The Proper Theory Of Relativity

[A-wal]

The Proper Theory Of Relativity

 

This is to show that the general theory of relativity is based on a false postulate and that the principles described by the special theory of relativity can also be used to describe gravitational acceleration. Gravitational free-fall is not an inertial frame of reference, it's an accelerated one. The argument that a free-falling object doesn't feel a force doesn't hold because it feels tidal force (the difference in the strength of gravity over the object caused by the fact that different parts of the object are at different distances from the source of gravitation). This is no different to the force felt by an accelerating object free from a gravitational field. Such an object wouldn't feel a force if the force were spread evenly throughout the object, in the same way that a flat object with all parts of it the same distance away from a source of gravity wouldn't feel any tidal force.

 

Energy pushes massive objects away from the source and mass pulls them towards the source. Other than that there's no difference in the way that they operate accept that the inwards force caused by mass is much weaker than the outwards force caused by the equivalent amount of energy, E = MC^2. There's also no physical difference between flat and curved spacetime. To infer that spacetime is curved you have to observe an object following a curved path through spacetime, and you could just as easily claim that the object is following a curved path through flat spacetime in the same way that objects accelerating free from gravitation are usually viewed. Mass causes objects to follow paths through spacetime that curve inwards towards the source while energy causes objects to follow paths that curve outwards away from the source.

 

 

To test the implications of general relativity we need to apply it to the most extreme cases of gravitational acceleration; black holes.

 

Different frames of reference can change when an event happen but not if it happens. If one set of coordinates shows objects crossing an event horizon and another shows them accelerating towards it but unable to ever reach it because of time dilation and length contraction then these coordinate systems can't both be right. Supposedly black holes accelerate objects beyond the speed of light relative to external objects once they cross the event horizon. That's not how relative velocities are added together, it would require infinite acceleration and it's impossible for the force of gravity to increase smoothly to infinity as the black hole is approached. It would also mean that the laws of gravity aren't reversible in time because objects would reemerge from inside the horizon if the arrow of time were reversed.

 

When objects approach the event horizon of a black hole they are length contracted and time dilated in such a way that they can never be observed reaching the event horizon. This means that from the frame of reference of any more distant observer it's always possible for the in-falling object to accelerate away from the black hole. If we take the frame of reference of the black hole itself and assume that it doesn't last forever and shrinks over time then the in-falling object can still never reach the event horizon, however small and close to the end of its life the black hole is. Any coordinate systems that allow in-falling objects to reach an event horizon are in direct contradiction with coordinate systems that don't. You can't change reality by switching coordinate systems.

 

The Schwarzschild coordinate system is the correct one, showing that a free-faller's acceleration towards a black hole causes the object be length contracted and time dilated in exactly the same way as described by the special theory of relativity so that its velocity relative to any more distant object and to the black hole itself can never reach the speed of light. To reach an event horizon an in-falling object would have been accelerate to the speed of light relative to the black hole and any object at rest relative to the black hole, and accelerated beyond the speed of light relative to the black hole and any object at rest relative to the black hole as it crosses the event horizon. This is an impossibility as described by the special theory of relativity. The fact that gravitation is the accelerating force is inconsequential.

 

Singularities are infinitely time dilated as well as infinitely length contracted, they're singular in time as well as space. This makes black holes perfect four dimensional spheres. The size of the sphere depends on the distance of the observer because gravitational acceleration causes it to become increasingly time dilated and length contracted as it's approached. The further away from the event horizon the observer is, the less time dilated and length contracted the black hole is in their frame of reference, so the size of the singularity is stretched in all four dimensions as distance increases, creating the appearance of a black hole. The event horizon is the edge of the singularity as viewed from a distance and a singularity is the black hole in its own frame of reference.

 

The standard view of black holes use coordinate systems in which the event horizon is expanding outwards but black holes aren't actual objects that are physically there in the traditional sense, they're just mass and acceleration caused by that mass and objects can't be accelerated to the speed of light because that would require infinite acceleration, so if an object were right next to a black hole as it formed then from their perspective the event horizon would be at its maximum radius at the moment they became aware of it. The event horizon of a black hole travels outwards at the speed of light in the black hole's frame of reference from the moment it first forms because all information propagates at that speed. The event horizon then moves inwards at the speed of light from the black hole's own frame of reference, making it unreachable.

 

 

It can also be shown that the event horizon is unreachable from the perspective of any object by using the Rindler horizon.

 

The Rindler horizon is the point behind an accelerating object where light from further away than the horizon will never be able to catch the accelerator as long it continues to accelerate at at least the same rate. If the accelerator maintains a constant rate of acceleration then the Rindler horizons stays at the same distance. If the accelerator decreases their rate of acceleration then the Rindler horizon moves further away and if they increase their rate of acceleration it will move closer to them but this isn't a linear scale. The harder they're accelerating, the less the Rindler horizon closes the gap in response to the same increase in acceleration. This is identical to the way that the same burst of acceleration doesn't increase relative by as much the faster the object's velocity relative to an object, ( A+B ) / ( 1 - ( AB ) ).

 

There's also a horizon in front of an accelerating object at exactly the same distance as the Rindler horizon is behind it. If the accelerating object were to shine a light in front of them then they would see that the light is moving away from them slower than the normal speed of light. The rate that they would close the gap on the velocity of their own light if they steadily increase their rate of acceleration is identical to the rate that the Rindler horizon would close on them from behind. If they were able to catch up to their own light then their Rindler horizon would have caught up to them. When an object is accelerated towards a black hole there is again a Rindler horizon behind them that works in exactly the same way and would overtake them if they were able to reach the event horizon, which would make no sense.

Edited July 20, 2015 by A-wal

[A-wal]

I need some advice. I'm not sure where to take this from here. I've written it in the best way that I can but I can't see it getting accepted to a scientific journal.

 

It deserves to be because it unifies special relativity and general relativity by describing acceleration due to mass in the same way as acceleration due to energy, they're two sides of the same coin. There's nothing to even suggest that free-fall is an inertial frame of reference. You could describe gravitation attraction as objects following curved paths through flat spacetime and acceleration due to energy as objects following curved paths through flat spacetime. It's a huge simplification, it does far more with far less and it does it a way that doesn't lead to coordinate systems that contradict each other.

 

I written some challenges to GR that I don't think are resolvable (http://www.scienceforums.com/topic/27224-can-you-answer-these-black-hole-questions/page-1) that I can add to it but other than that apart from just copying and pasting SR equations and the Schwarzschild and Rindler coordinate systems I'm not sure how to make it more acceptable.

[pgrmdave]

Have you tried going to a local university and enrolling in a PhD program in physics so that you can fill in the gaps where you're weaker and strengthen the parts you're stronger? It'll also give you the resources necessary to begin actual experimentation based on your thoughts - how would you go about falsifying your ideas?

[A-wal]

Thanks but a PhD isn't something I could go straight into, it's a very long road. Besides, I don't think that a person should need to be in the mainstream scientific community to make a contribution to science. If they have something worthwhile that it really shouldn't matter. GR makes an invalid and unsupported assertion and the description of gravity that's based on it is far more complicated than one that describes universal acceleration. I really don't think that GR has a leg to stand on if there's nothing at the moment that can test any contradicting predictions.

 

I'm not sure there's any practical experiments that could be done any time soon that could distinguish between the two but the onus shouldn't be on the postulate that I'm using, that gravitational acceleration is equivalent to acceleration free from gravity. GR's postulate that free-fall is inertial is the one that should need supporting evidence because it claims that gravitational acceleration is special. There's nothing to support this assertion when you consider that tidal force behaves in exactly the same way as the force felt by accelerating objects free from gravitation.

 

I think the only thing I can really do is submit it with the Rindler coordinates for an accelerating object and the Schwarzschild coordinates for an inertial one and see what happens.

[A-wal]

I made a graph showing that it would take an infinite amount of proper time for a free-falling observer to reach an event horizon of an everlasting black hole of constant spacial volume.

 

Scientists prefer pretty pictures to reading words, like small children. :)

 

 

Could someone tell me the equation for radius decrease to time dilation please? I'd like to do this properly.

 

Maybe it's not important, it shows the fact that proper time goes up in a curve with an ever increasing angle and becomes vertical at the horizon. Is that enough or will it get rejected out of hand for not being concise enough?

[A-wal]

I shouldn't have said proper time for the first graph, that's misleading. Proper time slows down as the event horizon is approached. I meant the time that passes in the rest of the universe in the free-fallers frame of reference, including the time that passes for the black hole in the free-fallers frame of reference. From the black hole's own frame of reference it doesn't exist for any length of proper time or occupy any amount of space because it's a singularity in all four dimensions.

 

This graph shows it better and incorporates the change in volume in all four dimensions over time as the event horizon is approached as well as showing the Rindler horizon.

[A-wal]

I worded it badly again. I shouldn't have said the time that passes on the black hole's watch from the free-faller's frame of reference. The time that passes on the black holes watch is zero from any frame of reference because it's the proper time experience by the infinitely time dilated singularity.

I want to turn this into a proper and concise coordinate system but I need a bit of help, I've never done anything like this before.

 

I've been looking around for how the contradiction in coordinate systems that show objects not being able to reach an event horizon and coordinate systems that show them crossing the horizon is resolved and I really can't believe some of the language that's used to attempt to brush it under the carpet. The Schwarzschild coordinates are "ill-behaved" at the event horizon so you need to switch to a coordinate system that's "well-behaved". Wtf? You can't just ignore what a coordinate system shows when it shows something inconvenient! If the Schwarzschild coordinates are accurate then they're accurate at the horizon. If they're not accurate at the horizon then they're not accurate anywhere else either! Unbelievable. That's supposed to be scientific! And another classic, it's okay for objects crossing the event horizon relative to to external objects (all of them in fact) because it's space that's moving moving faster than the speed of light not the falling object. :)

 

I want this coordinate system to show the falling object's velocity (represented by the blue line) relative to the singularity with the red lines for the two horizons and with a dotted line to show the time dilation experienced by the free-faller by showing the increase in amount of time that passes for a distant inertial observer from the free-faller's accelerating frame of reference. Then I want to show that it can be morphed into the Schwarzschild coordinates to show it from the perspective of a distant inertial observer without any contradictions. I don't see how that's possible with coordinates that allow objects to cross the event horizon because they'd have to cross back across the horizon.

 

So the the falling object's world line will curve to show acceleration being multiplied by four every time the distance is halved, the Rindler horizon will use ( A+B ) / ( 1 - AB ) and the event horizon will be the same thing the other side. Maybe I can do this myself, it's simpler than I thought. What's the time dilation formula so I can plot the dotted line? Anyone fancy making a graph? This is going to take me ages using paint.