Photon?

[quantum_wave]

...
Wrong. Empty space (or spacetime) is not a medium.

...

Technically that is true, but is it also true that nothing in GR or EM precludes that there is a medium filling otherwise empty space? Isn't it debatable that space might be filled with a medium of some kind; not the luminiferous particulate aether that was falsified by MM, but an undetectable wave carrying medium of some sort?

...

It is. Space is a medium. And it isn't what spacetime is. Spacetime is an abstract thing in which there is no motion. See this post where Quarkhead conceded that motion in spacetime has no mathematical meaning .

Thanks for addressing that point. How would you respond to the question I posed to James R?

 

[Farsight]

...you are forbidden by the ordinary rules of mathematics from writing $$p(t)=(x(t),y(t),z(t),ct(t))$$ as you cannot use the time-like coordinate to parametrize itself. So motion is spacetime is not allowed.

Hooray. Somebody has finally got it.

All: Have a google on move through spacetime. That gives an awful lot of hits, because an awful lot of people don't know the difference between space and spacetime. As an alternative google on eg move through spacetime Thorne or move through spacetime Wheeler. You soon appreciate that this issue runs deep.

 

[Farsight]

Thanks for addressing that point. How would you respond to the question I posed to James R?

Let's have a look:

Technically that is true, but is it also true that nothing in GR or EM precludes that there is a medium filling otherwise empty space?

It is. What James said isn't true. Space is a medium. It isn't nothing. See this which quotes Einstein's Leyden Address. That's where he said space isn't "empty", and says space is the ether of general relativity, and "the ether of the general theory of relativity is a medium". The next section quotes Robert Laughlin saying GR boils down to conceptualizing space as a medium, and "subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness". James will agree with this: when an ocean wave moves through the sea, the sea waves. When a seismic wave moves through the ground, the ground waves. When a gravitational wave moves through space, space waves. Now ask him again if he thinks space isn't a medium.

Isn't it debatable that space might be filled with a medium of some kind; not the luminiferous particulate aether that was falsified by MM, but an undetectable wave carrying medium of some sort?

Of course it is. But note this: space isn't filled with a medium. It is a medium. Have a read about LIGO:

"The space-time ripples cause the distance measured by a light beam to change as the gravitational wave passes by".

See that? The distance changes. Space waves. Yes. Now you can allow yourself a chuckle of irony, because LIGO is an interferometer. Just like the Michelson-Morley experiment.

 

[OnlyMe]

Technically that is true, but is it also true that nothing in GR or EM precludes that there is a medium filling otherwise empty space? Isn't it debatable that space might be filled with a medium of some kind; not the luminiferous particulate aether that was falsified by MM, but an undetectable wave carrying medium of some sort?

.... How would you respond to the question I posed to James R?

First, the M&M experiment did not prove that the Luminefierous Aether did not exist. It and many recreations of it, all returned null results. Meaning they failed to prove that the Luminefierous Aether exists. (That is not the same as proving that it does not exist.)

The possible existence of the Luminefiferous Aether continued right up to the introduction of general relativity. Before that the Lorentz Ether Theory stood side by side with Special Relativity. With the introduction of the theory of general relativity, the Lorentz ether theory as well as the concept of a Luminefierous Aether, together were unable to make a transition to a fully consistent explaintion of gravitation, with the same degree of descriptive and predictive success, as general relativity.

I am unsure what you meant in context by, and EM.., but I don't believe that GR itself posits any physical medium to space itself, no matter how Farsight misinterprets Einstein's comment near the end of his Leydon address. What it does imply is that, a gravitational field can be thought of as a medium, in as much as the local characteristics of a gravitational field, which fills space and is described by the spacetime of GR, affects the path of both massive objects and EM radiation that passes through it. (But be careful because even this description/definition could be misleading. It should be thought of only as a simplistic attempt to answer what I believe you were asking.)

To the question of something other than the gravitational field filling empty space, I do not believe that it is a question that can be approached or addressed within the context of GR. It appears to me something that could only be fully addressed within the context of QM and more specifically quantum gravity (QG).., and there we do not yet have a fully consistent approach to rely on. IOW from an intuitive perspective it seems a medium is needed to fully explain some of the verified predictions of GR (like frame-dragging), from a within the context of QG.., and as yet we have no model of QG that does not have significant unresolved problems.

 

[QuarkHead]

Hooray. Somebody has finally got it..

And I suppose you're going to take credit for "convincing" me. When all you made was an empty assertion, without any argument. When I supplied the argument for this assertion being true. When I have known this and the rest of differential geometry since before I had the mis-fortune to encounter your on-screen name.

You really do take the prize for arrogant ignorance

BTW I thought you had me on Ignore. Did you tell the truth about that?

 

[quantum_wave]

...

But note this: space isn't filled with a medium. It is a medium. Have a read about LIGO:

"The space-time ripples cause the distance measured by a light beam to change as the gravitational wave passes by".

See that? The distance changes. Space waves. Yes. Now you can allow yourself a chuckle of irony, because LIGO is an interferometer. Just like the Michelson-Morley experiment.

The three dimensional space of Euclidean geometry simply defines the volume, not what fills the volume. In that context, one could maintain that space could be empty. Where I make the distinction is between a volume in Euclidean geometry, vs. any given volume of space in the cosmos. Any theory or hypothesis that posits a medium, then could logically be said to mean that space is not empty, it is filled with a medium. The medium would be capable of hosting waves, and the waves could be said to carry energy.

 

[krash661]

Hooray. Somebody has finally got it.

All: Have a google on move through spacetime. That gives an awful lot of hits, because an awful lot of people don't know the difference between space and spacetime. As an alternative google on eg move through spacetime Thorne or move through spacetime Wheeler. You soon appreciate that this issue runs deep.

why is it referred to as a continuum ?
also, explain the difference of space and cosmos.
please ? i'm begging you, like always.

 

[quantum_wave]

First, the M&M experiment did not prove that the Luminefierous Aether did not exist. It and many recreations of it, all returned null results. Meaning they failed to prove that the Luminefierous Aether exists. (That is not the same as proving that it does not exist.)

I stand corrected. I should say that M&M did not prove the existence of a luminiferous particulate aether in absolute space. I don't think there is an aether the meets that description, but I don't reject the possibility of a different kind of aether, undetectable on its own, that fills space, and that hosts waves that traverse the medium, carrying energy.

The possible existence of the Luminefiferous Aether continued right up to the introduction of general relativity. Before that the Lorentz Ether Theory stood side by side with Special Relativity. With the introduction of the theory of general relativity, the Lorentz ether theory as well as the concept of a Luminefierous Aether, together were unable to make a transition to a fully consistent explaintion of gravitation, with the same degree of descriptive and predictive success, as general relativity.

That sounds like a realistic explanation of the history of it.

I am unsure what you meant in context by, and EM..,

Maxwell's equations of electromagnetism.

... but I don't believe that GR itself posits any physical medium to space itself, no matter how Farsight misinterprets Einstein's comment near the end of his Leydon address. What it does imply is that, a gravitational field can be thought of as a medium, in as much as the local characteristics of a gravitational field, which fills space and is described by the spacetime of GR, affects the path of both massive objects and EM radiation that passes through it.

I agree that GR does not posit a medium. I don't think it posits a gravitational field either, unless you interpret the curvature of spacetime to equate to a gravitational field, but I don't.

(But be careful because even this description/definition could be misleading. It should be thought of only as a simplistic attempt to answer what I believe you were asking.)

Ok, thank you for that.

To the question of something other than the gravitational field filling empty space, I do not believe that it is a question that can be approached or addressed within the context of GR.

Agreed.

It appears to me something that could only be fully addressed within the context of QM and more specifically quantum gravity (QG)..,

Very true.

... and there we do not yet have a fully consistent approach to rely on. IOW from an intuitive perspective it seems a medium is needed to fully explain some of the verified predictions of GR (like frame-dragging), from a within the context of QG.., and as yet we have no model of QG that does not have significant unresolved problems.

Yes, darn it, lol.

 

[krash661]

And I suppose you're going to take credit for "convincing" me. When all you made was an empty assertion, without any argument. When I supplied the argument for this assertion being true. When I have known this and the rest of differential geometry since bef

why is it referred to as a continuum ?
also, explain the difference of space and cosmos.

 

[quantum_wave]

why is it referred to as a continuum ?
also, explain the difference of space and cosmos.
please ? i'm begging you, like always.

FYI, I just ordered Idiocracy from NetFlix . I'll do a review later.

 

[krash661]

FYI, I just ordered Idiocracy from NetFlix . I'll do a review later.

, to this day, i love that movie.

 

[OnlyMe]

I agree that GR does not posit a medium. I don't think it posits a gravitational field either, unless you interpret the curvature of spacetime to equate to a gravitational field, but I don't.

GR and spacetime are descriptions of gravitation and a field theory, so they do in fact posit the existence of gravitational fields.

 

[quantum_wave]

GR and spacetime are descriptions of gravitation and a field theory, so they do in fact posit the existence of gravitational fields.

Thanks, I thought that the curvature equates to the gravitational field, but they differ as described by Wiki, which gives the impression that GR does not posit the force of gravity:

Gravitational field
In physics, a gravitational field is a model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenomena, and is measured in newtons per kilogram (N/kg). In its original concept, gravity was a force between point masses. FollowingNewton, Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century explanations for gravity have usually been taught in terms of a field model, rather than a point attraction.

In a field model, rather than two particles attracting each other, the particles distort spacetime via their mass, and this distortion is what is perceived and measured as a "force". In such a model one states that matter moves in certain ways in response to the curvature of spacetime,[1] and that there is either no gravitational force,[2] or that gravity is a fictitious force.[3]

 

[Aqueous Id]

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[nimbus]

That is the opposite of what Koks wrote (and what Einstein wrote). You are again lying about your citation.

Physbang, Don Koks doesn’t agree with Duffield when Duffield says…

Only once you appreciate that and read what Einstein said, you will then appreciate that the gravitational field is there because the speed of light varies. Not the other way around.

Duffield had to admit Don Koks doesn’t agree to this
Link Here

Don Koks doesn't agree with me, such is life.

At first Duffield had to bluff that Don Koks may had changed his mind since the book was written, but there later came on that thread the massage from Don Koks, that it's as true now as when the book was written.
See the following from Don koks book ‘Explorations in Mathematical-Physics: The Concepts behind an Elegant Language’.
Don Koks says…“spacetime is perfectly well behaved” at r = 2M
see image below of page 508

So with this time-space swap incorporated, the normalised Riemann components don’t diverge at r = 2M, and we know for certain that spacetime is perfectly well behaved there.

My underline in above quotes.
So, if spacetime is “perfectly well behaved” at r = 2M, then there’s no stopping of light there. ( r = 2M is the event horizon).
Image 501 below, explains how the slowing and stopping of light at event horizon is for Schwarzschild spacetime coordinates.

 

[nimbus]

Yes it is. Suppose for brevity we assume a Euclidean (flat) spacetime 4-manifold $$M$$ with coordinates x, y, z, ct. Then a curve - or path - in spacetime is given by a mapping, say, $$[0,1] \to M$$. Then for all $$p \in M$$ and all, say, $$s \in [0,1]$$ that $$p(s)=(x(s),y(s),z(s),ct(s))$$ exists as an image point in $$M$$ one calls this a curve or path with parameter $$s$$.

On the other hand, if you decide to use time as your parameter- i.e. describe motion - , you are forbidden by the ordinary rules of mathematics from writing $$p(t)=(x(t),y(t),z(t),ct(t))$$ as you cannot use the time-like coordinate to parametrize itself.

So motion is spacetime is not allowed

PS The curve or path I described above is not the same as a geodesic, that requires parallel transfer and all that sort of stuff, though it is related

Thanks for getting back, I have to admit the math is over my head.
When you said "Yes it is" was that in answer to my confusion between path and motion or the part aboutthe geodesic being a path in spacetime?

 

[QuarkHead]

When you said "Yes it is" was that in answer to my confusion between path and motion or the part aboutthe geodesic being a path in spacetime?

The former. A geodesic is most certainly a path in spacetime.

 

[Billy T]

Yes it is. Suppose for brevity we assume a Euclidean (flat) spacetime 4-manifold $$M$$ with coordinates x, y, z, ct. Then a curve - or path - in spacetime is given by a mapping, say, $$[0,1] \to M$$. Then for all $$p \in M$$ and all, say, $$s \in [0,1]$$ that $$p(s)=(x(s),y(s),z(s),ct(s))$$ exists as an image point in $$M$$ one calls this a curve or path with parameter $$s$$. ...

I'm not fully following your math /understanding your point, but it seems to me you may be more formally saying what I have said.
I.e. that objects have a trajectory in space time and for any one inertial reference frame, one can consider it a path in 3D (x,y,z) space with time parameter "t" marked along the 3D path to specify particular points by (x,y,x,t) in a 4D or spacetime coordinate system.

I have noted that instead of "t" which is regular seconds intervals (and sub-division), you could, for example, mark the 3D path with parameter "d" where d is also regular intervals (and subdivisions) of some constant distance (say in cm) along the path, just like "t" was constant intervals of time along the path.

If the object is not accelerating, then the "d" and "t" parameter marking systems are identical, but not so if the object is accelerating.

Is this basically what your more formal math is telling us? Or something quite different?

PS I don't know why even a copy of your text with the many "[ tex] ... [/ tex]" does not come out correct for me but seems to make the \ ... \ appear.[/tex]

 

[QuarkHead]

I don't think it posits a gravitational field either, unless you interpret the curvature of spacetime to equate to a gravitational field, but I don't.

Oh dear, quantum_wave, I am afraid you go back on my "standard crank list". What do your "beliefs" have to do with anything?
I thought we had agreed that spacetime curvature is given by a field of curvature tensors (i.e. possibly different at each point in spacetime) and that the same is true of the metric tensor field (again, possibly different at each point in spacetime)

Since these are the main elements that enter into Einstein's gravitational theory, and since each is a field (of tensors), I cannot see why you can doubt that GR is a field theory - i.e. a theory that describes a gravitational field

 

[quantum_wave]

Oh dear, quantum_wave, I am afraid you go back on my "standard crank list". What do your "beliefs" have to do with anything?
I thought we had agreed that spacetime curvature is given by a field of curvature tensors (i.e. possibly different at each point in spacetime) and that the same is true of the metric tensor field (again, possibly different at each point in spacetime)

Since these are the main elements that enter into Einstein's gravitational theory, and since each is a field (of tensors), I cannot see why you can doubt that GR is a field theory - i.e. a theory that describes a gravitational field

Alright, I stand corrected; it is a field theory then. I have no problem with changing my view of it in that regard. My argument is with the impression I have that spacetime tracks back to that tiny dense hot beginning, sometimes referred to as a point, and I can't get past the idea that such a point of infinite density is equivalent to something from nothing. There is where I simply start looking for alternatives, and I explore the possibilities of preconditions to the Big Bang. There are three major explanations for the existence of the universe, and I prefer "always existed" to "something from nothing".