# The Final Piece Of The Puzzle!

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### #1 Doctordick

Doctordick

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Posted 16 April 2010 - 03:32 PM

Well Anssi, in spite of the fact that I will be essentially out of contact for the next couple of months, following your recommendation, I decided to post this. Let's see what happens. If you have a lot of trouble following the Euler-Lagrange stuff, you might ask for help from either Erasmas00, Qfwfq, Pyrotex or perhaps modest.

I start with an attempt to communicate the issue of why gravity was thought perhaps to be a consequence of relativistic transformations.

Relativity is the mathematical transformation between two different geometric coordinate systems. Back in Newton's day, such transformations were quite straight forward as Euclidean coordinate systems were assumed applicable to reality. If the origin of a Euclidean coordinate system (coordinate system “b”) was at point (x0,y0,z0) in the original coordinate system (coordinate system “a”) then any point in coordinate system “a”, say point (xa,ya,za) was simply represented by the point (xa-x0,ya-y0,za-z0) in coordinate system “b”. This transformation was exactly the same even if the point being referred to as (x0,y0,z0) was moving in any arbitrary manner.

I would like to point out that, as opposed to Einstein's space time continuum, my paradigm results in a representation via a Euclidean coordinate system. The required transformation between any two different Euclidean coordinate systems are exactly what was introduced above. The difference between my system and Euclid's original system is that tau axis. Momentum quantization along that tau axis (mass) introduces some very subtle consequences when it comes to physical measurements such that the simple transformation above does not yield the measurements as taken by a person at rest in the moving system: i.e., special relativity is a necessary part of such a transformation in order to compensate for the effects of momentum quantization along the tau axis. Note that the transformation required by an observer in the original coordinate system to transform physical phenomena from one to the other has nothing to do with measurements made by the other observer; special relativity has to do with the apparent form of the transformed laws. Essentially, the “principal of relativity” as introduced by Galileo was the statement that the laws of physics were mathematically the same in any two coordinate systems so long as the only movement of one coordinate system relative to the other was at a constant velocity: i.e., as seen by the original rest observer, there should be no change in the laws of physics when transformed to another frame moving at a constant velocity. This is not quite the same as Einstein's paradigm; he sees the the laws themselves transforming, quite a different thing.

The form of the laws of physics was exactly the issue behind Newton's concept of an “inertial frame”. Newton's fundamental law, “things at rest tend to stay at rest and things in motion tend to stay in motion” is actually a special case of the more general (and simpler) inductive conclusion, “if something has been changing in a specific way up to now, it will most probably continue to change in the same manner in the future”. The value of my representation of that statement is that it actually has nothing to do with reality and everything to do with one's expectations. Newton further defined “a force” as the thing which changed that state and came up with the relationship $\vec{F}=m\vec{a}$ as a definition of how that rate of change changed. Acceleration is, after all, a change in the rate of change.

The reason I brought the above up is that I wanted to make it clear that Newton's $\vec{F}=m\vec{a}$ has to do with how things change and is not at all limited to things moving through space so to speak. The equation applies to geometric coordinate systems for the simple reason that coordinate systems are mental constructs created to display collections of information; as such, they are particularly valuable when it comes to displaying extremely large amounts of information. “A picture is worth a thousand words” is a rather extreme understatement of that fact. Essentially, Newton defined an “inertial frame” to be a coordinate system where $\vec{F}=m\vec{a}$ is a valid expression: i.e., the statement is “true” because “force” is actually defined by that very expression, so long as you are using an “inertial” frame of reference. You have to be very careful here because definitions such as that can tend to lead to circular reasoning if not handled properly.

That idea together with differential calculus created an extremely powerful mathematical method of predicting the dynamic behavior of objects (an object being any suitable stable defined collection of information). Since acceleration is the time derivative of velocity (where velocity is the time derivative of position in that “inertial frame”) force can be thought of as the time derivative of momentum (momentum being given by $m\vec{v}$). If m is a constant, the expression $\vec{F}=\frac{d}{dt}(m \vec{v})$ is identical to $\vec{F}=m\vec{a}$ and if m is allowed to change, that fact simply allows a rather simple mechanism to handle cases where identical forces cause different accelerations. As a consequence, m ends up being little more than a parameter allowing a more versatile definition of force.

What made Newton's expression so powerful was the fact that, when it came to what people commonly call “physical objects” that more versatile definition of force was quite limited. That parameter “m” (which we call mass) could be assigned to a physical object and essentially remained constant forever. As I said these equations are defined to be true in an inertial frame (which was essentially the same collection of Galilean frames asserted in his “principal of relativity”). Furthermore, the Euclidean transformations brought up in the first paragraph above made it quite easy to transform Newton's mathematical solutions to any frame moving in any arbitrary manner desired. Thus it is that Newton seemed to have solved the entire field of dynamic behavior of physical objects.

That brings up the interesting question, “what does the dynamic behavior look if one is using a non-inertial frame”. Clearly, a non-inertial frame is a frame which is accelerating relative to an inertial frame. It should be clear to the reader that any object at rest in any inertial frame (which then, by definition, has no forces accelerating it) will appear to be accelerating if its position is represented by coordinates in a non-inertial frame representation. It should also be quite clear that it is not really accelerating at all, it is only the reference frame which is actually changing (accelerating). The apparent motion of any force free physical object who's position is being represented via the non-inertial frame will be an exact mirror image of that frames acceleration.

That fact brings up a very important issue; if one has two objects of different mass at rest in an inertial frame, their acceleration, as seen in the accelerating frame, will be exactly the same (that fact follows directly from the fact that the acceleration is nothing more than the mirror image of the frames acceleration). From the perspective of Newton's definition of force, $\vec{F}=m\vec{a}$, the apparent force on such objects (when seen from the perspective of an accelerating frame) must be exactly proportional to the mass of the object of interest. When I was a student, such “apparent” forces (those which seemed to exist only because one was working in a non-inertial frame), were called “pseudo forces”; a term, according to Qfwfq, which is apparently no longer in common use. The most common examples of such forces are centrifugal and Coriolis forces.

From the above (the fact that all “pseudo forces” are proportional to the mass of the object being accelerated by that force), the physics community began to consider any case where the force was proportional to the mass of the object to be a possible example of a “pseudo force”: i.e., such behavior suggested the reference frame being used was not a proper inertial frame. Since the force of gravity appeared to be absolutely and always directly proportional to the mass of the object being accelerated, quite a number of theoreticians concluded that gravity should be explainable as a fictional force due to the researcher's failure to use the proper inertial frame of reference. What many of them tried to discover was, what was the “proper inertial frame” one should be using: i.e., what sort of geometry would make gravity a fictitious force. This interest lead to much work in the field of mathematical transformations between strange and unusual geometric frames of reference (which turned out to be an interesting field all on its own).

No such proper inertial frame of reference was ever found and, sometime in the middle of the eighteenth century, Pierre Louis Maupertuis proved, mathematically, that no such frame of reference could possibly exist. His proof pretty well stopped any efforts to continue the search; however, the work of generating transformations between strange and unusual geometric frames had already evolved into a field of its own and much valuable work stands quite independent of any interest in gravitational effects.

Astonishing methods of solving a great many very difficult dynamic mechanical problems can be traced directly to the early interest in such transformations. Hamiltonian mechanics was originally an extension of Lagrangian mechanics which was essentially a completely general mechanism (based upon Maupertuis' concept of action) for transforming Newtonian mechanics to an absolutely general reference frame represented by any set of abstract coordinates (q1,q2, ... qn). Hamilton extended Lagrange's work into what has come to be called Hamiltonian mechanics. And finally, analysis of Hamiltonian mechanics can be shown to be the underlying impetus which initially pushed physics towards modern quantum mechanics.

But that is all essentially beside the point here as our interest is in gravitational forces and the real impact of coordinate transformations upon that issue. It was exactly that issue which made Einstein's Relativity into an incontestable truth of the twentieth century. Einstein's general relativity yielded gravity as a consequence of geometric effects. Not exactly as a consequence of a geometric transformation (as were centrifugal and Coriolis forces) but rather through the idea that there was only one valid frame of reference under which correct physics could be generated (actually, in many ways, quite analogous to Newton's “inertial” frame). According to Adler, Bazin and Schiffer, (in their text book, Introduction to General Relativity, McGraw-Hill Co., New York, 1965, p. 7.) Einstein proved that "a reduction of gravitational theory to geodesic motion in an appropriate geometry could be carried out only in the four-dimensional space-time continuum of [Einstein's] relativity theory". It was, in fact, this astonishing achievement which made Einstein's approach to relativity so overwhelming a part of accepted modern theory.

The question then arises, how is it that Einstein's theory appears to circumvent Maupertuis' proof? The answer revolves around the principal of “least action” he invented as a means of calculating paths consistent with Newtonian physics (essentially minimizing the energy with respect to the path). Maupertuis showed that the problem was a consequence of the fact that, when it came to gravitational paths, different velocities led to different paths: i.e., two different objects behavior could not be reduced to geodesic motion in the same reference frame, something which must be true in the proper inertial frame. The inclusion of time in Einstein's space-time continuum allows this critical variation to be achieved; however, it turns out that this is exactly that same issue which creates the critical problems when it comes to “quantizing the gravitational field”. Thus it is that there are very real problems bringing quantum mechanics into Einstein's General Relativity theory. To date all attempts, that I am aware of, have resulted in failure.

Compare this to my presentation which is totally consistent with quantum mechanics from the very beginning. Beyond that, in my presentation, mass is defined to be momentum in the tau direction of a four dimensional Euclidean geometry. As a consequence, that hypothetical (see as unexaminable) tau dimension can be simply scaled to make the velocity of every elemental entity through that four dimensional geometry look exactly the same. That final fact totally circumvents Maupertuis' proof. It seems certainly reasonable to once again look at the consequences of general transformations and perhaps find that “non-inertial” geometry which yields gravity as a pseudo force. So let us proceed to examine some aspects of that circumstance.

To begin with, my fundamental equation does indeed require a specific frame of reference: that frame of reference being at rest with respect to the entire universe. In that particular frame, (remember, that frame is a standard Euclidean frame) any object (any collection of fundamental elements forming a stable pattern) which can be seen as essentially not interacting with the rest of the universe (i.e., those interactions may be ignored and we are looking at a “free” object) will obey Newton's laws of motion in the absence of a force (it will not accelerate in any way). That is, the only forces which appear in such a circumstance are those pseudo forces we want to examine in this analysis: i.e., apparent forces which are entirely due to the fact that our coordinate system is not at rest with respect to the universe.

True, we have created a situation which obviously circumvents Maupertuis' proof but, since energy is now not a function of velocity, we have also made the original formation of his principal of action into an unusable procedure (his relationship related velocities and we now have no relationship to minimize); however, there is another attack (actually the same attack but somewhat subtly different). If gravity is to be a mere pseudo force, we can use the fact that our model must reproduce the exactly the same classical pseudo forces produced by Newton mechanics. This is true as these forces are no more than a direct consequence of expressing the path in a non-inertial frame or, in my case, a reference frame not at rest with respect to the universe.

It is interesting to look at centrifugal force as a well understood Newtonian pseudo force. From the perspective of an observer at the center of the rotation, a string exerting a force equal to the centrifugal force will appear to maintain the object under the influence of that pseudo force at rest: i.e., a rock at the end of a string swinging in a circle will appear to be at rest in a reference frame rotating with that rock. We can then see the object as a test probe into the force field describing that specific pseudo force. Since my total interest is in explaining gravity as a pseudo force, I want to examine this force as seen from the perspective of being m times the negative gradient of a gravitational potential (which is the typical way of defining a gravitational potential). In this case $\vec{F}=-m\vec{\nabla}\Phi$ where $\Phi(\vec{x})$ is the gravitational potential. Any freshman physics text will provide an excellent derivation of centrifugal force. The result is the quite simple form, $\;\vec{F}=mr\omega^2\hat{r}\;$ where omega is the angular velocity and $\hat{r}$ is a unit vector in the radial direction. It follows that the analogous gravitational representation implies that the required $\Phi(\vec{x})$ (which, by the way, must by symmetry be a radial function) must obey the relationship

$-\frac{\partial}{\partial r}\Phi(r)=r\omega^2$.

This fact directly implies that $-\Phi=\frac{1}{2}(r\omega)^2=\frac{1}{2}|\vec{v}|^2$ or, multiplying by $\frac{2}{c^2}$, one can conclude that

$\frac{2}{c^2}\Phi(r)=-\left(\frac{|\vec{v}|}{c}\right)^2$.

In other words, the gravitational potential (as seen in the frame where the object being observed appears to be at rest) seems to be directly related to the actual velocity as seen from the correct frame (the frame at rest with the universe). This result is very interesting. As the observed object is actually moving in the correct frame, we should expect a clock (or any temporal physical process moving with that object) to proceed in accordance with special relativity. This implies that the correct relativistic transformation of the instantaneous time differentials should be given by

$dt'=dt\sqrt{1-\left(\frac{|\vec{v}|}{c}\right)^2}\equiv dt\sqrt{1+\frac{2\Phi}{c^2}}$

which happens to be exactly the standard gravitational red shift. This implies that any geometry which yields gravity as a pseudo force must also yield the standard gravitational red shift; or, alternately, gravitational red shift is not really a valid test of Einstein's general theory of relativity. This really isn't very enlightening as the gravitational red shift can be shown to be required by conservation of energy, but it does nonetheless imply that the above analysis is valid.

More importantly, the above suggests an attack towards determining the geometry which will yield gravity as a pseudo force in our four dimensional Euclidean geometry. I have already shown how static structures appear as three dimensional objects in this geometry so let us examine what is commonly called “a gravitational well”. The gravitational well consists of a vertical hole where there is a gravitational field in the vertical direction. If an experimenter in a gravitational well sets up a clock via a light pulse traveling back and forth between two horizontally displaced mirrors, since we can establish horizontal measure (since we are currently using a Euclidean geometry, simple vertical lines carry those measures to different heights in the hole) and his clock must run slow, we must see the apparent velocity of light to be

$c'=c\sqrt{1+\frac{2\Phi}{c^2}}$

(at least for small gravitational effects). The gravitational red shift (which we are using here) is an instantaneous differential effect whereas the expression above concerns the horizontal path of the light in the clock. To see that problem, consider the same experiment done in an accelerating elevator as seen from a rest observer (at rest with the universe; still ignoring everything except the objects explicitly under examination). From the rest observers perspective, the direction of the light cannot be parallel to the floor of the elevator; if it were it would miss the mirror on the other side of the elevator. It must be already have a component of its velocity in the direction the elevator is accelerating.

Secondly, the faces of the mirrors cannot be perpendicular to the floor of the elevator; it they were, the light would miss the original mirror on the return (the component of the elevator vertical velocity has changed, the vertical component of the light has not). It must now have an additional component of its velocity in the direction the elevator is accelerating. As a result, both mirrors must lean slightly towards the outside such as to assure that the reflected light always picks up that required change in velocity to keep up with the elevator. A little thought about the situation should be enough to prove to the reader that, at the instant immediately prior to reflection (as seen by the rest observer), the path of the light must be parallel to the floor of the elevator and immediately after reflection the path must be towards the position the other mirror will be in when the light gets to the other side.

So, with reference to the floor of the elevator, the light will initially rise as it will be going up faster than the elevator. The acceleration of the elevator will eventually bring this apparent rise rate to zero and then let the elevator catch up so that the light can reflect off the opposite mirror. Thus it is that the observer in the elevator (who will regard the floor as level) will see the light following a curved line. The pseudo force on the light seems to cause the light to follow a curved path. We can again note that curvature of the light in a gravitational field is not a test of Einstein's theory, any theory which yields gravity as a pseudo force must also require light to curve in a gravitational field.

Thus it is that the clock we have proposed will run even slower than what was predicted a few paragraphs ago. The error is clearly a function of the physical size of the clock. This effect can be eliminated by defining our clock's size to be small enough to make the error negligible. I point this out so that we can discuss further ramifications of those instantaneous relativistic effects.

Since, in my four dimensional geometry, it has already been shown that clocks actually measure tau, the above also implies any lower object will appear to proceed in the tau direction at a slower rate proportional to exactly that same factor: i.e., the fundamental velocity of any object in my geometry will appear to be slower in a lower gravitational potential. This immediately suggests that we should be using Fermat's principle to establish the metric which will yield the proper geodesics: i.e., we should consider the phenomena of refraction.

As an aside, it is quite clear that the proper adjustment to our geometry which will yield the standard concept of gravity as a pseudo force is a change in the presumed measure of that geometry: i.e., instead of seeing the speed of light as slower in a gravitational field we could just as well see the speed as unchanged and the distances as increased. After all, once time is defined, distances are reckoned via the speed of light. Though that satisfies the original goal expressed above, the idea of refraction (the speed of light being slowed in a gravitational field) is a much simpler expression of the solution. It is certainly most convenient method of finding the proper geodesics. In fact, there is a very simple view of the situation which will yield exactly that result.

With regard to the issue of refraction, my fundamental equation is a wave equation with Dirac delta function interactions. Clearly, in the absence of interactions, the probability wave representing an event will proceed at a fixed velocity. Any specific delta function interaction can be seen as an impact changing the direction and energy of that probability wave. What is important here is the fact that interaction will depend upon the distance between the two elements connected by that delta function interaction: i.e., the hypothetical element (which must be a boson) must carry the momentum and energy being transfered and the transfer must be consistent with the Heisenberg uncertainty principal: i.e., the uncertainty in momentum is directly related to the uncertainty in position. This implies that the further apart the interacting fermions are, the less momentum transfered must be (see virtual particle exchange).

Any physical object (any structure stable enough to be thought of as an object) must have internal forces maintaining that structure. Any interaction with another distant object must be via the virtual particle exchange I just commented about. Thus it is that one would expect the fundamental element of that physical object interacting via that delta function would have its momentum altered, not the whole object; however, that alteration would create a discrepancy in the structure of the object under discussion. Since that object must have internal forces maintaining its structure, it is to be expected that those internal interactions (which are also mediated by delta function exchange forces) will bring the trajectory of that interacting fundamental element essentially back to its original path (at least on average).

Thus it is that the path of that fundamental element can be seen as crooked as compared to its path in the absence of that distant object. Of issue is the fact that, if the influence of the distant object is ignored, the influenced element will inexplicitly appear to be proceeding at a slightly slower velocity than it would if the distant object didn't exist. What is important here is that this effect decreases as the distance from the distant object increases. That means that the net effect is to yield a very slight change in the speed of the elements which make up that object as one moves across the object. The net effect of such an interaction is to refract the wave function of the object under examination.

If the distant object and the object under observation are not moving with respect to one another (they are moving parallel to one another in the tau direction), the net effect of that refraction is to curve the paths of the two objects towards one another: i.e., there will be an apparent attraction between them. It is also evident that, since the mass of the source object (the source of these bosons external to the object of interest) is proportional to the total momentum of that object, one should expect the apparent density (as seen from the object of interest) should be proportional to its mass: i.e., one should expect the exchange forces to be proportional to mass.

Clearly the interaction just discussed arises from differential effects in the basic interactions thus it will amount to a force considerably less than the underlying force standing behind that differential effect. Thus it is that the two forces I have already discussed (the forces due to massless boson exchange: shown to yield electromagnetic effects and the forces due to massive boson exchange: shown to yield fundamental nuclear forces) will end up being split into four forces. Differential effects will yield a correction to both basic forces which correspond quite well with the forces observed in nature. The differential effect on massless boson exchange yields what appears to be a very weak gravitational force (weak when compared to the underlying electromagnetic effects) and the differential effect on massive boson exchange yields what appears to be a very weak nuclear force (weak compared to the underlying nuclear force). What is interesting is that the “weak nuclear force” can be shown to violate parity symmetry whereas the “weak electrical force” (gravity) does not. This is a direct consequence of the fact that the nuclear exchange bosons are massive.

But let us get back to gravitational effects. It is my position that gravity is a direct consequence of the fact that the presence of an object with momentum in the tau direction yields a secondary differential effect which causes the speed of elements through my four dimensional Euclidean space to slow: i.e., refraction of the wave solution to my fundamental equation occurs. In order to check my proposition, I need to be able to work out the geodesic paths implied by such a notion. To begin with, my assertion is that the four dimensional velocity of all elements can be seen as slowed in the presence of a gravitational potential. Thus it is that the “index of refraction” of a gravitational field is given by the instantaneous value of $n=\frac{c}{c'}$ evaluated a specific point in that field (where c is the velocity of light far removed from any massive influence). Geodesic paths can be obtained by minimizing nds where “ds” is the distance differential along that geodesic path in my four dimensional Euclidean geometry.

In order to accomplish that result, we need to use what is called “the calculus of variations”. We want the variation of the path integral along the geodesic to vanish: i.e.,

$\delta \int^{P_2} _{P_1}nds = 0\quad\quad where \quad\quad n=\frac{1}{\sqrt{1+\frac{2}{c^2}\Phi(\vec{x})}}$.

Thankfully this is a problem already solved by the physics community. The vanishing of the path integral occurs when the function being integrated satisfies the Euler-Lagrange equation.

In order to simplify the problem, I would like to turn to a spherically symmetric case. Essentially a point source with a very large momentum in the tau direction and negligible momentum in the other three dimensions. This is in order to look at geodesic paths in the vicinity of a single very massive object where the other properties of the object can be ignored. In such a case, I can write $\Phi(\vec{x})$ in a very simple form consistent with standard notation:

$\Phi(\vec{x})=-\frac{\kappa M}{r}$

where $\kappa$ is the proper proportionality constant to yield the correct potential generated by the mass M. This expression can be further simplified by changing to cylindrical coordinates (omit z as by symmetry we need only consider motion in the x-y plane). Thus it is that the differential of the path along which our metric is to be minimized is given by $ds=\sqrt{(d\tau)^2+(dr)^2+r^2(d\theta)^2}$. It follows that the metric to be minimized to yield gravity consistent with a pseudo force is $dl=nds$ which can be written

$dl={\left[1-\frac{2\kappa M}{c^2r}\right]^{-\frac{1}{2}}}\left[(d\tau)^2+(dr)^2+r^2(d\theta)^2\right]^{\frac{1}{2}}$

Using the standard Euler-Lagrange notation, the path integral over which the variation is to vanish (“J” in equation #1) is given by

$J =\int f(t,y,\dot{y})dt=\int^{P_2}_{P_1}\frac{1}{\sqrt{1-\frac{2\kappa M}{c^2r}}}\left[(\dot{tau})^2+(\dot{r})^2+r^2(\dot{\theta})^2\right]^{\frac{1}{2}}dt$

Since “t” in my reference frame is actually a path length measure (essentially a reference as to where one is on the referenced path) I have changed the “ds” into “dt” thus converting the original expression given for ds, $\left[(d\tau)^2+(dr)^2+r^2(d\theta)^2\right]^{\frac{1}{2}}$, into $\left[(\dot{\tau})^2+(\dot{r})^2+r^2(\dot{\theta})^2\right]^{\frac{1}{2}}dt$. Following the standard Euler-Lagrange attack, if the expression

$f(t,y,\dot{y})=\frac{1}{\sqrt{1-\frac{2\kappa M}{c^2r}}}\left[(\dot{\tau})^2+(\dot{r})^2+r^2(\dot{\theta})^2\right]^{\frac{1}{2}}$

satisfies the Euler-Lagrange equation, the variation of the integral over the implied path will vanish. In this case we have three independent variables to deal with (note that “y”, in this case, stands for the variable of interest) which leads to three independent differential equations. However, we have one additional constraint which simplifies the problem considerably: $(\dot{\tau})^2+(\dot{r})^2+r^2(\dot{\theta})^2=c^2$. The partials of f with respect to tau and theta vanish leading to the fact that the first integrals of the Euler-Lagrange equation for those variables are trivial. Substituting c for $\left[(\dot{\tau})^2+(\dot{r})^2+r^2(\dot{\theta})^2\right]^{\frac{1}{2}}$, one has the following two first integrals:

$\int \frac{d}{dt}\left(\frac{\partial}{\partial \dot{\tau}}\left\{\left[ \frac{1}{1-\frac{2\kappa M}{c^2r}}\right]^{\frac{1}{2}}\sqrt{(\dot{\tau})^2+(\dot{r})^2+r^2(\dot{\theta})^2}\right\}\right)dt = \left[ \frac{1}{1-\frac{2\kappa M}{c^2r}}\right]^{\frac{1}{2}}\frac{\dot{\tau}}{c}=\;$
a constant $=\;\frac{1}{cl}$

and

$\int \frac{d}{dt}\left(\frac{\partial}{\partial \dot{\theta}}\left\{\left[ \frac{1}{1-\frac{2\kappa M}{c^2r}}\right]^{\frac{1}{2}}\sqrt{(\dot{\tau})^2+(\dot{r})^2+r^2(\dot{\theta})^2}\right\}\right)dt = \left[ \frac{1}{1-\frac{2\kappa M}{c^2r}}\right]^{\frac{1}{2}}r^2\dot{\theta}\frac{1}{c}=$
a constant $=\;\frac{h}{cl}$.

I have chosen to represent the two constants as I have, in terms of the constants l and h, because this notation will bring my solution into exactly the same form as the standard Schwarzschild solution to the Einsteinian field equations (with one very important difference).

From this solution we can presume that

$\dot{\tau}=\frac{1}{l}\sqrt{1-\frac{2\kappa M}{c^2r}}\quad\quad and \quad\quad \dot{\theta}=\frac{h}{r^2l}\sqrt{1-\frac{2\kappa M}{c^2r}}$

Using $(\dot{\tau})^2+(\dot{r})^2+r^2(\dot{\theta})^2=c^2$, we can write

$\frac{1}{l^2}\left(1-\frac{2\kappa M}{c^2r}\right)+(\dot{r})^2+\frac{h^2}{r^2l^2}\left(1-\frac{2\kappa M}{c^2r}\right)=c^2.$

This differential equation (relating r and t) can be transformed to the actual differential equation of interest (that would be r versus $\theta$) through the following well known replacement

Since $\quad r'=\frac{dr}{d\theta}=\frac{\dot{r}}{\dot{\theta}}, \quad \dot{r}=\dot{\theta}r'=\frac{h}{r^2l}r'\sqrt{1-\frac{2\kappa M}{c^2 r}},$

and the equation for the geodesic can be directly written as

$\frac{1}{l^2}\left(1-\frac{2\kappa M}{c^2 r}\right)+\frac{h^2}{r^4l^2}(r')^2\left(1-\frac{2\kappa M}{c^2 r}\right)+\frac{h^2}{r^2l^2}\left(1-\frac{2\kappa M}{c^2 r}\right)= c^2$

which can be rearranged to yield:

$\left(1-\frac{2\kappa M}{c^2 r}\right)=c^2l^2 -\frac{h^2}{r^4}(r')^2-\frac{h^2}{r^2}\left(1-\frac{2\kappa M}{c^2r}\right)+\left[\frac{h^2}{r^4}(r')^2\left(\frac{2\kappa M}{c^2r}\right)\right],$

which, except for the final term in square brackets, is precisely the Schwarzschild solution to Einstein's field equations for a spherically symmetric case (see Adler, Bazin and Schiffer, Introduction to General Relativity, McGraw-Hill Co., New York, 1965, p. 180.).

I have certainly shown gravitational forces can be reduced to geodesics in my geometry by virtue of the fact that I have just done so. The fact that my result is not exactly the same as that obtained from Einstein's theory is not too troubling. It is possible that I have made a subtle deductive error in the above as none of my work has ever been checked by anyone competent to follow my reasoning; however, in the absence of an error, my result must be correct as it is deduced and not theorized as Einstein's solution is.

In order to comprehend exactly what the impact of that extra term is, I would like to compare the Schwarzschild solution to to the classical Newtonian result. Note that, if one differentiates the classical elliptical solution to the Newtonian problem, $\frac{1}{r}=\frac{1}{r_0}(1-\epsilon \;cos (\theta))$, and chooses the appropriate constants; the Newtonian solution can be written:

$\left(1-\frac{2\kappa M}{c^2 r}\right)= c^2l^2-\frac{h^2}{r^4}(r')^2-\frac{h^2}{r^2}.$

It may then be seen that the Schwarzschild solution amounts to a small adjustment to the energy contribution of the angular momentum term of Newton's solution (the most important consequence being the experimentally verified precession of the orbit of Mercury).

$-\frac{h^2}{r^2}\quad\Rightarrow\quad -\frac{h^2}{r^2}\left(1-\frac{2\kappa M}{c^2r} \right).$

In the same vein, my "error" (if indeed it is an error) amounts to an equally small adjustment to the energy contribution of the radial momentum term. It should be noted that both Einstein's change to Newton's solution and my change to Einstein's solution are not only small but they also both contain an additional factor of one over r relative to their respective base terms. Whereas Einsteins theory makes no changes whatsoever in the radial term of Newton's equation,

$-\frac{h^2}{r^4}(r')^2\quad\Rightarrow\quad -\frac{h^2}{r^4}(r')^2,$

my solution makes a very small change to that term:

$-\frac{h^2}{r^4}(r')^2\quad\Rightarrow\quad -\frac{h^2}{r^4}(r')^2\left(1-\frac{2\kappa M}{c^2r} \right).$

Since the energy attributable to the radial momentum of Mercury is very small compared to the energy attributable to its orbital angular momentum, the perhelic shift of Mercury is certainly not a test of the validity of Einstein's theory as, within the accuracy of experiment, I obtain exactly the same result. The only test which could possibly remain is the deflection of star light. In that regard, please notice that in the above deduction, I selected my constants l and h so as to reproduce the exact form of Schwarzschild's solution. By doing so I forced my two constants of first integration to be related.

Under normal circumstances, one would simply write the first integrals as equal to an arbitrary constant: i.e., one would ordinarily write,

$\frac{\partial f}{\partial \dot{\tau}}= \left(1-\frac{2\kappa M}{c^2r}\right)^{-\frac{1}{2}}\frac{\dot{\tau}}{c}=\frac{A_1}{c} \quad and \quad \frac{\partial f}{\partial \dot{\theta}}= \left(1-\frac{2\kappa M}{c^2r}\right)^{-\frac{1}{2}}r^2\frac{\dot{\theta}}{c}=\frac{A_2}{c}$

In this case, one would obtain a differential equation for the geodesic of the form

$A^2_1\left(1-\frac{2\kappa M}{c^2 r}\right)=c^2 -\frac{A^2_2}{r^4}(r')^2-\frac{A^2_2}{r^2}\left(1-\frac{2\kappa M}{c^2r}\right)+\left[\frac{A^2_2}{r^4}(r')^2\left(\frac{2\kappa M}{c^2r}\right)\right].$

In this representation, the geodesic for a photon is immediately obtained by setting A1 equal to zero (which corresponds to no initial motion in the tau direction: i.e., the photon has zero rest mass). Again, except for the term in square brackets, the result is exactly the same result Schwarzschild obtains by setting his invariant interval to zero and resolving the problem. Here also, the term in square brackets can be seen as an energy adjustment related to that part of the photons energy which can be seen as due to it's radial motion. Clearly the deflection of star light by the sun does not test the existence of my additional term as, in grazing the sun, the impact of this term is negligible as the radial motion of the photon is only comparable to the angular motion for large r.

With this final result, I have clearly demonstrated that Einstein's assertion of Minkowski space-time is in no way necessary to explain the validity of either the Lorentz transformations or the so called tests of general relativity. I think it is very possible that Einstein would have given me some serious thought had he lived to see what I have done.

after failing to unify the electro and gravity field, Einstein wrote ...

All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken. … I consider it quite possible that physics cannot be based on the field concept, i.e., on continuous structures. In that case, nothing remains of my entire castle in the air, gravitation theory included, [and of] the rest of modern physics. (Albert Einstein, 1954)

I find it interesting that Einstein himself had doubts concerning field theory. In particular with regard to Qfwfq's insistence that the correct way of doing quantum mechanics was to quantize the fields: i.e., he considered field theory to be more fundamental than quantum mechanics whereas my position was quite the reverse. (Qfwfq never responded to that post.)

In addition to the above, there might be some evidence that Einstein's theory is actually wrong. Note that, if my work is correct (and I certainly admit I could be wrong) the difference between my solution and Einstein's solution would be that simple factor multiplying the $(r')^2$ term

$\left(1-\frac{2\kappa M}{c^2r}\right)$.

If you solve the Schwarzschild solution to Einstein's field equations for “dr” and then divide by “dt” you will obtain

$\frac{dr}{dt}= \frac{r^2}{h}\left[c^2l^2-\left(1-\frac{2\kappa M}{c^2 r}\right)\left(1+\frac{h^2}{r^2}\right)\right]^{\frac{1}{2}}\frac {d\theta}{dt}$

Add to this the fact that conservation of angular momentum requires $v_\theta = r\frac{d\theta}{dt}$ = a constant or $\frac{d\theta}{dt}=\frac{C}{r}$ and we have,

$\frac{dr}{dt}= \frac{r}{h}\left[c^2l^2-\left(1-\frac{2\kappa M}{c^2 r}\right)\left(1+\frac{h^2}{r^2}\right)\right]^{\frac{1}{2}}C=F(r).$

If you use exactly the same procedure to solve my equation for $\frac{dr}{dt}\sqrt{1-\frac{2\kappa M}{c^2 r}}$ you will obtain exactly the same result: i.e.,

$\frac{dr}{dt}\sqrt{1-\frac{2\kappa M}{c^2 r}}=F(r),$

where F( r ) is exactly the same function obtained from Schwarzschild's solution. This implies that the radial velocity obtained from my solution multiplied by $\sqrt{1-\frac{2\kappa M}{c^2 r}}$ must be exactly Schwarzschild's solution. That, in turn, implies that the radial velocity for a given radius will be greater in my case than it was in Schwarzchild's solution (or Newton's solution for that matter); however, if the object is far far away, the accurate measurement here is the radial velocity itself, not the exact value of r. The radial velocity is determined via the Doppler effect and, with an accurate clock on board the object, its velocity can be measured quite accurately.

The radius on the other hand would be estimated by solving for the orbital motion of the object (using either Einstein's field theory or Newtonian gravitational theory). Since the velocity is slowing as an object leaves the solar system, if my equation is the correct calculation, Schwarzschild would presume the object was somewhat further away than I would (I would have obtained that same value at a somewhat closer radius). If the object were actually slightly closer to the sun than they thought, its deceleration would be slightly greater. That is apparently what the measurements on that recent satellite leaving the solar system have yielded.

It appears (at least to me at the moment) that the effect of that extra term in my solution is to make the gravitational field appear to be slightly stronger than estimated via Einstein's field theory. If that conclusion is correct, then it could also explain the “dark matter” problem.

My final comment is, once again, that my presentation is not a theory but a purely deductive conclusion from required symmetries and thus stands on much firmer ground than any theory including Einstein's. Of course, I could have made a mistake in my deductions but, if no one ever checks that deduction, how will anyone ever know? Am I really a crackpot? Or have I gone where no one else has tread?

Anssi, if you find any errors, I of course put them there to test you.

Have fun -- Dick
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### #2 freeztar

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Posted 16 April 2010 - 06:51 PM

Well Anssi, in spite of the fact that I will be essentially out of contact for the next couple of months, following your recommendation, I decided to post this. Let's see what happens. If you have a lot of trouble following the Euler-Lagrange stuff, you might ask for help from either Erasmas00, Qfwfq, Pyrotex or perhaps modest.

I start with an attempt to communicate the issue of why gravity was thought perhaps to be a consequence of relativistic transformations.

Relativity is the mathematical transformation between two different geometric coordinate systems. Back in Newton's day, such transformations were quite straight forward as Euclidean coordinate systems were assumed applicable to reality. If the origin of a Euclidean coordinate system (coordinate system “b”) was at point (x0,y0,z0) in the original coordinate system (coordinate system “a”) then any point in coordinate system “a”, say point (xa,ya,za) was simply represented by the point (xa-x0,ya-y0,za-z0) in coordinate system “b”. This transformation was exactly the same even if the point being referred to as (x0,y0,z0) was moving in any arbitrary manner.

Excellent post, DD!

I look forward to the responses from the people you mentioned.

### #3 coldcreation

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Posted 16 April 2010 - 10:22 PM

[...]my presentation is not a theory but a purely deductive conclusion from required symmetries and thus stands on much firmer ground than any theory including Einstein's. Of course, I could have made a mistake in my deductions but, if no one ever checks that deduction, how will anyone ever know? Am I really a crackpot? Or have I gone where no one else has tread?

Well, I wasn't one of the people you mentioned above, but I do have a remark or two to make before responding fully.

How, Doctordick, would you falsify, disprove your purely deductive conclusion? After all, what makes theories, such as general relativity, so powerful is that they are falsifiable, testable, or refutable, i.e., there are logical possibilities that an assertion or conclusion can be shown false by an observation or a physical experiment.

I might be wrong, but it seems you've concocted a deductive conclusion the falsehood of which could be demonstrated by no finite amount of observation.

The beauty of relativity, of course, is not just that is is falsifiable, but that it has passed every test thrown at it (within its macroscopic domain of applicability), except perhaps for the gravitational wave prediction.

What exactly are you offering that the differences or appearances be statistically significant from measurements of events, things, or phenomena observed in the physical world that makes you think your conclusion stands on "much firmer ground than any theory including Einstein's"?

Perhaps I simply fail to see the objective criteria upon which you base your conclusion, and how that would present a definitive falsification of generally accepted universal statements of the kind general relativity has to offer.

It seems to me that even purely deductive conclusions from required symmetries (however probabilistic in nature) must be in principle empirically verifiable in order to be both meaningful and scientific.

What makes your conclusion different from any other simple uncircumscribed existential statement, such as there exists a purple duckbill platypus?

Thanks in advance for your response which should actually assist us (and ultimately you) in determining to what extent such a conclusion might be evaluated.

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### #4 Doctordick

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Posted 16 April 2010 - 11:35 PM

Perhaps I simply fail to see the objective criteria upon which you base your conclusion, and how that would present a definitive falsification of generally accepted universal statements of the kind general relativity has to offer.

The objective criteria? I have the entire experimental consequences of modern physics as objective criteria on which to base my conclusion. Please examine my earlier post to pyrotex.

Have fun -- Dick

### #5 coldcreation

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Posted 17 April 2010 - 12:47 AM

The objective criteria? I have the entire experimental consequences of modern physics as objective criteria on which to base my conclusion. Please examine my earlier post to pyrotex.

Have fun -- Dick

How, Doctordick, would you falsify (disprove) your purely deductive conclusion?

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Posted 17 April 2010 - 09:50 AM

How, Doctordick, would you falsify (disprove) your purely deductive conclusion?

I think you may be looking at it from the wrong direction. It is my opinion that DD offers another interpretation of relationship between space, time, things that exist, and relationship of gravity to all three.
I think he would say, look, when the experimental data collected years ago showed Einstein's General Theory of relativity held to be true to experimental facts, well, that exact same data can be used to show that DD "deductive conclusion" also holds true. It is like getting an answer to the question--what is quantum reality ? Well, what approach do you as a physicist agree with ? All of them, some, one ? (Copenhagen, Undivided Wholeness of Heitler, Many-Worlds of Davis, Two-World-Duplex of Heisenberg).

Also, there is a very important use of language by DD. Please note that he specifically makes the point that his "deductive conclusion" is NOT a scientific THEORY. This is a key statement--it gets to the root of how his mind does science and philosophy ! A theory for a scientist has a very specific meaning and it is arrived at following a very specific method. The "deductive conclusion" of DD does NOT follow the scientific method that leads to a "theory" ! DD method is use of pure reason to arrive at a "deductive conclusion", which, if he is correct in his thinking (??) gives the same logical outcome as a theory derived from scientific method. Logically, it makes no sense to hold DD to falsify anything---in fact---since his use of pure reason "deductive conclusion" approach is not a scientific theory there is nothing to falsify, not as the word is used by Popper.

Thus, imo, there are two ways to question the "deductive conclusion" approach of DD. (1) show that the "deductive conclusion" is derived from use of a false premise(s), using logic; (2) show that the argument he presents about gravity is mathematically incorrect (that is, he adds wrong or incorrectly uses a constant, etc) or is based on false understanding of laws of physics. For example, someone must show how his use of the "tau" concept to derive mass and gravity is is in error.

So, unless I am missing something, what DD is claiming is that his approach (derived using pure logical deduction) reaches the exact same conclusion as say the Feynman's sum-over-history theory of quantum mechanics AND AT THE SAME TIME it reach the same conclusion as Einstein's General Theory of Relativity. That is, his deductive reason approach unites all thinking in physics. And if he is then "correct", then he truly has done something of historic importance.

This is how I see it, and for sure I may be in complete error on my understanding of what DD is (and has been for many years ) claiming.

### #7 coldcreation

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Posted 17 April 2010 - 12:14 PM

Please note that he specifically makes the point that his "deductive conclusion" is NOT a scientific THEORY. This is a key statement--it gets to the root of how his mind does science and philosophy ! [...] The "deductive conclusion" of DD does NOT follow the scientific method that leads to a "theory" ! DD method is use of pure reason to arrive at a "deductive conclusion", which, if he is correct in his thinking (??) gives the same logical outcome as a theory derived from scientific method. Logically, it makes no sense to hold DD to falsify anything---in fact---since his use of pure reason "deductive conclusion" approach is not a scientific theory there is nothing to falsify, not as the word is used by Popper.
.

Oh, but there is something to falsify.

Falsifiability is not only an important concept in science. It is also important within the philosophy of science. Had DD been practicing theology or theosophy the question of falsifiability would obviously not have surfaced (on my behalf).

The fact that DD appears to be practicing science (as observed in the OP, with or without a dash of philosophy) leads me to believe his work should be subject to the same rigorous scrutiny as any scientific theory, (it should be testable) regardless of how he reaches a conclusion. Otherwise DD's exercise would be meaningless.

For example, gravity can and has been seen over the centuries from several different viewpoints: as an attractive force in Euclidean space, as a repulsion from space, as gravitons, as due to the expansion of matter, as a curved spacetime phenomena and any combination of the above. These interpretations of gravity (whatever the operational mechanism) differ dramatically, yet they produce the same observations, or nearly the same.

The question is which is the most accurate representation of gravity?

Simply arriving at the same observations in a representation via a Euclidean coordinate system carries nothing revolutionary in itself. Nor does the introduction of a tau axis (mass) or even a fourth spatial dimension (or 21 dimensions), if that be the case.

Feynman once wrote, “No machinery has ever been invented that “explains” gravity without also predicting some other phenomenon that does not exist.” (Six Easy Pieces 1994 pp. 107-109)

The only way to distinguish between competing views of gravity is empirically. Which brings us right back to falsifiability.

_____________________

DD has a pseudo-gravitational force in a Euclidean space, with a hypothetical (unexaminable) "tau dimension." It also has the requirement that a specific frame of reference be at rest with respect to the entire universe (to be or not to be ignored). That is certainly a question (judging from the OP). But it is not a fact that such a "tau dimension" exists in the real world, in the physical universe, nor that there exists a gods-eye reference frame. Scaling or replacing one mainstream arbitrary parameter, term or constant with a new "tau" dimension seems only to add artificial flavor to the generally accepted view of gravitation (or rather what used to be the generally accepted view: i.e., pre-relativity).

So to differentiate between DD's hypothesis (or "purely deductive conclusion") and what is really transpiring in the universe, or with, say, Einstein's general relativity, DD will have to find a way (at least in principle) to test, falsify or corroborate his idea based on physical evidence. Until then I see little that differs from hand-waving.

Simply stating that a presentation or proposition is "not a theory" should by no means imply that the conclusion arrived at is somehow beyond (or should be exempt from) scrutiny of the scientific method. Certainly philosophy of science is not exempt from that rigor. This is after all the Philosophy of Science section of Hypography.

_____________________

Back to DD. If indeed the effect of that extra term in your solution is to make the gravitational field appear slightly stronger than estimated by Einstein's general postulate of relativity there must be something less mundane than the Pioneer anomaly (something usually associated with conspiracy theories or strange claim fora) that can be tested and ultimately falsified, refuted or accepted. Surely that must be your wish. I doubt you've gone through all this trouble for nothing.

I notice you mentioned the dark matter problem. But I don't see how quantitatively you can account for the so-called missing mass (for galactic rotation curves, galaxy clusters or cosmological redshift observations) when your pseudo-force is only fractionally (or slightly) stronger than estimated by GR. The dark matter component appears too large to be satisfied by your concept.

If you really want to go where no one else has tread it seems only logical to take your conclusion to the next step. Make predictions that can be tested empirically.

Once again Doctordick:
How would you falsify (disprove) your purely deductive conclusion?

Edit:

I have certainly shown gravitational forces can be reduced to geodesics in my geometry by virtue of the fact that I have just done so. The fact that my result is not exactly the same as that obtained from Einstein's theory is not too troubling. It is possible that I have made a subtle deductive error in the above as none of my work has ever been checked by anyone competent to follow my reasoning; however, in the absence of an error, my result must be correct as it is deduced and not theorized as Einstein's solution is.

Have fun -- Dick

The most useful approach is likely to be one that attempts to look for complete corroboration with empirical evidence, as Einstein had done, with broad themes as a foundation—general postulates or principles from which one deduced conclusions. His work fell into two parts: foremost, that of establishing the principles that were to serve as a starting point for the deductions, then drawing conclusions that followed from them.

That was fun.

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Posted 18 April 2010 - 06:12 PM

Feynman once wrote, “No machinery has ever been invented that “explains” gravity without also predicting some other phenomenon that does not exist.” (Six Easy Pieces 1994 pp. 107-109)

Do you think Feynman would include "time" alone as being such a phenomenon that "does not exist" as realted to the explanation ? Seems to me the answer should be yes as I define "exist".

### #9 coldcreation

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Posted 19 April 2010 - 11:27 AM

Do you think Feynman would include "time" alone as being such a phenomenon that "does not exist" as realted to the explanation ?

No.

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### #10 coldcreation

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Posted 19 April 2010 - 11:40 AM

My final comment is, once again, that my presentation is not a theory but a purely deductive conclusion from required symmetries and thus stands on much firmer ground than any theory including Einstein's. Of course, I could have made a mistake in my deductions but, if no one ever checks that deduction, how will anyone ever know? Am I really a crackpot? Or have I gone where no one else has tread?

Several things come to mind. Firstly, Doctordick, I want to congratulate you. It's important for the progress science that theories be put continually to the test, and that when errors are found, or improvements can be made and misinterpretations illuminated, one should not resist the temptation to set things right. For that it is always worth it to review and critique the generally accepted scientific theories. Both your work and your dedication have served a purpose, and will for a very long time be available to specialist and the lay public for further review. However, and secondly, there's an old saying that goes something like:

If you think you've discovered something fundamentally new, you must not read your predecessors.

Indeed, since the inception of Einstein's special and general postulates of relativity there has been a laborious effort (for whatever motivation) to disprove, falsify and/or confirm the contentions inherent in Einstein's work, as you know. Certainly the concept of gravity as a curved spacetime phenomena did not please everyone. After all, there is something remarkably nonintuitive implicit in 'curved' space, let alone curved spacetime. The idea that, perhaps, Einstein had been mistaken about curvature, about gravity (amongst other things), had been prevalent in the literature even before the name Einstein became a household word. In another way, the idea that space both locally and globally is perfectly Euclidean has been with us for an eternity, so it seems. Even now we can find the idea circulating in the corridors of physics departments (and now on the Web) all over the globe. The old Aristole/Galilean dream of a perfect Euclidean world seemed somehow more pure, more intuitive, simpler. I understand.

There are many examples of efforts to thwart the apparently inevitable results of Herr Albert over the years. One of those efforts is encapsulated in the writings of R. d'E. Atkinson (1963). Perhaps, though I didn't see the credit, you are familiar with his work. It seems he tread a half a century ago the same ground upon which you are currently treading.

General Relativity in Euclidean Terms

Abstract
The relativistic equations for the deflexion of light, the motion of a particle, and the red shift of spectral lines, in the neighbourhood of a single stationary mass, are rigorously derived on the basra of a strictly Euclidean space and an independent time. Only two ad hoc assumptions are needed, in addition to two very obvious extensions of the special theory; one of these assumptions is already familiar, but the other, involving the mass of a stationary test particle, is believed to be new. The particle equations are derived from a Lagrangian m the usual way. Expressions for the kinetic and potential energies are also readily obtained. It is shown (by what is believed to be a new argument) that matter with an infinite Young's modulus cannot exist, and the fact that actual measuring rods may therefore be affected by tidal forces, even when they are 'unconstrained', is considered. It is shown that in principle observations in the solar system should be made in a tune system which is not Shat in which the clocks of distant observatories are synchronized at present; the difference is below the present errors of the best time signals, but not very much below. A rigorous expression is derived for the numerical value of the radial co-ordinate r, in terms of quantities directly observable by the crew of a space-ship (of negligible mass) moving in a circular orbit at the appropriate circular velocity. Further progress along these lines will depend on their extension to the two-body problem.

For the life of me, I find nothing that differs fundamentally in the work of Atkinson and what you DD have presented above.

But that's not all. Hans Montanus, too, argued along strikingly similar lines.

Arguments Against the General Theory of Relativity and For a Flat Alternative

Phys. Essays 10, 666 (1997) (14 pages); doi: 10.4006/1.3028746, Received 23 December 1996, Bunuellaan 16, 1325 PL Almere, the Netherlands

In this paper we will offer decisive arguments against the general theory of relativity. We will also offer an alternative model for gravitation; that is, we will construct the appropriate Lagrangian for the description of gravitational dynamics in an absolute Euclidean space-time. This Lagrangian leads to the correct predictions for the gravitational time dilation, the gravitational redshift, the deflection of light, and the precession of the perihelia of planets. In this alternative model for gravitation we do not need the concept of a curved space-time. Our flat, absolute, and Euclidean alternative excludes the possibility of blackholes, Einstein-Rosen bridges, and other exotic consequences of the theory of relativity. ©1997 Physics Essays Publication.

Also for your interest, although dealing primarily with SR, you may find appealing the work of Alexander Gersten (Department of Physics, Ben-Gurion University of the Negev 84105 Beer-Sheva, Israel), if you have not already delved into it.

Euclidean Special Relativity

Abstract
New four coordinates are introduced which are related to the usual space-time coordinates. For these coordinates, the Euclidean four dimensional length squared is equal to the interval squared of the Minkowski space. The Lorentz transformation, for the new coordinates, becomes an SO(4) rotation. New scalars (invariants) are derived.

A second approach to the Lorentz transformation is presented. A mixed space is generated by interchanging the notion of time and proper time in inertial frames. Within this approach the Lorentz transformation is a 4 dimentional rotation in an Euclidean space, leading to new possibilities and applications.

Keywords: Special relativity, Euclidean 4-space-time, mixed space, Lorentz transformation.

(Oct. 27, 2002)

There are others too: I'm sure you are more than familiar with these. Source: General principles and other sources on Euclidean relativity.

• Prof. Jose Almeida, 5-dimensional space-time (website with links to arXiv.org for most articles). Talk at the Moscow conference Number Time Relativity 2004. Talk at the PIRT IX conference Londen 2004.

• Carl Brannen, Papers on Proper Time Geometry and the Geometry of Fermions.

• Dr. Giorgio Fontana, The Four Space-times Model of Reality (arXiv.org, physics/0410054A); Hyperspace for Space Travel, Video of presentation at the STAIF 2007 by Dr. Eric Davis (American Institute of Physics, C.P. 880, pp. 1117-1124); Gravitational Waves in Euclidean Space (Excerpt from AIP Conference Proceedings 969, 1055 (2008)); On the foundations of Gravitation Inertia and Gravitational Waves(Scribd); Towards an Unified Engineering Model for Long (and short?) Range Forces and Wave Propagation.

• Dr. Anthony Crabbe, Alternative conventions and geometry for Special Relativity (Annales de la Fondation Louis de Broglie Vol 29 no 4, 2004); The Limitations of the Minkowski Model of Space-time, talk at the 13th Triennial Conference of the International Society for the Study of Time, (Monterery, CA July 28-Aug 3 2007)

• Dr. Phillips V. Bradford, Alternative ways of looking at physics, A space-time, geometric interpretation of the beta factor in Special Relativity.

• Dr. Witold Nawrot, Is the space-time reality Euclidean?

• Subramaniam Kanagaraj, Euclidean Special Relativity

• Rob van Linden, Dimensions in special relativity theory (Galilean Electrodynamics Vol 18 nr 1, Jan/Feb-2007). Mass particles as bosons in five dimensional Euclidean gravity. Minkowski versus Euclidean 4-vectors. Propulsion without propellant using four-momentum of photons in Euclidean special relativity.

There's something dramatically ironic (rococo even) about bringing back Aristole/Galilean gravitation (in Euclidean 4-space), a trail that had already been pioneered a generation ago, and where the wagon-wheel ruts are still perfectly visible by individuals with a knowledge of the literature. It is addressing a devices of fiction: Tau in this case. For sure, Tau involves irony and is probably self-reflective, metafiction. I'm referring to the effect, also, when a story is interrupted to remind the reader that it is really only a story ("not a theory"), often explored in a philosophical context.

There are many notable attempts to sustain metafiction throughout the history of philosophy, metaphysics (and physics), in which none of the additional terms, arbitrary constants, extra dimensions, or ad hoc parameters are real and exist only within the writer's imagination, where the fictional device comes to life and accompanies the author throughout the story.

It can be seen as a technique that uses the juxtaposition of loaded evocations and empty symbolism to create a theory (or to arrive at purely deductive conclusions) whose roots lie not so much in the lampooning of any one theory (e.g., general relativity) or theorist (e.g., Einstein) so much as in lampooning the 'stupidity' that resides at the core of the propagation of modern physics.

It is clever too that the irony presented in the OP ensures endless reflection and incomprehensibility. Not surprisingly, this tactic is the favorite textual property of those who have favored the deconstruction of Einstein's general relativity theory; almost like Marcel Duchamp painting a Dada mustache on the Mona Lisa.

Sure, the truth matters . But the problem is not really whether DD's idea is true or false, right or wrong, fact or fantasy, valid or invalid. Nor is it particularly important that DD's deductive conclusion is a rhetorical tautology derived from the use of a false premise, or faulty logic (if that be the case). Or that the arguments he presents about gravity are mathematically correct or incorrect (or that he adds a wrong term, or incorrectly uses a constant or fourth spatial dimension) or that it is based on false understanding of the physical laws. It's not even a problem that others had planted the flag first. What is important is that DD believes in what he/she is doing, that he/she enjoys what he/she is writing and is having fun doing it. And if others along the way (Rade, Anssi, myself and others) share his/her passion for philosophy along the way, then so much the better.

Keep :)ing

Something has only just begun.

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### #11 coldcreation

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Posted 20 April 2010 - 07:22 AM

Do you think Feynman would include "time" alone as being such a phenomenon that "does not exist" as realted to the explanation ? Seems to me the answer should be yes as I define "exist".

The short answer was no (so as not to deviate too far from DD's hypothesis).

But it might be worth it, in the absence of DD, to deviate slightly off topic.

For a longer answer check out this video of Richard Feynman - The Distinction of Past and Future. Part 1

The discussion covers reversibility, irreversibility, natural laws and time.

You'll notice he goes to great length to emphasize the reversible nature of physical laws. But toward the end of this video he begins to describe a situation that is clearly irreversible, i.e., there is a distinction between the past and future. I have not seen Part 2 (if anyone can find it let me know), but is appears he is turning towards thermodynamics, notably the second law, the natural law that introduces the concept of irreversibility, the direction of time...

YouTube - Richard Feynman - The Distinction of Past and Future. Part 1

As far as the context of gravitation, see the reference Six Easy Pieces above. I gave you the page numbers related to gravity.

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### #12 IDMclean

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Posted 20 April 2010 - 08:46 AM

CC,
You present DD's piece as if the whole thing was one giant hypothesis (assumption, axiom). I don't think this is the case. What DD has presented amounts to a formal theory which itself is composed of axioms, definitions, and theorems.

The trick would be to identify the axioms upon which DD's theory rests and find the cases in which those axioms might be false. The rest of it is subject to proofs by logic (deduction). Scientifically speaking from the Popperian perspective, DD's only in trouble if his axioms aren't subject to falsifiability. IE if there is no case in which the axioms might be false.

According to Popperian scientific method, DD's theory wouldn't be admissible as scientific if such were the case; though, his theory might still be admissible under computing, mathematics, and logic.

On that note, his approach to this and the criterion under which his analytical theory is derived isn't too far off of what String theorist use. In fact, your criticism of DD's piece would apply equally to virtually any work done by String theorists and even some of the interpretations of quantum mechanics.

Popper's falsifiability isn't the only criterion nor the most used criterion for a scientifically valid theory. Seems, DD's approach is more along the lines of the positive scientist described by Charles S. Peirce. Given all the above, it seems to me that DD's got a pretty good constructive proof of a possible explanation of phenomena in the world. Perhaps then, it would be more productive if you were to see if the theory conforms to your view of scientific method, and if it does, let us know exactly where and how. If not, ditto. Otherwise, I'm more of the instrumentalist school of interpretation here: "shut up and calculate".

Enjoy,
Ian

### #13 coldcreation

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Posted 20 April 2010 - 12:48 PM

CC,
You present DD's piece as if the whole thing was one giant hypothesis (assumption, axiom). I don't think this is the case. What DD has presented amounts to a formal theory which itself is composed of axioms, definitions, and theorems.

Hello Ian,

It was Doctordick (not Coldcreation) who wrote the "presentation is not a theory but a purely deductive conclusion from required symmetries and thus stands on much firmer ground than any theory including Einstein's."

I contest that the hypothesis, conjecture, assumption, axiom, deductive conclusion (or whatever it is) DD presents stands on firmer ground than any theory, not the least of all Einstein's general principle of relativity.

The trick would be to identify the axioms upon which DD's theory rests and find the cases in which those axioms might be false. The rest of it is subject to proofs by logic (deduction). Scientifically speaking from the Popperian perspective, DD's only in trouble if his axioms aren't subject to falsifiability. IE if there is no case in which the axioms might be false.

I argue that DD's "tau axis" of a four dimensional Euclidean geometry is ad hoc, untestable, nonexistent in the real world, imaginary.

It could be viewed as fortunate that DD's hypothetical (unexaminable) tau dimension can be manipulated (scaled) to make observations agree (to some extent) with his hypothesis. His result would have been much more attractive (not to say elegant) had that tau device not been a necessary feature of the equations. Thus, it is unfortunate that without the hypothetical or fictitious "tau dimension" there is no agreement with observations. Indeed the validity of the entire edifice presented by DD hinges on the veracity of this so-called tau device: something that by its very nature seems to be unverifiable.

Essentially, DD's theorizing, with a healthy dose of fragmentary dissent, is a bravura exercise: Two parallel worlds, two plots, two set designs, two lighting proposals, two choreography sections, one of which is the real world, and the other, a world entirely invented by the human mind (that latter is the tau dimension of course).

On that note, his approach to this and the criterion under which his analytical theory is derived isn't too far off of what String theorist use. In fact, your criticism of DD's piece would apply equally to virtually any work done by String theorists and even some of the interpretations of quantum mechanics.

This is true. I've done my share of critiquing the 21 (or so) dimensions inherent in string theory. I guess a little more can't hurt.

With such ideas as string theory (you choose the version) late twentieth-century physics had begun to manifest its own destiny. With its collection of dimensions (soon to be 21) it was on its way to becoming nothing more and nothing less than fiction pure and simple, numbers and words on a page, literature undamaged by observation, there was nothing to be seen, to be felt, to be touched. The extra dimensions were invisible, pure imagination, nihilism, empty, godlike, vacuous, naked beyond words, beyond reason, beyond nature. The was no substantiation via empirical evidence, direct or indirect.

The same goes for tau, with one fundamental difference;
DD's dimension is flat.

You see Ian, with DD's tau dimension (or with string theory for that matter) nothing was impossible anymore. And yet, the final frontier has not been attained. There is still no unified theory of quantum gravity, no theory of everything. This is finally, then, a fable far more forbidding than sought-after.

The error of thinking that an extra dimension (tau in this case) represents, both in practice and in principle, is to transcend with artificial convention the very essence of what it is supposed to accomplish: the development of a better understanding of gravity (the topic of the OP) and how pseudo-Euclidean space could explain what is observed in the environment better than Einstein's general relativity. But all efforts at conceptual shorthand appear to fall flat.

DD's surreal tau dimension, Dadaistic pseudo-forces and wanton melodrama conspire to produce a succession of completely gratuitous (and how) problematically interconnected Galilean scenes dependent on one imperceptible common denominator, elevated not by its lack of rigor to the status of pure, unadulterated art.

I see it as entertainment, with a definite shift in the design strategy. Compared with observational or experimental physics it is almost anti-research. There is no pressure from competing theories (or even from other purely deductive conclusions) because there’s no way to prove it wrong, no way to test it.

You can’t have one foot is physics and the other outside.

Popper's falsifiability isn't the only criterion nor the most used criterion for a scientifically valid theory. Seems, DD's approach is more along the lines of the positive scientist described by Charles S. Peirce. Given all the above, it seems to me that DD's got a pretty good constructive proof of a possible explanation of phenomena in the world. Perhaps then, it would be more productive if you were to see if the theory conforms to your view of scientific method, and if it does, let us know exactly where and how. [snip] Enjoy,
Ian

This seems to be a classic case where those with a particular belief (say, in Euclidean space) often see things as reinforcing their belief, even if to another observer they would appear not to do so. Belief alters observations.

Some useful hypotheses will enable the formulation of predictions, by reasoning (including deductive reasoning). They might predict the outcome of an observation of natural phenomena, or of an experiment in a laboratory setting (or be statistical, referring only to probabilities).

Once a prediction is made, it can be tested. If results contradict the prediction, then the hypotheses is called into question and explanations may be sought.

The failure of a hypothesis to produce a testable prediction leads to reconsideration of the hypothesis. In this case I've asked DD how one would go about falsifying or verifying, even in principle, his hypothesis (that gravity is a pseudo-force operating in a Euclidean 4-space). This would be especially important for DD considering the competition (Einstein's postulate of general relativity where gravity is a curved spacetime phenomenon) has passed every unambiguous observational and experimental test (again save for gravitational waves). So far, and not particularly surprisingly, those posts addressed to DD have gone unanswered.

This is one feature of the scientific method that aims to protect against bad science.

Any attempt by DD to have this work peer reviewed will likely run into the same dilemma exposed above. I don't think these problems are insurmountable though. Referees may or may not recommend DD's work for publication, with or without suggested modifications. After all, he only adds one extra dimension, not 21 of them.

The main problem is going to be: The Return of Euclidean Geometry
(sounds like a B-series movie sequel, I know)

But either way, DD will likely be confronted once again with falsifiability (the infamous F-word), or at the very least verifiability. His hypothesis must be (at least in principle) empirically verifiable in order to be either meaningful or scientific (or both).

In any case, and for the purpose of continuing an interesting discussion, it would be useful for DD to present a program of how to falsify (empirically) his hypothesis, thus showing us where to look when attempting to criticise his deductive conclusion (regarding e.g., gravitation). It can only help us help him.

In the absence of such, one can only conclude that phenomena such as gravitational lensing, gravitational time dilation and frequency shift, light deflection and gravitational time delay, orbital effects and the relativity of direction (precession of apsides, orbital decay, geodetic precession and frame-dragging) are consequences of Einstein's general theory of relativity that describes a curved 4-dimensional spacetime manifold.

________________________

CC

### #14 Doctordick

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Posted 21 April 2010 - 05:11 PM

Anssi, if you are reading this, Eyjafjallajokull canceled our European trip so I will be here for a while. But, meanwhile, we seem to have some attention I didn't expect.

How, Doctordick, would you falsify (disprove) your purely deductive conclusion?

All you have to do is find an error in my proof, an error in my deduction or a good reason to discount my representational notation: i.e., understanding what I am saying is the first step.

Had DD been practicing theology or theosophy the question of falsifiability would obviously not have surfaced (on my behalf).

Then you regard theology and theosophy to be facts not requiring support?

The fact that DD appears to be practicing science (as observed in the OP, with or without a dash of philosophy) leads me to believe his work should be subject to the same rigorous scrutiny as any scientific theory, (it should be testable) regardless of how he reaches a conclusion.

Scrutiny? Then why don't you provide a little scrutiny? Make some attempt to understand my proof. Testable? As I said above, the results are almost totally in alignment with all known modern physics. Since what I present is a logical tautology, it implies modern physics is itself a mere tautology: i.e., it tells us nothing about reality and is thus a religion, not a science in spite of its seemingly unassailable arguments.

Your diatribe is a religious argument and if you can't see that, you have no comprehension of what I am talking about. You have clearly made no attempt whatsoever to understand my presentation. Rade has managed to make my ignore list and, if you keep up these utterly thoughtless posts you can achieve that status also. Please, if you want to discuss these issues, make some attempt to understand my proof.

The most useful approach is likely to be one that attempts to look for complete corroboration with empirical evidence, as Einstein had done ...

”Complete corroboration with empirical evidence”? Are you insane? Neither Einstein or any other physicist has even come close to “complete corroboration with empirical evidence”. As far as I am aware, I have come closer than anyone. At least I have shown how that issue can be logically attacked (as opposed to the "guess and by golly" attack used by the current practitioners of the field).

Feynman's lecture is an example of exactly what I am talking about. “All the laws of physics we have found so far” (the rules of the religion called modern science) “are time reversible” ... and “yet films run backwards are laughable”. And you are taking that to imply physics has achieved “complete corroboration with empirical evidence”? It is easy to show that my paradigm does not yield time reversibility simply via my definition of time. The definition of time is simply not taken as a serious issue by anyone. They “think” they know what they are talking about! It amounts to personally enforced ignorance: i.e., though they put their work forward as science, the field is actually a religion as they take a great number of things (time and space in particular) as articles of faith.

The old Aristole/Galilean dream of a perfect Euclidean world seemed somehow more pure, more intuitive, simpler. I understand.

What you seem to fail to comprehend is the fact that all non-Euclidean geometries include presumed relationships between the variables being plotted. Those relationships are presumed axioms of the theory being presented. If one sticks to “the facts and nothing but the facts” the only proper plot for a collection of independent variables is a Euclidean plot. Oh, if you have found a relationship which seems “universal” with regard to your data then use of a non-Euclidean geometry can be defended but not otherwise.

For the life of me, I find nothing that differs fundamentally in the work of Atkinson and what you DD have presented above.

Mine is based upon my “fundamental equation” which I have proved to be correct. I don't believe his presentation is based on that fact in any way. I can only presume that you don't have the slightest idea as to what I am talking about.

But the problem is not really whether DD's idea is true or false, right or wrong, fact or fantasy, valid or invalid.

Then you have no interest in facts of any kind? Why don't you just go away?

The trick would be to identify the axioms upon which DD's theory rests and find the cases in which those axioms might be false.

Except for the “theory” thing you are correct. I can only presume you have never examined my proof.

The rest of it is subject to proofs by logic (deduction). Scientifically speaking from the Popperian perspective, DD's only in trouble if his axioms aren't subject to falsifiability. IE if there is no case in which the axioms might be false.

Oh, so I am in big trouble if what I have proved can not be falsified am I? What are they going to do, institute a scientific inquisition and burn me at the stake?

On that note, his approach to this and the criterion under which his analytical theory is derived isn't too far off of what String theorist use.

You have utterly no idea as to what I proved have you?

I argue that DD's "tau axis" of a four dimensional Euclidean geometry is ad hoc, untestable, nonexistent in the real world, imaginary.

I take that as solid evidence that you have never looked at my proof at all. You have no idea as to why it is there do you?

Once a prediction is made, it can be tested. If results contradict the prediction, then the hypotheses is called into question and explanations may be sought.

What I call the “guess and by golly” approach to explaining things. How about thinking, just a little, about the underlying assumptions in your approach.

This is one feature of the scientific method that aims to protect against bad science.

And what about protection against stupid presumptions. Do you think that is not worth thinking about?

Any attempt by DD to have this work peer reviewed will likely run into the same dilemma exposed above. I don't think these problems are insurmountable though. Referees may or may not recommend DD's work for publication, with or without suggested modifications. After all, he only adds one extra dimension, not 21 of them.

I discovered the proof of my fundamental equation when I was still a graduate student back in the sixties but it seemed pretty worthless because I couldn't solve the equation. I discovered the first solution around 1983 and after some work, I attempted to publish my proof about twenty years ago. I don't think it made it past any of the referees. The physicists said it was philosophy, the philosophers said it was mathematics and the mathematicians said it was physics. The only physicist I knew who showed any interest at all in what I was doing was Richard Feynman. He promised me he would check the thing out carefully when he finished with the Challenger hearings. The next thing I knew he had died. It was quite clear, God didn't want me to be recognized!

I ran across some of my work when I was cleaning the attic sometime after the turn of the century. I read it with a fresh eye (having not thought about it for many years) and commented that it still made a lot of sense to me. My son-in-law suggested I publish on the web (he was a professional web site designer). So far I have met only one person, AnssiM, who seems to even comprehend the problem I had solved but he knows very little math. Its been an education and I believe I am beginning to comprehend what people find confusing about it.

His hypothesis must be (at least in principle) empirically verifiable in order to be either meaningful or scientific (or both).

My fundamental hypothesis is quite simple: an explanation must be internally self consistent! Since you are so bright, suppose you tell me how to falsify that hypothesis. Again, what I have put forth is a proof, not a theory.

If you have no interest in rational thought, why don't you just go away. If you are interested in thinking things out, wait for the post I mentioned to Pyrotex in “the nature of time” thread. If you have no interest in rational thought, why don't you just go away.

Have fun -- Dick

### #15 coldcreation

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Posted 21 April 2010 - 07:08 PM

Had DD been practicing theology or theosophy the question of falsifiability would obviously not have surfaced (on my behalf).

Then you regard theology and theosophy to be facts not requiring support?

Au contraire. I regard tenets of theology and theosophy to be fiction, not able (even in principle) to provide support. There is no way to falsify something that can't be tested. Let's hope that your "tau axis" doesn't fall into the same category.

Scrutiny? Testable? As I said above, the results are almost totally in alignment with all known modern physics. Since what I present is a logical tautology, it implies modern physics is itself a mere tautology: i.e., it tells us nothing about reality and is thus a religion, not a science in spite of its seemingly unassailable arguments.

I guess the key word there is "almost". There is where you might be able to test a prediction.

Obviously I disagree with your statement: "modern physics is itself a mere tautology: i.e., it tells us nothing about reality and is thus a religion."

For example, Einstein's general relativity tells us many things about the physical universe, 'reality' (and is thus not a religion).

What you seem to fail to comprehend is the fact that all non-Euclidean geometries include presumed relationships between the variables being plotted. Those relationships are presumed axioms of the theory being presented. If one sticks to “the facts and nothing but the facts” the only proper plot for a collection of independent variables is a Euclidean plot. Oh, if you have found a relationship which seems “universal” with regard to your data then use of a non-Euclidean geometry can be defended but not otherwise.

Mine is based upon my “fundamental equation” which I have proved to be correct. [...]

Yet two hours ago in another thread ("the nature of time") you wrote "I am in the process of writing out my proof of my fundamental equation."

My fundamental hypothesis is quite simple: an explanation must be internally self consistent! Since you are so bright, suppose you tell me how to falsify that hypothesis. Again, what I have put forth is a proof, not a theory.

Your hypothesis is not solely that "an explanation must be internally self consistent!" There is more involved than just that.

If you are interested in thinking things out, wait for the post I mentioned to Pyrotex in “the nature of time” thread.

I thought this thread was supposed to be The final piece of the puzzle!

CC

### #16 IDMclean

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Posted 21 April 2010 - 09:31 PM

To DD,

[...]

The trick would be to identify the axioms upon which DD's theory rests and find the cases in which those axioms might be false.

Except for the “theory” thing you are correct. I can only presume you have never examined my proof.

The rest of it is subject to proofs by logic (deduction). Scientifically speaking from the Popperian perspective, DD's only in trouble if his axioms aren't subject to falsifiability. IE if there is no case in which the axioms might be false.

Oh, so I am in big trouble if what I have proved can not be falsified am I? What are they going to do, institute a scientific inquisition and burn me at the stake?

On that note, his approach to this and the criterion under which his analytical theory is derived isn't too far off of what String theorist use.

You have utterly no idea as to what I proved have you?

[...]
Have fun -- Dick

DD, Some here's some context for my comments. First off, I'll admit mistake. As I saw it, you were presenting a formal theory or axiomatic system. In which case, I assumed it would follow the format of logic: axioms, theorems, definitions, and proofs. As far as I know, axioms can't be proven consistent in any logic powerful enough to express Peano arithmetic as per Gödel's Proof (with notable exceptions pioneered by Dan Willard). The standard stance put forward in the logic texts I read is that logic isn't about proving the truth of the assumptions that's the job of somebody else like a physicist. My suggestion then of identifying the axioms is intended for CC who seems bent on drawing a Popperian hypothesis out of your work.

Pardon my error, I'm still getting used to the difference of lingo for logic and mathematics. I started all this as a self-taught biologist and then a self-taught physicist. I'll probably never reach the point where I don't mistakes. It's nothing that can't be corrected with ample doses of study and research.

Second off, once again, the comment about "from the Popperian perspective, you'd be in trouble" is directed at CC. He's the one who's imposed the constraint of falsifiability on your method, so if he really wants it, he'll find it or prove that it has no case in which it would be false, or he'll go do something better with his time like as Kleene says "acrostics or beekeeping." I don't take the Popperian perspective with your work because you work logically, so the methods that apply to the critique at this point are deductive not inductive. Similarly, you don't take falsifiability to a mathematic problem. Wrong tool for the job.

Finally, third off, the context for the last quoted comment is that you use methods similar to String theorists IE mathematics and logic. CC's criticism that your axiomatic system (not just this, but the theorems and proofs it rests on) may not be falsifiable applies equally to other axiomatic systems (like the theory of computers and String theory).

As for your comment regarding what I do and do not comprehend, no I don't fully comprehend what you've proved. Chances are few people at this point do other than you. Give me time to mature in logic and mathematics, and I will understand it if for no other reason than I want to understand it. I get the intuitive, informal gist of it. It's the formal techniques of proof that floor me. When I get to that maturity, I'll see if I can add something; until then, I literally have nothing to add, subtract, or modify regarding your proof. It looks good to me.

Enjoy,
Ian

### #17 Doctordick

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Posted 21 April 2010 - 11:34 PM

Coldcreation, I really wish I knew why you feel compelled to post to this thread. You obviously have not the first hint of what I am talking about.

I guess the key word there is "almost".

That “almost” is there for honesty. There exist aspects of modern physics which I have not yet proved are indeed implied by my fundamental equation. It is not an easy equation to solve. I have shown that Schrödinger's equation (and thus Newtonian mechanics) is an approximate approach to solving my fundamental equation, Dirac's equation is an approximate approach to solving my fundamental equation, Maxwell's equations are an approximate approach to solving my fundamental equation and finally, (as the last piece of the puzzle of identifying constraints implied by my equation with supposed conclusions of modern physics) showing that Einstein's theory of General Relativity is essentially an approximate solution to my fundamental equation. I have not yet achieved “complete corroboration with all empirical evidence” but I have certainly deduced enough to convince me that modern physics is a tautology (as it is quite clear that my fundamental equation is certainly a tautology). As I said, it is not exactly an easy equation to solve.

There is where you might be able to test a prediction.

Yes, and I will make a prediction: there probably exists other empirical evidence which can be shown to be approximate solutions to my fundamental equation.

Obviously I disagree with your statement: "modern physics is itself a mere tautology: i.e., it tells us nothing about reality and is thus a religion."

Of course you do because you have absolute faith in the validity of the standard “by guess and by golly” approach used by modern physics.

For example, Einstein's general relativity tells us many things about the physical universe, 'reality' (and is thus not a religion).

Yeah, I know! That is exactly what you are convinced of and you would like the rest of us to believe. I say it is no more than another consequence of internal self consistency of the argument (but as I get something a little different, either I have made a deductive error, which is certainly possible, or Einstein's theory is not internally consistent). The fact that no one has succeeded in presenting a quantized version of that theory is somewhat indicative of its failure to be internally consistent.

Yet two hours ago in another thread ("the nature of time") you wrote "I am in the process of writing out my proof of my fundamental equation."

Perhaps I should have said, “rewriting”. If you had read that post you would have seen the passage

So far I have met only one person, AnssiM, who seems to even comprehend the problem I had solved but he knows very little math. Its been an education and I believe I am beginning to comprehend what people find confusing about it.

I am trying to put it in a form comprehensible to the average mind.

Your hypothesis is not solely that "an explanation must be internally self consistent!" There is more involved than just that.

You clearly have never read the proof as, if you had, you could explicitly point out the other hypotheses.

I thought this thread was supposed to be The final piece of the puzzle!

As I have commented earlier, you seem to have utterly no comprehension of what puzzles are under discussion. And, as an aside, if you were at all aware of my proof you would clearly comprehend the nature of that tau axis. Again, I have utterly no idea as to why you think any of your comments have anything to do with this thread. Either go read some of my earlier stuff, wait for the new post of my proof or just go away.

Just for your information, I went into physics because only physicists seemed to think their ideas needed a logical defense. I found most other subjects essentially gobs of undefendable assertions. (Oh, mathematics seemed quite well defended but it also seemed to have little to do with reality; at least no mathematician I knew claimed it did.) I wanted to understand the world I found myself in and physics seemed to be the best bet. Until I got into graduate school when they also began to feed me undefendable bullshit. Before I went to graduate school I thought “theorists” thought about the problem of creating theories and that problem interested me very much.

After I got there I found out that absolutely no one thought about the fundamental issues of that problem. The actual presumed purpose of “theorists” was to work out the details necessary to check out theories someone else had invented by, what I call the, “guess and by golly” approach so that experimentalists wouldn't have to. My Ph.D. thesis concerned writing a computer program to calculate the outcome of a nucleon-nucleus scattering problem under the assumption that the current “guess and by golly” theories of nuclear structure of the time were correct: i.e., a programing problem consisting of designing a good approximation calculable on mainframe computers of the day (which, compared to the machine I am typing this on, were absolute crap). I told my thesis advisor that our time would be much better spent drinking beer for twenty years while computer hardware made these issues trivial. (I think it is quite evident that I was right!) The theorists work of the 1960's was quite analogous to people caluculating pie out to a thousand decimal places by hand back in the eighteen hundreds (people actually did that).

At any rate, when I was awarded my degree, I left physics to earn my living outside the field because I was of the opinion they had nothing to offer regarding the problem which interested me. I think I pissed off my thesis advisor as, ten years later (when I asked him for assistance in getting my proof published) he said, “no one will ever read your stuff because you haven't paid your dues” and he refused to even look at it himself. It turned out that he was pretty well right.

Hi Ian, I appreciate your post; thanks for clarifying your position. Sorry, I haven't answered your private message. I haven't done so because you posted here and I think I can make my position clear with this post.

It's the formal techniques of proof that floor me. When I get to that maturity, I'll see if I can add something; until then, I literally have nothing to add, subtract, or modify regarding your proof. It looks good to me.

I suspect very strongly that you have never actually examined my proof. It is essentially embedded in the “What can we know of reality?” thread and is apparently quite confusing to most everyone. Why don't you just wait for my new (hopefully less confusing) post on that subject? I am an old man and not mentally quick any more but, I promise, it will eventually show up. If you wish, you can read my posts to the “What can we know of reality?” thread but I really suspect you will find them confusing. The lines along which I think are not at all the same lines along which most people think. As I have said earlier, only Anssi appears to have asked himself the same questions which bothered me since I was a child; everyone else seems to jump to assorted erroneous presumptions of what I am saying.

Have fun -- Dick