boboe Posted October 20, 2010 Posted October 20, 2010 Density: Time dilation due to velocity = (the Lorentz-Fitzgerald equation) Let's look at density as it pertains to, let's say, a rug occupying an area inside a room, in order to see what percentage of the room the rug does NOT occupy. Density = sqrt (1 - area of rug / area of room) Assuming that the length and width are always equal: D = sqrt (1 - Length of Rug^2 / Length of Room^2) Of course, to get this to pertain to time dilation due to velocity, we can simply replace "Length" with measurements of spacetime - velocities. (Any object which occupies 'x' amount of space, also occupies 'x' amount of time - they are equal) So we can make the conclusion that measuring the relative velocity of an object is measuring it's occupation of spacetime - a form of density where c (the speed of light) is the maximum. Having a maximum velocity allows us to use any form of measurement of velocities- kilometers/hr, miles/hr, meters/hr, etc. etc. etc. The universe understands these measurements because they can all be compared to a maximum value - c. I'm well aware of the equation: And to be brutally honest, this equation can, in no way, shape or form exist with the Lorentz-Fitzgerald equation above. That is, either one of the equations is wrong, or the Equivalence Principle is wrong. So examining the equation I have severe problems with Mass. Mass has no maximum value. So what is mass? An objects occupation of spacetime - compared to what? Nothing. It's some arbitrary measurement - how does the universe know what 1 kilogram is, whereas, it knows what 1 mile is, because 1 mile is some fraction of 186,282 miles. In the Lorentz-Fitzgerald equation, results which change an object's mass are based on a percentage change, so results have been accurate, however we are using our arbitrary value of mass in this equation to define gravity. How were units of mass derived? Was the occupation of spacetime taken into consideration at their creation? The only forms of measurement which the universe understands deal with the occupation of spacetime in distances. Mass can, and should, be a measurement of spacetime but it needs to relate to distance, not the weight of a grain or whatever. What I'm saying is that gravity, like velocity, should be based on a measure of the density (occupation) of spacetime. (As I believe the Equivalence Principle is correct) If you have an object moving the speed of light relative to you, the object is calculated to have 0 length; HOWEVER, if you were that object which was moving that speed of light, you wouldn't measure any change in your length. So in a gravitational field where time is dilated to 0, observers outside would measure the body as having 0 length, whereas someone inside that body would measure everything as it's proper size. If we take our lesson from the Lorentz-Fitzgerald equation, we should find that a black hole is merely 100% dense. I'm neither mathematician nor physicist by trade. I have no equation to explain gravity, though I'm certain it will be easily discovered with changed perspectives about mass. This is a small piece of a much larger picture, which I may be willing to discuss, but for now, this will do.
imatfaal Posted October 20, 2010 Posted October 20, 2010 Boboe - not sure about why you would call your first idea Density, it seems to be a measure of occupancy, and a slightly strange one at that. Personally I would say the rug occupies area_rug/area_floor and not any form of the square root. I think you also need to engage with lorenz boosts rather than just time dilation. Both x and t are transformed by lorenz boosts in a very similar way (x' = (x-vt)gamma and t'=(t-vx)gamma - but they are not the same. The second formula you give is not an equation - as you give it, but does seem to be the factor for calculating proper time through gravitational time dilation. The major question is - why can the two equations for time dilation due to velocity and time dilation due to gravitational effects not co-exist? You state they cannot - but dont give a reason. Not sure about your problem with mass - a kilogram can be viewed as a multiple of the planck mass which is formed from the fundamental universal constants. Many properties of matter do not have maximum finite values. Gravitational effect time dilation has, i believe, been verified in many everyday situations - if it is incorrectly formulated you need to show why experimental data fits. 2
Janus Posted October 20, 2010 Posted October 20, 2010 Density: Time dilation due to velocity = (the Lorentz-Fitzgerald equation) Let's look at density as it pertains to, let's say, a rug occupying an area inside a room, in order to see what percentage of the room the rug does NOT occupy. Density = sqrt (1 - area of rug / area of room) Assuming that the length and width are always equal: D = sqrt (1 - Length of Rug^2 / Length of Room^2) Of course, to get this to pertain to time dilation due to velocity, we can simply replace "Length" with measurements of spacetime - velocities. (Any object which occupies 'x' amount of space, also occupies 'x' amount of time - they are equal) So we can make the conclusion that measuring the relative velocity of an object is measuring it's occupation of spacetime - a form of density where c (the speed of light) is the maximum. Having a maximum velocity allows us to use any form of measurement of velocities- kilometers/hr, miles/hr, meters/hr, etc. etc. etc. The universe understands these measurements because they can all be compared to a maximum value - c. I'm well aware of the equation: And to be brutally honest, this equation can, in no way, shape or form exist with the Lorentz-Fitzgerald equation above. Sure it can. It is a simple fact that gravitational time dilation is due to gravitational potential. The factor in the equation relates to the time dilation at a given point in a gravity well as compared to a point infinite removed. Gravitational potential also determines the velocity of a falling object. A particular velocity related to gravitational potential is the escape velocity, or the initial velocity an object has to have at a point in a gravity well in order to escape to infinity. This is also the velocity of an object dropped from infinity when it reaches that point in the gravity well. The escape velocity is found by: [math]v = \sqrt{\frac{2GM}{R}}[/math] Note that if we substitute this value for v into the Lorentz-Fitzgerald equation, we get the gravitational time dilation factor.
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