On 04/02/2010 08:28 AM, Roarty, Francis X wrote: > Stephan, > > No, Like Harry I am having trouble too but I think you are simply > making a distinction between different sources of time dilation. I > know that time dilation is much greater sitting on the surface of a > dead star vs. a small planet and therefore would agree with Harry > that it is proportional to gravitational strength.
I see what you're saying. However, I know of two ways to view gravitational time dilation (outlined below, just after the asterisks), and both lead to the conclusion that, as I said, variations in measured field strength simply aren't in the picture. As to the surface of the dead star, of course the dilation is much greater there than the surface of a planet -- but you're much deeper in a steeper gravity well. The difference, again, is due to the Newtonian potential energy difference, not the measured field strength. As you also point out, an observer in the middle of the same dead star will experience even more dilation than the observer on the surface, despite the fact that the measured field strength at the center of the star is nil! > I also had a > thread on one of the science forums regarding this Cavity at the > center of a planet before but I took the position that the > gravitational vectors “cancelled” pulling the observer equally in all > directions but still experiencing time dilation based on the absolute > sum of the vectors regardless of orientation. Is this “potential” > field what I was calling cancellation? The cavity at the center of a > dead star and a small planet should both exhibit microgravity but the > time dilation should be much greater for the dead star. By "potential" I just meant the measured potential energy difference in the Newtonian gravity model. Around a spherical mass, G goes as 1/r^2, potential goes as 1/r, as I recall. As to the field at the center of the star really being very strong but canceling itself out, I don't know how to interpret that. When I use the term "field strength" I mean the strength of the field as measured by an observer, and that's all. In a microgravity environment, the "field strength" is essentially nil, by that definition. Whether there's really some "field fabric" present which is causing effects even though it can't be measured directly, I couldn't say; I don't know how to model that. Similarly, if we dig a spherical chamber in a uniformly dense planet, but we place it *off* *center* (somewhere well off to the side of the planet's middle), the G field in that chamber will not be nil. However, it will be *totally* *uniform*! (This is very cool, IMO.) Despite the uniformity of the field in the chamber, time will still run slower at the "bottom side" of the chamber than it does at the "top side" of the chamber. We can see that it must, from the Einstein-on-a-stepladder argument. So, this is another example where there's dilation associated with a potential difference with no difference in measured field strength. * * * The two ways I know of to look at this are via conservation of energy, and via the metric. The conservation of energy argument is the one I gave earlier, with Einstein on the stepladder, and it leads immediately to the conclusion that the dilation *must* be proportional to the Newtonian gravitational potential. The second way to look at it is to choose a coordinate system and find the metric tensor in that coordinate system. (Note that time dilation is a non-local phenomenon -- your own time rate always matches your own time rate! So, you need to choose a "global" coordinate system against which to measure your "local" time to find the dilation.) Look at the components of the metric tensor in that coordinate system. The actual *values* of the components at each point in space tell you how much things are physically contracted, and tell you what the time dilation is. The strength of gravity that you measure at any point, on the other hand, shows up as the *first* *derivatives* of those components. So, anyplace where the components of the metric tensor are constant in some volume, you won't measure any G-field there -- but there could still be enormous time dilation relative to a distant observer, depending on the values of the components in that region. Similarly, if you could arrange things so that a strong G field starts abruptly at some location, you'd find that the derivative of the metric tensor components in that region of high G was substantial, but, near the edge of the high-G region, the *values* of the components would not be very different from the values outside that region. And so the dilation at that location would be very small. > In science > fiction we can store the terminally ill in a deep gravitational well > until medical science catches up with the disease. This isn’t meant > to be philosophical but if these fields meet in the cavity and there > is no mass there for them to fight over, will the fields even sum or > just pass through each other? I never got a satisfactory answer on > any of the forums but while following this f/h thing I came across > that Beck-Mackey work proposing that vacuum fluctuations under 2 thz > are more gravitationally active then above and for a while thought > that this might be a hint to this time dilation/microgravity at the > center of a mass question. Then I realized the time dilation kills > that idea because the changes in vacuum fluctuation frequency would > themselves be relativistic and the greater proportion of longer > vacuum fluctuations would probably only be seen from the observer on > the planet surface while they would seem unchanged to the observer > inside the cavity – I think this may be an unresolved issue with the > Beck – Mackey paper but it did give me a “relative” way of modeling > time dilation. If their paper holds any water at all then the ratio > of flux >2thz / < 2Thz should be reduced the lower into a gravity > well you travel and reflect how much mass is at the bottom (From the > perspective of an observer at the top of the well). > > Regards > > Fran > > > > > > > > > >>> it doesn't > >> depend in any way on *variations* in the *strength* > >>> of the > >> gravitational field. > > > > To paraphrase: > > > > The **VARIATIONS** in the > >> field STRENGTH are not relevant to > > gravitational time dilation. > > > > >
