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A wal
  • A wal
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The Proper Theory Of Relativity

Everything below is based on a new fundamental law that I figured out. If you reverse everything within a system then relativity everything stays exactly the same unless it's viewed from an external frame of reference. The curved space-time caused by gravity in the general theory of relativity also applies to ordinary acceleration. There is absolutely no difference between an object following a straight line in curved space-time and an object following a curved path in flat space-time. Gravity creates inwards curvature which pulls all masses towards each other, rather than conventional acceleration caused by outwards curvature. Gravity is a force of mass rather than energy which is why it's so much weaker than electro-magnetism.

The reason why General Relativity and Quantum Mechanics don't work together is because General Relativity's wrong. Singularities are not places where the laws of relativity break down. They're places that the laws of relativity prevent from ever being reached. A black hole is a four dimensional bubble of space-time, with the event horizon representing the physical boundary imposed by the speed of light that increases size the more space-time there is between the it and the observer. The concept of curved space-time hasn't been applied correctly and the result is a description of gravity that treats falling objects as equivalent to objects at rest in the sense that a falling object isn't under the influence of a force. This leads to objects being able to accelerate beyond a relative velocity of the speed of light when the pass the event horizon of a black hole, which is impossible.

Set the posts to newest first and start from the top to read the rest.

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  • Ofj Smith

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    Oct 19 2012: Hi A Wal,
    There's a question that's been puzzling me:
    Relative to a stationary observer,how does one calculate/determine the rate at which an object observed 'decreases' in size when viewed by that observer as it moves away at a contact speed?
    This is because objects are viewed as 'smaller' as they move away from an observer.
    Thanks!
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    A wal

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    Oct 10 2012: Short version:

    Introduction
    If you reverse everything within a system then relativity everything stays exactly the same unless it's viewed from an external frame of reference. The general theory of relativity introduces the concept of curved space-time, which basically means viewing motion as a change in the distances between objects rather than movement of the objects themselves. There is absolutely no difference between following a curved path in flat space-time and following a straight line in curved space-time. The reason why quantum mechanics and general relativity are incompatible is because general relativity doesn't treat them as physically equivalent. It describes a free-falling object as the equivalent of an inertial object because the force is acting on the space-time that the object is moving through instead of the object itself. This is incorrect. Length contraction and time dilation also change the space-time that objects are moving through when they accelerate in the conventional sense and this can be used to explain the force they feel as the difference in the curvature of space-time that the different parts of the objects are moving through in the same way that general relativity describes tidal force. Massive objects cause inwards curvature, making them gravitate towards each other, while energy causes outwards curvature, making objects move away the the source. Energy equals mass times the speed of light squared, so gravity is that much weaker.
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      natasha nikulina 50+

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      TED Translator
      Oct 16 2012: Hi, A wal !
      The real difficulty we have in understanding space on the material level is due to the fact that, while material bodies exist in space, space also exists in these same material bodies.
      Taking into consideration that an atom is 99. 9999...% empty space , an object, no matter how big is separated from ' outer' space by a thin vernier , it's more like an image; space carries images, not objects move in the space. Would you agree that the idea of ' unbroken wholeness ' holds the key to the Theory of Everything ?
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    A wal

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    Oct 10 2012: ...
    Black Hole Geometry
    When a black hole forms it expands outwards at the speed of light until it's reached its maximum size and then immediately contracts inwards at the speed of light creating a four dimensional sphere. Information moves at the speed of light as well so an observer would see it appear at its full size and then rush inwards. It's size in all four dimensions increases as the distance of an observer increases, and at an ever decreasing rate the further away the observer. At zero distance the black hole has no size at all. A singularity is a point in time and space and so can never be reached by an object, even one accelerating towards it because the closer an object gets, the smaller it is. A black hole is just what a singularity looks like from a distance as length contraction and time dilation decrease.

    Horizons
    When an object is observed free-falling towards a black hole it becomes more length contracted and time dilated as it's relative velocity increases in exactly the same way as an object accelerating away using energy, and light from an ever decreasing distance will never reach them as long as they keep accelerating at at least the same rate in the same way as the Rindler horizon approaches an accelerator if their acceleration increase. If an object were able to reach an event horizon then light from behind it would start from in front of it as the two horizons cross over, in exactly the same way that a Rindler horizon and light emitted from the front of an accelerator would cross over if it were able to accelerate to a relative velocity of c.
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    A wal

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    Oct 10 2012: ...
    Event Horizon Paradox
    It can't be possible for an object to reach an event horizon from the perspective of any external object, even one accelerating towards the black hole. If it was then then that object would have to escape from the black hole and come back across the event horizon from the external objects perspective if it accelerates away, so if objects can't possibly reach the event horizon while there still is an event horizon. In others words black holes are unreachable.

    Rope Paradox
    A spaceship attached by a rope to a another spaceship maintaining a constant distance from the black hole free-falls towards the event horizon. The rope goes taut after the free-falling ship crosses the event horizon from its own perspective and then the other ship then tries to pull away. The free-falling ship is still outside the event horizon from the perspective of the ship pulling it out so it can be done from the perspective of this ship, but not the free-falling ship. General relativity isn't even self consistent.

    Universal Curvature/AccelerationThe universe is also a four dimensional sphere, but one that we can't exit rather than enter. It's curved just like the surface of the Earth but in time as well as space. We see red shift because we're looking across this curvature, and objects become more red shifted the further across it we look. Everything funnels into a singularity if we look across to the opposite side of the universe in time or in space, creating the illusion of dark flow and the big bang. I don't think the physical constants are independent variables, they're relative. If you were to adjust one then the others would also change, so that in fact there would be no change at all.
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      natasha nikulina 50+

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      TED Translator
      Oct 16 2012: " black holes are unreachable."
      And now let's try to reconcile your statement with another : black hole is ubiquitous.
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    natasha nikulina 50+

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    TED Translator
    Oct 4 2012: By mistake I've deleted my previous post.
    So... once more .
    Thanks for your kind response in you closing statement :)
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    natasha nikulina 50+

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    TED Translator
    Oct 4 2012: Re : I do believe in the determinism.
    Would you agree that it is just a 'model' your mind feels comfortable with ?
    If you take 'no spacetime ' zone , it's 'determined' to all possible probabilities and the very notion ' determinism' makes no sense under the circumstances.
    If you take the 'perception' zone, which is unfolding in spacetime , hypothetically it can be determined by the ' attractor' and we can see the most likely development , "everything that CAN happen does", so it is limited by 'can' but still it is not cut off from all possibilities completely. It gives slim but still an opportunity for ' can't ' being converted into 'can' Sorry, it's really a kind of unlanguagable, at least for me :) Here is the quantum measurement problem : the observer and the observed are not distinct , the very act of observation changes the picture and the observer as a part of the picture . So, certainty is a kind of impossible condition. It is not only the failure of our human mind but the very nature of the Whole, 'it's constantly branching into alternate possibilities ' in a sense it is never complete, though it is everything . Iow. we can see the road but we don't know how the scenery will look like. As I understand it, the 'fabric' of the whole existence in its all seeming complexity can lead to some more likely to occur outcome, but it is not written down it is not certain. It gives the room for an 'unconscious' choice while conscious choice ( decision ) is always in the main stream motion and in a sense is not choice at all.
    And it is also just a model my mind feels more or less comfortable with, nothing more.
    Thanks for reading this :)
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      A wal

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      Oct 4 2012: We become part of any system that we try to measure so it's the fact that we try to know in the first place that makes the situation inherently unknowable, so the it's not really uncertain. It's just uncertain to anyone who tries to know. I think that made sense. My brain hurts.
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        natasha nikulina 50+

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        TED Translator
        Oct 5 2012: Maybe it is not necessary to achieve the closure with this
        stuff ? And in fact any belief system ( which we erroneously call knowledge ) that offers closure - meaning final answers- is sure to be wrong.
        So, one of the ideas I'd like to put out is the idea ( and it may seem strange in this menu, but perhaps not ) that we should feel comfortable not to know. Just enjoy the way with no place of destination :)
        Cheers !
        Thanks for the conversation !
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    A wal

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    Sep 26 2012: Short version using a quick thought experiment. I love these. (:

    Two objects start along side each other and fall towards a black hole. Before they reach the event horizon one accelerates away. What you have is simply two objects accelerating away from each other. They can't ever reach the speed of light relative to each other no matter how much energy is used because time dilation and length contraction prevent it. No amount of gravity can make that happen because no amount of energy can. General relativity says the falling object does reach the speed of light relative to one accelerating away, but not the other way round. That's the equivalent of the object accelerating away reaching the speed of light. Length contraction can create potentially infinite distance between any object and the event horizon and time dilation slows any object doing it just as they keep any object from reaching the speed of light by creating more distance and giving them less time to cover it. It's exactly the same situation except one is being caused by an outward force and the other by an inward one. You can view acceleration in flat space-time as curvature just as easily as with gravity. The difference is that gravity is positively/inwardly curved and energy is negatively/outwardly curved. The falling object still feels acceleration, it's just called tidal force. General relativity ignores the force felt by the falling object and says look, it's at rest. Well that can just as easily be done with acceleration as well. Acceleration is just as relative as velocity. If acceleration were smoothly distributed thought a body then all that object would feel is the difference in the strength of that acceleration over the different parts of the object. Feeling acceleration is indistinguishable from feeling tidal force. There isn't one example of how they differ, which means that special relativity is a universal theory of acceleration, explaining gravity just as easily as any other force.
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    A wal

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    Sep 25 2012: BUGGER! I forgot you can change the order of the posts. I really should have explained that for this to make sense it has to be set to newest first and read from the the top down. Sorry. (: That explains it. It should be easier to follow now. I'm such a plonker.
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    A wal

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    Sep 23 2012: I think this could also explain dark matter. Black dwarves are burned out white dwarves but in the current model there hasn't been anywhere near enough time for one to exist, but in an eternal universe there could be loads out there.
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    Justin Elkin

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    Sep 22 2012: What's your thoughts on Hawking's Unified theory? What of the "lawlessness" of quantum mechanics?
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      A wal

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      Sep 22 2012: I don't know what you mean by lawlessness. Is that an actual term for something or are you speaking generally? Quantum mechanics can seem very weird but it still follows laws, the conservation of energy for example.

      I didn't even know Hawking had a unified theory. What's he trying to unify?
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    Justin Elkin

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    Sep 22 2012: What's your thoughts on how Time factors in? I was under the understanding that going towards the event horizon would cause that frame of reference to view the outside universe at an ever increasing speed. Isn't it possible that nothing has crossed over a event horizon in this universe? just transformed into some sort of Energy reciprocal of mass?
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      A wal

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      Sep 22 2012: Yep! That's exactly right. That's what gamma ray bursts are. (:

  • Richard Krooman 50+

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    Sep 22 2012: First of all it is quite confusing how the text is cut up in many pieces (I haven't attempted to read this as seeing how you posted them all within minutes I take it that you have written this out in a document). Could you please add a link to your post towards your own document such that it is easier to read?

    Secondly I've read that if you can't explain your idea in 1 line it's not a good idea.
    Could you try to summarize what the concept is you're talking about? (perhaps you've already done this but I haven't read it that detailed because of the 1st point)
    I have a feeling like it is a very basic concept (just like the special relativity is actually not a hard concept) by just skipping through most text. In the parts that I've skipped through you're mainly explaining what phenomena are not correctly explained etc.
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      A wal

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      Sep 22 2012: Copy and paste it.

      General relativity is wrong. Special relativity is right. It's so right that it can do what general relativity tries and fails to do. It can describe gravity almost effortlessly and without the weird stuff associated with singularities, and in over a century no ones bloody noticed! Einstein spent over a decade coming up with a failed attempt to reformulate his own theory. Whoops!

      • Richard Krooman 50+

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        Sep 22 2012: 1) ok then I won't read it.

        2) I doubt that. But I hope you're right.
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          A wal

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          Sep 23 2012: I would have thought that fact that's broken up into bite sized chunks would make it easier to read.

          That's perfectly understandable. I'd think the exact same thing if I didn't know better. You'll never know if you don't read it though.

      • Richard Krooman 50+

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        Sep 23 2012: I get confused from time to time where you are refering to. When I read the posts some of them do not refer to the previous post at all while others partially do and a few seem to be directly continue the previous post.
        So for me it's kind of a jigsaw puzzle that I don't want to solve in order to be able to read it.

        It is not even clear if I should read the oldest one first or the newest one first (although that is because I have not made any real effort to do so).
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          A wal

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          Sep 23 2012: Oh crap! Yea they may be in the wrong order actually. It's because I coppied it to another site and then coppied it from there backwards so it would be in the right order, but I think I messed it up. (: Whoops. Why do I always make stupid mistakes like that? I'll sort it out and let you know when it's done. Sorry people. No wonder people have been saying it's confusing. DOH!

      • Richard Krooman 50+

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        Sep 23 2012: I think I'm the only guy saying that it's somewhat confusing but imo you would do better if you just write a document and put it up on the web somewhere and just put the link up in the origional post.

        Do like: Hey dudes "General relativity is wrong. Special relativity is right. It's so right that it can do what general relativity tries and fails to do. It can describe gravity almost effortlessly and without the weird stuff associated with singularities, and in over a century no ones bloody noticed! Einstein spent over a decade coming up with a failed attempt to reformulate his own theory. Whoops!" and here is why link to document.

        That way the few people that are interrested in the topic will still read it.
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          A wal

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          Sep 23 2012: It was in the right order from the top down but the paragraph breaks were in stupid places because of the character limit from before, I forgot about that but it's sorted now. Somebody else said it was hard to follow in the cause of gravity topic. Anyway, most people who read these conversations don't post. In fact this topic has gotten lots of responses because my other topics are all different aspects of this. A lot of people probably just look at the title and think yea right and don't bother. I can't say I blame them. It could do with a rewrite and trimming but that's why I broke it up into separate topics. Which parts do you think are hard to follow?
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    A wal

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    Sep 21 2012: When an object accelerates away from a black hole it can't pass other falling objects at a relative velocity greater than the speed of light no matter how fast it moves away from the black hole. But in General Relativity the relative velocity between them does exceed the speed of light when the falling object reaches the event horizon. This is because a falling object is wrongly considered to be equivalent to an object at rest in the absence of gravity. In this definition gravity becomes a pseudo-force because it's the space-time between them being affected rather than the objects that occupy that space-time. There is absolutely no difference between describing objects as being accelerated by a force and correctly describing the curvature between them as the mechanism for acceleration. There is a universal law of acceleration. When an object accelerates it creates a Rindler horizon which is mistakenly considered as being equivalent to the event horizon of a black hole. There is a gravitational equivalent of the Rindler horizon but it's not an event horizon. The event horizon is the gravitational equivalent of the light speed horizon. The problem is that General Relativity is a failed attempt to formulate Special Relativity, describing gravity as the curvature of the space-time between objects. In other words describing the space-time between objects as changing instead of the objects being accelerated by a force, but if it's done properly it will lead to exactly the same predictions as using Special Relativity to describe gravity as a traditional force because it's equivalent. Acceleration itself is what causes curved space-time, regardless of the cause. To travel along a curved path you have to move through two dimensions simultaneously.
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    A wal

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    Sep 21 2012: If one of those dimensions is time then you feel yourself being pushed back in one spacial dimension in the opposite direction that you're traveling in and you feel yourself being pushed in time instead of feeling yourself being pushed in the opposite direction of two spacial dimensions. Acceleration in a straight line in three dimensions creates a curved path in four dimensions. Galilean Relativity says that there can be no such thing as absolute motion because if an object is heading towards you then you could equally view yourself as moving towards the other object which is static. You can only view motion as the change in the distance between objects. It doesn't even make sense to ask which ones are static and which ones are moving. We normally measure motion relative to the ground, but ground speed is different to air speed because you're measuring your motion relative to a different background. Whenever you look at an object you're seeing it as it was in the past because you're looking further back in time the further away that light is coming from. The relative velocity of the light itself isn't an issue because it was discovered later that the speed of light is constant. It's impossible to even approach the speed of light from your own perspective and it's impossible for anything with mass to move as fast as light relative to anything else with mass. Light moves at the same velocity relative to every object in the universe regardless of the objects velocities relative to each other or the relative velocity of the source of the light. That means that two objects with different relative velocities are seeing the same light moving at different speeds after their velocity relative to the object producing the light is taken into account.
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    A wal

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    Sep 21 2012: If an object is one light year away from you and heading towards you at half the speed of light then you're going to have to see three years of its history in the two years it takes to reach you so it will look to you as though it's moving quickly through time, so the light waves will be more frequent. The higher frequency of the light waves squashes them making their colour blue shifted. It's called Doppler shift. If it's moving away from you then the light waves get stretched which reduces their frequency, red shifting them and making it look to you like it's moving slowly through time. It doesn't mean their speed through time is actually altered because it's relative and they would see you moving just as quickly or slowly through time because the situation is symmetrical. A spaceship leaves Earth and and accelerates to half the speed of light. From Earths perspective the ship is constantly traveling through space-time that's more and more length contracted and time dilated as its acceleration increases so the same amount of energy is moving it over a shorter distance, so its mass has increased (E=mc^2). It would take an infinite amount of energy for the ship to accelerate to a relative velocity of the speed of light. Earth is also covering less distance (length contraction) and is moving slower through time (time dilation) from the perspective of the ship because both frames of reference are equally valid. It would look the same for the ship if Earth were another ship with its headlights pointing in the opposite direction. What separates them is acceleration. In this case the ship started off in the same frame as Earth and then accelerated to half the speed of light.
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    A wal

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    Sep 21 2012: If they were to accelerate back into Earths frame then more time (time dilation) would have passed on the clocks on Earth, so people who were the same age as you will now be older than you. And you would have traveled further through space (length contraction) by Earths measurements, so the distance between the ship and any object in the direction it was accelerating would have been shortened when moving towards it at half the speed of light relative to Earth.

    So you can travel great distances (because length contracts) very quickly (because time dilates) from the perspective whichever frame you happen to be in and do it in a short amount of time by your own watch if you accelerate enough but for those who stayed behind it would take longer for you to travel the same distance and you would have further to go. When an object accelerates relative to a magnetic field the electrons get closer together giving the field a negative charge and turning it into an electric field, which is how electricity and magnetism were unified into the electro-magnetic force. That's Einsteins Special Theory Of Relativity. The ship heads back towards Earth at half the speed of light so is seeing us moving towards it at half the speed of light and sees the bubble of light/radio and whatever waves we're emitting as warped with respect to Earth because the light coming towards the ship directly between them is moving away from Earth at half the speed of light from the ships perspective, and the light moving directly away from the ship and Earth is moving away from Earth at one and a half times the speed of light from the ships perspective to keep the speed of light constant. For the ship to come home it needs to accelerate into Earths frame.
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    A wal

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    Sep 21 2012: From the ships perspective the Earth is heading towards it at half the speed of light and the ship needs to be at rest relative to Earth when the Earth reaches them so it's going to have to accelerate in the same direction that the Earth is traveling, which is the opposite direction to where Earth is now so that when Earth catches up with the ship they will be moving at the same speed and it doesn't get a rock so heavy that it has a cloud of gas held to it by gravity, a magnetic field generated by the molten core to protect itself and spaceship building moss smashing into it at half the speed of light. From Earths perspective the ship needs to break. That warped bubble is going to become a perfect sphere from the ships perspective when it reaches the same relative velocity as Earth and becomes static relative to it. To start with the ship sees the light heading towards them between them and Earth as heading away from Earth at half the speed of light, because Earth's moving towards them at half the speed of light which gives the correct combined relative velocity of the light coming towards the ship. When the ship lands it's going to be in a frame of reference where the light was always moving away from Earth at the speed of light, not half the speed of light. Relative velocity is a measurement of distance over time. So the light had further to travel and/or took longer to do it in the ships previous frame so that the light could speed up relative to Earth from the ships perspective when the ship moved into Earths frame to keep the speed of light the same relative to the ship.
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    A wal

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    Sep 21 2012: Either the ship was measuring less distance over the same amount of space (length contraction) in its previous frame making the light travel through less space in the same amount of time, or it was measuring less distance over the same amount of time (time dilation) than Earth was measuring, making the light take longer to travel the same distance. It's actually half of each because any two objects are separated in time and one spacial dimension because you can draw a straight line between any two objects. The light was moving away from Earth at half the speed of light so the extra distance multiplied by the extra time made up the other half. As the ship was braking from Earths perspective it was measuring the same amount of space and time (when the ship was seeing the light moving away from Earth at half the speed of light in the ship previous frame) covering a greater distance (when the ship was seeing the light moving away from Earth at the full speed of light when they're in the same frame after it landed). So it was getting less and less length contracted and time dilated from Earths frame as it accelerated into it, so more time had passed for the Earth than for the ship when the ship returned because it was the ship that accelerated. The way the amount of length contraction and time dilation changes between different frames is called the Lorenz transformations. Basically length contracts and time dilates for any accelerator to keep all of the different velocities of light relative to the same objects from all the different frames of reference consistent with each other.
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    A wal

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    Sep 21 2012: When an object travels along a curved path it's traveling through two dimensions at the same time which is felt as g-force pulling it to one side. Time is also a dimension so an object can travel along a curved path through time and one spacial dimension. This is acceleration and is felt as g-force pulling an object in the opposite direction to its motion. As an object uses constant acceleration to maintain a constant velocity following a curved path through two spacial dimensions it experiences shortening of its initial two dimensions approaching zero as the angle reaches ninety degrees. The same thing happens in the form of time dilation and length contraction when using acceleration to follow a curved path in time and one spacial dimension which are also at right angles to each other, with ninety degrees representing infinite acceleration at a velocity of the speed of light. When an object moves through two spacial dimensions, if you add up the distance it moved through one dimension to the distance it moved it moved through the other spacial dimension then the total is greater than an object that follows a curved path to reach the same point. An observer at rest is moving through one spacial dimension (as long as you're not at rest relative to it) and one temporal dimension (not that there's any real physical difference between them) and because they're not following a curved path it means that they're taking a longer rout than an object that starts off in the same place as them and then accelerates away, then accelerates back along side them. So more time would have passed for the object that accelerated because they followed a curved path, effectively taking a short cut into the future.
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    A wal

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    Sep 21 2012: General Relativity introduces the concept of curved space-time to explain gravity but it assumes that it's somehow fundamentally different to the other forces and applies only to gravity, and leads to different results than it would if you were to view gravity as a force in flat space-time. One of the postulates of General Relativity says acceleration and gravity are equivalent, but it doesn't describe them as equivalent in every sense. General Relativity describes an object in free-fall as equivalent to an object at rest in flat space-time. This creates an area of space-time where gravity overpowers the other outward pushing forces to produce a black hole. The Earth is a solid object which means there's an electro-magnetic force to counteract the Earths gravity and accelerate us upwards. We can't feel gravity pulling us down which is why we can't feel our weight when we're in free-fall, but we can feel the acceleration that's used to resist gravity which is why we feel our weight when we're not falling. Apparently this distinction is able to explain how it's possible for an object to move past a point in space-time where no amount of acceleration will be able to resist the pull of gravity when it reaches the event horizon of a black hole, because curved space-time is able to move them at a relative velocity of the speed of light and beyond because it's doing it without accelerating them and this creates objects of infinite density called singularities, which is where the laws break down. A group of inwardly contracting objects can't become infinitely dense any more than a group of outwardly expanding objects could become infinitely diffuse because that would literally take forever.
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    A wal

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    Sep 21 2012: Instead length contraction and time dilation allow for an unlimited amount of room to accelerate before that could happen, just as they allow for an unlimited amount of room to accelerate before you could reach the speed of light. When there's no force to oppose gravity it causes objects to keep on accelerating indefinitely while the mass is there. This is why Quantum Mechanics and curved space-time don't work together. Quantum Mechanics shows that gravity needs to be quantisized as well, so the whole concept of curved space-time must be the exact equivalent of a traditional force using particles to interact in flat space-time. Objects under different amounts of gravity accelerate away from each other in the same way they would if they were using different amounts of energy to accelerate. The reason you're not supposed to be able to escape from a black hole is because you can't accelerate away because you're relative velocity increases slower from the perspective of an object that's not accelerating (length contraction and time dilation) to keep the relative velocity below the speed of light, which isn't enough to escape because supposedly gravity has accelerated the objects in the opposite direction to a relative velocity faster than the speed of light. That's ridiculous because acceleration is a change in the relative velocity between two objects. No amount of acceleration would allow an object to reach a point where no amount of acceleration in the opposite direction will move them that way because that would mean that it's reached a relative velocity of the speed of light and that would mean that take an infinite amount gravity.
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    A wal

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    Sep 21 2012: If two objects accelerate in opposite directions enough then of course they'll keep moving away from each other no matter how much gravity they're in. Curved space-time just means viewing the space between objects as changing over time instead of viewing the objects themselves as moving, and it should make no difference to the result of anything because they're exactly equivalent. You can clearly see that acceleration and curvature are the same thing if you look at an accelerating object from the perspective of an object with a different relative velocity. When two objects have the same relative velocity they're always following a straight path because you can always draw a straight line between any two objects, but one of them accelerates then the other object will see the accelerating one following a curved path. This is how gravity curves space-time and it obviously doesn't make any difference whether the curvature is caused by a force of energy or a force of mass unless there's reason to think it does, and there just isn't! You could view all acceleration as a curvature of space-time. The fact that an object can feel acceleration when it's caused by an ordinary force but apparently not gravity because it's special is used to justify why the falling object is equivalent a non-accelerating object in flat space-time. There is an equivalent to the g-force you feel when you accelerate called tidal force. Tidal force is caused by the difference in gravitational strength between two parts of the same object. Well so is acceleration when it's caused by energy.
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    A wal

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    Sep 21 2012: The reason we can feel the downwards force of the acceleration of the ground pushing us up but not the upwards force of gravity pulling us down is because the g-force pulling us down is due to all the upwards force of Earth pushing on us being concentrated on our feet when we stand, which is why we feel like we weigh less when we're lying down and decrease the difference in the amount of energy over the different parts of our body. But the tidal force caused by the difference in strength of gravity over the different parts of our body is always very small, so we don't feel it. You can see that acceleration, curvature and gravity are all the same thing if you imagine two objects orbiting in perfect circles on the same plane in opposite directions. If you just look at the relative velocity between two orbiting objects and ignore everything else then as they move apart the curvature of their orbits causes them to accelerate away from each other at an increasing rate until they're on opposite sides of their orbits, and then they accelerate towards each other again. Their watches always match when they pass because their rate of acceleration is always the same as each others. Any object outside the system watching from a distance would be aging quicker because they're not length contracted and time dilated because they're not accelerating.
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    A wal

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    Sep 21 2012: A force can reduce the space-time between objects or it can create space-time between them, in the same way that space-time can be curved inwards, pulling objects in, or curved outwards, pushing them away. Energy pushes matter outwards and mass pulls matter inwards and because E=mc^2 you would expect gravity to be vastly weaker than a force of energy. I'm guessing gravity has exactly the same strength as the equivalent amount of electro-magnetism if you times it by the speed of light and square it. From the perspective of an object that's using constant acceleration to hover at a constant distance it's impossible for anything to reach an event horizon of a black hole because it's equivalent to an object reaching the speed of light. This is called the Schwarzchild coordinate system. From the perspective of an outside object it's never too late for a falling object (or even an object constantly accelerating towards the black hole) to turn round and come back as long as it has access to an unlimited supply of energy. Gravity increases as an inverse square of the distance so the relative velocity of a free-falling object quadruples when the distance is halved from the perspective of any object that's static relative to the black hole. Length contraction and time dilation continually increase at an increasing rate the closer they look to the horizon, in exactly the same way that it would if they were watching an accelerating object approaching the speed of light relative to them.
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    A wal

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    Sep 21 2012: An object that's quadrupling its acceleration every time the distance between you is halved would never be able to reach you because if the distance between you were to reach zero then the object would be infinitely accelerated and would have reached the speed of light relative to you, but in General Relativity it is supposedly possible for a falling object to reach the speed of light relative to the singularity and every outside object in the universe, which is why not even light can escape from inside an event horizon. General Relativity describes a falling object as equivalent to an object at rest and an object at rest relative to the black hole as equivalent to an accelerating object. It's true that the hovering object is constantly accelerating to maintain a constant distance but the fact that it's consistent means that a hovering object is the equivalent of an object at rest in the absence of gravity because the pull of gravity in one direction is being canceled out by the push of the engines in the opposite direction. For every action there is an equal and opposite reaction. Whenever an object accelerates it creates what's know as a Rindler horizon following behind it. It marks the point past which nothing, not even light would be able to catch an accelerating object as long as it keeps accelerating at at least the same rate.
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    A wal

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    Sep 21 2012: If the object keeps its acceleration constant then the Rindler horizon stays the same distance behind them. It starts off very far away at low acceleration and gets closer to the object if its acceleration increases and would catch up to them if they were able to accelerate to the speed of light, since light from behind this horizon could never reach reach them, which is why it's paradoxical to reach the speed of light. Objects can't ever reach the Rindler horizon from the accelerators perspective. They just get more and more length contracted and time dilated as their velocity increases relative to the accelerating object in exactly the same way that the accelerating object gets more and more length contracted and time dilated from the perspective of an object at rest. They do however cross the Rindler horizon from their own perspective at the point when light from them will never catch up to the accelerating object as long as they don't decrease their rate of acceleration and this is the reason for the difference on their watches when they meet up because it means the accelerator is measuring less distance in space and time the further they look towards the Rindler horizon so that nothing reaches it from their perspective. An object moving past a Rindler horizon from their own perspective is often compared to a falling object moving past the event horizon of a black hole from their own perspective, but that doesn't follow because that's the equivalent of saying objects can reach a velocity of the speed of light relative to every object in the universe when they reach the event horizon of a black hole, but only from their own perspective.
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    A wal

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    Sep 21 2012: Apparently the Schwarzchild coordinates don't cover the entire manifold and that's why a falling object can't reach an event horizon from the perspective of an outside object. A coordinate system that doesn't cover the entire manifold isn't valid. It would mean that there's no absolute truth even within the context of your own frame of reference because objects would be both inside and outside the event horizon and moving above and below the speed of light at the same time when other coordinate systems are taken into account. It's the falling object that's experiencing increasing length contraction and time dilation, and at an ever increasing rate as they approach the speed of light. Less time would have passed for the falling object if they were to pull away and compare watches with the hovering object, so the falling object is obviously equivalent to an accelerating object. There's no distinction between being accelerated by gravity (mass) and being accelerated by energy other than the cause and the fact that mass attracts and energy repels, or mass curves space-time inwards and energy curves it outwards, depending on how you want to look at it. The event horizon isn't equivalent to the Rindler horizon, it's equivalent to the light speed horizon, which would make perfect sense considering the event horizon is the point when any falling object would have accelerated to the speed of light relative to any outside object, which no amount of gravity should be able to do just as no amount of energy can. The equivalent to a Rindler horizon is a horizon that follows behind a faller that even light can't reach them from behind as long as they keep falling at at least the same rate that objects can't reach from the fallers perspective because they just get more and more time dilated and length contracted without ever reaching the horizon.
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    A wal

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    Sep 21 2012: The falling object is being accelerated purely by gravity, so is moving towards an unreachable horizon that's moving away from them at the speed of light and would be length contracted and time dilated from the perspective of a non-accelerating object, exactly like an object approaching the speed light. This horizon would cross them in the opposite direction if they were able to reach the event horizon so that no object in front of them up to an ever increasing distance would be able to catch them. That's the exact equivalent of an objects Rindler horizon overtaking it in the opposite direction if they were able to accelerate to the speed of light so that no object in front of them up to a certain distance would be able to catch them, and it makes exactly the same amount of sense. If nothing can reach a falling object from beyond this horizon then an object following behind them would never be able to reach them no matter how much they accelerate as long as the faller keeps falling at at least the same rate, so what happens when an object from behind this horizon approaches a falling object that they can never catch but also an object that can never reach the event horizon?
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