtekar and colleagues report they have been able to develop a model that describes a transition from a previous universe, through the Big Bang to an expanding universe that exhibits physics similar to the one that exists today.Reporting in the current issue of Physical Review Letters, the team said their calculations reveal that prior to the Big Bang, there was a contracting universe with space-time geometry otherwise similar to the current expanding universe.As gravitational forces pulled this previous universe inward, it reached a point at which the quantum properties of space-time cause gravity to become repulsive, rather than attractive.Here Ashtekar and team are using a combination of quantum physics and general relativity to develop a model where the calculations reveal that prior to the Big Bang, there was a contracting universe with space-time geometry otherwise similar to the current expanding universe.
"QED" Richard P Feynman - chapter 2: Photons: Particles of Light - page 55 & 56Quote : FeynmanThis is an example of the 'uncertainty principle': there is a kind of "complementary" between knowledge of where the light goes between the blocks and where it goes afterwards - precise knowledge of both is impossible.I would like to put the uncertainty principle in its historical place: When the revolutionary ideas of quantum physics were first coming out, people still tried to understand them in terms of old-fashioned ideas (such as, light goes in straight lines). But at a certain point the old-fashioned ideas would begin to fail, so a warning was developed that said, in effect, "Your old-fashioned ideas are no damn good when..." If you get rid of all the old-fashioned ideas and instead use the ideas that I'm explaining in these lectures - adding arrows for all the ways an event can happen - there is no need for an uncertainty principle!(I think this notion may be compatible with non-commutative geometry)
"The Trouble with Physics" chapter 13: Surprises from the Real World - pages 204 ,205, 207 & 208.Quote :Lee SmolinLet us start with the cosmological constant, thought to represent the dark energy accelerating the universe's expansion. As discussed in chapter 10, this energy was not anticipated by string theory, nor by most theories, and we have no idea what sets its value. Many people have thought hard about this for years, and we are more or less nowhere. I don't have an answer either, but I have a proposal for how we might find one. Let's stop trying to account for the cosmological constant's value in terms of known physics. If there is no way to account for the phenomenon on the basis of what we know, then maybe this is a sign that we need to look for something new. Perhaps the cosmological constant is a symptom of something else, in which case it might have other manifestations. How are we to look for them, or recognize them?The answer will be simple. because universal phenomenon are ultimately simple. Forces in physics are characterized by just a few numbers - for example, the distance over which a force travels and a charge to tell us how strong it is. What characterizes the cosmological constant is a scale, which is the distance scale over which it curves the universe. We can call this scale R. It is about 10 billion light years, or 10power27 centimeters. What is weird about the cosmological constant is that its scale is huge compared with other scales in physics. Scale R is 10power40 times the size of an atomic nucleus and 10power60 times the Planck scale (which is about 10power-27 times the size of a proton). So it's logical to wonder whether scale R might reflect some totally new physics. A good approach would be to look for phenomenon that happen on the same vast scale.Does anything else happen on the the scale of the cosmological constant? Let's start with cosmology itself. The most precise cosmological observations we have are the measurements of the 'cosmic microwave background'. This is the radiation left over from the Big Bang, which comes to us from all directions of the sky. The radiation is purely thermal - that is, random. It has been cooling as the universe expands, and it is now at the temperature of 2.7 degrees Kelvin. The temperature is uniform across the sky to a high degree of precision, but at the level of a few parts in 100 000 there are fluctuations in it. The patterns in these fluctuations gives us important clues to the physics of the early universe.Over the last decades, the temperature fluctuations of the microwave background have been mapped by satellites, balloon-borne detectors, and ground based detectors. One way to understand what these experiments measure is to think of the fluctuations as if they were sound waves in the early universe. It is then useful to ask how loud the fluctuations are at different wavelengths. The results give us a picture, which tells us how much energy there is at various wavelengths.The picture is dominated by a large peak, followed by several smaller peaks. The discovery of these peaks is one of the triumphs of contemporary science. They are interpreted by cosmologists to indicate that matter filling the early universe was resonant, much like the head of a drum of the body of a flute. The wavelength at which a musical instrument vibrates is proportional to its size, and the same is true of the universe. The wavelengths of the resonant modes tell us how big the universe was when it first became transparent: that is, when the initial hot plasma developed, or 'de-coupled'. into separate realms of matter and energy some three hundred thousand years after the Big Bang, at which time the microwave background became visible. These observations are extremely helpful in tying down the parameters of our cosmological models.Another feature we see in the data is that there is very little energy in the largest wavelength. This may be just a statistical fluctuation, because it involves a small number of pieces of data. But if it is not a statistical fluke, it can be interpreted as indicating a cut-off, above which the modes are much less excited. It is interesting that this cutoff is at the scale of R, associated with the cosmological constant.The existence of such a cutoff would be puzzling from the point of view of the most widely accepted theory of the very early universe, which is 'inflation'. According to the theory of inflation, the universe expanded exponentially fast during one extremely early period. Inflation accounts for the observation that the cosmic background radiation is so nearly uniform. It does this by ensuring that all parts of the universe we see now could have been in causal contact when the universe was still a plasma..The theory also predicts the fluctuations in the cosmic microwave background, which are hypothesized to be remnants of quantum effects during the period of inflation. The uncertainty principle implies that the fields dominating the energy of the universe during inflation fluctuate, and these fluctuations become imprinted on the geometry of space. As the universe expand exponentially, they persist, causing fluctuations in the temperature of the radiation produced when the universe becomes transparent.Inflation is believed to have produced a huge region of the universe with relatively uniform properties. This region of the universe is thought to be many orders of magnitude larger than the observable region, because of a simple argument about scales. If inflation had stopped just at the point where it created a region as large as we now observe, there must have been some parameter in the physics of inflation that selected a special time to stop, which just happens to be our era. But this seems improbable, because inflation took place when the universe had a temperature ten to twenty orders of magnitude greater than the center of the hottest star today; thus the laws governing it must have been different laws, which dominate physics only in those extreme conditions. There are many hypotheses about the laws that govern inflation, and none of them say anything about a time scale of 10 billion years. Another way to put this is that there seems no way for the present value of the cosmological constant to have anything to do with the physics that caused inflation.Thus if inflation produced a uniform universe on the scale that we observe, it likely produced a universe that is uniform on much larger scales. This in turn implies that the pattern of fluctuations produced by inflation should go on and on, no matter how far you look. If you could see beyond the present size of the observable universe, you should continue to see small fluctuations in the cosmic microwave background. Instead, the data hint that the fluctuations may cease above the scale of R.Indeed, as cosmologists have examined the large-scale modes in the microwave background, they have found more mysteries. It's an item of faith among cosmologists that at the largest scales the universe should be symmetric - that is, any one direction should be like any other. This is not what is seen. The radiation in these large-scale modes is not symmetric; there is a preferred direction. (It has been called "axis of evil" by the cosmologists Kate Land and Joao Magueijo). No one has any rational explanation for this effect.These observations are controversial because they disagree profoundly with what we would expect on the basis of inflation. Since inflation explains so much of cosmology, many prudent scientists suspect that there is something wrong with the microwave data. Indeed , it is always possible that the measurements are just wrong. A lot of delicate analysis is applied to the data before they're presented. One thing that's done is to subtract the radiation known to come from the galaxy that we live in. This may have been done incorrectly, but few experts familiar with the details of how the data are analyzed believe that to be the case. Another possibility, as noted, is that our observations are just statistical anomalies. An oscillation at a wavelength of the scale R takes up a huge part of the sky - about 60 degrees; consequently we see only a few wavelengths, and there are only a few pieces of data, so what we are seeing may just be a random statistical fluctuation. The chances of the evidence for a preferred direction being a statistical anomaly have been estimated at less than 1 part in 1000. But is may be easier to believe in this unlikely bad luck than to believe that the predictions of inflation are breaking down.These issues are currently unresolved. For the time being, it is enough to say that we went looking for strange physics on the scale of R and found it.My contracting cyclic model gives physical cause and effect mechanics for it's Big Bangs and Inflation periods, and this data of a preferred direction will correspond to those mechanics.Given that anyone can understand that a 'contracting' universe will eventually result in all the mass of the universe being in the same location, i.e. a super-massive black hole, and that a super-massive back hole with no counterpart gravitational force acting upon it will explode it's plasma in an outward trajectory in an inflation like manner, I will continue onto the next few pages of Lee Smolin's book concerning the R scale with respect MOND.
:Lee SmolinThese issues are currently unresolved. For the time being, it is enough to say that we went looking for strange physics on the scale of R and found it...Are there any other phenomenon associated with this scale? We can combine R with other constants of nature to see what happens at scales defined by the resulting number. Let me give an example. Consider R divided by the speed of light: R/c. This gives us a time, and the time given is roughly the present age of our universe. The inverse, c/R, gives us a frequency - a very low note, one oscillation per lifetime of the universe.The next simplest thing to try is c^2/R. This turns out to be an acceleration. It is in fact the acceleration by which the rate of the expansion of the universe is increasing - that is, the acceleration produced by the cosmological constant...
: Lee Smolin - page 209 continued......Compared to ordinary scales, however, it is a very tiny acceleration: 10-8 centimeters per second. Imagine a bug crawling across the floor. It manages to go perhaps 10 centimeters per second. If the bug doubled it's speed over the lifetime of a dog, it would be accelerating as much as c^2/R, a very small acceleration indeed.But suppose there is a new universal phenomenon that explains the value of the cosmological constant. Just by the fact that the scales match, this new phenomenon should also affect any other kind of motion with an acceleration this tiny. So anytime we can observe something moving with such tiny acceleration, we would expect to see something new. Now the game starts getting interesting. We do know things that accelerate this slowly. One example is a typical star orbiting in a typical galaxy. A galaxy orbiting another galaxy accelerates even more slowly. So, do we see anything different about the orbits of stars with accelerations this tiny, compared to the orbits of stars with larger accelerations? The answer is yes, we do, and dramatically so. This is the problem of Dark Matter.
:Lee Smolin continued...So, do we see anything different about the orbits of stars with larger accelerations? The answer is yes, we do, and dramatically so. This is the problem of dark matter...As we discussed in chapter 1, astronomers discovered the dark matter problem by measuring the acceleration of stars in orbit about the center of their galaxies. The problem arose because, given the measured accelerations, astronomers could deduce the distribution of the galaxy's matter. In most galaxies, this result turned out to disagree with the matter observed directly.I can now say a bit more about where the discrepancy arises. (For the sake of simplicity, I'll restrict the discussion to spiral galaxies, in which most stars move in circular orbits in a disk.) In each galaxy where the problem is found, it affects only stars moving outside a certain orbit. Within that orbit, there's no problem - the acceleration is what it should be if caused by visible matter. So there seems to be a region in the interior of the galaxy within which Newton's laws work and there is no need for dark matter. Outside this region, things get messy.The key question is: Where is the special orbit that separates the two regions? We might suppose that it occurs at a particular distance from the center of the galaxy. This is a natural hypothesis, but it is wrong. Is the dividing line at a certain density of stars or starlight? Again, the answer is no. What seems to determine the dividing line, surprisingly, is the rate of acceleration itself. As one moves further out from the center of the galaxy, accelerations decrease, and there turns out to be a critical rate that marks the breakdown of Newton'slaw of gravity. As long as the acceleration of the star exceeds this critical value, Newton's law seems to work and the acceleration predicted is the one seen. There is no need to posit any dark matter in these cases. But when the acceleration observed is smaller than the critical value, it no longer agrees with the predictions of Newton's law.What is this special acceleration? It has been measured to be 1.2x10-8 centimeters per second per second. This is close to c^2/R, the value of the acceleration of the cosmological constant!This remarkable twist in the dark matter story was discovered by an Israeli physicist named Mordelhai Milgrom in the early 1980's. He published his findings in 1983, but for many years they were largely ignored. As the data have gotten better, however, it has become clear that his observation was correct. The scale c^2/R characterizes where Newton's law breaks down for galaxies. This is now called Milgrom's law by astronomers.I want you to understand how weird this observation is. The scale R is the the scale of the whole universe, which is enormously bigger than any individual galaxy. The acceleration c^2/R occurs on this cosmological scale; as noted, it is the rate at which the universe's expansion accelerates. There is no obvious reason for this scale to play any role in the dynamics of an individual galaxy. The realization was forced upon us by the data. I recall my amazement when I first learned about it. I was shocked and energized. I walked around for an hour in a daze, muttering incoherent obscenities. Finally! A possible hint from experiment that there is more to the world than we theorists imagine!How is this to be explained? Apart from coincidence, there are three possibilities. There could be dark matter, and the scale of c^2/R could characterize the physics of the dark matter particles. Or the dark matter halos could be characterized by the scale of c^2/R, because that is related to te density of dark matter at the time they collapsed to form galaxies. In either case, the dark energy and dark matter are distinct phenomenon, but related.The other possibility is that there is no dark matter and Newton's law of gravity breaks down whenever accelerations get as small as the special value of c^2/R. In this case there needs to be a new law that replaces Newton's law in these circumstances. In his 1983 paper, Milgrom proposed such a theory. He called it MOND for "modified Newtonian dynamics." According to Newton's law of gravity, the acceleration of a body due to a mass decreases in a specific way when you move away from that mass - that is, by the square of the distance. Milgrom's theory says that Newton's law holds, but only until the acceleration decreases to the magic value of 1,2x10-8cm/sec^2. After that point, rather than decreasing with the square of the distance, it decreases only by distance. Moreover, while normally the Newtonian force is proportional to the mass of the body causing the acceleration times a constant (which is Newton's gravitational constant), MOND says that when the acceleration is very small, the force is proportional to the square root of the mass times Newton's constant.If Milgrom is right, then the reason that the stars outside the special orbit are accelerating more than they should be is that they are feeling a stronger gravitational force than Newton predicted! Here is brand-new physics - not at the Planck scale, and not even in an accelerator, but right in front of us, in the motions of the stars we see in the sky.As a theory, MOND does not make much sense to physicists. There are good reasons why the gravitational and electrical forces fall off with the square of the distance. It turns out to be a consequence of relativity combined with the three dimensional nature of space. I won't go into details here, but the conclusion is drastic. Milgrom's theory appears inconsistent with basic physical principles, including those of special and general relativity.
Milgrom's theory says that Newton's law holds, but only until the acceleration decreases to the magic value of 1,2x10-8cm/sec^2. After that point, rather than decreasing with the square of the distance, it decreases only by distance. Moreover, while normally the Newtonian force is proportional to the mass of the body causing the acceleration times a constant (which is Newton's gravitational constant), MOND says that when the acceleration is very small, the force is proportional to the square root of the mass times Newton's constant.
I have explained in previous posts how my model describes causality for both the attraction of gravity (mass internal GR&SR timing)
and the acceleration of gravity (3rd aspect time dilation of open space)
:post 49If you travel one metre at a constant speed that is held relative to a longer or shorter 'variable' second. Then the distance remains the same, and it just takes a longer or shorter amount of 'time' to travel that metre.