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Author Topic: An essay in futility, too long to read :)  (Read 281345 times)

Offline yor_on

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Re: An essay in futility, too long to read :)
« Reply #1325 on: 15/07/2013 22:05:21 »
That boundary is inside you, and me, and everything we can magnify, except 'space'. You're welcome to show me a piece of magnified 'space', also to prove what differ it from it unmagnified macroscopic brother. Referring to a 'energy' inside a 'space' is also something unprovable. Assume you can magnify a patch of 'space', would you now have diluted the 'energy' inside it too?
 

Offline yor_on

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Re: An essay in futility, too long to read :)
« Reply #1326 on: 15/07/2013 22:32:14 »
What you call magnifying I might call a 'inflation' :)

But maybe? Maybe everything is about 'densities', 'space' being some 'neutral' density, without 'friction'. Or maybe 'space' is 'gravity'? Wasn't this what Einstein thought, as he looked at particles and tried to explain them. As if they too was formed from gravity? "The purpose of the paper of Einstein and Rosen was not to promote faster-than-light or inter-universe travel, but to attempt to explain fundamental particles like electrons as space-tunnels threaded by electric lines of force. " That speaks to me about gravity. from The Einstein-Rosen Bridge.

How would gravity create 'space tunnels' for particles?

"Fundamental interactions, sometimes called fundamental forces or interactive forces, are described in fundamental physics as patterns of relations in physical systems evolving over time, whose descriptions appear not reducible to relations among entities more basic. The known fundamental interactions are gravitation, electromagnetism, strong nuclear, and the weak nuclear, which are all non-contact forces.

The electromagnetic and weak interactions were modeled together as the electroweak interaction, inferred to operate only at such high temperatures as soon after the presumed Big Bang, although as the early universe cooled, the electroweak interaction split into electromagnetism and the weak interaction. Both forces together with the Higgs field are described by the Standard Model. In particular the Higgs component has been verified only recently by experiments, with some details -- such as the exact form of the Higgs field Hamiltonion -- still being under debate. There is a considerable theoretical effort to extend the Standard Model to include also the strong nuclear, which includes the interactions listed above as a low energy approximation to an underlying unified force. These models are usually referred to as Grand Unified Theory.

With the possible exception of gravitation, these interactions can usually be described in a set of calculational approximation methods known as perturbation theory, as being mediated by the exchange of gauge bosons between particles. However, there are situations where perturbation theory does not adequately describe the observed phenomena, such as bound states and solitons." Fundamental interaction.

Now, I won't discuss renormalization in perturbation theory more than say that I find it a circular process, in where you use experimentally known boundaries to define 'theoretical' limits for your solutions, all as I get it. Renormalization Made Easy "Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory." Renormalization. 
 

Offline yor_on

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Re: An essay in futility, too long to read :)
« Reply #1327 on: 15/07/2013 23:26:33 »
So, how about it. Is all particles of a same type identical? Can they share a space? Are they 'individuals'?
Identical particles.
 

Offline yor_on

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Re: An essay in futility, too long to read :)
« Reply #1328 on: 15/07/2013 23:43:08 »
Assume you have a device that can compress a perfect vacuum. Then assume that it also can be used to uncompress that vacuum. Let it start at its most compressed level, opening a valve to let in a perfect vacuum in that recess. You close the valve and start to uncompress the device. What do you expect to happen with that perfect vacuum? Have you 'magnified' it by increasing its volume?
 

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Re: An essay in futility, too long to read :)
« Reply #1329 on: 15/07/2013 23:47:26 »
We don't need to discuss if you do it on earth or if you and your device too are in a perfect vacuum. We're only interested in what happens as you uncompress that initially small volume of a vacuum into a larger volume. Do you expect the 'vacuum energy' to 'increase' too, to keep a equilibrium here?
 

Offline yor_on

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Re: An essay in futility, too long to read :)
« Reply #1330 on: 15/07/2013 23:57:11 »
well, if you, as I, think we both exist you better bet on that your particles are 'individuals', although in a rather strange way. On the other tentacle :)  You better read this. Identity and Individuality in Quantum Theory.
 

Offline yor_on

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Re: An essay in futility, too long to read :)
« Reply #1331 on: 18/07/2013 10:02:13 »
So, how crazy am I :)

Crazy enough to try to understand physics. It's not the easiest proposition is it? To understand it? Then again, to me it's incredibly close to philosophy, as Stanford university is such a brilliant example of. And what we all share reading and writing is a deep interest in why we are here, wouldn't you agree? Sharing our ideas we all have something to say, and we all want to be understood, don't we? So here we are, on a small ball resting in a infinite darkness, lighted by a burning fire called a sun. And it's time that interest me, probably because I know I'm mortal, just as you.

So, how crazy can I become :)

I know that energy is mass, mass becoming energy, a 'convertible' without 'loss'. I know where we got it from and how we define it. But I find it incredible hard to accept that there isn't a cost involved in those transformations. So, if it now is a convertible without a measurable loss, meaning that we find it transform from usable to unusable 'energy'? So, can you guess what I'm thinking of as a, possible, cost?

The arrow of time.
 

Offline yor_on

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Re: An essay in futility, too long to read :)
« Reply #1332 on: 18/07/2013 10:07:03 »
Some call it change.
 

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Re: An essay in futility, too long to read :)
« Reply #1333 on: 18/07/2013 10:12:29 »
It goes so well with what I felt allready as I started to write, some years ago. That you can't ignore the arrow. It's a symmetry, just as Planck scale
 

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Re: An essay in futility, too long to read :)
« Reply #1334 on: 18/07/2013 10:14:22 »
Heh, soon the oh , so friendly men in white coats will pass me a visit, won't they? Anyway, we have a cost.
 

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Re: An essay in futility, too long to read :)
« Reply #1335 on: 24/07/2013 15:39:25 »
We have a universe don't we? And in it we have 'energy'. Is there a 'outside' too? Let us assume gravity to be a definer of what we can measure, would that mean that where gravity is not, nothing exist? And does that 'nothing' differ from the nothing we call a vacuum?

I'm not fanatical when it comes to anything, I hope? except possibly my ideas of 'locality' then :) and 'democracy' naturally. When it comes to the question of a God I just don't know. I see that as a matter of faith, of a very personal kind, up to each person to decide for themselves.

Let us consider the universe from two points of view. One is the one I would like to call a Newtonian, the other I think of as a result from Relativity, not only Einsteins but a growing idea, called 'symmetry'. In Newtons universe we have cause and effect, don't you agree? Something doesn't come from nothing, it need a cause. But when looking back at some origin of a universe that view becomes problematic to me. Because, where would it end? Wherever you set your foot down, calling this the 'origin', a further question can be added. "But, where did that come from?"

Then we have 'symmetries". Symmetry is to me a little as a analogue to our idea of 'energy', constantly of a same magnitude, going from 'useful' to un-useful", transforming. Both those ideas build on, as I see it then, an assumption that there is not really needed a cause and effect, not in a linear procession anyway. Although what we see normally is our Newtonian universe, in where we expect us able to backtrack a effect to a cause. Now, you also have non-linear effects, unable to backtrack to causes, as following all parameters back becomes just too much, but you might be able to argue that having the perfect computer, and all parameters defined it should be possible (macroscopically this is). Then we can add QM, and the way that describes it as statistics and probabilities, as well as uncertainty on a microscopic plane.

Well, in a universe defined by symmetries, each 'half' is dependent on the other 'half' as I think. To me it becomes a 'merry go round', and in the end. It does not answer how this situation can be. So, either way, it neither confirm, nor disagree with any 'shaper of the universe' as I see it. Myself I doubt, but that is from aesthetics mostly. I mean, who in his or her right mind would want to be responsible for so much suffering?
« Last Edit: 24/07/2013 15:43:11 by yor_on »
 

Offline yor_on

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Re: An essay in futility, too long to read :)
« Reply #1336 on: 24/07/2013 16:01:39 »
there is another way to think of it, possibly :) Assuming a arrow to be a 'local definition', creating cause and effect. That should also imply that the universe we measure on will be restricted by a clock and a ruler. Because all our measurements use it. So how would you prove such an idea?
 

Offline yor_on

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Re: An essay in futility, too long to read :)
« Reply #1337 on: 24/07/2013 16:25:38 »
Then again, if I refer to a arrow as being a cost created through 'change', or 'symmetries' interacting, as when 'energy' goes from 'useful to un-useful' in a transformation? I just as easily can turn that around, can't I? and define the arrow as being 'cause and effect'? It all depends on what you think the arrow is, and also if you differ that idea from a idea of 'time'. I differ them, and anyone reading about quantum computers most probably do, as it involves something 'taking all paths simultaneously' (Feynman if I remember rightly here) to then present us with one final path. The one we measure, using our clock and ruler, calling a outcome.

Either you argue that everything, all paths taken, has to do so under a existing arrow, before presenting us with a outcome. Or you, as me ,think of it as something 'timelessly coexisting' falling out into a outcome, becoming part of our arrow.

The first assumption, to me that is, suggest 'coexisting universes' though.
 

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Re: An essay in futility, too long to read :)
« Reply #1338 on: 24/07/2013 16:32:23 »
The point I'm trying to make is that if you assume a arrow to continuously exist, also defining it as taking all possible paths, then all those paths should be realized, in some weird manner. If you don't define it that way, instead defining it such as it is outcomes defining a arrow, then what happens 'between outcomes' isn't a arrow at all.
 

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Re: An essay in futility, too long to read :)
« Reply #1339 on: 28/07/2013 23:42:27 »
Is "Gravity" "Energy"?

What about gravitational waves?
Tidal forces, as tides? Isn't that 'energy'?

But first, what is "Energy"?

What about a 'geodesic' then. If I'm in a space-probe, uniformly moving, passing Jupiter, am I in a geodesic? Gravity is both 'passive' as well as 'active', meaning that all mass acts on all mass. And if a geodesic is defined by gravity's "energy', Am I in a geodesic? Defined by no 'resistance' and no 'friction'?

And if we then go down in scale to 'test particles', are they in a geodesic?
 

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Re: An essay in futility, too long to read :)
« Reply #1340 on: 28/07/2013 23:49:24 »
Let's exchange 'gravity' for 'energy', just for a while :)

We are then defined by "Energy", as our "SpaceTime" also should be. So what would then a vacuum be? Something created in and through that "Energy"? Or yet another property, co-existing? If you define 'gravity' as the metric of space, you also must assume that it is what defines it, the way it behaves.

I don't know what 'energy' is, and I doubt you do either.
 

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Re: An essay in futility, too long to read :)
« Reply #1341 on: 28/07/2013 23:50:48 »
Or you have a equation showing how to transfer a vacuum to energy?
 

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Re: An essay in futility, too long to read :)
« Reply #1342 on: 28/07/2013 23:59:05 »
That one I would like to see, practically proved that is :)
Getting 'energy' driving a flashlight, out of a vacuum.

The closest I get to 'energy' seems to be transformations? And getting a tide could be seen as a transformation. Then again, if fermions and bosons both are representations of that 'energy', shouldn't  it have a 'ground state', somehow, somewhere? What would that ground state be then?

And if it all is observer dependent?
Gravity in a free fall is without 'Energy' as nothing is acting on you, locally measured. And that's how you measure, however you turn.
 

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Re: An essay in futility, too long to read :)
« Reply #1343 on: 29/07/2013 00:23:29 »
Gravity is observer dependent.
Motion is observer dependent, still we define 'c', stating that no matter can reach that speed. So how do we define it? We can do it locally, am I not right? Strictly, locally, defined, as in a 'acceleration' getting close to 'c'. But we also, to get a logic, need to assume that another observer, no matter his speed, as defined by us or by some other observer, will agree on us now being close to 'c'. And as we accelerate our relative mass grows. So how do you measure? If you would like to define a SpaceTime 'globally'? You need a coordinate system that you simplify to as few parameters as possible, preferably, I think? Or, you add more degrees of freedom, finding something that simplify it, making it observer independent?

Because that's what you need to get away from, to define this 'common universe'.
Observer dependencies.

And to do that you also must explain why 'c' always is a local constant I think.
Not many that tries for that.
 

Offline yor_on

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Re: An essay in futility, too long to read :)
« Reply #1344 on: 29/07/2013 00:45:07 »
"Einstein went on to discover a more general theory of relativity which explained gravity in terms of curved spacetime, and he talked about the speed of light changing in this new theory.  In the 1920 book "Relativity: the special and general theory" he wrote: . . . according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [. . .] cannot claim any unlimited validity.  A curvature of rays of light can only take place when the velocity of propagation of light varies with position.  Since Einstein talks of velocity (a vector quantity: speed with direction) rather than speed alone, it is not clear that he meant the speed will change, but the reference to special relativity suggests that he did mean so.  This interpretation is perfectly valid and makes good physical sense, but a more modern interpretation is that the speed of light is constant in general relativity.

The problem here comes from the fact that speed is a coordinate-dependent quantity, and is therefore somewhat ambiguous.  To determine speed (distance moved/time taken) you must first choose some standards of distance and time, and different choices can give different answers.  This is already true in special relativity: if you measure the speed of light in an accelerating reference frame, the answer will, in general, differ from c.

In special relativity, the speed of light is constant when measured in any inertial frame.  In general relativity, the appropriate generalisation is that the speed of light is constant in any freely falling reference frame (in a region small enough that tidal effects can be neglected).  In this passage, Einstein is not talking about a freely falling frame, but rather about a frame at rest relative to a source of gravity.  In such a frame, the speed of light can differ from c, basically because of the effect of gravity (spacetime curvature) on clocks and rulers.

If general relativity is correct, then the constancy of the speed of light in inertial frames is a tautology from the geometry of spacetime.  The causal structure of the universe is determined by the geometry of "null vectors".  Travelling at the speed c means following world-lines tangent to these null vectors.  The use of c as a conversion between units of metres and seconds, as in the SI definition of the metre, is fully justified on theoretical grounds as well as practical terms, because c is not merely the speed of light, it is a fundamental feature of the geometry of spacetime.

Like special relativity, some of the predictions of general relativity have been confirmed in many different observations.  The book listed below by Clifford Will is an excellent reference for further details.

Finally, we come to the conclusion that the speed of light is not only observed to be constant; in the light of well tested theories of physics, it does not even make any sense to say that it varies."

The speed of light.
 

Offline yor_on

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Re: An essay in futility, too long to read :)
« Reply #1345 on: 29/07/2013 00:50:45 »
So light follows geodesics, or 'gravity', and although you can define its 'velocity' as 'varying' relative you being on a frame at rest relative to a source of gravity, its 'speed' in a 'flat space' is a constant, called 'c', using our definitions of clocks and rulers. But it does not answer why it is 'c', does it?
 

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Re: An essay in futility, too long to read :)
« Reply #1346 on: 29/07/2013 01:21:30 »
Using 'c' we then must find a way to define what doesn't change under a Lorentz transformation, as one way to that 'commonly shared' SpaceTime. That is, if we want a global solution.

"In physics, Lorentz symmetry, named for Hendrik Lorentz, is "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space". Lorentz covariance, a related concept, is a key property of spacetime following from the special theory of relativity. Lorentz covariance has two distinct, but closely related meanings:

    A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group. According to the representation theory of the Lorentz group, these quantities are built out of scalars, four-vectors, four-tensors, and spinors. In particular, a scalar (e.g., the space-time interval) remains the same under Lorentz transformations and is said to be a "Lorentz invariant" (i.e., they transform under the trivial representation).

An equation is said to be Lorentz covariant if it can be written in terms of Lorentz covariant quantities (confusingly, some use the term "invariant" here). The key property of such equations is that if they hold in one inertial frame, then they hold in any inertial frame; this follows from the result that if all the components of a tensor vanish in one frame, they vanish in every frame. This condition is a requirement according to the principle of relativity, i.e., all non-gravitational laws must make the same predictions for identical experiments taking place at the same spacetime event in two different inertial frames of reference."

But..

"Local Lorentz covariance, which follows from general relativity, refers to Lorentz covariance applying only locally in an infinitesimal region of spacetime at every point. There is a generalization of this concept to cover Poincaré covariance and Poincaré invariance." Lorentz covariance.

General covariance and the foundations of general relativity: eight decades of dispute, by J. D. Norton.
 

Offline yor_on

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Re: An essay in futility, too long to read :)
« Reply #1347 on: 29/07/2013 02:46:12 »
So do I  think that as you can transform gravity it won't exist?
Depends on where I stand looking, doesn't it?

From a local point of view it must be gone. If I instead adapt a global definition it can't be gone, you might define it such as if you have two observers, one finding no gravity free falling, the other defining it as 'gravity' being there, attracting the one falling, then we must have gravity, even when 'transformed away' locally for the free falling observer.

But, if using a strictly local definition it is gone for the free falling observer, as far as I can see.

Using a local definition, but adding in 'gravity's' presumed 'infinite reach' then? If I assume the free falling observer to be in a geodesic, it shouldn't matter if you use Mach definitions or some other. That guy still shouldn't be able to find any gravity, acting on him, ignoring tidal forces for this. So where is that infinite reach locally defined?

but we can all observe gravity acting, looking out in the universe, no matter if we are inertially uniformly 'free falling' or 'gravitationally uniformly accelerating', according to some other observer.
 

Offline yor_on

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Re: An essay in futility, too long to read :)
« Reply #1348 on: 29/07/2013 13:53:16 »
Then again.

" There are many instances of later accounts misrepresenting Einstein’s ideas.

None is as universal and complete as the later treatments of Einstein’s principle of equivalence. In his 'Meaning of Relativity', Einstein gives a statement of the principle typical of all his writing. K is an inertial system in special relativity and K‘ a system of coordinates uniformly accelerating with respect to K. Having noted ’that free masses in K are accelerated‘ just as if a gravitational field were present and  K‘ unaccelerated’,  Einstein  (1922a.  p57-8)  then writes:

". . . there is nothing to prevent our conceiving this gravitational field as real, that is, the conception that K is ‘at  rest’ and a gravitational field  is present we can consider as equivalent to the conception that only K is an ‘allowable’ system of co-ordinates and no gravitational field is present. The assumption of the complete physical equivalence of the systems of coordinates, K and K, we call the  ‘principle of  equivalence’;  . . . [it] signifies an extension of the principle of relativity to co-ordinate systems which are in non-uniform motion relatively to each other. In fact. through this conception we arrive at the unity of nature of inertia and gravitation."

Einstein, however, is nearly universally understood as urging a rather different principle, which I shall call the  ‘infinitesimal principle of equivalence’. A canonical formulation is given in Pauli (1921,pl45): "For every infinitely small world region (i.e. a world region which is so small that the space and time-variation of gravity can be neglected in it) there always exists a coordinate system K0(X1 X2 X3 X4) in which gravitation has no influence either on the motion of particles or any other physical process."
 
The key idea here is that in adopting a sufficiently small region of  spacetime, an arbitrary gravitational field becomes homogeneous and can be transformed away by a suitable choice of coordinate system. This principle exists in many variant forms. Sometimes it is strengthened to require that when the gravitational field is transformed away, we recover special relativity locally (for example, Misner et al., 1973, ~386).

With somewhat different qualifications, Pauli’s infinitesimal principle correspond to Dicke’s ‘strong  equivalence principle (Roll et al., 1964, p444). Dicke’s ‘weak equivalence principle’, however, requires only the uniqueness of gravitational acceleration, which amounts to requiring that the trajectories of free fall of suitably idealized bodies are independent of  their constitutions. Unlike most other writers, Pauli (1921,  p 145) acknowledged that his infinitesimal version of the principle of equivalence differed from Einstein’s, suggesting that, where Einstein’s principle applied only to homogeneous gravitational fields, Pauli’s version was for the ‘general case’. However the differences ran far deeper than Pauli allowed and pertain to quite fundamental questions of the role of the principle of equivalence in general relativity. These differences can be summarized in three  essential aspects of the principle which remained fixed throughout Einstein’s writings on general relativity, from the earliest moments in 1907 to his final years in the 1950.

..Einstein’s principle of equivalence was a covariance principle..

Special relativity required the complete physical equivalence of all inertial coordinate systems; for Einstein, general relativity required the complete equivalence of all coordinate systems.

Einstein’s principle of equivalence required the complete equivalence of a set of coordinate systems of intermediate size: inertial coordinate systems plus uniformly accelerated coordinate  systems. That is, the principle sanctioned the extension of the covariance of special relativity beyond Lorentz covariance but not as far as general covariance. Thus, for Einstein, the principle of equivalence was a relativity principle intermediate in range between the principle of  relativity of special relativity and of general relativity. The point is so important for our concerns here that it is helpful to have it in Einstein’s own words of  (1950, p347):
 
"This is the gist of the principle of equivalence: In order to account for the equality of inert and gravitational mass within the theory it is necessary to admit non-linear transformations of the four coordinates. That is, the group of Lorentz transformations and hence the set of ‘permissible’ coordinate systems has to be extended."

Or, more succinctly, in an article devoted to explicating precisely what he intended with his principle of equivalence, Einstein (1916a, p641) wrote in emphasized text: "The requirement of general covariance of equations embraces that of the principle of equivalence as a quite special case."

The function of the alternative, infinitesimal principle of equivalence is to stipulate that a spacetime of general relativity with an arbitrary gravitational field is in some sense locally, that is, in infinitesimal regions, like the spacetime of special relativity. Einstein objected in correspondence with Schlick to the latter’s use of this idea, pointing out to Schlick that the sense in which special relativity holds locally must be so weak that accelerated and unaccelerated particles cannot be distinguished. For details, see Norton (1985, section 9).)

As a covariance principle, Einstein’s version of the principle served no such function. Therefore it was invariably restricted in the following related ways: Einstein’s principle of equivalence was applied only in special relativity to what we now would call Minkowski spacetimes. That is, the inertial coordinate system K of Einstein’s formulation of the principle is not some kind of free fall coordinate system of general relativity. It is simply an inertial coordinate system of special relativity. Thus the coordinate systems K and K’ are both coordinate systems of a Minkowski spacetime. Because of this, we would now be inclined to picture the entire principle as operating within special relativity.

This seems not to have been Einstein’s view. He seems to have regarded special relativity supplemented with the principle of equivalence as having more physical content than special relativity alone. The supplemented  theory had a wider covariance and it dealt with a new phenomenon, homogeneous gravitational fields. Einstein’s principle of  equivalence was not a prescription for transforming away arbitrary gravitational fields; it was just a recipe for creating a special type of gravitational field. Einstein’s principle of equivalence gave a recipe for creating a homogeneous gravitational field by transforming to a uniformly accelerated coordinate system. 

The infinitesimal principle gives a recipe for transforming away an arbitrary gravitational field: one first homogenizes it by considering an infinitesimal region of spacetime and then transforms it away by the reverse transformation of Einstein’s principle. Einstein repeatedly insisted that his principle of equivalence did not allow one to transform away an arbitrary gravitational field, but only gravitational fields of a quite special type, those produced by acceleration of the coordinate system.  (Einstein devotes a paragraph of near page length to this point (1916a. pp640-I). See Norton (1985, section2) "

From 'General covariance and the foundations of general relativity: eight decades of dispute, by J. D. Norton.' And if you didn't have a headache before I hope you'll find it now :)
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Scanning this text puts in 'spaces' between words, so bear with it.
« Last Edit: 29/07/2013 14:27:58 by yor_on »
 

Offline yor_on

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Re: An essay in futility, too long to read :)
« Reply #1349 on: 29/07/2013 14:52:07 »
What is striking ( to me that is :) in this text is the way we think of SpaceTime, as a 'commonly shared space' in where we all exist, even though 'observer dependently, locally defined'. Viewed 'globally' if I may, we find Einstein defining gravity quite clearly. It is the metric of the space we exist in, non-splittable from a vacuum. The idea of magnifying a space until it becomes 'flat', no gravity there, seems to me to be an idea that Einstein did not share.

Gravity becomes a vacuum.
 

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Re: An essay in futility, too long to read :)
« Reply #1349 on: 29/07/2013 14:52:07 »

 

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