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## Summary:

- Is there a relative motion between a moving massive gravitational object with respect to the curved spacetime it produces in its vicinity?

What is Gravitational dragging ?

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## Summary:

- Is there a relative motion between a moving massive gravitational object with respect to the curved spacetime it produces in its vicinity?

What is Gravitational dragging ?

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A.T.

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In the spacetime viewpoint, objects don't "move" and spacetime doesn't "change". Spacetime is a 4-dimensional geometry that already includes the entire history of the object and the spacetime curvature it produces. A spacetime with an object that produces frame dragging simply has a somewhat different geometry from a spacetime with an object that doesn't.I don’t know the mathematics or the phenomenology in terms of what happens to curved spacetime when the massive object moves

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Please explain moreSpacetime is a 4-dimensional geometry that already includes the entire history of the object

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You're basically asking for an entire course in General Relativity. That's beyond the scope of a PF thread.Please explain more

Can you ask a more specific, narrower scope question?

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Mathematically, frame-dragging is rather similar to the way that a moving charge creates a magnetic field as well as an electric one.

So frame dragging is rather like the gravitational analogue of magnetism in electromagnetism. It's a pretty weak effect though. Gravity probe B detected the frame dragging due to the Earth's rotation, which provides a field analogous to that of a spinning charge. However, this effect is tiny, it took extrodinary measures to be able to detect it for the rotating Earth.

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In the spacetime viewpoint, objects don't "move" and spacetime doesn't "change". Spacetime is a 4-dimensional geometry that already includes the entire history of the object and the spacetime curvature it produces. A spacetime with an object that produces frame dragging simply has a somewhat different geometry from a spacetime with an object that doesn't.

but a moving charge creates a magnetic or electric field when it moves through a medium. If the medium moves with the charge no effect can be found.Mathematically, frame-dragging is rather similar to the way that a moving charge creates a magnetic field as well as an electric one.

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Ibix

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No it doesn't - there's no medium for electromagnetic fields. The supposed "ether" was found inconsistent with experiment over a century ago.but a moving charge creates a magnetic or electric field when it moves through a medium.

Peter's point was that spacetime can't change with time because time is just a direction in spacetime. You can imagine 'slicing' 4d spacetime into 3d 'sheets' which are each all of space at a single time. These sheets may have different geometries, but that's not because anything is being "dragged around" by mass.

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I apologize for not being careful when I said medium. I meant “field”. Lorentz force; if a charged particle q moves with velocity v in the presence of an electric field E and a magnetic field B then it will experience a force F. If no velocity no force. Do you agree?No it doesn't - there's no medium for electromagnetic fields. The supposed "ether" was found inconsistent with experiment over a century ago.

Peter's point was that spacetime can't change with time because time is just a direction in spacetime. You can imagine 'slicing' 4d spacetime into 3d 'sheets' which are each all of space at a single time. These sheets may have different geometries, but that's not because anything is being "dragged around" by mass.

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So do you mean these 3D sheets at a single time (hypersurfaces?) which have a specific flat local metric do not change with the presence of a massive object from point to point either according to world postulate(world line) or according to Einstein’s “ mollusk”?Peter's point was that spacetime can't change with time because time is just a direction in spacetime. You can imagine 'slicing' 4d spacetime into 3d 'sheets' which are each all of space at a single time. These sheets may have different geometries, but that's not because anything is being "dragged around" by mass.

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Ibix

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Not if the electric field is non-zero. And you seem to be positing a particle having a velocity with respect to the field. This is no such thing. The velocity in the Lorentz force equation is the velocity with respect to the reference frame in which the field is measured.Do you agree?

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Ibix

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I didn't say they were flat. They won't be in general. And no, they cannot change because they aren't equipped with a notion of time. You can compare one slice to another at a later time (with some care, there are a lot of traps for the unwary) and they may have a different geometry, yes.So do you mean these 3D sheets at a single time (hypersurfaces?) which have a specific flat local metric do not change with the presence of a massive object from point to point either according to world postulate(world line) or according to Einstein’s “ mollusk”?

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Nugatory

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No. One component of the force is ##q\vec{E}##, which is independent of velocity.If no velocity no force. Do you agree?

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Nugatory

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We can speak of an object's position in space changing over time - that's what we mean by "moving". However, this situation is represented in four-dimensional spacetime by a stationary curve - nothing moves or changes.Please explain more

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“Stationary curve”in what? Relative to what frame of reference is this curve stationary and what is the definition of “stationary”? A photons trajectory is can be straight line or curved depending on the chosen frame. But how do you explain it’s motion from Big Bang and across universe? Please help with more explainingWe can speak of an object's position in space changing over time - that's what we mean by "moving". However, this situation is represented in four-dimensional spacetime by a stationary curve - nothing moves or changes.

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If a charged particles velocity is parallel to the magnetic field, then there is no net force and the particle moves in a straight lineNo. One component of the force is ##q\vec{E}##, which is independent of velocity.

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jim mcnamara

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Ignore the math, it has a movie

Try this:

Try this:

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I am trying to understand this “week effect “. What is it’s mechanism ? How does it affect a free falling object in the curved space time in the vicinity of a massive object. How are the hypersurfaces of that space time affected. How are these effects communicated throughout the spacetime. I apologize for asking Too many questions.It's a pretty weak effect though. Gravity probe B detected the frame dragging due to the Earth's rotation, which provides a field analogous to that of a spinning charge. However, this effect is tiny, it took extrodinary measures to be able to detect it for the rotating Earth.

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Not if there is an electric field. See, for example:If a charged particles velocity is parallel to the magnetic field, then there is no net force and the particle moves in a straight line

http://farside.ph.utexas.edu/teaching/em/lectures/node33.html

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I agree.Not if there is an electric field. See, for example:

http://farside.ph.utexas.edu/teaching/em/lectures/node33.html

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If I may add that my original question included Linear motion as well as rotational motion dragging which gravity probe B detected.I am trying to understand this “week effect “. What is it’s mechanism ? How does it affect a free falling object in the curved space time in the vicinity of a massive object. How are the hypersurfaces of that space time affected. How are these effects communicated throughout the spacetime. I apologize for asking Too many questions.

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Ibix

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A curve in spacetime.“Stationary curve”in what?

You are misunderstanding @Nugatory's use of "stationary". He just means that the curve is a curve in spaceRelative to what frame of reference is this curve stationary and what is the definition of “stationary”?

Objects are modelled as a bundle of paths in spacetime, and what you probably think of as an object is a 3d slice through that bundle.Please help with more explaining

Unless there is an electric field, as has been pointed out multiple times now.If a charged particles velocity is parallel to the magnetic field, then there is no net force and the particle moves in a straight line

Spacetime is a curved manifold. Depending on the geometry, which depends on the distribution of stress-energy, the geodesic paths (the curved manifold equivalent of straight lines) are different. And free-falling objects follow geodesics.I am trying to understand this “week effect “. What is it’s mechanism ?

There is no lower-level explanation than that at our current level of knowledge. We hope a quantum theory of gravity might provide further insight.

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The 3D sheet at any given time does not change, no. That would make no sense. It would be like saying that what you did at noon today "changed". What you did at noon today is whatever it was; it can't change. Similarly, a 3D sheet at a given time can't change; it is whatever it was at that time.these 3D sheets at a single time (hypersurfaces?) which have a specific flat local metric do not change

The 3D sheet at some time ##t_2## might be different from the 3D sheet at some earlier time ##t_1##. In the spacetime viewpoint, this just means 4D spacetime as a whole is a stack of such sheets, and the ##t_2## sheet is higher in the stack than the ##t_1## sheet, and the ##t_2## sheet has a different shape than the ##t_1## sheet does. (And, as @Nugatory noted, it might be that none of the sheets have a flat shape; they might all be curved.)

The limitation of this "stack of sheets" analogy is that there is not one unique way to slice up 4D spacetime into a stack of 3D sheets. There are an infinite number of different ways of doing it, corresponding to the infinite number of ways of choosing coordinates, and there might not be any useful correspondence between the "spaces" (sheets) or "time" (direction from one sheet to another) in the different coordinate choices. (In fact, there are choices of coordinates which do not even lead to a "stack of sheets" where each 3D sheet is a "space" and the direction from one sheet to another in the stack is a "time"; but that level of complication is probably out of scope for this discussion.)

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timmdeeg

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Imagine freely falling test particles toward a mass (a planet, a star, ...). Then there are two cases, the mass isI am trying to understand this “week effect “. What is it’s mechanism ? How does it affect a free falling object in the curved space time in the vicinity of a massive object.

a) not rotating: the trajectory of the particles is a straight line towards the center of the mass.

b) rotating: the trajectory of the particles is slightly bent in the direction of the rotation.

This is what happens, its not the "mechanism".

Experts: please correct if my wording is misleading.

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