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Author Topic: How much does the Earth weigh?  (Read 56633 times)

Foolosophy

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How much does the Earth weigh?
« Reply #200 on: 16/12/2010 00:27:26 »
Photons are 'mass less' according to mainstream physics, so why do they bend?

Photons do however possess a value for momentum, p and do impart pressure.

Photons bend because according to the theory of general relativity, space is bent or warped in the presence of a body's mass and so the photons follow the warped space. That's what gravity is, the warping/distortion effect of space (and time) by mass etc.

.........interesting

« Last Edit: 16/12/2010 00:29:18 by Foolosophy »

yor_on

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« Reply #201 on: 16/12/2010 00:38:46 »
Yes, but the momentum is also what is expected to 'push' on 'stuff', isn't it?
That seems to make them unique in some motto. when proper matter 'push' we call it 'kinetic energy' and it can be described in form of 'springs' compressing and recoiling as 'proper mass' meets 'proper mass', But if we talk about light it seems as if the momentum is expected to both be able to 'push' and 'attract', aka distorting SpaceTime?

Or what am I missing?
==

I should stop using 'attract' huh :)

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SteveFish

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How much does the Earth weigh?
« Reply #202 on: 16/12/2010 00:56:04 »
Shrunk
Yor_on:

OK, now I think I understand what you are about. In the future I will, as much as I can bear, try not to disturb you in your secret room.

Steve

JP

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« Reply #203 on: 16/12/2010 01:38:41 »
Heh.  I think I see what Yor_on was getting at.  Geodesics are shortest-paths (actually they're extremal paths, so they could be longest paths too) within general relativity's curved space-time.  Freely falling objects follow geodesics and gravity isn't treated as a force within that framework.

I'm not sure that defining weight is really useful within that framework, but maybe you could define it as the force required to hold an object at a constant position?  I can't imagine a use for defining a concept of weight in GR, though...

yor_on

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« Reply #204 on: 16/12/2010 03:31:45 »
Yeah, I found myself in deep trouble trying to find a decent definition of weight JP. And it's 'energy' not 'momentum' that distorts 'SpaceTime' isn't it? I have used momentum so long that suddenly it felt as if a photon only was its momentum there :) Senility my middle-name (I'm a collector of those too:)
==

extremal paths I mean?

Seems quite serious, the ones I found :)

« Last Edit: 16/12/2010 03:42:38 by yor_on »

JP

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« Reply #205 on: 16/12/2010 04:09:47 »
And it's 'energy' not 'momentum' that distorts 'SpaceTime' isn't it? I have used momentum so long that suddenly it felt as if a photon only was its momentum there :) Senility my middle-name (I'm a collector of those too:)
==

extremal paths I mean?

Seems quite serious, the ones I found :)

One of the points of GR is that it works no matter what reference frame you're in.  In other words, the basic equations of GR have to work no matter what frame you're in, and in different frames, energy and momentum can change.  The correct formulation of GR requires using a stress-energy tensor, which includes energy and momentum as well as the flow of energy and momentum in all four space-time coordinates and shear stresses.  In lay terms, this means that energy and momentum might be enough in one reference frame, but they aren't necessarily enough in all reference frames.  I can't go into a lot more detail than that, since I don't know GR in a lot of detail, but I do know that energy and momentum alone aren't enough except in special cases.

As for extremal paths and geodesics, I get it from something like this:
http://en.wikipedia.org/wiki/Geodesics_as_Hamiltonian_flows#Geodesics_as_an_application_of_the_principle_of_least_action

I see geodesics described as "extremal paths," "shortest paths," and "the closest thing to a straight line in a curved space."  I've been thinking about them as extremal paths because that's a technique used to solve a lot of problems in classical mechanics as well as to make approximations in quantum mechanics and electromagnetism.  In those cases, you look for paths that are basically the shortest or longest, so I've been assuming that's how GR works.  I haven't found a derivation proving that a geodesic can be the longest path, but neither have I seen one proving that it's the shortest...

yor_on

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« Reply #206 on: 16/12/2010 04:39:44 »
Well, I guess it depend on how you would define a 'longest path' wouldn't it? You could easily see a geodesic as a 'longest path', if you define it from a 'flat plane' I presume? But then again, that's not what you're talking about, is it?:) It's more of a rigorous mathematical definition, or approximative technique I guess in where one have to take in consideration the type of 'space' described in that path, whatever I may mean by that :)

I've always like the idea of energy myself, it seems to fit somehow. But there is also the idea of least force or action, maybe they all are equally correct. But for any action taken in SpaceTime I would expect you to have to expend energy. So I'll keep it :)

As for the tensions and stress inside some specific location of SpaceTime? That should mean other gravitational 'influences' acting on the photons path, except their own I presume? And possibly also covering how to define it depending on where you are watching the 'events'? Different 'frames of reference' in SpaceTime observing different causality chains?

Awh, any which way, time for me to get some sleep here.
My pleasure JP :)

JP

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« Reply #207 on: 16/12/2010 07:25:31 »
Well, I guess it depend on how you would define a 'longest path' wouldn't it?

I don't think so.  The "extremal path" description comes from the mathematical description that the derivative of the path length with respect to slight variations in the path equals zero.  If a derivative of a path equals zero, all you know is that it's either a minimum or a maximum length path, but not which until you get further information.

I don't know if this same treatment holds up in GR.  I'm confused by the fact that shortest path, extremal path and closest path to a straight line are all used...

yor_on

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« Reply #208 on: 16/12/2010 13:09:36 »
Ok :)
A mathematical definition in where certain attributes of your equation need to equal zero for it to fit the description of a extremal path, But how?

You have two points that you want to connect 'A' and 'B', then what?
If you look at the path between those two, practically you will need to consider what kind of 'space' they exist in right? Like drawing it on a paper the shortest way is a '2-dimensional flat plane' And in SpaceTime you have three (and time).

What more do you need to weight in for getting a description?
And how do you get to a longest path in SpaceTime?
Assuming that it is a 'sphere' the longest path have to be go around?

Or am I just confusing the concept?

yor_on

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« Reply #209 on: 16/12/2010 14:04:45 »
Thinking of the concept of 'force'. That is F=ma right?
And what it refers to is the concept of 'inertia' which is a objects tendency to stay in whatever motion, or position, it has unless acted upon by some external 'influence'. 'Influence' as we want to include gravity in the concept.

(Thinking about it, I should avoid to say external 'influence' and just call it 'change' instead. That as you can turn on your space engine which is entirely internal acting at the walls of your engine, 'pushing' at them.)

Still, what it all comes down to has to be the idea of 'energy expended'.
Correct me if you think I'm wrong here.

==
Here you can find another explanation of that apple, explained in form of geodesics.
Straight lines in a curved SpaceTime.
« Last Edit: 17/12/2010 02:15:08 by yor_on »

yor_on

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« Reply #210 on: 17/12/2010 03:46:52 »
I don't know, maybe you could look at gravity as an expression of time too?

Light that have no proper mass and is intrinsically time-less will have a 'shorter' SpaceTime path than Matter as 'proper mass' have a time-dilation, as seen from a outside 'frame of reference', and so have a longer Space-Time path? As even though with a 'time dilation' matter would still have a arrow 'ticking' intrinsically whilst light would have none?

Or if you like to see light as 'mass' too, relative or momentum, there still would be a 'mass difference'. But then I would say that it was light having to travel the 'longer path' according to the 'outside observer' as with a bigger 'time dilation' matter should have to be the 'faster'? As the idea of a intrinsic timelessness would be gone?

And the equivalence should hold for Lorentz contraction too, as observed from the 'inside' of their respective frames, assuming that light also meet that phenomena of course? Which it should if you assume a mass to it. But in the first case I'm not sure what light 'sees'?
==

One way around it would be to give only proper mass a time dilation, and ignore relative mass and momentum as having any importance for a time dilation? Then you can let light have a 'mass' and still not be affected by any intrinsic time? Light is so strange :)

I like it best not propagating at all :)

But if I do so I would have to assume that 'motion' in itself have some time dilating property, unrelated to relative mass and momentum? Nahh, that one was too weird..
==
Or maybe not?

Momentum shouldn't have a time dilation?
Because if it did it should invalidate the photons timelessness, shouldn't it?
And then we have relative mass left?

which in a way is a equivalence to 'potential energy'.
And I don't like 'potential energy' as a 'force' :)
Heh.

Which leaves 'motion'

And if i assume that light don't 'move'.
But matter does?

With should make 'motion' time dilation in itself.

Stop throwing things at me :)
==

Maybe 'energy' need to be looked at though?

We can't say that 'matter' gains 'energy' as such by motion. That is, the atoms doesn't start to 'jiggle' in my spaceship just because it 'moves' faster, do they? But there have to be a relation anyway. But I do 'bend' SpaceTime, contracting it, and also getting a time dilation as seen from 'outside' my frame of reference.

Could I assume that I gain 'energy' by a Lorentz contraction?
That is that if I assumed that the energy in the 'field' around my ship due to motion have increased?

« Last Edit: 17/12/2010 05:10:44 by yor_on »

JP

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« Reply #211 on: 17/12/2010 03:54:52 »
What more do you need to weight in for getting a description?
And how do you get to a longest path in SpaceTime?
Assuming that it is a 'sphere' the longest path have to be go around?

You look at the length of the path from point A to point B as the path taken varies.  Then you look for places where slight variations in the path don't change its length.  This happens at a local maxima or minima of the path length.  I don't know if it's possible in GR for an object to take a maximal path, but in other cases which use the same mathematics these paths are important.

yor_on

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« Reply #212 on: 17/12/2010 03:58:35 »
Sweet, now I see what you mean :)

JP

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« Reply #213 on: 17/12/2010 05:04:09 »

In SR, velocity alone determines time dilation.  Mass isn't useful in doing so.  Velocity is also determined by the ratio of energy to momentum, so you could determine time dilation if you know energy and momentum.  For photons velocity is always c and the energy-momentum ratio is always constant.  Of course, there is no mathematical theory for the point-of-view of photons, so no physical theory is going to answer the question of how they experience the universe.

In GR, time dilation is also caused by curvature of space-time, so mass does get involved, but as I mentioned elsewhere it gets involved through the stress-energy tensor, so the fundamental quantities are still energy and momentum.  I don't know the details as well in GR, though.

yor_on

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« Reply #214 on: 17/12/2010 05:14:58 »
Nah it's just me having assumed that they all was involved in it, well, not momentum maybe :) I haven't thought of it like this before. Strange..

But it makes sense, if it is this way then I don't need the concept of 'potential energy' I think? And neither do I need 'relative mass'?

That is because the 'potential energy' is a direct effect of motion and not 'potential' at all but very real. It's not so much as invalidating the concept, more like you have a 'sea' of energy that when contracted will increase. But it fits well in with how I think 'potential energy' is described with the difference of it not being 'potential' but 'real' :) If you get my drift..

And to then 'fit it' against other 'frames of reference' you just need to remember that all of them have their own 'SpaceTime', moving relative you or not. In them they will observe the same effects as you do. And as all of them are 'uniquely' their own, with a 'own SpaceTime' aka 'frame of reference' the 'potential energy' you expect to be released with a impact will be there as a relation.

It's moving me into a really weird universe if it's correct. Every 'frame of reference' a direct expression of a unique 'room time geometry' possibly swimming in a sea of 'energy' that we only get access to through 'motion' but still to us representing a 'whole 'smooth' SpaceTime' as far as we can observe having no 'borders' between what we know to be those 'frames of reference'. And then we have matter? A black hole create a very strange 'room time geometry', doesn't it? Or a Neutron star? And the Bekenstein bound as a description of the amount of 'states' possible, and possibly also 'energy' available(?), in your 'frame of reference'

But hey :)
It's late..

And momentum is then a very specialized description of photons 'pushing'.
And suddenly those Rindler observers starts to make a new sense..
==
I need to get some sleep huh :)
Anyway, for me its opening new ground as I reasoned it out all by myself ::))

However wrong I may be :)
==

And thanks JP, you have a flair for making your explaining succinct.
It's a very nice sign of knowing what one speaks of..

Same as me in fact... N 0t :)
« Last Edit: 17/12/2010 06:09:34 by yor_on »

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How much does the Earth weigh?
« Reply #214 on: 17/12/2010 05:14:58 »