[fontwell]

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.

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.

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]

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]

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]

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 (OP)]

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]

I'm glad you are finding this helpful

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]

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 (OP)]

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]

3 minites

[gem (OP)]

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]

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.)

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]

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.

[JP]

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 (OP)]

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]

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."*

[Geezer]

Anyway, I suspect Geo Driver is quite correct. If you want a three minute egg, time it for three minutes. (I'm assuming we are conducting the experiment at something close to one atmosphere and boiling the egg in water rather than molten iron.)

The timing device and the egg will both experience three minutes in, well, three minutes, or did we conclude the answer would be different?

[fontwell]

yor_on, you seem to have it in your grasp. The trouble is that some examples you use jump between GR and SR. A free falling body (or orbiting) compared to the Earth's surface (or centre) has time dilation due to the relative velocities (ignores mass). This is an SR effect. There is also another effect due to being near mass, this is a GR effect.

@Geezer, yes three minutes is three minutes but don't use an hour-glass style egg timer

[Geezer]

@Geezer, yes three minutes is three minutes but don't use an hour-glass style egg timer

Ah yes! I suppose any device that relied on gravity (pendulums etc) would be suspect  []

[gem (OP)]

@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 ??

[yor_on]

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.

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'?