[Geezer]

Assuming minor details like temperature and pressure have negligible influence on gravity, would not the gravitational effect at the centre (of mass) of the Earth be almost the same as the gravitational effect at a very great distance from the Earth?

In either location, a body would be unlikely to alter its distance from the centre of the Earth because of the Earth.

Perhaps this is a fancy way of saying that the Earth produces no gravitational effects at its centre.

[yor_on]

Are you thinking that the geodesics might look the same at a far spot in space, as it does inside the middle Geezer? I had that disturbing feeling too yesterday thinking of it, like a flat paper (two dimensional) with mass creating the three dimensions we see. Then mass could make a 3D description of a 2D space..

Kind of like that, although as I think of it, what we see as 3D is 'whole patterns', not 'cut & paste' So my universe would then be a 'flat-land', with matter creating 3D as times arrow binds it together for us into a seamless experience.

Ahem..

with some weird kind of 'bumps' making up what we call 3D? Alternatively it could be times arrow that then produce the effect of what we call matter and also what we see as a 3D environment?

(Well, they're waiving at me over there, better go, the doctor gets so irritated when I don't:)

[Geezer]

Yoron: My thought was a bit more Newtonian I'm afraid. []

It was more along the lines of the net effect of gravity at the center of mass (due to the Earth) will be zero.

[yor_on]

Ah well. Prosaic is cool too
And I can proudly say that I'm one step behind

My view is turning into an Copernican one )

[gem (OP)]

I'm still not sure I understand the concept we're discussing Gem Sometimes I think I do but then, just as sudden, I feel that I lost all sight of it again.

Sorry yor on that's probably my fault my  thinking of time is probably along the ethereal lines so i struggle with statements like ' time actually runs faster there or atomic clocks run faster showing that gravity bends time'.

hence the post to put space time theory to a few tests,[I think its my way of kicking the tyres of the vechicule that is space time before i buy in to the idea] when i mention time and speed at the back of my logic is the laws of conservation of energy and wether i can use them to show space time theory contravenes them.
 
Because it is said if a theory is right it gives the confidence to make other theory's [or question others ] and i believe the laws of conservation of energy hold in the physical world, so i will try and come up with a scenario of placing a horse in a space suit in different values of gravity and time and see if we get the same values as Mr Watt.

getting back to where  we are up to J p has summed up very nicely indeed in his last two posts, so we have to consider does what is postulated on this post have any  specific impact on space time theory by bringing newton physics in to space time theory. [has it really not been considerd before?]

Are you thinking that the geodesics might look the same at a far spot in space, as it does inside the middle Geezer? I had that disturbing feeling too yesterday thinking of it, like a flat paper (two dimensional) with mass creating the three dimensions we see. Then mass could make a 3D description of a 2D space..

On that note you have to consider that at the centre of earth the sun and the moons gravity field [space time] still exist UN altered and given that earths core is said to be a solid within a fluid it is probably held in place or comes up against the fluids pressure gradient {but i am straying in to something else there that i will be posting later] many thanks for the posts so far

[Geezer]

Ah well. Prosaic is cool too
And I can proudly say that I'm one step behind

My view is turning into an Copernican one )

"Prosaic". Was that a typo? Perhaps you meant Prozac? http://en.wikipedia.org/wiki/Prozac

[yor_on]

Ah?
Prozac??

Now, would that be a invitation, or a theory??

My dear friend, in a true Copernican manner I just have to state. "I am the world" That as I just follow it to the logical end, as did our first royal Copernican, Louis XIV when he stated "I am the state". He also said "There is little that can withstand a man who can conquer himself." Which I agree wholeheartedly too even though it sounds a mite lonely? Let me finish with his immortal words. "It is legal because I wish it." which should cover most of my views, I hope?

[fontwell]

Just to repeat my previous post on this topic, I think that bending of space-time, and thus time dilation, is caused by mass. Gravity is an effect of bent space-time, not the other way round. And mass bends space-time.

The famous analogy is to place a heavy metal ball on a rubber sheet, or a  mattress, or even a rubber sheet on a mattress The sheet is only two dimensions but represents space-time for our purpose.

The heavy ball makes a dip in the sheet and also for some distance around it. This bending of the sheet is analogous to how a mass bends space-time in GR. We would see that objects roll down into this dip as if attracted to it. The way that objects fall down the dip is analogous to gravity in GR. They look as if they are attracted to the mass but actually they are following a path due to bent space-time. It just happens that the mass bent the space-time.

Note that near the ball the dip has a steep gradient. This really pulls objects in. Further away, the dip has less gradient and so the pull toward the dip is weaker. The gradient of the dip is analogous to gravity.

Note that if you just look at the shape of the dip, there is no gravity at the bottom of the dip because the sheet is flat at this single point. So just like with Newton we get zero gravity at the balls centre (or the earth's centre). However, at this same point, the sheet itself is at its most stretched, and it is the stretching that makes time appear to run differently.

I know that the ball and sheet thing is only an analogy and that you can stretch an analogy too far but I think this is how it works. So, the time differences will continue all the way to the centre because that is where the space-time is most stretched, but gravity will fall to zero because it is caused by the gradient of the stretching.

The result is, don't use a gravity egg timer.

Also, I can't see it now but did someone ask how to tell if you are in an inertial frame? Well the answer is, you pick up the egg with your hand and then open your hand. If the egg moves away from your hand you are not in an inertial frame. If it stays inside your open hand you are in an inertial frame.

[yor_on]

Fontwell, it's interesting the way you think of gravity. You seem to split it in stretching/stressing(?) SpaceTime and its gradient that then will equal an gravity?. Using that analogy seems to leave me two ways to see what we call that 'flatness' area. Either I associate it with 'levels' like invincible layers upon layers where the so called 'flatness' aka non gravity can exists on all levels, like our dip with that new 'flatness level' on its bottom. Or one could imagine one 'flatness level' only, and there I wonder how those gradients would look? It's intriguing. Is there anything speaking more in the favor of time moving faster or slower 'down there'? Like some analogue experiment pointing to one way or another? Or does it build on the math describing gravity. That as I've seen the same idea at other places. And Gem do you have any thought experiment drawn up yet?

"Damn that doctor.." he mutters as he has to run again.

[gem (OP)]

Just to repeat my previous post on this topic, I think that bending of space-time, and thus time dilation, is caused by mass. Gravity is an effect of bent space-time, not the other way round. And mass bends space-time

 

If gravity is only an effect of space time what property of mass is bending space?

yor on, just a quick one because something in j p posts has got my attention
[Einstiens seems to have got a double error that got him closer than newton to what we actually observe will be posting in 'is this the source of the pioneer anomally' later this week]

Right, that horse or engine equal to one horse power forgive the imperial measurements but that's what watt used.

WE WILL USE THREE PLANETS ALL WITH THE SAME RADIUS AND  ROTATION SPEED AND THEY ALL ORBIT THE SUN AND THE ENGINE/HORSES WORK FROM DAY BREAK TO NIGHT FALL.

on earth one horse power is equal 550 foot pounds per second  now lets put that same engine on a planet with half the gravitational force that should mean that that same one horse power should be able to lift 1100 pounds per second ,

However if the atomic clock runs faster it would seem that the engine was not quite operating at its full 1 hp.

And if we reversed the scenario and placed the engine on a planet with a gravitational force twice times earth then the said same 1 hp should be able to lift 275 pounds per second  but the atomic clock is running slower and so it would seem that the 1 hp engine is operating at an efficiency greater than 1 hp.

So it would seem that space time theory contravenes the laws of conservation of energy
or does that stretchy rubber sheet help lift the mass in some way. 

so one which planet would i get more miles to the gallon

[fontwell]

 


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?

[yor_on]

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?

[JP]

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]

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]

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]

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.

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]

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.

[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.

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]

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!

[yor_on]

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..