[lean bean]

"Transformed away" in physics normally means that you perform a mathematical operation, or change coordinate systems but keep whats happening the same!  You have not transformed away the acceleration - you have changed the physical situation.  an accelerated frame of reference is not an inertial frame

Thanks for pointing that out. 

  I can look at a rock travelling at a constant velocity from my "fixed" position or I can mathematically show what I look like from the rest frame of the rock (ie the rock is no longer moving).

I can understand that.


imatfaal 

What I cannot do is a mathematical operation that allows me to say that the one point of view the earth has a gravitational field - but from another frame of reference, or coordinate system describe the earth without that field

Very late edit:Been doing some googling.
 Apparently, it is to do with not being able to transform away the tidal gradients of the earth's gravitational field, no matter how small your frame the gradients still exist.
So your right imatfaal, there is no mathematical operation you can do to transform the gradients away.

[LetoII]

i see really long and complicated answers here.
Isn't it as simple as this: the shortest path (a straight line) is not the path of least resistance?

[yor_on]

Maybe, depends on how you define gravity and space-time. Gravity is just a preferred direction to me though, nothing 'touchable', and nothing definable to conglomerations of different bosons for example. But we might find it otherwise, considering if we can prove a Higgs boson. That seem to open for 'densities'.

[Pmb]

"Transformed away" in physics normally means that you perform a mathematical operation, or change coordinate systems but keep whats happening the same!

When it comes to GR it means the following: Suppose there is a gravitational field in the current frame of reference, The presence of the gravitational field manifests itself by letting an object go free by dropping it. If the body accelerates with respect to the current frame of reference it means that there is a gravitational field present. Now invoke a change of the system of coordinates corresponding to a locally inertial frame of reference, If a body is let free and it remains at rest and doesn’t accelerate then there is no gravitational field present. That is what it means to “transform the gravitational field away.” At least according to Einstein. Obviously the reverse is true in that you can produce a gravitational field by an appropriate change in coordinate systems.

[AndroidNeox]

"Transformed away" in physics normally means that you perform a mathematical operation, or change coordinate systems but keep whats happening the same!  You have not transformed away the acceleration - you have changed the physical situation.  an accelerated frame of reference is not an inertial frame

  I can look at a rock travelling at a constant velocity from my "fixed" position or I can mathematically show what I look like from the rest frame of the rock (ie the rock is no longer moving).  What I cannot do is a mathematical operation that allows me to say that the one point of view the earth has a gravitational field - but from another frame of reference, or coordinate system describe the earth without that field

Right.

Equivalence principle allows one to equate a gravitational field with linear acceleration only if the field is uniform... for example, for someone standing on an infinitely wide plane of mass in an otherwise empty universe. Real world gravitational fields only approximate this, locally.

[imatfaal]

"Transformed away" in physics normally means that you perform a mathematical operation, or change coordinate systems but keep whats happening the same!

When it comes to GR it means the following: Suppose there is a gravitational field in the current frame of reference, The presence of the gravitational field manifests itself by letting an object go free by dropping it. If the body accelerates with respect to the current frame of reference it means that there is a gravitational field present. Now invoke a change of the system of coordinates corresponding to a locally inertial frame of reference, If a body is let free and it remains at rest and doesn’t accelerate then there is no gravitational field present. That is what it means to “transform the gravitational field away.” At least according to Einstein. Obviously the reverse is true in that you can produce a gravitational field by an appropriate change in coordinate systems.

Sorry Pete but can you run that again?  How can you produce a gravitational field by a coordinate transform - you can show that acceleration is indistinguishable (tidal aside) but after that I am flummoxed; it is the "elevator car" that is either in a gravitational field or accelerating - you cannot just transform that away. 

[Spacetectonics (OP)]

@ Pmb:

 Obviously the reverse is true in that you can produce a gravitational field by an appropriate change in coordinate systems.
[/quote]

Thanks Pmb,

Would it it be possible for you ,to define "Appropriate"; where you have mentioned "an appropriate change in coordinate systems" please?

[Pmb]

Equivalence principle allows one to equate a gravitational field with linear acceleration only if the field is uniform... for example, for someone standing on an infinitely wide plane of mass in an otherwise empty universe. Real world gravitational fields only approximate this, locally.

In Newtonian gravity it is quite possible set up a distribution of mass to get a perfectly uniform field, at least in principle. Nothing is ever perfect to a zillion decimal places, right?   I created a web page describing such an example. It’s a cavity inside a spherical body whose center is offset from the center of the spherical body (which otherwise has uniform mass density). See http://home.comcast.net/~peter.m.brown/gr/grav_cavity.htm

In GR there are stresses to take into account and those stresses contribute to the gravitational field. However the field is still uniform to a large degree of accuracy.

Sorry Pete but can you run that again?  How can you produce a gravitational field by a coordinate transform - you can show that acceleration is indistinguishable (tidal aside) but after that I am flummoxed; it is the "elevator car" that is either in a gravitational field or accelerating - you cannot just transform that away. 

First let’s look at where I got that notion from just so that the world can be sure that it’s not pmb who has been creating wild fantasies in his mind.

From The Foundations of the General Theory of Relativity by A. Einstein, Annalen der Physik, 49, 1916.

It will be seen from these reflexions that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to “produce” a gravitational field merely by changing the system of co-ordinates.

If you were to invoke a spacetime coordinate transformation that is changes from an inertial frame of reference S in flat spacetime to a uniformly accelerating frame S’ then observers in S’ will observe that there is a uniform gravitational field in their frame of reference.

If you were in a frame of reference in which there was a gravitational field of the Earth’s gravitational field then you can only transform the gravitational field away locally (i.e. in a small region of spacetime). Please explain what your objection is and what the talk about the elevator has to do with it? I.e. please explain why it can’t be transformed away? You do understand, don’t you, that when the spacetime is curved then you can only transform the field away locally? What local means has to do with the precision of the instruments that you’re using to detect the tidal forces.

Thanks Pmb,

Would it it be possible for you, to define "Appropriate"; where you have mentioned "an appropriate change in coordinate systems" please?

You’re most welcome Sir!

Appropriate means that not all changes of spacetime coordinates will work. Only those of a special kind will work. Obviously changing only the spatial coordinates from Cartesian coordinates to spherical to polar coordinates won’t be able to produce a gravitational field. But changing from one set of spacetime coordinates to a set of spacetime coordinates corresponding to a frame of reference which is accelerating relative to an inertial frame is an appropriate transformation. Mind you, these are changes from one set of spacetime coordinates to another set of spacetime coordinates. Not merely from one set of spatial coordinates to another.

[lean bean]

If you were in a frame of reference in which there was a gravitational field of the Earth’s gravitational field then you can only transform the gravitational field away locally (i.e. in a small region of spacetime). Please explain what your objection is and what the talk about the elevator has to do with it? I.e. please explain why it can’t be transformed away? You do understand, don’t you, that when the spacetime is curved then you can only transform the field away locally? What local means has to do with the precision of the instruments that you’re using to detect the tidal forces.

That’s answered something I was wondering about earlier.
Those tidal gradients are still there, it’s just a question of the precision of the instruments that you’re using to detect the tidal forces. Thanks.

[Pmb]

That’s answered something I was wondering about earlier.
Those tidal gradients are still there, it’s just a question of the precision of the instruments that you’re using to detect the tidal forces. Thanks.

You’re welcome Sir! There are two opinions on this subject. One side says that the equivalence principle is wrong because you can detect the tidal forces while the other side says its right because you can ignore them. I’ve explained the “it’s right” side. Here is the “it’s wrong” side.

What is the principle of equivalence?, Hans C. Ohanian, Am. J. Phys. 45(10)), October 1977. The abstract reads

The strong principle of equivalence is usually formulated as an assertion that in a sufficiently small, freely falling laboratory the gravitational fields surrounding the laboratory cannot be detected. We show that this is false by presenting several simple examples of phenomena which may be used to detect the gravitational field through its tidal effects: we show that these effects are, in fact, local (observable in an arbitrarily small region). Alternative formulations of the strong principle are discussed and a new formulation of strong equivalence (the "Einstein principle") as an assertion about the field equations of physics, rather than an assertion about all laws or all experiments, is proposed. We also discuss the weak principle of equivalence and its two complimentary aspects: the uniqueness of free fall of a test particles in arbitrary gravitational fields ("Galileo principle") and the uniqueness of free fall of arbitrary systems in weak gravitational fields ("Newton's principle").

[imatfaal]

Sorry Pete but can you run that again?  How can you produce a gravitational field by a coordinate transform - you can show that acceleration is indistinguishable (tidal aside) but after that I am flummoxed; it is the "elevator car" that is either in a gravitational field or accelerating - you cannot just transform that away. 

First let’s look at where I got that notion from just so that the world can be sure that it’s not pmb who has been creating wild fantasies in his mind.

From The Foundations of the General Theory of Relativity by A. Einstein, Annalen der Physik, 49, 1916.

It will be seen from these reflexions that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to “produce” a gravitational field merely by changing the system of co-ordinates.

If you were to invoke a spacetime coordinate transformation that is changes from an inertial frame of reference S in flat spacetime to a uniformly accelerating frame S’ then observers in S’ will observe that there is a uniform gravitational field in their frame of reference.

If you were in a frame of reference in which there was a gravitational field of the Earth’s gravitational field then you can only transform the gravitational field away locally (i.e. in a small region of spacetime). Please explain what your objection is and what the talk about the elevator has to do with it? I.e. please explain why it can’t be transformed away? You do understand, don’t you, that when the spacetime is curved then you can only transform the field away locally? What local means has to do with the precision of the instruments that you’re using to detect the tidal forces.

But Pete that section is dealing with an object at rest with respect to an accelerated non-inertial reference frame - that is indistinguishable from a uniform gravitational field - and as AE states a co-ordinate change will create the gravitational field BUT only in a frame that could otherwise be thought of as a non-inertial accelerating frame (K') .  I still do not understand how you could create a grav field with is identical locally to a non-inertial frame (with pseudoforces etc) from an inertial frame via coordinate transformations.

[Pmb]

But Pete that section is dealing with an object at rest with respect to an accelerated non-inertial reference frame - that is indistinguishable from a uniform gravitational field - and as AE states a co-ordinate change will create the gravitational field BUT only in a frame that could otherwise be thought of as a non-inertial accelerating frame (K') .

That’s correct. Perhaps you think that the creation of the gravitational field is something which is independent of the coordinate system and intrinsic to spacetime? Many physicists today don’t things which have an existence which is frame dependant.

In fact you said it yourself – Invoke a change in spacetime coordinates from an inertial frame to a non-inertial frame and you can have a gravitational field.

I still do not understand how you could create a grav field with is identical locally to a non-inertial frame (with pseudoforces etc) from an inertial frame via coordinate transformations.

I don’t understand where your confusion lies. You do understand, don’t you, that the term  “coordinate transformation” refers to changes in spacetime coordinates between two frames of reference including those changes in reference from an inertial frame of reference to an accelerating frame of reference, right?

Think of this as you would an electric field. If you have a frame of reference in which there is no electric field but there is a magnetic field present then you can change coordinates and “produce” an electric field. In the same way that you can “produce” an electric field by a change in spacetime coordinates you can also change spacetime coordinates to “produce” a gravitational field.

Note #1: Just in case you’re one of those people who think that in relativity there is no such thing as an electric field but only an electromagnetic field then let me warn you that such an assumption is not true. All it means is that the electric field produced is observer dependant. As I recall, the electric field 4-vector is proportional to the contraction of the Faraday tensor,  aka the electromagnetic field tensor, and the observer’s 4-velocity.

Note #2: Just because you can produce such things by a change in spacetime coordinates it doesn’t mean that you actually do create such things. Just as you can change from one inertial frame to another in the presence of a magnetic field and produce an electric field it doesn’t mean that just any old change in spacetime coordinates will produce such a gravitational field. Obviously if your in an inertial frame of reference in flat spacetime you can’t produce a gravitational field by invoking a Lorentz transformation. In the same way there are transformations which won’t give you an electric field in certain kinds of magnetic fields.

[Pmb]

imatfaal - You have me curious. What is it you think Einstein meant when he said

It will be seen from these reflexions that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to “produce” a gravitational field merely by changing the system of co-ordinates.

?

[imatfaal]

imatfaal - You have me curious. What is it you think Einstein meant when he said

It will be seen from these reflexions that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to “produce” a gravitational field merely by changing the system of co-ordinates.

?

He was talking about a non-inertial / accelerating frame of reference.  the whole of that section is about the way a coordinate transform can allow one to view an accelerating frame of reference as one that is in a uniform gravitational field.   You have said that a co-ordinate transform can allow one to view an inertial /constant velocity frame as one which is in a uniform gravitational field.  If you perform a coordinate transform to change an inertial frame to an accelerating frame then you have created a uniform fictitious field; the only way that an object or observer will recognize that field is if the object is accelerated to be at rest in that frame and frankly accelerating an object is not my idea of a coordinate transform.

[Spacetectonics (OP)]

Thanks .

Or May be we are measuring something Erroneously!!:)

[yor_on]

Hmm, to me that's more about what ground you choose to define it from, than what experiments tell you Imatfaal. the definitions Einstein used was all about experimental evidence as I remember. And enclosed inside his famous 'black box' uniformly accelerating, ignoring tidal forces, you too would find a 'real gravity', undifferentiated from any other type of 'gravity'.

Calling it 'pseudo' is correct from some other frame of reference ('inertial frame' as they call it).
But locally it is real, if we define our reality from experiments.

When reading people defining such forces as 'pseudo forces' I mostly assume that they think of it from the conception of  'one whole undivided SpaceTime', same for us all. But that's not the whole truth as I see it, we have one thing joining our observer dependencies, well, as I think of it nowadays, and that's the constant 'c'. But if experiments are the tellers of truth then Einsteins definition must be the correct one.

[yor_on]

To see why I make the point about experiments crucial, one need to consider how we make them. We can only make them locally, there is no other way that I know of. And what they tell me will then be the very real ground I go out from, theorizing about why, and how, those effects are possible. If I don't trust what my local experiments tells me then, by fault, I also must question physics, and if it/they are built on the wrong premises. So, as far as I know all experiments are local, and they also tell me what my reality looks like.

[Spacetectonics (OP)]

Imagine a big mass between an observer and a star, light reaches the witness” eye where it has to stop by the bulk but because of the bend he sees the star .up to now everything looks normal and I guess simply correct!
Now let’s change the mass to a black hole!
What our witness meant to see? How much “the bend “changes? How we could figure a ratio for the change?
 

[relgycandy]

Thank you for this report.If they see them, I asked the legal character ... maybe I will end back up with me ... or someone ... ... things happen ..