On the Hypotheses which lie at the Bases of Geometry





The non-Euclidean geometries are called geometries, because they have been developed from the Euclidean geometry. The non-Euclidean geometries are called geometries, because they employ the methods and the axioms and the rules of the Euclidean geometry. The non-Euclidean geometries are called geometries, because the educated folks have agreed to call them geometries. And the non-Euclidean geometries are called geometries, because of very cogent arguments like the strong argument below.


In a lecture entitled 'On the Hypotheses which lie at the Bases of Geometry', Bernhard Riemann argues very convincingly in favor of non-Euclidean geometries:

It is known that geometry assumes, as things given, both the notion of space and the first principles of constructions in space. She gives definitions of them which are merely nominal, while the true determinations appear in the form of axioms. The relation of these assumptions remains consequently in darkness; we neither perceive whether and how far their connection is necessary, nor a priori, whether it is possible. From Euclid to Legendre (to name the most famous of modern reforming geometers) this darkness was cleared up neither by mathematicians nor by such philosophers as concerned themselves with it. The reason of this is doubtless that the general notion of multiply extended magnitudes (in which space-magnitudes are included) remained entirely unworked. I have in the first place, therefore, set myself the task of constructing the notion of a multiply extended magnitude out of general notions of magnitude. It will follow from this that a multiply extended magnitude is capable of different measure-relations, and consequently that space is only a particular case of a triply extended magnitude. But hence flows as a necessary consequence that the propositions of geometry cannot be derived from general notions of magnitude, but that the properties which distinguish space from other conceivable triply extended magnitudes are only to be deduced from experience. Thus arises the problem, to discover the simplest matters of fact from which the measure-relations of space may be determined; a problem which from the nature of the case is not completely determinate, since there may be several systems of matters of fact which suffice to determine the measure-relations of space - the most important system for our present purpose being that which Euclid has laid down as a foundation. These matters of fact are - like all matters of fact - not necessary, but only of empirical certainty; they are hypotheses. We may therefore investigate their probability, which within the limits of observation is of course very great, and inquire about the justice of their extension beyond the limits of observation, on the side both of the infinitely great and of the infinitely small.

http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/WKCGeom.html

That man called 'Riemann' was just trying to make name for himself by shouting 'darkness' in the middest of lights!


In any case, those 'general notions of magnitude', the main topic of Riemann's Lecture, are what algebra is all about.


All in all, there is absolutely no difference between those non-Euclidean geometries and this matrix algebra:

http://people.hofstra.edu/stefan_waner/realworld/Summary3.html


Also, there is no difference of any kind between matrix algebra and this geometry of General Relativity:

http://www.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf


So, those non-Euclidean geometries are, in the final analysis, geometries in name and only in name and nothing else.

Hello AAF,

>>So, those non-Euclidean geometries are, in the final analysis, geometries in name and only in name and nothing else.<<

You seem touched very wide and general questions especially with this somewhat simplified conclusion of yours. Well, both non-euclidean geometries (hyperbolic and elliptic respectively) can be postulated and INTERPRETED in many different might be counterintuitive but logicaly fully justified and even amazing ways.

For example, Lobachevskie-Bolyai hyperbolic geometrie can be seen as a system raised over axiom of no-parallels through any point, OR, as a space with constant negative curvature. Similary goes with Gauss-Riemann elliptic geomtries. Both of them possess their PRESENTATIONS on the parabolic (Euclid) geometrie but vice versa as well.

The other pair of sleavs is physical interpretaion (of even USAGE) of such systems. SR/GR via Minkowski space-time and later on the so-called GR tensorial field as metric one are interpretations of the kind and those seems are, in the end, among the biggest blunders throughout entire "history of science". Simply put, realistic cosmic dynamics cannot be expressed in geometrical manner at all. Only problem is how to honestly admit that simple thruth and finally reject one utterly wrong and in fact sterile "paradigm".

However, rejecting that way doesn't and simply cannot mean a comeback under secure Newton's arm.

Best regards

Hello Turanyanin:




Yes, it's a simplified conclusion, but it's true.


Using the Euclidean conic sections as analogies, Lobachevsky & Bolyai & Gauss have come up with a “non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the parallel postulate, which is modified to read: For any infinite straight line L and any point P not on it, there are many other infinitely extending straight lines that pass through P and which do not intersect L”:

http://mathworld.wolfram.com/HyperbolicGeometry.html


However, from the standpoint of geometry, these analogies of theirs as well as that of Riemann are flawed and false. Since it's impossible to demonstrate in any way or manner the reality and logical consistency and coherence of any other type of surfaces, except one-dimensional and two-dimensional surfaces:

http://www.carliner-remes.com/jacob/math/project/math.htm


And so, it follows that every non-Euclidean geometry is no geometry at all and mere algebraic construction based mainly on alphabetical symbols and algebraic principles and rules.


As algebraic systems, non-Euclidean geometries are indeed consistent and rigorous; but as geometries, those so-called 'non-Euclidean geometries' are non-coherent, non-logical, and absurd, and don't make any sense at all.

You may call these multi-spatial geometries matrix algebra, even though matrix algebra is an independent and highly developed field in its own right.


However, no one can justify labeling the geometry of general of relativity as algebraic & non-geometrical.


That is because, unlike other non-Euclidean geometries, the geometry of general relativity has only three spatial co-ordinates.
And since its fourth co-ordinate geometrical is a time co-ordinate, the geometry of general relativity is a true geometry
that can be used and has been successfully used to describe the physical world.

It's quite the opposite.

As a matter of fact, the geometry of General Relativity is the least physical and the least self-consistent among all non-Euclidean geometries:

http://www.friesian.com/curved-1.htm


With exception of the pseudo-Riemannian geometry of Einstein's theory, the co-ordinate axes of other non-Euclidean geometries are of the spatial type. And this dimensional homogeneity gives those geometries some degree of consistency as closed systems of axioms and symbols.


The geometry of Einstein's General Relativity, by comparison, is composed of three spatial co-ordinates and one temporal co-ordinate. And this makes it inconsistent right for the beginning.


Within this inhomogeneous system of mixed co-ordinates, Einsteinians switch frequently and silently between the treatment of the time co-ordinate as a real time co-ordinate in the conventional sense and the treatment of the time co-ordinate as the fourth spatial co-ordinate just like the other three spatial co-ordinates as it suits their purposes.


In short, the pseudo-Riemannian geometry of General Relativity is incoherent and inconsistent and pseudo and pseudo out and out and completely unsuitable for describing anything inside the Universe or outside the Universe.

AAF: The geometry of Einstein's General Relativity, by comparison, is composed of three spatial co-ordinates and one temporal co-ordinate. And this makes it inconsistent right for the beginning.

Within this inhomogeneous system of mixed co-ordinates, Einsteinians switch frequently and silently between the treatment of the time co-ordinate as a real time co-ordinate in the conventional sense and the treatment of the time co-ordinate as the fourth spatial co-ordinate just like the other three spatial co-ordinates as it suits their purposes.

cinci: Time is never treated as a coordiante equivalent to spatial coordinates. The metric can be written as follows

(ds)^2 = (dx)^2 + (dy)^2 + (dz)^2 - (cdt)^2.

Notice the minus sign...it means you're wrong. Nobody is "switching" anything unless it's you switching from one inane argument against relativity to another.

Cincirob: "AAF at it again”.



AAF: And Cincirob is under it and below it and beneath it all over again!



Cincirob: “Nobody is "switching" anything unless it's you switching from one inane argument against relativity to another”.



AAF: They are doing it all the time! The geometry of Einstein's General Relativity is composed of three spatial co-ordinates and one temporal co-ordinate. And this makes it inconsistent right from the beginning. Within this inhomogeneous system of mixed co-ordinates, Einsteinians switch frequently and silently between the treatment of the time co-ordinate as a real time co-ordinate in the conventional sense and the treatment of the time co-ordinate as the fourth spatial co-ordinate just like the other three spatial co-ordinates as it suits their purposes.



Cincirob: “Time is never treated as a coordinate equivalent to spatial coordinates. The metric can be written as follows (ds)^2 = (dx)^2 + (dy)^2 + (dz)^2 - (cdt)^2. Notice the minus sign...it means you're wrong. Nobody is "switching" anything unless it's you switching from one inane argument against relativity to another”.



AAF: Don't be stubborn & wrong-headed! This equation is the Metric Equation of Einstein's Special Relativity, where the space and time co-ordinates are supposed to be Euclidean. But even here, the incoherence and the mixing up of different types of co-ordinates are very obvious. You believe wrongly the minus sign can make the difference. It doesn't; it says only that whenever the space co-ordinates point upwards, the time co-ordinate points downwards; and when they point to the right, it points to the left; and so on. Accordingly, your weak and 'inane' defensive argument does not and cannot help Relativity:

http://www.answers.com/topic/spacetime

[AAF]: "This equation is the Metric Equation of Einstein's Special Relativity, where the space and time co-ordinates are supposed to be Euclidean."

No, ignoramus. In special relativity the space is Minkowski. So is the metric.
Ans so are the coordinates. Obviously you don't know the difference.

AAF: This equation is the Metric Equation of Einstein's Special Relativity, where the space and time co-ordinates are supposed to be Euclidean.


Anticrank: "No, ignoramus. In special relativity the space is Minkowski. So is the metric. Ans so are the coordinates. Obviously you don't know the difference”.



AAF: So according to your 'cranky and very 'dumb' comment above, Einstein was ignoramus; I like that!

In his 1916 paper, Einstein wrote:


"In a space which is free of gravitational fields we introduce a Galilean system of reference K (x, y, z, t), and also a system of co-ordinates K' (x', y', z', t') in uniform rotation relatively to K. Let the origins of both systems, as well as their axes of Z, permanently coincide. We shall show that for a space-time measurement in the system K' the above definition of the physical meaning of lengths and times cannot be maintained. For reasons of symmetry it is clear that a circle around the origin in the X, Y plane of K may at the same time be regarded as a circle in the X', Y' plane of K'. We suppose that the circumference and diameter of this circle have been measured with a unit measure infinitely small compared with the radius, and that we have the quotient of the two results. If this experiment were performed with a measuring-rod at rest relatively to the Galilean system K, the quotient would be [ð]. With a measuring-rod at rest relatively to K', the quotient would be greater than [ð]. This is readily understood if we envisage the whole process of measuring from the "stationary" system K, and take into consideration that the measuring-rod applied to the periphery undergoes a Lorentzian contraction, while the one applied along the radius does not. Hence Euclidean geometry does not apply to K'. The notion of co-ordinates defined above, which presupposes the validity of Euclidean geometry, therefore breaks down in relation to the system K'. So, too, we are unable to introduce a time corresponding to physical requirements in K', indicated by clocks at rest relatively to K'. To convince ourselves of this impossibility, let us imagine two clocks of identical constitution placed, one at the origin of co-ordinates, and the other at the circumference of the circle, and both envisaged from the "stationary" system K. By a familiar result of the special theory of relativity, the clock at the circumference -- judged from K -- goes more slowly than the other, because the former is in motion and the latter at rest. An observer at the common origin of co-ordinates, capable of observing the clock at the circumference by means of light, would therefore see it lagging behind the clock beside him. As he will not make up his mind to let the velocity of light along the path in question depend explicitly on the time, he will interpret his observations as showing that the clock at the circumference "really" goes more slowly than the clock at the origin. So he will be obliged to define time in such a way that the rate of a clock depends upon where the clock may be. We therefore reach this result: -- In the general theory of relativity, space and time cannot be defined in such a way that differences of the spatial co-ordinates can be directly measured by the unit measuring-rod, or differences in the time co-ordinate by a standard clock".

Imbecile, Einstein is talking about a Galilean System of Reference (as in Frame of Reference).
Besides, the 1916 paper you are citing is about General relativity, NOT special relativity. Your incorrect post was about the space of Special relativity.
I just explained to you that in SR, the spacetime is Minkowski, the metric is Minkowski and the coordinates are also Minkowski, you dumbass.
How does an imbecile like you get everything wrong is wondrous.

Cincirob: “AAF at it again”.



AAF: And Cincirob is under it one more time!



Cincirob: “Nobody is "switching" anything unless it's you switching from one inane argument against relativity to another”.



AAF: The geometry of Einstein's General Relativity is composed of three spatial co-ordinates and one temporal co-ordinate. And this makes it inconsistent right from the beginning. Within this inhomogeneous system of mixed co-ordinates, Einsteinians switch frequently and silently between the treatment of the time co-ordinate as a real time co-ordinate in the conventional sense and the treatment of the time co-ordinate as the fourth spatial co-ordinate just like the other three spatial co-ordinates as it suits their purposes.



Cincirob: “Time is never treated as a coordinate equivalent to spatial coordinates. The metric can be written as follows (ds)^2 = (dx)^2 + (dy)^2 + (dz)^2 - (cdt)^2. Notice the minus sign...it means you're wrong. Nobody is "switching" anything unless it's you switching from one inane argument against relativity to another”.



AAF: Don't be stubborn & wrong-headed! This equation is the Metric Equation of Einstein's Special Relativity, where the space and time co-ordinates are supposed to be Euclidean. But even here, the incoherence and the mixing up of different types of co-ordinates are very obvious. You believe wrongly the minus sign can make the difference. It doesn't; it says only that whenever the space co-ordinates point upwards, the time co-ordinate points downwards; and when they point to the right, it points to the left; and so on. Accordingly, your weak and 'inane' defensive argument does not and cannot help Relativity:

http://www.answers.com/topic/spacetime



Anticrank: “No, ignoramus. In special relativity the space is Minkowski. So is the metric. Ans so are the coordinates. Obviously you don't know the difference”.



AAF: So according to your cranky & dumb' comment above, Einstein was ignoramus; I like that!

In his 1916 paper, Einstein wrote:

"In a space which is free of gravitational fields we introduce a Galilean system of reference K (x, y, z, t), and also a system of co-ordinates K' (x', y', z', t') in uniform rotation relatively to K. Let the origins of both systems, as well as their axes of Z, permanently coincide. We shall show that for a space-time measurement in the system K' the above definition of the physical meaning of lengths and times cannot be maintained. For reasons of symmetry it is clear that a circle around the origin in the X, Y plane of K may at the same time be regarded as a circle in the X', Y' plane of K'. We suppose that the circumference and diameter of this circle have been measured with a unit measure infinitely small compared with the radius, and that we have the quotient of the two results. If this experiment were performed with a measuring-rod at rest relatively to the Galilean system K, the quotient would be [π]. With a measuring-rod at rest relatively to K', the quotient would be greater than [π]. This is readily understood if we envisage the whole process of measuring from the "stationary" system K, and take into consideration that the measuring-rod applied to the periphery undergoes a Lorentzian contraction, while the one applied along the radius does not. Hence Euclidean geometry does not apply to K'. The notion of co-ordinates defined above, which presupposes the validity of Euclidean geometry, therefore breaks down in relation to the system K'. So, too, we are unable to introduce a time corresponding to physical requirements in K', indicated by clocks at rest relatively to K'. To convince ourselves of this impossibility, let us imagine two clocks of identical constitution placed, one at the origin of co-ordinates, and the other at the circumference of the circle, and both envisaged from the "stationary" system K. By a familiar result of the special theory of relativity, the clock at the circumference -- judged from K -- goes more slowly than the other, because the former is in motion and the latter at rest. An observer at the common origin of co-ordinates, capable of observing the clock at the circumference by means of light, would therefore see it lagging behind the clock beside him. As he will not make up his mind to let the velocity of light along the path in question depend explicitly on the time, he will interpret his observations as showing that the clock at the circumference "really" goes more slowly than the clock at the origin. So he will be obliged to define time in such a way that the rate of a clock depends upon where the clock may be. We therefore reach this result: -- In the general theory of relativity, space and time cannot be defined in such a way that differences of the spatial co-ordinates can be directly measured by the unit measuring-rod, or differences in the time co-ordinate by a standard clock".



Anticrank: “Imbecile, Einstein is talking about a Galilean System of Reference (as in Frame of Reference). Besides, the 1916 paper you are citing is about General relativity, NOT special relativity. Your incorrect post was about the space of Special relativity. I just explained to you that in SR, the spacetime is Minkowski, the metric is Minkowski and the coordinates are also Minkowski, you dumbass. How does an imbecile like you get everything wrong is wondrous”.



AAF: You 'idiot'; you gambled all your savings away in one week and got your moronic self stranded in Las Vegas! The space-time continuum of Special Relativity is flat and Euclidean according to Einstein himself. Read very carefully the following passage by Einstein:

IN classical mechanics, as well as in the special theory of relativity, the co-ordinates of space and time have a direct physical meaning. To say that a point-event has the X₁ co-ordinate x₁ means that the projection of the point-event on the axis of X¹, determined by rigid rods and in accordance with the rules of Euclidean geometry, is obtained by measuring off a given rod (the unit of length) x₁ times from the origin of co-ordinates along the axis of X₁. To say that a point-event has the X₄ co-ordinate x₄=t, means that a standard clock, made to measure time in a definite unit period, and which is stationary relatively to the system of co-ordinates and practically coincident in space with the point-event, will have measured off x₄>=t periods at the occurrence of the event. This view of space and time has always been in the minds of physicists, even if, as a rule, they have been unconscious of it. This is clear from the part which these concepts play in physical measurements; it must also have underlain the reader's reflexions on the preceding paragraph for him to connect any meaning with what he there read. But we shall now show that we must put it aside and replace it by a more general view, in order to be able to carry through the postulate of general relativity, if the special theory of relativity applies to the special case of the absence of a gravitational field".



Cincirob: “Sure it sounds fishy to you because you don't have a clue about how real physics is done. It's done openly and shared freely across international borders. There aren't any cults protecting Einstein or anybody else. It's time for you and Pentcho to grow up”.



AAF: It doesn't just sound fishy; it's outright fishy! Cincirob has never shown any interest in the Quantum mechanics or its fundamental particles. So what is the real reason behind leaving his beloved Cincinnati for three days and paying his way and the hotel in Chicago? To attend some boring lectures at Fermilab? http://ed.fnal.gov/
No; Cincirob does not make trips for an inane and silly reason like that; or does he?

You're, probably, just saying that because the pseudo-Riemannian geometry of general relativity is a tough subject to learn; let alone to criticize!


As I pointed out before, the three spatial co-ordinates give the geometry of general relativity all the realistic characteristics and ease of picturing and comprehension of the Euclidean geometry. At the same time, time as the fourth co-ordinate gives it the generality and versatility of higher geometries.


And so far from rendering it incoherent and inconsistent, the mixed co-ordinates allows general relativity to have the best of both worlds: the Euclidean world and the non-Euclidean world.

This great theory of Einstein has passed so many tests including this most recent one:

"A system like this, with two very massive objects very close to each other, is precisely the kind of extreme 'cosmic laboratory' needed to test Einstein's prediction," said Victoria Kaspi, leader of McGill University's Pulsar Group.

And Einstein’s greatest scientific theory, general relativity, has passed its latest test with flying colours.

The finding has come as a great relief to most scientists who are happy with the status quo, though is tinged with the disappointment of a few theorists who want to see Einstein fail, which may offer a glimpse of the next "theory of everything."

General relativity is a theory of gravity that overturned the ideas of Sir Isaac Newton and, when his radical new idea was first backed after World War 1 by a British expedition, propelled Einstein to international fame so that he became as well known as Charlie Chaplin.

When Einstein himself first glimpsed the truth, which he unveiled as a fully fledged theory in 1915, he said: "Something snapped inside me. The feeling was so extreme. I couldn’t work for days. I was beside myself. In all my life, I never felt such joy."

Scientists are of two minds about experiments to test such theories: it is great to confirm that general relativity works but could be even better if it is shown to fail sometimes, since that points towards new theories. But, in a study published today by an international team in the journal Science, observations of unique dead star system show that Einstein still rules the cosmos.

(1) http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2008/07/03/scieinstein103.xml

(2) http://www.universetoday.com/2008/07/03/theory-of-relativity-passes-another-test/

Re: Stanley 16, On the Hypotheses which lie at the Bases of Geometry July 24 2008, 5:02 PM

As I pointed out before, the three spatial co-ordinates give the geometry of general relativity all the realistic characteristics and ease of picturing and comprehension of the Euclidean geometry. At the same time, time as the fourth co-ordinate gives it the generality and versatility of higher geometries.

And so far from rendering it incoherent and inconsistent, the mixed co-ordinates allows general relativity to have the best of both worlds: the Euclidean world and the non-Euclidean world.

Thanks for the link Stanley, a very interesting read. I do think it would have been a bit more professional of them to at least quote the passage from GR where Einstein made that prediction, it could very well be that Einstein was relying on Newtonian mechanics for the effects on those gravitational bodies. Again, thanks for the link.

bob s

Bob;

I haven't read their Science report yet; but I assume this new experiment is a repetition of the same experiment for which Hulse & Taylor were rewarded the Nobel Prize in physics in 1993:

http://nobelprize.org/nobel_prizes/physics/laureates/1993/press.html

Re: Stanley 16, On the Hypotheses which lie at the Bases of Geometry July 25 2008, 12:59 AM

I haven't read their Science report yet; but I assume this new experiment is a repetition of the same experiment for which Hulse & Taylor were rewarded the Nobel Prize in physics in 1993:

Actually Stanley, there were two different Pulsar systems; Hulse & Taylor was PSR 1913 + 16 and the latest is PSR J0737-3039A/B. But what I would like to read is where in Einstein’s GR he made the twin pulsar prediction and I thought that since you are so well versed in GR you could direct me to the passage. You see, the problem I have (among others) is that GR is 1915 yet pulsars were not discovered till 1967 so what they are saying (at least to me) is that Einstein predicted something that was not even known to exist in 1915.

bob s

bob s: Actually Stanley, there were two different Pulsar systems; Hulse & Taylor was PSR 1913 + 16 and the latest is PSR J0737-3039A/B. But what I would like to read is where in Einstein’s GR he made the twin pulsar prediction and I thought that since you are so well versed in GR you could direct me to the passage. You see, the problem I have (among others) is that GR is 1915 yet pulsars were not discovered till 1967 so what they are saying (at least to me) is that Einstein predicted something that was not even known to exist in 1915.

cinci: I don't think they say that Einstein knew about or calculated anything about pulsars. Inthe article cited I find this sentences:

"This change was presumed to occur because the system is emitting energy in the form of gravitational waves in accordance with what Einstein in 1916 predicted should happen to masses moving relatively to each other." In fact he first rejected the idea of black holes as being too bizarre. I don't know if he changed his mind later.

So I think they're just saying he predicted the effect. He may have done it to estimate the effect of these waves on planets in the sloar system to see if they should all be spiraling into the Sun. That would be a check on the reality of his theory. We know for instance that the precession of the planet Mercur's orbit was calculated using relativity (but perhaps not by Albert himself). So there were astronumical calculatins being done relating org\biting bodies and relativity.

Re: Cincirob, On the Hypotheses which lie at the Bases of Geometry July 25 2008, 4:48 PM

So I think they're just saying he predicted the effect. He may have done it to estimate the effect of these waves on planets in the sloar system to see if they should all be spiraling into the Sun. That would be a check on the reality of his theory. We know for instance that the precession of the planet Mercur's orbit was calculated using relativity (but perhaps not by Albert himself). So there were astronumical calculatins being done relating org\biting bodies and relativity.

Thank you Cincirob, I know “what” they (they, being the authors of the two articles linked by Stanley) are saying “Einstein predicted the effect” but “they” did not cite their source. I assume (which is not always the best thing to do) that the prediction is from General Relativity however, my question to Stanley was ‘where’ can I read what Einstein said and how he made the prediction. Stanley 16, has shown remarkable insight of GR and I was hoping he could point out the proper passages. I can, and have, read GR but it would be somewhat easier, and avoid any misunderstanding, if I could focus on the proper section in which the prediction is to be found, if in fact it is to be found in GR; Einstein has written many papers and follow-ups to his Relativity(s).

I too reject Black Holes, as are presently modeled, because, among other reasons, gravity can not collapse into itself (explode...possible! Implode...can’t happen!). GR may predict the capture of light but to do so would invalidate SR which would then invalidate GR.

bob s

Bob s.: I too reject Black Holes, as are presently modeled, because, among other reasons, gravity can not collapse into itself (explode...possible! Implode...can’t happen!).

cinci: I've never heard this description of a black hole.
******************************

Bob s. GR may predict the capture of light but to do so would invalidate SR which would then invalidate GR.

cinci: I don't think "capturing" quite describes it. There is a region outside the event horizon where light can orbit the black hole. A photon moving away from a black hole loses energy s it overcomes the gravity so that it becomes redshifted. The effect gets mor pronuounced when the phton begins its journey closer to the event horizon. At the horizon, time stands still and photons cannot be emitted or looked at another way, would have to have infinfite energy to be emitted.

As far as invalidating SR goes, SR isn't valid in the presence of a gravitatinal field. It is predicated on no gravity. It turns out the low level of gravity in the vicinity of the Earth causes very little departure from the predictions of SR.
****************************

Re: Cicirob, On the Hypotheses which lie at the Bases of Geometry July 26 2008, 12:35 AM

Bob s.: I too reject Black Holes, as are presently modeled, because, among other reasons, gravity can not collapse into itself (explode...possible! Implode...can’t happen!).

cinci: I've never heard this description of a black hole.
******************************

Collapse and implode are synonymous; to explode would be the antonym of either.

Bob s. GR may predict the capture of light but to do so would invalidate SR which would then invalidate GR.

cinci: I don't think "capturing" quite describes it. There is a region outside the event horizon where light can orbit the black hole. A photon moving away from a black hole loses energy s it overcomes the gravity so that it becomes redshifted. The effect gets mor pronuounced when the phton begins its journey closer to the event horizon. At the horizon, time stands still and photons cannot be emitted or looked at another way, would have to have infinfite energy to be emitted.

Light can only be omitted at the event horizon because that is where the event happens.

Light can orbit a Black Hole! Wow...I didn’t see that coming. According to Relativity an object can not attain the speed of light because to do so would require infinite energy; it must follow then that if light is already at that speed then it (light) already has infinite energy; Relatively speaking of course. And yes, "capture" describes it quite well.

Cinci: As far as invalidating SR goes, SR isn't valid in the presence of a gravitatinal field. It is predicated on no gravity. It turns out the low level of gravity in the vicinity of the Earth causes very little departure from the predictions of SR.

No, SR is not predicated on “no gravity”, SR is predicated on the speed of light. However, General Relativity is predicated on Special Relativity hence the title Relativity: The Special and General Theory. And furthermore, if SR is not valid in a gravitational field then a clock at the equator running slower than a clock at the pole is a pointless experiment...Right! And if it is not pointless then SR is valid in a gravitational field...Right!

bob s

When it comes to testing Einstein's theories, it's always the same old story!


Some upstarts in physics come up with some experiment or observation to verify one of Einstein's predictions. Their result is hailed as a triumph and vindication of Einstein and his theories. After a decade or so, their result turns out to be wrong. And so on ...

This current observation on the binary pulsars is no different. And most certainly, it will turn out to be flawed and way wrong as well.


Take, for example, the fabled gravitational redshift of General Relativity.
At first, the Relativists solemnly thought it's verified and vindicated by the sun.
As it turns out, the surface of the sun is in turmoil and the minute gravitational redshift of Einstein, if any, is completely masked by and cannot be separated from the ordinary Doppler effect of atoms in turbulence and random motion:

http://www.greatdreams.com/solar/sun.htm


Einsteinians, however, moved on to the white dwarfs in pursue of their holy grail of gravitational redshift. And they thought they found it there. But it turns out their observation is a mirage and those dwarfs are too tiny and dim and faraway to be useful in this regard:

http://imagine.gsfc.nasa.gov/docs/science/know_l1/dwarfs.html


But Einsteinians didn't give up and moved on to search for their elusive gravitational redshift in the O stars. And you bet; they were wrong again; and it turns out that those stars are so hot and too faraway to be useful for this purpose:

http://cfa-www.harvard.edu/~pberlind/atlas/htmls/ostars.html


More recently, however, Einsteinians have been hooked on pulsars as a means of proving their 'messiah' was right:

http://esciencenews.com/sources/physorg/2008/07/03/einstein.was.right.unique.stellar.system.provides.laboratory.testing.relativity


The main problem, here, is that pulsars are too mysterious and of uncertain nature to do them any good.

What are the pulsars? All the possibilities, in this regard, are still wide open; and they range from being radio beacons by extraterrestrial civilizations: http://www.etheric.com/LaVioletteBooks/Book-Pulsars.html
to simply being kinematic mirages caused by the variable speed of light.


And among all these scenarios for the pulsars, the Relativistic scenario of them as extremely dense dead stars is the least plausible and the least scientific. And so using the unknown to test the unknown can never work for the Einsteinians and the non-Einsteinians.


It follows, therefore, that this 'old man of the sea' is absolutely right:


The three consequences stemming from Einstein's theory of gravitation, that are usually brought forward as supporting it, are also not impressive. The movement of the perihelion of Mercury was known before and can be explained in various ways (Whittaker 1953). The 'bending of light' round the Sun had been suggested before, and the much advertised confirmation in the eclipse of 1919 involved assuming Einstein's law of 'bending' to obtain the 'scale constants', with the help of which the results were derived which were supposed to prove it. The deflections of stars that moved transversely or in the opposite direction to that predicted were omitted. The mean deviation and its direction varied from plate to plate during the eclipse, suggesting refraction in a turbulent diffuse 'atmosphere'. Nevertheless a mean value was obtained "in exact accord with the requirements of the Einstein theory" (Lick Observatory Bulletin 1922, No. 346). Later attempts have given different values. This must be one of the most extraordinary self-deceptions in the whole history of science (see Poor 1930). The gravitational red shift of light now appears to be confirmed, but this follows from Mach's hypothesis. [fn. Einstein and others call it Mach's principle, but it is not a principle—it is a physical hypothesis.] that inertial forces are due to interaction with the distant bodies of the Universe [fn. Newton considered this possibility (see Brown 1943)], and does not require 'relativity' as the author has shown (Brown 1955). We see, then, that the general theory is based physically on a fallacy (principle of equivalence) and on a principle that is barren (covariance) and which is also, mathematically, almost intractable. Genuine physicists may well agree with Fock that it is not a major contribution to physics.


http://homepage.ntlworld.com/academ/whatswrongwithrelativity.html

Re: On the Hypotheses which lie at the Bases of Geometry July 26 2008, 2:02 AM

Re: Cincirob, On the Hypotheses which lie at the Bases of Geometry July 26 2008, 12:35 AM

Bob s.: I too reject Black Holes, as are presently modeled, because, among other reasons, gravity can not collapse into itself (explode...possible! Implode...can’t happen!).

cinci: I've never heard this description of a black hole.

Bob s: Collapse and implode are synonymous; to explode would be the antonym of either.

cinci: Yes, you're correct about what the words mean, but I've never heard anyone say that it was gravity that implodes. Material implodes, but the gravity is still there.
**************************************

Bob s. GR may predict the capture of light but to do so would invalidate SR which would then invalidate GR.

cinci: I don't think "capturing" quite describes it. There is a region outside the event horizon where light can orbit the black hole. A photon moving away from a black hole loses energy s it overcomes the gravity so that it becomes redshifted. The effect gets more pronuounced when the photon begins its journey closer to the event horizon. At the horizon, time stands still and photons cannot be emitted or looked at another way, would have to have infinfite energy to be emitted.

Bob s: Light can only be omitted at the event horizon because that is where the event happens.

cinci: Actually that is where events cease to happen. Time stands still.
********************************

Bob s: Light can orbit a Black Hole! Wow...I didn’t see that coming. According to Relativity an object can not attain the speed of light because to do so would require infinite energy; it must follow then that if light is already at that speed then it (light) already has infinite energy; Relatively speaking of course. And yes, "capture" describes it quite well.

cinci: We know the path of light can be bent by gravity and sufficient gravity will make it go in a circle so perhaps you should have seen it coming. And capture does describe this pretty well but it wasn't what you were talking about earlier. The energy of light is a function of photons is a function only of their frequency and nothing make them infinite.
**************************

Cinci: As far as invalidating SR goes, SR isn't valid in the presence of a gravitatinal field. It is predicated on no gravity. It turns out the low level of gravity in the vicinity of the Earth causes very little departure from the predictions of SR.

Bob s: No, SR is not predicated on “no gravity”, SR is predicated on the speed of light. However, General Relativity is predicated on Special Relativity hence the title Relativity: The Special and General Theory. And furthermore, if SR is not valid in a gravitational field then a clock at the equator running slower than a clock at the pole is a pointless experiment...Right! And if it is not pointless then SR is valid in a gravitational field...Right!

cinci: SR is valid for inertial frames and inertial frames are defined as having constant velocity, no rotation, and no gravity. GR is an extension of SR to include gravity. The gravitational field at the pole is the same as the gravitational field at the equator. The difference is that the clock at the equator is traveling at about 1000 miles per hour relative to the one at the pole. That differential velocity causes the equatorial clock to run slower. As I noted, the gravitaitonal field of the earth can be ignored for many SR experiments.
*******************************************

Re: On the Hypotheses which lie at the Bases of Geometry July 26 2008, 4:41 PM

AAF: When it comes to testing Einstein's theories, it's always the same old story!

cinci: I agree. And the story is they relativity always comes through with flying colors. Thanks for reminding everyone.
***********************

AAF: Some upstarts in physics come up with some experiment or observation to verify one of Einstein's predictions. Their result is hailed as a triumph and vindication of Einstein and his theories. After a decade or so, their result turns out to be wrong. And so on ...

cinci: This is your persistent dream I supose...it certainly isn't reality.
******************************

AAF: This current observation on the binary pulsars is no different. And most certainly, it will turn out to be flawed and way wrong as well.

cinci: Is this from the crystal ball in your secret Early Einstein Shrine? You now think you can predict the future as well as rewrite the past.
****************************

AAF: Take, for example, the fabled gravitational redshift of General Relativity.
At first, the Relativists solemnly thought it's verified and vindicated by the sun.
As it turns out, the surface of the sun is in turmoil and the minute gravitational redshift of Einstein, if any, is completely masked by and cannot be separated from the ordinary Doppler effect of atoms in turbulence and random motion:

http://www.greatdreams.com/solar/sun.htm

cinci: You posted a site entitled "WHY ARE WE SO AFRAID OF THE SUN?" whose author is "Red Ravager" and as far as I can see it doesn't say anything about realtivity at all. What is "fabled" is that you ever had any eveidence against relativity.
********************************

AAF: Einsteinians, however, moved on to the white dwarfs in pursue of their holy grail of gravitational redshift. And they thought they found it there. But it turns out their observation is a mirage and those dwarfs are too tiny and dim and faraway to be useful in this regard:

http://imagine.gsfc.nasa.gov/docs/science/know_l1/dwarfs.html

cinci: Here you have just posted a site describing white dwarfs and it says nothing about any relativistic experiment. And the article shows they are "so far away" by having a picture of one.
****************************

AAF: But Einsteinians didn't give up and moved on to search for their elusive gravitational redshift in the O stars. And you bet; they were wrong again; and it turns out that those stars are so hot and too faraway to be useful for this purpose:

http://cfa-www.harvard.edu/~pberlind/atlas/htmls/ostars.html

cinci: Another score for AAF. These stars are "so far away" that the article sited gives a detailed graph of their spectrum. Nice try......for you.
******************************

AAF: More recently, however, Einsteinians have been hooked on pulsars as a means of proving their 'messiah' was right:

http://esciencenews.com/sources/physorg/2008/07/03/einstein.was.right.unique.stellar.system.provides.laboratory.testing.relativity


The main problem, here, is that pulsars are too mysterious and of uncertain nature to do them any good.

cinci: Right on target here AAF. The title of this one is "Einstein was right: Unique stellar system provides 'laboratory' for testing relativity". What's happening in the universe you inhabit? Up is down? Left is right? Are you sure you arne't Alice from Lewis Carrol's "Through the Looking Glass"?
*******************************

AAF: What are the pulsars? All the possibilities, in this regard, are still wide open; and they range from being radio beacons by extraterrestrial civilizations: http://www.etheric.com/LaVioletteBooks/Book-Pulsars.html
to simply being kinematic mirages caused by the variable speed of light.

cinci: typical! First you say we can't use them to demonstrate relativity and now you admit you don't even know what they are.
*************************

AAF: And among all these scenarios for the pulsars, the Relativistic scenario of them as extremely dense dead stars is the least plausible and the least scientific. And so using the unknown to test the unknown can never work for the Einsteinians and the non-Einsteinians.

It follows, therefore, that this 'old man of the sea' is absolutely right:

The three consequences stemming from Einstein's theory of gravitation, that are usually brought forward as supporting it, are also not impressive. The movement of the perihelion of Mercury was known before and can be explained in various ways (Whittaker 1953). The 'bending of light' round the Sun had been suggested before, and the much advertised confirmation in the eclipse of 1919 involved assuming Einstein's law of 'bending' to obtain the 'scale constants', with the help of which the results were derived which were supposed to prove it. The deflections of stars that moved transversely or in the opposite direction to that predicted were omitted. The mean deviation and its direction varied from plate to plate during the eclipse, suggesting refraction in a turbulent diffuse 'atmosphere'. Nevertheless a mean value was obtained "in exact accord with the requirements of the Einstein theory" (Lick Observatory Bulletin 1922, No. 346). Later attempts have given different values. This must be one of the most extraordinary self-deceptions in the whole history of science (see Poor 1930). The gravitational red shift of light now appears to be confirmed, but this follows from Mach's hypothesis. [fn. Einstein and others call it Mach's principle, but it is not a principle—it is a physical hypothesis.] that inertial forces are due to interaction with the distant bodies of the Universe [fn. Newton considered this possibility (see Brown 1943)], and does not require 'relativity' as the author has shown (Brown 1955). We see, then, that the general theory is based physically on a fallacy (principle of equivalence) and on a principle that is barren (covariance) and which is also, mathematically, almost intractable. Genuine physicists may well agree with Fock that it is not a major contribution to physics.


http://homepage.ntlworld.com/academ/whatswrongwithrelativity.html

cinci: One more time, http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html.

Just start working your way through all of these. My guess is taht you'll end up saying they're all bogus because we can't set clocks, make mirrors, build lasers, and a myriad other nonsense objections to established science. I'd think by now youwould have learned something by accident but I guess not.
*****************

Re: bobs, On the Hypotheses which lie at the Bases of Geometry July 25 2008, 8:32 PM

In re: Cincirob, On the Hypotheses which lie at the Bases of Geometry July 25 2008, 4:48 PM

Cincirob: So I think they're just saying he predicted the effect. He may have done it to estimate the effect of these waves on planets in the sloar system to see if they should all be spiraling into the Sun....

bob s: Thank you Cincirob, I know “what” they (they, being the authors of the two articles linked by Stanley) are saying “Einstein predicted the effect” but “they” did not cite their source. I assume (which is not always the best thing to do) that the prediction is from General Relativity [H]owever, my question to Stanley was ‘where’ can I read what Einstein said and how he made the prediction. Stanley 16, has shown remarkable insight of GR and I was hoping he could point out the proper passages. I can, and have, read GR but it would be somewhat easier, and avoid any misunderstanding, if I could focus on the proper section in which the prediction is to be found, if in fact it is to be found in GR; Einstein has written many papers and follow-ups to his Relativity(s).

Cincirob, and/or Stanley 16, can you, or can you not, tell me where and when Einstein mad the prediction in question. If you can I would appreciate it and if you can not I will understand.

bob s

From

There are principally two distinct methods whereby gravitational radiation can be estimated in the theories. First, the EIH (Einstein, Infeld, Hoffmann) method (8) consists in solving the equations of motion in a power series in a suitable parameter such as v/c .

AAF: When it comes to testing Einstein's theories, it's always the same old story!
Some upstarts in physics come up with some experiment or observation to verify one of Einstein's predictions. Their result is hailed a triumph and vindication of Einstein and his theories. After a decade or so, their result turns out to be wrong. And so on ... This current observation on the binary pulsars is no different. And most certainly, it will turn out to be flawed and way wrong as well.


Cincirob: “I agree. And the story is they relativity always comes through with flying colors. Thanks for reminding everyone. This is your persistent dream I suppose...it certainly isn't reality. Is this from the crystal ball in your secret Early Einstein Shrine? You now think you can predict the future as well as rewrite the past”.


AAF: The theory of Relativity can never come through with flying colors or non-flying colors, because it's false and flawed at every level; and it has not chance in hell of being true even remotely. Take, for example, the fabled gravitational redshift of General Relativity. At first, the Relativists solemnly thought it's verified and vindicated by the sun. As it turns out, the surface of the sun is turmoil and the minute gravitational redshift of Einstein, if any, is completely masked by and cannot be separated from the ordinary Doppler effect of atoms in turbulence and random motion: http://www.greatdreams.com/solar/sun.htm




Cincirob: “You posted a site entitled "WHY ARE WE SO AFRAID OF THE SUN?" whose author is "Red Ravager" and as far as I can see it doesn't say anything about relativity at all. What is "fabled" is that you ever had any evidence against relativity”.



AAF: That website is intended to show you that the sun surface is turbulent and in turmoil; but as usual, you didn't get it! Anyway, Einsteinians moved on to the white dwarfs in pursue of their holy grail of gravitational redshift. And they thought they found it there. But it turns out their observation is a mirage and those dwarfs are too tiny and dim and faraway to be useful in this regard: http://imagine.gsfc.nasa.gov/docs/science/know_l1/dwarfs.html



Cincirob: “Here you have just posted a site describing white dwarfs and it says nothing about any relativistic experiment. And the article shows they are "so far away" by having a picture of one”.



AAF: This website, too, is intended to show you that white dwarfs are very dim and hard to spot; but you didn't get it as usual! In any case, Einsteinians didn't give up and moved on to search for their elusive gravitational redshift in the O stars. And you bet; they were wrong again; and it turns out that those stars are so hot and too faraway to be useful for this purpose: http://cfa-www.harvard.edu/~pberlind/atlas/htmls/ostars.html



Cincirob: “Another score for AAF. These stars are "so far away" that the article sited gives a detailed graph of their spectrum. Nice try......for you”.



AAF: Also, this website is intended to show you that the O stars are very faraway and very hot; so much so that it's absolutely impossible to sort out Doppler shifts as great as that caused by the galactic motion of the Solar System; let alone Einstein's tiny prediction. More recently, however, Einsteinians have been hooked on pulsars as a means of proving their 'messiah' was right:
http://esciencenews.com/sources/physorg/2008/07/03/einstein.was.right.unique.stellar.system.provides.laboratory.testing.relativity
The main problem, here, is that pulsars are too mysterious and of uncertain nature to do them any good.




Cincirob: “Right on target here AAF. The title of this one is "Einstein was right: Unique stellar system provides 'laboratory' for testing relativity". What's happening in the universe you inhabit? Up is down? Left is right? Are you sure you aren't Alice from Lewis Carrol's "Through the Looking Glass"? typical! First you say we can't use them to demonstrate relativity and now you admit you don't even know what they are. One more time, http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html.
Just start working your way through all of these. My guess is that you'll end up saying they're all bogus because we can't set clocks, make mirrors, build lasers, and a myriad other nonsense objections to established science. I'd think by now you would have learned something by accident but I guess not.”.




AAF: You bet; I'm right on target; this website is intended to show you that Einsteinians have been recently hooked on the pulsars; and this time, you did get it1 Now, what are the pulsars? All the possibilities, in this regard, are still wide open; and they range from being radio beacons by extraterrestrial civilizations: http://www.etheric.com/LaVioletteBooks/Book-Pulsars.html to simply being kinematic mirages caused by the variable speed of light. And among all these scenarios for the pulsars, the Relativistic scenario of them as extremely dense dead stars is the least plausible and the least scientific. And so using the unknown to test the unknown can never work for the Einsteinians and the non-Einsteinians. It follows, therefore, that this 'old man of the sea' is absolutely right:

The three consequences stemming from Einstein's theory of gravitation, that are usually brought forward as supporting it, are also not impressive. The movement of the perihelion of Mercury was known before and can be explained in various ways (Whittaker 1953). The 'bending of light' round the Sun had been suggested before, and the much advertised confirmation in the eclipse of 1919 involved assuming Einstein's law of 'bending' to obtain the 'scale constants', with the help of which the results were derived which were supposed to prove it. The deflections of stars that moved transversely or in the opposite direction to that predicted were omitted. The mean deviation and its direction varied from plate to plate during the eclipse, suggesting refraction in a turbulent diffuse 'atmosphere'. Nevertheless a mean value was obtained "in exact accord with the requirements of the Einstein theory" (Lick Observatory Bulletin 1922, No. 346). Later attempts have given different values. This must be one of the most extraordinary self-deceptions in the whole history of science (see Poor 1930). The gravitational red shift of light now appears to be confirmed, but this follows from Mach's hypothesis. [fn. Einstein and others call it Mach's principle, but it is not a principle—it is a physical hypothesis.] that inertial forces are due to interaction with the distant bodies of the Universe [fn. Newton considered this possibility (see Brown 1943)], and does not require 'relativity' as the author has shown (Brown 1955). We see, then, that the general theory is based physically on a fallacy (principle of equivalence) and on a principle that is barren (covariance) and which is also, mathematically, almost intractable. Genuine physicists may well agree with Fock that it is not a major contribution to physics.
http://homepage.ntlworld.com/academ/whatswrongwithrelativity.html

cinci: At http://www.davis-inc.com/relativity/index.shtml I found the quote below.

"There are principally two distinct methods whereby gravitational radiation can be estimated in the theories. First, the EIH (Einstein, Infeld, Hoffmann) method (8) consists in solving the equations of motion in a power series in a suitable parameter such as v/c . "

The (8) refers to this footnote: A. Einstein, L. Infeld, and B. Hoffmann, Ann. Math., 39, 65 (1938). I searched on this footnote and got a lot of references to this article. This may be what you're looking for but you need access to Ann. Math.

I also found this quote: (at http://www.ligo.caltech.edu/LIGO_web/about/factsheet.html )
"Albert Einstein predicted the existence of these gravitational waves in 1916 in his general theory of relativity, but only since the 1990s has technology become powerful enough to permit detecting them and harnessing them for science. Although they have not yet been detected directly, the influence of gravitational waves on a binary pulsar (two neutron stars orbiting each other) has been measured accurately and is in good agreement with the predictions. Scientists therefore have great confidence that gravitational waves exist."

So maybe there's a version in his 1916 paper. Here is a site that claims to have teh paper but it won't open for me. Maybe you'll have better luck: http://www.alberteinstein.info/gallery/gtext3.html

Re: Cincirob, On the Hypotheses which lie at the Bases of Geometry July 26 2008, 6:59 PM

Bob s: I too reject Black Holes, as are presently modeled, because, among other reasons, gravity can not collapse into itself (explode...possible! Implode...can’t happen!).

cinci: I've never heard this description of a black hole.

Bob s: Collapse and implode are synonymous; to explode would be the antonym of either.

cinci: Yes, you're correct about what the words mean, but I've never heard anyone say that it was gravity that implodes. Material implodes, but the gravity is still there.
**************************************

Yes! And you could have been more clear as to what it was you did not understand. The phenomena is referred to as “gravitational collapse”. I went the semantics route whit some Bozo some time back who claimed he did not understand what I meant by “void”. We can argue physics, we can argue grammar or we can just argue, your choice! (By ‘argue’ I mean a discussion of opposing view points)


Bob s. GR may predict the capture of light but to do so would invalidate SR which would then invalidate GR.

cinci: I don't think "capturing" quite describes it. There is a region outside the event horizon where light can orbit the black hole. A photon moving away from a black hole loses energy s it overcomes the gravity so that it becomes redshifted. The effect gets more pronuounced when the photon begins its journey closer to the event horizon. At the horizon, time stands still and photons cannot be emitted or looked at another way, would have to have infinfite energy to be emitted.

Bob s: Light can only be omitted at the event horizon because that is where the event happens.

cinci: Actually that is where events cease to happen. Time stands still.

Bob s: Light can orbit a Black Hole! Wow...I didn’t see that coming. According to Relativity an object can not attain the speed of light because to do so would require infinite energy; it must follow then that if light is already at that speed then it (light) already has infinite energy; Relatively speaking of course. And yes, "capture" describes it quite well.

cinci: We know the path of light can be bent by gravity and sufficient gravity will make it go in a circle so perhaps you should have seen it coming. And capture does describe this pretty well but it wasn't what you were talking about earlier. The energy of light is a function of photons is a function only of their frequency and nothing make them infinite.
**************************

Time ‘may’ stand still going in; light on the other hand ‘should’ stop coming out and the subject on point was ‘light’ and ‘the orbiting of same’ not ‘time’. You said light orbits a Black Hole; an orbit can only happen ‘around’, or outside of an orbited body, and light is not suppose to be able to escape a Black Hole (the orbited body in question) so it ‘may’ follow then; “Wow!...I didn’t see that coming” which means your statement took me by surprise. I don’t know of any scientific expression for surprise except “Eureka” so I will amend my statement to read; Eureka!!! Cincirob has revealed that light orbits a Black Body.


Cinci: As far as invalidating SR goes, SR isn't valid in the presence of a gravitatinal field. It is predicated on no gravity. It turns out the low level of gravity in the vicinity of the Earth causes very little departure from the predictions of SR.

That is a self contradictory statement Cincirob, SR either has ‘some’ validity in a gravitational field or it has ‘no’ validity in a gravitational field.


Bob s: No, SR is not predicated on “no gravity”, SR is predicated on the speed of light. However, General Relativity is predicated on Special Relativity hence the title Relativity: The Special and General Theory. And furthermore, if SR is not valid in a gravitational field then a clock at the equator running slower than a clock at the pole is a pointless experiment...Right! And if it is not pointless then SR is valid in a gravitational field...Right!

cinci: SR is valid for inertial frames and inertial frames are defined as having constant velocity, no rotation, and no gravity. GR is an extension of SR to include gravity. The gravitational field at the pole is the same as the gravitational field at the equator. The difference is that the clock at the equator is traveling at about 1000 miles per hour relative to the one at the pole. That differential velocity causes the equatorial clock to run slower. As I noted, the gravitaitonal field of the earth can be ignored for many SR experiments.
*******************************************

First I would suggest you look up the meaning of “predicated” and then look up the meaning of “inertial frames”, an inertial frame does not forbid gravity; SR does not forbid gravity, it (SR) just does not use gravity so therefor; SR is not predicated on the use, or non use, of gravity it (SR) is predicated on the consistency of the speed of light and the Laws of physics in an inertial frame. If you will read the postulates of Special Relativity it holds for ‘all’ Laws of physics, of which, gravity is one. If Einstein had wanted to omit gravity he should have said (some) Laws of physics.

I am often amused that non-relativists understand SR an GR better than relativists. We, the non-relativists, try to argue what Einstein ‘did’ say as opposed to relativists who just want to argue or play the semantics game.

bob s