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I saw an explanation on it somewhere where every 'bit' of matter was treated as having, that is if I remember right now, an equal effect on every other bit? I think it was a Newtonian concept though? But it came to the conclusion that in the middle they would 'negate' the 'attraction', or as we say the 'bending of space'? Hyperphysics takes this approach when digging a hole to the problem.
As for the metric tensor JP? Want to explain how you think for us more , ah, solid ones there? No, not 'thick headed' solid I said. By 'curvature involves derivatives' you would then mean that? It measures difference instead of magnitude for those points in space? Or am I getting it all wrong? That's a subtle one JP
If it helps, try to imagine that instead of being solid, the earth was made out a big sphere of liquid (which is probably true near the centre anyway. If you were at the centre you would be crushed by the pressure of all the mass but still feel no gravity.
Even if things "curve" the same way at the center of the earth (since you're experiencing no net gravity), the entire space is squashed down. Think of a piece of graph paper in deep space. As you move down towards the center of the earth, it distorts because of the curvature and gets squashed, so it's no longer flat and the lines aren't parallel to each other. At the center of the earth, it's flat again and all the lines are parallel but it's been squashed to a smaller size
Yes, that's what I'm wondering too. Pressure and Gravity. You will have a pressure at the middle, that much seems clear but you can't equal that to a 'gravity', can you?
So one could say that in a mathematical sense the steeper the slope the slower the clock?
Ah, in the Jules Vernian sense I mean, measuring time differences. And then we have two different types of 'weightlessness' if this is correct, don't we? Or maybe not? You could compare it to an uniform acceleration giving you a constant gravity?? Nah, that's not being weightless, weightless is a 'free fall' as I understands it? In what way does that 'weightlessness' in the middle have anything to do with a free fall if so?? Awh..
So in what way would I be able to differ the weightlessness inside my black box at the middle of our earth, against being in a free fall? You could argue that pressure will do it, but you can set up a equal situation in a free fall I think, creating that pressure, can't you? Either it will differ or?Consider the definition of gravity as being equal to a uniform accelerating?This one is still strange to me, even though your point of view makes eminent sense Mr fontwell And the idea of equivalence doesn't build on looking at a situation with 'the eye of a God' as I understands it? It builds on the opposite, being in a black box unable to define anything except from your own frame?
The difference is that near a mass everyone agrees clocks run slower than further away. But this does not create a privileged position, just different positions. The clock near the mass still measures local seconds but he measures clocks further away as running as too fast. Who is correct? There is no correct.It is like we look at the clock on a GPS satellite and correct it to our local time. But the Sun affects us both, so the Sun thinks we are both too fast. But the centre of the Galaxy thinks the Sun is too fast. Even our observable universe is perhaps too fast for someone else!
Does this mean there is not a universe standard law of conservation of energy [work heat equivilance] ?
Just to say something on the issue of the zero gravity at the earth's centre versus 1G at the surface. I think the bending of space-time and slowing of clocks is due to mass, not gravity. Gravity is an effect of curved space-time. The centre of the earth is at the bottom of a local curve and so there is no gravity there. However, the actual curve is at its lowest point so the time is most slowed down. I think.
Well, the GR view of gravity is that it is only an effect of curved space-time. The GR view is that mass curves space-time. And the equations for time dilation refer to the centre of mass. The clock at the earth's centre is slowed by the combined pressure of all that mass around it.
I will say again in case the relevance of my previous question was not understood if the equations for time dilation were referring to the centre how is it possible that the time dilation is any different one radius away?, the values should be the same according to the radius squared part of the equation.
Also i don't see how mass applies pressure other than as a consequence of gravity
OK another question, how is time slowest at the center ? Because as i understand it Einstein used inverse square law and the earths radius, and one times one equals one. So it would seem to be the same as at earths surface, or am i missing something ? [i must be otherwise there would be no more down once your on earths surface]
Time dilation occurs wherever gravity curves space-time so that one point in space experiences a different rate of time than another...
Please! I thought we had agreed that mass curves space-time! Gravity doesn't do anything to space-time, it is a consequence of how curved it is.
@Geezer, yes three minutes is three minutes but don't use an hour-glass style egg timer
Quote from: fontwell on 23/03/2010 09:08:41@Geezer, yes three minutes is three minutes but don't use an hour-glass style egg timer Not if it contravenes the laws of conservation of energy it isn't. below is an extract from a link J P provided in regards to wether G R voilated energy conservation ...........An infinitesimal piece of spacetime "looks flat", while the effects of curvature become evident in a finite piece. (The same holds for curved surfaces in space, of course). GR relates curvature to gravity. Now, even in newtonian physics, you must include gravitational potential energy to get energy conservation. And GR introduces the new phenomenon of gravitational waves; perhaps these carry energy as well? Perhaps we need to include gravitational energy in some fashion, to arrive at a law of energy conservation for finite pieces of spacetime?.........Looks to me like there turning gravity back in to a force field.Anyone else come up with a way to test wether gravity is an attractive force or a bending of time ??
We think we have indirect evidence of gravitational waves acting as a energy Gem. "The smoking gun is a system of orbiting neutron stars with the catchy name PSR1913+16. Einstein's theory predicts that gravitational waves carry away energy. For a system of orbiting stars, such a decrease in total energy leads to an ever faster and closer orbit. Over decades, radio astronomers have monitored the time that it takes the stars of PSR1913+16 to complete each successive orbit, and lo and behold: this orbital period decreases over time exactly as predicted by general relativity. This is strong evidence that the speed-up is indeed due to the radiation of gravitational waves, and the reason Russell Hulse and Joseph Taylor were awarded the Nobel prize for physics for the year 1993." Gravitational waves.
Why is energy conservation suddenly coming up and what does it have to do with time dilation? All you really need to know is what Geezer was saying--that if you put your timer and egg next to each other, then they should both agree on what three minutes is.
But, what exactly is this 'energy' we're speaking of, is it the same type we find in our combustible engine? and furthermore, if there exist this kind of phenomena, why couldn't we speak about gravity as a 'force'?
So you will notice time is a factor in the measurement of the work heat equivalence and as we have already noted earlier in this post at the center where in GR time is slower will the energy interactions there not disagree with the International System of Units as regards the laws thermodynamics.
You know Geezer, I think you're right. That thoughts too are regulated by time I mean. They seem so unrelated to what we deem as being materially 'there', as if they wasn't connected to anything materialistic, but they are.
The general rule of thumb is that locally, space-time is flat, so you only need to use special relativity, not GR.
An infinitesimal piece of spacetime "looks flat", while the effects of curvature become evident in a finite piece. (The same holds for curved surfaces in space, of course). GR relates curvature to gravity. Now, even in newtonian physics, you must include gravitational potential energy to get energy conservation.
If you use an atomic clock to time your egg for three minutes, the atomic clock measures local time, so it will "tick" exactly the same number of times in three minutes, regardless of its location.
By "everything" I really mean everything. All atomic activity, every chemical process, human thought, human metabolism, all physical motion etc. etc. is governed by the local time.
And also if space time is flat locally there would be no gravity according to fontwell that is what happens only at the centre.
Please explain how ALL PHYSICAL MOTION IS GOVERNED BY LOCAL TIME because according to the atomic clocks the mass at the centre is traveling faster.
Quote from: Geezer on 24/03/2010 21:39:44 By "everything" I really mean everything. All atomic activity, every chemical process, human thought, human metabolism, all physical motion etc. etc. is governed by the local time.Please explain how ALL PHYSICAL MOTION IS GOVERNED BY LOCAL TIME because according to the atomic clocks the mass at the centre is traveling faster.
If you had some amazing device that allowed you to observe the two egg timers simultaneously, if both started simultaneously, you would be able to observe that the one at the center of the earth would finish before the one at the surface.
(Actually for egg timing, the time dilation of the earth isn't even important since microseconds don't matter).
Local time is time measured locally. The local time at the center faster than the local time at the surface.
It's not really correct to say it's travelling faster. Locally, it's travelling at the same speed. Speed is distance in time. Everything is governed by local time, so locally speed would be the same at the two locations.If you had some amazing device that allowed you to observe the two egg timers simultaneously, if both started simultaneously, you would be able to observe that the one at the center of the earth would finish before the one at the surface.
Quote from: JP on 26/03/2010 00:47:02Local time is time measured locally. The local time at the center faster than the local time at the surface. Slower.
That is, if you accept my definition of the universe as a 'whole experience' aging of course. Otherwise you might say that there are things/objects aging 'faster' than you. But if it is that way then the experience of being able to observe a 'whole universe' have to be explained from something else it seems to me?Can you see what I think here? That what we call 'times arrow' then is a very localized phenomena and that our 'universal arrow of time' then becomes even more remarkable, as will all causality-chains observed, following our 'entropy'.