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Author Topic: Why Light folows the space-Time curve?Not the the shorthest Line?  (Read 12394 times)

Offline imatfaal

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Quote from: 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.
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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.
 

Offline Pmb

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Quote from: imatfaal
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.

Quote from: imatfaal
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.

 

Offline Pmb

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

Offline imatfaal

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

« Last Edit: 12/02/2013 16:24:22 by imatfaal »
 

Offline Spacetectonics

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Thanks .

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

Offline yor_on

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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.
 

Offline yor_on

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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.
 

Offline Spacetectonics

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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?
 :)
 

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Offline relgycandy

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Shrunk


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 ..



 

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