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### Author Topic: how should i time my eggs  (Read 24702 times)

#### fontwell

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« Reply #50 on: 17/03/2010 23:25:57 »

Having hunted around it seems to be accepted that mass bends space-time, and bends in space-time cause gravity e.g. see http://en.wikipedia.org/wiki/Gravity#General_relativity [nofollow]  -> "the effects of gravitation are ascribed to spacetime curvature"... "Einstein proposed that spacetime is curved by matter." By 'matter' he implies mass.

I have only found a few places where they explicitly say the gradient (derivative) of space-time is gravity but it always seems to be understood this way.

Famous quote: ‘Matter tells space how to curve. Space tells matter how to move.’
Translation: Mass bends space-time. Bent space-time causes gravity.

I feel pretty confident to say:

Mass curves space-time, the gradient of the space-time curve is gravity. Time dilation is a function of the space-time curve's magnitude, not its gradient.

To be honest, I haven't ever come across any discussions on GR where anyone thought other than this, its just mainstream GR isn't it?

« Last Edit: 18/03/2010 13:44:19 by fontwell »

#### yor_on

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« Reply #51 on: 18/03/2010 00:54:17 »
No worrys :) it's just that I haven't thought of it that way before, I have always seen those geodesics as the true 'straight paths' sort of. To me mass and space are very much the same thing, I haven't really thought to separate them. Like we say that a black hole (Schwarzwild solution) opens to infinite (?) distances inside the EV according to some thoughts, and even more so for a spinning one. To me it seems that they go together (Space and mass), so when you used the sheet analogy this way it made me curious. I can see the idea, but then my thought visually became how to set this flat sheet 'pulled together' and wonder how mass could be represented from such a view. That is if we assume that a free fall is equivalent to another free fall, no matter internal time rates differing, and that both represent the same 'flat sheet' ?
==

Or is there some way of describing that 'weightlessness' without using the idea of a free fall? Uniform motion for example, when the motion is zero relative something else, like we have in those innards of our earth, we can still say that A even if at rest with B still have a uniform motion when compared to C, right? So that thingie in the middle do have an uniform motion, even if not relative Earth? So in one way you might say that it share a free fall with our Earth, but as it also is 'weight less' relative Earth its equivalence seems to have more to do with 'space' than with our Earth?
« Last Edit: 18/03/2010 01:04:18 by yor_on »

#### JP

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« Reply #52 on: 18/03/2010 01:12:55 »
Doesn't time dilation/length contraction have to do with how you measure space-time distances, which is in turn defined by the metric tensor?  http://mathworld.wolfram.com/MetricTensor.html  The metric tensor appears to measure curvature, which involves derivatives, rather than magnitudes.

#### JP

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« Reply #53 on: 18/03/2010 02:27:23 »
By the way, I think there is an error in my previous reasoning about drilling into the earth, as the Schwarzschild solution assumes that you're solving the equations in a vacuum (where the stress-energy tensor is zero).  Inside the earth, this wouldn't be the case.  I don't know what the proper form of the solution would be or if it's solvable without numerical simulations.

#### yor_on

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« Reply #54 on: 18/03/2010 04:04:06 »
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.

Another question relating to that middle of out Earth? If I assume that it is equivalent to a free fall, can there be a pressure acting at that point? There can, right? As it is a part at rest in a bigger system Earth / 'It' :) Analogous to your black box can be inside a bigger pressurized black box..

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 :)

#### JP

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« Reply #55 on: 18/03/2010 05:12:31 »
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.

That works in Newtonian gravity.  That's what I tried to apply to GR.  I have a feeling you can't simply apply those ideas to GR, though.

Quote
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 :)
A metric tensor is a mathematical object that tells you about the curvature of a "surface" (or in mathematics what is called a manifold) at a point in space.  You use it to define lengths on that manifold.

In general relativity, you have to measure  "lengths" in space-time, and they are called intervals, since they involve events separated in time and in space.  The metric tensor tells you how to define intervals locally (the definition depends on your reference frame).  Since you're measuring intervals in space and time, it therefore tells you how the definitions of length and of time differ.  The definition of the metric tensor involves derivatives, and derivatives tell you about slopes instead of magnitude.  It seems to me that because the metric tensor involves derivatives, it's probably based on how space-time curves rather than on the magnitude of the space-time curve.  By the way, there's a number called curvature that you can calculate from the metric, which isn't what we're talking about here.

In addition to the link I posted above, there's this description: http://en.wikipedia.org/wiki/Metric_tensor_%28general_relativity%29#Local_coordinates_and_matrix_representations

#### fontwell

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« Reply #56 on: 18/03/2010 08:58:26 »
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.

Although this is a dubious way to think about the situation here it does indicate how mass can have an effect that is not detectable by measuring local gravity.

The idea of every piece of matter affecting every other piece by a gravitational pull is a Newtonian way to sum the net effects of masses. This kind of calculation results in a Newtonian explanation for zero gravity at the centre of a mass. But in GR gravity is caused by the bending of space-time and the bending of space-time is caused by mass. So in GR we do not ask how every piece of matter affects each other, we ask how do all the pieces curve space-time. Gravity is then derived from the curvature of space-time.

Really, this whole thing comes down to this; Is time dilation caused by mass, which bends space-time, thus making the centre of mass the most dilated place? Or is it caused by gravity, which is caused by the curve of space-time?

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. It does not care that it is in an inertial frame with zero gravity.

Also, distant orbiting satellites have faster clocks compared nearer to orbiting satellites, due to being further from the mass of the earth. But they also experience themselves as being in an inertial frame with zero gravity.
« Last Edit: 18/03/2010 18:17:25 by fontwell »

#### JP

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« Reply #57 on: 18/03/2010 11:34:51 »
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.

Yes, and I think that what you're saying here agrees with the reason my earlier reasoning was wrong.  The extra forces you're describing are likely components of the stress-energy tensor which we can't ignore within the earth.  Therefore you can't just extrapolate from the solution outside the earth to get the solution within the earth--the form of the equations changes.

I also think I see how the timer within the earth should measure time differently than the timer in deep space.  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.  You can kind of see that if you look at the left-hand figure you show here: http://www.thenakedscientists.com/forum/index.php?topic=29156.msg304011#msg304011 .

I have to think a bit more to get it to make sense with the (little) mathematics of GR that I know, but it seems right...

#### fontwell

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« Reply #58 on: 18/03/2010 13:43:20 »
Quote
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!
« Last Edit: 18/03/2010 13:45:30 by fontwell »

#### yor_on

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« Reply #59 on: 18/03/2010 13:57:47 »
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? Thanks for the explanations btw :) they're helpful. So one could say that in a mathematical sense the steeper the slope the slower the clock? And as all sides are extremely steep at a VMO f.ex you will have a very slow time where those slopes come together, no matter if they plan out there. Like some sort of 'gravitational vectors' pointing towards that 'flat point' in the middle of our VMO?

Hah I refuse to accept that, I just have to find some paper and a pencil, just wait and see:)

Nah, I'm sort of joking. But yes I can see how that view comes naturally from treating it as slopes with vectors pointing to the middle, that is if I got it correct ::)) But I still would like to see an experiment proving the concept?
==

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..
« Last Edit: 18/03/2010 14:08:23 by yor_on »

#### fontwell

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« Reply #60 on: 18/03/2010 15:32:38 »
Quote
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?

Correct, you can't. But it makes the point that an effect due to mass (pressure) can occur in a region where there is no gravity. Indicating that time dilation due to mass can occur in a place with no gravity.

Quote
So one could say that in a mathematical sense the steeper the slope the slower the clock?

No. Not if you mean the slope of curved space-time. You could say the steeper the slope the stronger the attraction of masses - which we observe as gravity. Gravity would be the steepness, time dilation would be the amount of stretch.

Quote
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..

Exactly!

As I understand it 'weightlessness' is 'weightlessness' but also 'mass' is 'mass' :)

By which I mean, free fall and being weightless in the centre of a large mass are the same in that an observer in either condition can't do a local experiment which would give different results (to him).

However, the presence of mass is a real thing which makes the two situations unequal. They will both agree on who has the faster clock - the one furthest from the mass. This is unlike inertial frames in SR where both parties observe the other to have a slow clock. Mass allows the situation to be absolutely unbalanced.

#### yor_on

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« Reply #61 on: 18/03/2010 15:52:16 »
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?

#### fontwell

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« Reply #62 on: 18/03/2010 17:26:47 »
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?

I agree, to my understanding, inside a block box there is no difference between the two situations, that is why relativity is still 'relativity'.

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!

#### yor_on

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« Reply #63 on: 18/03/2010 18:55:04 »
Yep :)
You're all to fast for me.

*Oh no, Those men in their white coats again, where do they grow them?*
Ah, gotta run now Mr Fontwell :)
==

I'll be back ::))

#### gem

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« Reply #64 on: 18/03/2010 21:20:10 »
Hi all
gosh you have all been busy, font well certainly has helped clarify space time theory a little clearer for me as to how it can come to the same conclusions for different reasons. such a lot to take in i have read through every ones posts but will have to read through some more to make sure i have understood it all properly,

At the moment my grasp on it is 'newton' mass causes gravitational attraction force and when within a sphere of mass the attraction vectors cancell each other giving a resulting zero force on a body within.

Einstein separates gravity from the mass, gravity does not attract and the reason mass acceleration diminishes as you get nearer the center is because the curve of space becomes less

one question that comes to mind straight away though is about this statement that G R postulates

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] ?

#### fontwell

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« Reply #65 on: 19/03/2010 00:41:03 »

Quote
Does this mean there is not a universe standard law of conservation of energy [work heat equivilance] ?

I'm pretty certain that conservation of energy is one of the few laws that always works. I'm not really very clear about energy in SR or GR but isn't it the case that everything works due to differences in potential energy (what ever that is!). So if it turns out that we are  all affected (more or less) the same by a huge but distant mass it doesn't affect the local differences in potential.

This is actually our experience anyway - when we raise 1kg by 1m it takes 1Joule. We do not notice that this raising took place in the context of the Sun's gravity, that just adds an equal potential energy to both positions.

#### JP

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« Reply #66 on: 19/03/2010 02:27:56 »
We've had a few discussions about conservation of energy in GR lately.  (There isn't a problem with conservation of energy in SR as far as I know.)  Basically, GR has issues defining an energy, since when you include gravitational energy, the quantity that acts like a conserved energy doesn't transform appropriately when you change reference frames.

The two links I include below were useful in trying to understand this:
http://www.phys.ncku.edu.tw/mirrors/physicsfaq/Relativity/GR/energy_gr.html
http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html

#### gem

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« Reply #67 on: 19/03/2010 20:17:47 »
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.

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]

#### geo driver

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« Reply #68 on: 19/03/2010 20:34:03 »
3 minites

#### gem

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« Reply #69 on: 21/03/2010 23:26:20 »

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.

Meaning no curvature from the centre to the surface.
[Newton addressed this issue did Einstein]

Also i don't see how mass applies pressure other than as a consequence of gravity

#### JP

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« Reply #70 on: 22/03/2010 01:21:11 »
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.
Time dilation occurs wherever gravity curves space-time so that one point in space experiences a different rate of time than another.  Since gravity starts curving space-time well outside of the earth and continues all the way down to the center, you would expect time dilation to occur between any two all radial points you chose.  Only if you chose two points the same radial distance from the earth's center would you get the same rate of time.  (And all this assumes the earth is a perfect sphere--in reality it would be slightly different.)

Quote
Also i don't see how mass applies pressure other than as a consequence of gravity
There's a term in the equations of general relativity called the stress-energy tensor.  This is the term that tells space-time how to bend.  Mass contributes to this term.

#### fontwell

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« Reply #71 on: 22/03/2010 09:17:28 »

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]

I'm not quite sure what you are asking. Inside the earth, distances from the mass of the earth are less than one earth radius. So time runs slower. There are some pictures near the top of the page in one of my earlier  posts indicating the way that space-time is warped by mass. The warping isn't the same at the surface and the centre.

Also i don't see how mass applies pressure other than as a consequence of gravity

Of course. I may have confused the issue here by using an analogy comparing regular pressure of a liquid with the bending of space-time due to mass.

In a normal Newtonian way of thinking the pressure at the centre of the earth is huge. But there is zero local gravity (if you dropped a stone while at the centre it would not accelerate away from you). The only point of this is to show that just because a location has no gravity itself, it is not free from the surrounding effects of gravity and mass, even in Newton's world. So, just because there is zero gravity it doesn't mean we can say it is the same as a point at infinite distance, either for Newton or Einstein.

In GR thinking, mass bends space-time in an analogous way to the pressure inside a Newtonian Earth. But the GR curving isn't caused by being squashed under a mass by gravity. Space-time bending is caused purely by the presence of mass. A 'way you could think' about this is as a 'pressure' to due to mass - like in the pictures above. This is a mental model of 'pressure' due to mass, and this pressure slowing down time. But it isn't an actual pressure in the everyday meaning. The 'GR pressure' which bends space-time is highest at the centre of the Earth because in this location the effect of all the mass of the Earth is at is maximum (the sum of the 1/r^2 equations over all the mass), not anything to do with gravity.

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.
« Last Edit: 22/03/2010 12:21:15 by fontwell »

#### JP

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« Reply #72 on: 22/03/2010 09:59:42 »
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.

True.  Poor choice of words on my part in trying to simplify things. To be more precise, the stress-energy tensor (which includes mass) is the source of the curvature and the curvature is a mathematical description of gravity.

#### gem

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« Reply #73 on: 22/03/2010 21:15:21 »
Right i have got the concept of mass pressure in the way it applies in general relativity, and it answers my question as to how it is postulated that time runs slowest at the centre.

So the difficulty is how to get nature to ask a question of both theory's that will separate out which one is closest to what is observed,

And because both theory's include the same dynamics happening, albeit for different reasons it would seem at first glance to be insurmountable.

However i can think of one which could isolate there differences

#### yor_on

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« Reply #74 on: 22/03/2010 21:43:37 »
Yep I can follow that thinking, gravity would then be the consequence of SpaceTimes geodesics (dips, bends and heights) called forward by the stress-energy tensor that is the direct result (expression) of mass acting on space.

The problem here being that both the geodesics and the stress energy tensor are mathematical descriptions versus gravity that really is what we feel :) I mean, we don't say, "Hey Alex, watch out for that stress energy tensor man, you're gonna fall !!" Do we, huh? ... "Why thanks Charles, that geodesic really took me by surprise."

:)

But it do make sense, all the way down to how to accept the idea that a free fall in the middle won't be equal to a free fall outside, time dilation wise that is. But then again, if they're not then it seems to me that the same should hold for free falling frames outside too. And if that would be right then different velocity in free fall (uniform moving) will be able to create different time dilations relative a common originator (like starting two rockets from Earth)?

Awh..

1+1= *White coats again? Why do they persecute me. "I'm innocent I say, innocent."*
« Last Edit: 22/03/2010 21:58:08 by yor_on »

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« Reply #74 on: 22/03/2010 21:43:37 »