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Four days ago I discovered something interesting which I've been trying to rule out ever since. Perhaps someone else can help with this, because it's putting up a strong fight. The key idea here is that if the path of light is deflected slightly by the existence of a massive object nearby (through any mechanism, including the one in General Relativity), it looks as if it could lead to an imbalance of forces in matter which will result in a force being generated that would accelerate it towards the massive object. In the case of GR, this would accelerate matter off the geodesic which it should be following.I happened upon this mechanism while thinking about length contraction in LET (Lorentz Ether Theory) and what might happen in a gravity well, so the best place to start is there. Start out by imagining a room in which all walls, floor and ceiling are square. There is a light in the middle which illuminates all these surfaces equally, though each square surface will be a little brighter in the middle and darker in the corners due to the distance the light has to travel before it reaches them - the further it goes, the more it will spread out and the dimmer it will be when it arrives.If the room is moving along at high speed, the light will have further to go before it can reach the leading wall, but it will also have less far to go to reach the trailing wall, so you would expect the leading wall to get dimmer with higher speed of the room and the trailing wall to get brighter, but that doesn't happen - the way the light is emitted is affected by the speed of travel of the lamp, so more light is concentrated forwards and less backwards, helping to reduce the difference in brightness between these two walls, but they will both be dimmer unless the room contracts in the direction of travel.[This concentration of light forwards and reduction backwards can be understood mechanistically if you imagine sending the light out sideways and reflecting it off a flat mirror - the movement of the mirror will make it act as if it is curved. If you think things through with lenses, you'll find similar effects which ultimately show you why light has to be concentrated forwards and reduced backwards whenever a light source moves.]But why should the room contract? Well, the forces holding atoms apart are also transmitted at the speed of light and they spread out in the same way, weakening over distance. This means that the atoms will naturally settle closer together in the direction of travel whenever they find themselves too far apart. By the time the forces have pulled all the atoms into the right places, the illumination will be equal again on both the leading and trailing walls, just as if the room was stationary.Now we can turn to a situation involving gravity where we have a very slight curvature of the paths followed by photons (caused by the nearby presence of a massive object like a star or planet), but these deviations will affect force carriers in the same way as they do with light. The result will be an extra spreading out of the forces in the direction away from the massive object and a reduced spreading towards the massive object. With light, this means that the wall furthest from the massive object will be dimmer than the wall nearest to the massive object, and it will be the same with the forces being applied. The result of this is that the wall furthest from the massive object will be pulled inwards towards the centre of the room because it's sitting further out from where the balance of force requires it to be, but the wall nearest the massive object will be pushed outwards away from the centre of the room because it's sitting to close in from where the balance of forces requires it to be. Both walls are being pushed by this towards the massive object.It wouldn't work quite like that, of course, because rather than a room we should be thinking about forces moving about within the atom nucleus, or even within electrons and quarks. The distances travelled by these force carriers would be very short and would have little opportunity to bend, but the effect would still build up rapidly over time as these forces are being applied continually, so the imbalance would be absolutely real and must generate a force towards the massive object.So, can anyone shoot this down?
I have worked it through and see your point exactly. Isn't this just a description of gravity? What makes you think this wouldn't follow a geodesic?
It is special relativity where no forces act. General relativity is different.http://csep10.phys.utk.edu/astr162/lect/cosmology/gravity.html
David have a look at this video and in the still frame before the slow motion look at the compression of the slinky at the bottom compared to the top. Think of this in relation to you mass deviation.//www.youtube.com/watch?v=rCw5JXD18y4Now how would this change with altitude? If at all.
Quote from: jeffreyH on 05/03/2015 18:15:19It is special relativity where no forces act. General relativity is different.http://csep10.phys.utk.edu/astr162/lect/cosmology/gravity.htmlBut in GR, gravity is not a force - time and space are warped in such a way that things can just follow straight lines and make it look as if there's a force acting when there isn't one. It may be that things are so warped by this though that the room in my thought experiment is distorted in such a way that there is no imbalance of forces, but I'm still trying to work out whether that's possible.Quote from: jeffreyH on 05/03/2015 18:35:20David have a look at this video and in the still frame before the slow motion look at the compression of the slinky at the bottom compared to the top. Think of this in relation to you mass deviation.//www.youtube.com/watch?v=rCw5JXD18y4Now how would this change with altitude? If at all.Nice video - I was wanting to find one like that, but I'm not sure how it relates to this. You aren't seeing compression there, but the opposite, and the stretching at any point is just a measure of the mass further down.[Someone should do a video of a slinky being dropped alongside a ball (dropped from the same height as the top of the slinky, and released at the same moment). I'd like to see if the top of the slinky would descend much more quickly than the ball.]
But in GR, gravity is not a force - time and space are warped in such a way that things can just follow straight lines and make it look as if there's a force acting when there isn't one.
Quote from: David CooperBut in GR, gravity is not a force - time and space are warped in such a way that things can just follow straight lines and make it look as if there's a force acting when there isn't one.That's a common misconception, David.
To see how to obtain the expression for the gravitational force in GR please see:http://home.comcast.net/~peter.m.brown/gr/grav_force.htm
People think that the gravitational force is really a manifestation of curved spacetime.
In the first place that has to do only with tidal forces and not gravitational forces in general. And spacetime curvature is quite literally just another name for tidal forces.
But you can certainly have gravitational forces in the absence of spacetime curvature. I've calculated it myself here:http://home.comcast.net/~peter.m.brown/gr/uniform_force.htmIf you'll notice Eq. (12) you'll see that it's identical to the Newtonian expression.
The only think that GR introduces is the notion that all gravitational forces are inertial forces and that in GR inertial forces are "real" whereas in Newtonian mechanics they're mostly considered to be a manifestation of the coordinate system being a non-inertial one.
I thought that was the whole point of GR - gravity explained by things following straight paths through a curved Spacetime without any need for any actual force of gravity to be applied at all.
Due to a crucial year spent with one of the world's worst maths teachers, that's just a page of meaningless squiggles to me. However, it is always possible to get past such obstacles with a bit of help in translating them into normal language.
When you talk about an expression for the gravitational force in GR, what exactly do you mean?
Is this an expression for working out the apparent gravitational force ...
when treating space as having Euclidean geometry (as used in LET) or is this a force within the non-Euclidean geometry of Spacetime?
If the latter, then it appears to be in conflict with the whole idea of things simply following geodesics, and that means a lot of experts are misleading the public.
That's because the experts keep telling the public that it is.
Is there anywhere I can read a reliable explanation of all this written in ordinary language which doesn't send the reader down the wrong path with misinformation? Every time I think I've finally got to the truth, someone tells me it's all wrong.
Quote from: David CooperI thought that was the whole point of GR - gravity explained by things following straight paths through a curved Spacetime without any need for any actual force of gravity to be applied at all.Not according to Einstein.
A body in free-fall will always follow a geodesic in spacetime, always. What I said doesn't change that one bit.
Think of a transparent tube upon the surface of which we have drawn a spiral that appears from a particular direction to be a sine wave. Then consider that we have started from the left hand side with a small wavelength and let this become progressively longer until it reaches its maximum at the right hand end. If we rotate this tube about the axis through its length then the wave will appear to move. The left hand end will then represent the maximum length contraction and the right hand end the minimum length contraction. However it will apear to take exactly the same time for a wave to traverse one wavelength at the left hand end as at the right.
Now consider that the time dilation is represented by a change in the angular momentum along the length of the tube so that the left hand end rotates more slowly than the right hand end. If this was one continuous wave the length of the tube there would be stresses along the wave as it is twisted tighter by the difference in rotation. This is like a twist in spacetime.EDIT: Actually it might make more sense for the left hand end to be rotating faster than the right hand end.
Quote from: jeffreyH on 09/03/2015 00:45:31Think of a transparent tube upon the surface of which we have drawn a spiral that appears from a particular direction to be a sine wave. Then consider that we have started from the left hand side with a small wavelength and let this become progressively longer until it reaches its maximum at the right hand end. If we rotate this tube about the axis through its length then the wave will appear to move. The left hand end will then represent the maximum length contraction and the right hand end the minimum length contraction. However it will apear to take exactly the same time for a wave to traverse one wavelength at the left hand end as at the right.I'm not sure it's correct to apply length-contraction to light (unless a slowing is imposed by an atmosphere). Length contraction of light requires the speed of light to change or the frequency to shift, and the frequency cannot change - only the perceived frequency can change due to time dilation.QuoteNow consider that the time dilation is represented by a change in the angular momentum along the length of the tube so that the left hand end rotates more slowly than the right hand end. If this was one continuous wave the length of the tube there would be stresses along the wave as it is twisted tighter by the difference in rotation. This is like a twist in spacetime.EDIT: Actually it might make more sense for the left hand end to be rotating faster than the right hand end.I don't think that's going to work either, because you're going to break the light by having different frequencies at different ends of it, and that's again impossible. It fits in with what someone might think if they measure the frequency at different altitudes and they insist on ignoring time dilation as an explanation for the apparent frequency changes.
The point is the wave will never be that spread out. It was a hypothetical analogy to show how spacetime could twist. This twisting could in theory be the mechanism that draws matter together. I am not entirely sure if this is anything like twistor space. This twisting could also explain induced rotation in orbiting bodies.
Quote from: jeffreyH on 09/03/2015 17:45:43The point is the wave will never be that spread out. It was a hypothetical analogy to show how spacetime could twist. This twisting could in theory be the mechanism that draws matter together. I am not entirely sure if this is anything like twistor space. This twisting could also explain induced rotation in orbiting bodies.A photon cannot spread out, but a group of photons can and will spread out. That is why the walls are darker the further the light has to go before hitting them, but each photon still delivers its full punch wherever it lands.