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Whereas current theory sets the theoretical "fastest" rate in the change in time due to gravity field at 0 gravity field, my model sets the theoretical "slowest" rate in the change of time to a 0 gravity field. The concept of time dilation for coordinate time is inverted, so coordinate time now runs fast in a black hole and slow out in space.
In the mean time, if you are a mathematician or have a computer program that you can plug these parameters into that would calculate this theory and you are interested, I'd dearly love to "know" if my model is viable..!
You would have to invert relativistic gamma in order for this to work. Although you say you ignore relativistic mass you can't in fact do that unless it is due to a constraint that you are applying upon the system for some reason. The other major issue is the fact that this would cause relativistic mass to decrease with velocity meaning it would get easier to accelerate the nearer to light speed a mass was traveling. I can't accept that one I'm afraid. The only way this could work would be at a turning point of some kind. It may be useful to study your theory with respect to the ergosphere of a black hole. However I am not sure what the results would be as I would need to work it out.
I am using the term "coordinate time" to describe the time at any coordinate in the universe according to its gravity field.
I use the inverse velocity equations twice. Once to calculate time dilation due to gravity (time gets slower in space by the same amount that distances get longer) and using these equations again, taking these increasing distances and inversely cubing them to create the geodesic structure of space.
...are the same equations used to calculate length contraction except in their inverse form.
"Coordinate time" is time dilation due to gravity field. (This time dilation departs from SR and GR in that it has been inverted. An increase in gravity field speeds time up)
"Actual time" needs coordinate time and proper time as a function to determine actual time. Taking coordinate time (predetermined by strength of gravity field) and subtracting proper time (determined by velocity) from it.
David...are the Lorentz transformations for time dilation due to motion that are inverted for length contraction the same equations as the Lorentz transformations for time dilation due to gravity that are inverted for velocity transformations? In that they hold the same values?
Quote from: timey on 03/06/2015 00:41:27I am using the term "coordinate time" to describe the time at any coordinate in the universe according to its gravity field.So in the scenario I presented in my previous post, I have a normal coordinate time ticking out 100 ticks while the hovering rocket only experiences 90 ticks of proper time (meaning its own time) [if you count that as proper time - it's running at a slowed rate due to gravity rather than movement], and you have it undergoing perhaps 110 ticks of your own special kind of coordinate time. I want to understand how that faster ticking rate of this special coordinate time relates to anything that's going on where the rocket is. It certainly can't be measured as 110 ticks by the rocket, and it doesn't show up as 110 ticks to any observer of the rocket, so what is this special kind of time actually doing? Who can measure it and how? If it can't be measured but is important for something, what is its role? What is it useful for?QuoteI use the inverse velocity equations twice. Once to calculate time dilation due to gravity (time gets slower in space by the same amount that distances get longer) and using these equations again, taking these increasing distances and inversely cubing them to create the geodesic structure of space.I can't follow this without seeing some actual numbers being put to specific events. What are these distances that are getting longer? What are these distances between and what do you have to be doing to make them appear longer?Quote...are the same equations used to calculate length contraction except in their inverse form.I need to see worked examples of what you're doing - I can only follow something like this when the numbers are put in front of me.Quote"Coordinate time" is time dilation due to gravity field. (This time dilation departs from SR and GR in that it has been inverted. An increase in gravity field speeds time up)It sounds as if you should have two kinds of proper time - one which clocks record when they're moving in deep space and another which clocks record when they're in a gravity well, but I can't work out whether you count that one at all, because your strange coordinate time which deals with "time dilation" due to gravity field does not tell you what a clock will record in a gravity well as it does the opposite, asserting that time is faster when the clock is ticking slower and that time is slower when the clock is ticking faster. This is making it difficult to understand your model because you haven't pinned down what the different kinds of time are in it and you haven't named them correctly.Quote"Actual time" needs coordinate time and proper time as a function to determine actual time. Taking coordinate time (predetermined by strength of gravity field) and subtracting proper time (determined by velocity) from it.Again I need to see a worked example or two with the actual numbers for some situation/event/scenario which I can visualise.QuoteDavid...are the Lorentz transformations for time dilation due to motion that are inverted for length contraction the same equations as the Lorentz transformations for time dilation due to gravity that are inverted for velocity transformations? In that they hold the same values?I don't use the Lortentz transformations, but work everything out through trigonometry instead. I get a value for time dilation and length contraction by the following method: speed = 0.866c --> arcsin 0.866 = 60 degrees (the angle that light will actually travel at if a moving light clock is lined up across the direction of travel) --> cos 60 = 0.5, so 0.5 is both the time dilation and the length contraction for that speed. There is no inversion involved for calculating either of them. The way(s) of calculating time dilation under gravity look quite different and I don't know if they can be shown to be equivalent in any way. I'm looking at one in which proper time for an object in a gravity well is calculated by taking coordinate time from some distant clock and multiplying it by the square root of 1-(2GM/rc^2) taken from http://en.wikipedia.org/wiki/Gravitational_time_dilation. Clearly this formula will give you proper time under gravity and not your special kind of coordinate time, so if you're wanting a formula for the latter, you can use whatever you find fits your needs. Then you need to explain what your special kind of coordinate time is useful for in some way that will help me get the point, because at the moment I'm at a complete loss as to what it's for.
David, to clarify, in my model a gravity well has a faster rate of time because an increase in gravity field makes the frequency of stuff faster. It makes the frequency of light faster, the cessium atoms frequency runs faster. Gravity is compressing the length of everything, including the length of a moment.
Of course it would be stupid to think that time runs faster when a clock is telling you that it is running slow or the opposite.
My model states that clocks tick faster in elevation because they are experiencing a greater gravity field because of the relationship of their associated mass in relation to earths mass.
Apart from clocks ticking faster in elevation, there is no other reason to think that an increase in gravity field slows time down and there is, within the Pound Rebka experiment every reason to think that it doesn't.
I now look at this relativistic gamma quantity as being relevant to the gravitational relationship between the associated mass of that elevated clock in relation to the mass of the earth and an increase in the clocks gravity field...and so on.
If we take the equation for gravitational acceleration:We can integrate this:Since the term GM is a constant we can rewrite as-GMThen as-GMThis can then be integrated as-GMThis then changes the signSo like escape velocity the direction is away from the source. Since escape velocity for a black hole is c we we can divide by this velocity to obtain the minimum velocity required to remain stationary near the horizon.I have attached a graph of the results for an earth sized mass. The tidal forces are so strong that the effects on time are to slow it down.Edit: Normally we would end up with where C is the constant of integration. I am assuming a value of zero for C so it vanishes.