Problems With General Relativity

Initially, the light passes from the star, through some point P and then all the way to your eye. However the sun will block the light from the star by having part of itself occupy point P. The supposed 'curvature of space' takes the point P away from any part of sun, in the process, so that the light now moves curvilinearly without any blockage from the sun. But if the movement of point P was due to the 'movement of space' itself as it curves, then it was supposed to take the sun itself alongside it, making the sun larger! The scenario would not have resulted in revelation of any star otherwise blocked by the sun.

The usual 'force' explanation of a bending of trajectory of an object, differs significantly from the 'bending of space itself' explanation in the following way: Supposing that the force acting on the moving particle is present only at some region, call it R. So should the particle move through R, the force will act on the object only briefly during its period of the entry and exit from R. This force will bend the trajectory of the object (assume that the direction of the force is perpendicular to the direction of the moving object). However the direction of the moving object thereby changes permanently so that after moving for a vast distance, it lands in a place completely far from where it would have landed, had it moved rectilinearly, i.e. without encountering any force. The corresponding notion of 'force acting only at region R' in the 'curvature of space' explanation is problematic. The space must be 'distorted' only at region R and it must 'return to normal' elsewhere. Therfore an object moving through R changes its trajectory only at around R and immediately comes back to its original trajectory. For an object to develop a parmanently new trajectory, all the 'space portions' throughout the universe must be altered! For light bent by gravity in andromeda to hit at your eye rather than landing on pluto, or even on the Pleiades, the portion of 'space' that sits in Pleiades must be brought all the way to your eye by 'bending of space itself'! This is because in such a theory, light is 'embedded' in space so that it can only bend when the space itself bends! Is this reasonable? Does a star in andromeda bends the space of the rest of the universe?

So we can now critically exermine the second, possible attempt to explain how stars otherwise 'behind the sun' are revealed due to the fact that the light moves around the sun curvilinearly. Initially, the light that hits your eye would have landed elsewhere had it kept moving rectilinearly rather than it getting bent all the way to your eye. Call the place it would have landed at 'Q'. In the 'curved space' explanation, the space portion Q is bent all the way to your eye! But this doesn't make any sense because if the space itself was the one getting curved, your eyes alongside your body would have been taken elsewhere too by the very 'bending of space'!

At this point, you might have noted that it is not easy at all to determine that 'space is curved' by taking measurements within the space itself. To notice a 'curvature of spcae', so it seems, one must move 'outside of space' and then find another 'space' relative to which the space in question is 'curved'. So you might have wondered what it is that physicists are talking about! You are right! What we can measure within the curved space is surverly restricted. If you bend a piece of paper, a 'bed bug' trapped in it,( so that it cannot in anyway see anything that the paper is bent relative to) cannot notice any change! However, if the 'bed bug' was living near the vertex of a cube, he will discover something 'strange' there. He will notice that unlike in 'elsewhere', you can fill the whole of supposedly '2 dimensional space' (unaware of the third dimension) by summing up only three 90 degrees angles (the three rectangular faces meeting at the vertex)! This is the nature of what it can, and how it is discovered about 'curvature of space' all while stuck inside that space. If the curvature is of the type that 'you need to cut the paper' to make it, then the 'bed bug' can discover the 'missing angles' by walking around the surface. There is nothing else that the 'bed bug' can discover! Have this one intact in your mind when criticaly examining the alleged 'measurement' done by relativists that supposedly shows that 'spacetime' is curved.

In the case of alleged discovery of 'curvature of spacetime' by observing how the starlights are deflected by the sun's gravity, the relativist wants you to believe that the 'bed bug' can tell that lines are bent by the bending of 'space' itself. In the picturesque of 'hammock' that is 'weighed down' by a spherical object, it is easy to see that the otherwise straight lines (geodescics) are actually curved around the spherical object. But this is all because we are seeing it in 3 dimensions and against the back drops relative to which, the lines are 'curved'. But for the 'bed bug', he can only see things curved relative to the things stuck within. He absolutely has no way of telling that one geodesic of 'curved differently' from another simply because the whole of space itself is curved. So here, the relativists confuse themselves with the very same 'analogies' that they claim are 'simplifications for laymen'!

Now lets consider the alleged measurement of 'gravitational time dilation'. First ask 'a clock is ticking slowlier near the earth surface relative to what clock'? relative to the one at the satellite? Then how do you compare these clocks? At first, this look straightfoward. But this is only because we make assumptions about 'spacetime' that the very relativist are trying to deny! Relativity denies us the ability to compare distant clocks as the light has to travel between them. In the case of 'rate of clocks ticking', the light suffers the same 'distortion' as the clocks as it travels from the satellite to the earth surface. So it is not clear at all what rate a clock in satellite will appear to tick as seen all the way from earth. As you will see, there must be a 'Doppler shift' like effect. That corrects any ticking difference between the clock on earth and that in the satellite.

This is how to see it even more clearly: consider two pulses of light emitted, at some point in space, P, one after the other. let T be the time period between the two pulses. These two pulses will travel away from P towards another point, Q. If nothing affect the spacetime in between P and Q, then for every point,R, along line PQ, there will be the same period T between one pulse arriving at R and the other pulse's arival. But if time is 'dilated' at around R, this same 'dillation' will affect the period between the two pulses. This renders the period between the two pulse arriving at R be T', so that T/T' is the 'time dilation between clocks at P and the clocks at R'. Therefore you cannot observe how a clock at P is 'dilated' relative to a clock at R by 'looking at the information about the rate of the clock at P is ticking, as conveyed by light'. The two clocks will simply appear to be ticking at the same rate by whatever way we obtain information from P!

But when you see the alleged 'measurements' by relativists, they fail to consider the effect of 'time dilation' on the light conveying the information itself! To be precise, they assume that the same period, T is maintained throughout the space no matter how spacetime is 'distorted' locally! This is both unreasonable and contradict their other allegation that they can measure 'Doppler shift' due 'expansion of the universe'. The 'time dilation' is supposed to be the effect primarily on spacetime itself, not on anything in it. The other things follows the suit because they are supposedly 'embeded' in space. If you 'stretch space' at some region, the wavelength of light passing that region must increase. If you 'stretch time' there, the frequency of light passing there must similarly reduce. This is how they explain 'red shift' due to alleged 'expansion of the universe' and they must not be allowed to switch back and forth whenever it suits them!

As you might have noted, generally, the relativist's trick is to decide in an ad oc manner what is affected by 'curveture' and what it is not so that they find an observable 'back drop' relative to which, the one affected by the 'curvature' supposedly reveals the curvature of the 'space time' in which it is supposedly embeded! You wonder how the nature can make the choice of what to 'embed' and what not to do it is done on the same spot, in favour of the relativist! In the starlight near the sun example, the sun itself is not 'distorted allongside the spacetime' and/or the observer's eye etc is not similarly 'distorted'. In the case of 'gravitational time dilation', the light emited by a distant clock does not undergo the 'dilations' even as it travels through supposedly distorted spaces! In the case of 'expansion of the universe', as you will notice, the objects themselves are not undergoing the 'expansion' even as 'space' itself is the one that is supposedly expanding!

Of course if the objects underwent expansion, by the same scale as the 'spacetime' itself, we will not notice any change by observing wavelengths of the light that is supposedly 'stretched' by the expansion of space! If you stretch a ruler alongside the object you are measuring, you will not notice any change! So how does then 'spacetime' expands without the expansion of the objects into which, they are embedded.? Why doesn't this exemption affect the light itself? After all the light too, according to the same relativity, have mass.

To begine understanding how wrong the relativists are, consider the difference between ordinary 'Doppler Effect' and the one due to 'expansion of space'. If a moving person firers a bullet away from the direction he is miving in at some time, t1, at some point in space, x1, and then firers the second shot at some time, t2 and at some point in space, x2 then by the time he fires the second shot, the person will have moved towards the bullet by distance: x2-x1= v (t2-t1), where v is his speed. Meanwhile, the bullet will have moved by distance x3-x1=c (t2-t1), where c is the bullet's speed. The difference, x3-x2 =(c-v)(t2-t1) will be the space interval seperating the person from the first bullet by the time he firers the second bullet. This spacing is seen by a stationary observer. So the ratio (x2-x1)/(x3-x2)=(c-v)(t2-t1)/(x3-x1)=(c-v)/c =1-v/c will be the ratio of the pacing of the bullets as seen by the moving observer to the spacing as seen by the stationary observer. This is the usual Doppler shift where the 'bullets' are 'the wave crests' and 'bullet spacings' are 'wavelengths'.

In the Doppler shift due to 'expansion of space' (or contraction in our case), the gun man does not fire the gun and then chase the bullet. Rather, the space 'shrinks' during the period between t1 and t2. So not only is it the case that the standing by observer will not notice any chang in wavelength (due to his ruler shrinking too), there is no reason that the same shrunk interval between the bullets will be maintained throughout the rest of the univers even as the 'bullets' passes through spaces that are shrunk or stretched by different amounts. If anything, we expect the interval to alter in perfect synchronicity with the alterance in the space they are embedded in. After all the reason the interval shrunk in the first place was due to the shrinking of space itself. Clearly we cannot choose when the shrinking or expansion of space affects the wavelengths and when it doesn't affect it.

With this understanding, we only have two scenarios, both of which debunks the relativists. First is that either the whole of the universe expands evenly, and we will not notice any Doppler shift because our light too is similarly expanded, or the space near our atmosphere etc does not expand and the light enterring it must 'shrink back' to 'normal' upon entering it and we will not notice any difference either! A 'Doppler shift' due to 'expansion of space' is simply unobservable from the point of view of the expanded space itself.

 

 

Like we have briefly seen, the only thing a 'bed bug' can tell about the corner of a cube is the apparent absurdity where only 3 90 degrees angles are enough 'to add up to 360 degrees'! The explanation is obvious when we see a cube from 3 dimensions. The corner, not being flat, it is farther away than what a 2 dimensional 'bed bug' might infer. In short, the 2d 'bed bug' takes a bent or a curved surface as though it were flat, and so makes false inferences as to how far places are. Distance along a curve, is, of course longer than distance along a straight line.

So when we consider a smoother curve, eg a sphere (preferably the earth), we can draw a circle on the earth's surface. if we think that the earth is flat, we will be surprised to learn that the circumference of the circle we have just drawn does not equal 2pir. This is because the radius along what is actually a portion of a sphere rather than of a flat plane, is longer than along a flat space. More bluntly, we are realy not dealing with a circle at all. we are dealing with something like a pan cake or a bowl, giving it a wrong radius by measuring it along the curvature.

Considering this simple fact then, if relativist wanted to suggest that we live in a 4 dimensional analogy of the 2 d surface, and that thus we are prone to the same tendency not to notice the 'pan-cake' nature of our so called circles (or even spheres etc). All he neaded, from scientific angle, is to spit out an equation that relates how much a circle's circumference deviates the simple 2pir formula (lets call it 'the pan cake deviation'). He would then relate this deviation say to the 'mass' at the center in forming a 'curved space' theory of gravity! It would be a very simple equation, with only a single term at the left side, and the 'mass' term on the right side, understandable even by an high school child!

The important thing about this equation is that all the parameters appearing in it, which are just radiuses and circumferences, are all measurable within 3d. So the only thing of scientific interest will be the 'pan cake deviation'. But relativists, instead went for the complex equations that were meant to show that such deviations indeed measures the 'curvutures' of surfaces, a show that only make sense to an hypothetical 'higher dimensional' 'observer'. Now, be sure you understand this. So I will keep re-wording it. It is obvious to anyone, not just the mathematician, that if you draw a circle on a generally curved surface, there will be the 'pan cake deviation'. But the equation that relates this deviations to the curvature of the surface is complex and not many people understands it. Since the curvarture is in 'higher dimensions', some of the parameters appearing in the equation are actually distances that goes 'outside of space', and so those that can never be measured. In relating the curvature to the measurable parameters on the 'surface', the mathematican must equate terms that only include the measurable parameters (ie radiuses and circumference of the 'pan cakes' incongruously dubbed 'circles') with another term that includes parameters that cannot be measured. This second term is complex, a complex combinations of the rates of changes in gradients, of the curves (that is, for instance, considering the curves as 'graphs' embeded in a 'flat', coordinate system, eg a cartesian). The complexity is necesitated by the need to include gradient terms that are necesary to calculate the circumfrences on the surface. The relativist, instead of relating the first simple term on the left, with mass, he opted to relate the mass to the complex term appearing on the right, a needless complexity because they are mathematically equated! In effect, the relativist dwelt solely in a relationship that should have only been of interest to a mathematician, in order to drive firm the unprovable assertion that we are actually living in a curved space! Without being able to see the 'higher dimensions', we could adopt other explanations for the 'pan cake deviation'.

 

But even more problematic is how the relativist end up confusing themselves with their own vodka! Now the gradient of the point on graph (derivative in calculus), as uses to calculate lengths lieing on the surface of the curve using Pythagoras Theorem is given a fancy name termed 'the metric'. So they are squares of gradients, which when you take their second and third derivatives (rate of change in gradients), the rules of calculus spits out terms that includes the products of rates of change in gradients, which they call them 'curvatures'. This product is called 'Gaussian curvature'. It is just a mathematical exercise that adds no more physical insight to the main idea, which is that there is relationship between gradients of graphs and lenghts of lines drawn on the surface, a fact that is obvious without the need for any calculation! A physicist can just proceed to take measurements for 'pan cake deviations', relate this with 'masses' (if any), proceed empirically, and leave out the details of 'Gaussian curvatures' in terms of derivatives of metrices to pure mathematicians, since the parameters in the metrics include 'Cartesian coordinate system' that extends 'outside of space' that is beyond the reach of a physicist, and show the latter should not make speculations along those lines.

Since metrics, as gradients, includes parameters that are measurements of distances 'outside of space', the metric on its own is empirically useless! To describe 'curved space' using metric is to ask us to imagine an higher dimensional ' flat coordinate system' in which the 'curved space' is 'curved' relative to. So why are 'physicist' preoccupied with solving for the metrics as the bread and butter for 'general relativity', instead of being preoccupied with calculating the 'pan cake deviations' associated with a given mass, the way it is done in usual physics? The answer seems to be that they are confused! In schwarzchild metric, for instance, the 'raduses' appearing in it are actually distances in some backround 'flat' coordinate system that can be easily discerned by close exerminning 'spherical coordinate system'. They are not distances in a curved manifold at all! To obtain distances in the curved manifold, we must do some integrations, from which we will see that the manifold described by Schwarzchild metric does not have lengths corresponding to regions less than the so called 'schwarzchild radius'. The curve, instead, is a torus-like structure with a 'hole' in the center whose radius is Schwarzchild radius!

The correct calculation of the shape of the manifold described by Schwartzchild metric also shows another problem with Einstein's General relativity. Einstein's Field Equations EFE actually describes how matter 'curves the space time' it is sitting on, and tells us nothing about what the matter does to the space outside of itself! The EFE as applied to Schwarzchild metric in no way does it 'place the point matter at the center of the spherical coordinate' as it is asserted! The mass is freely chosen by the physicist to fit some experiment, hammered into the center, and then hope is made that it will fit other unknown data that is called 'confirmation of GR'! But then we have now seen that the Schwarzchild's Space Time actually has a hole around its center, and therefore there is nowhere to place the 'point mass'!

To solve Schwarzchild metric, the relativist is forced to say 'the Ricci Curvarture of spacetime equals zero'! He does not reference the alleged cause of the Ricci curvature in the mathematical statement hailed to completely describe our universe! He does not reference the 'point mass' because it is distant from the space, and as I said, EFE only describes how matter supposedly curves space time in situ! This should not be the case! If the distant mass is the cause of the curvature, EFE should be an equation that relates curvutes with masses AND with distance, like how Newton's law relates accelerations to distances and to the mass. Then we will see how the maths is stating that 'the cause of a curvarture at place x is the mass at place y. Or a mass of such and such amount, distorts spacetime to such and such extend, at such and such distance away from the mass. So in deed the mass distorts the space time at a distance. But if you just say Ruv=0, then we are just contemplating on a pure geometrical exercise that is yet to be inteprated in the real world. It might as well describe a completely empy world! it doesn't tell us where the 'mass' is. They latter allege that 'it is at the center' but after amusingly failing to see that the manifold is a featureless structure with a hole around the center!

It is easy to see why relativist got this confused. The formed a false analogy with Newton's gravity. In the latter, there are two equivalent ways of stating the law. One is the familiar inverse square law, and the other one is called 'poisson's equation'. The latter describes how masses gravitational affect masses in situ. But the two equations are related by a so called 'divergence theorem', so that even if we use poisson's equation to describe the gravity in the empty space away from matter, we can still relate the gravity with the mass via divergence theorem. This is cuptured well in Gauss's law description for gravity, where Gauss talks of the total gravitational flux crossing a Gaussian Surface that encloses the mass. Since the Gaussian Surface extends arbitrarily upto the 'empty space', then yes, the poison's equation does relates gravity to the distant source. But the curved space nature of the maths of GR does not allow us to even compare distant vectors, let alone form an analogy of divergence theorem. Therefore any comparison between EFE and Poisson's equation is misleading!

Relativists say that gravity is not a force. But then they also say that they have a task to reconcile gravity with the other forces of nature, eg electrodynamics, in forming a quantum theory for gravity! This is problematic because in quantum theory of particle interactions, fermions must 'exchange momentums' with bosons. This 'momentum' is problematic if gravity is not a force! To say that spacetime can morph into a graviton particle that delivers a momentum is to now deny that gravity is due to a 'curvature of spacetime'. You are now saying that 'spacetime exerts a force on the particle' just like all other 'fields' does!

Furthermore, to quantize gravity, one must be able to say what amount of energy is in a given portion of space, just like in quantizing gravitational field to form photons. The photons 'carry energy' which is in quanta. So we must similarly calculate the energy somehow 'stored' in the 'curvature of space' (like the energy stored in a bent bow?). We then quantize this energy by making it descret chunks of E=hf. But GR forbids us from thinking of a 'curved space' as though to 'store energy' because the curvature is relative. Gravity being completely equivalent to accelerating means that it only has what looks like 'kinetic energy' which is zero as seen from the co moving frame.

There are still more daunting problems with GR, but let me stop there for now, to allow you to absorb these!

 

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