Gravity waves and the aether

[Mike Smith Cosmos]

Yes. Me and many others said this some time ago. (Although, personally, I think using the word "aether" is unnecessarily confusing as it was originally used for something completely different.)

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Yes well that is great !

I have only been temporarily using the word ' aether' as it was in the original post , posted by someone else . ( MoonTanMan)

 

I wouldn't mind knowing who first coined the rubber sheet analogy . Was it Einstein or a more recent scientist . As it does offer some interesting possible insights , if it was the great master himself ? Einstein ?

 

Mike

 

Ps this is almost on a par with ( "which is more important ? the medium ? Or the message? " ) bandied around some years ago!

Edited August 18, 2016 by Mike Smith Cosmos

[geordief]

So absolutely everything is affected by gravity?

 

And the gravity field extends the length and breadth of the known Universe,possibly being considered as the largest thing that exists? (it is continuous and entirely extensive with the possible exception of black holes )

 

Is it a kind of mirror image of the distributed mass/energy in the Universe?

[Strange]

I wouldn't mind knowing who first coined the rubber sheet analogy . Was it Einstein or a more recent scientist . As it does offer some interesting possible insights , if it was the great master himself ? Einstein ?

 

I have no idea who thought of it.

 

But as it is horribly misleading in so many ways, I would not spend any time on it.

So absolutely everything is affected by gravity?

 

And the gravity field extends the length and breadth of the known Universe,possibly being considered as the largest thing that exists? (it is continuous and entirely extensive with the possible exception of black holes )

 

As gravity IS [the curvature of] space-time then, yes, it extends wherever there is space (and time!)

 

 

 

Is it a kind of mirror image of the distributed mass/energy in the Universe?

 

Interesting analogy. I guess it could be considered an image of the mass-energy distribution.

[Mike Smith Cosmos]

I have no idea who thought of it.

 

But as it is horribly misleading in so many ways, I would not spend any time on it.

 

As gravity IS [the curvature of] space-time then, yes, it extends wherever there is space (and time!)

 

 

 

Interesting analogy. I guess it could be considered an image of the mass-energy distribution.

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Well , obviously with All analogies they have their limitations. But if one was to consider far ends of the model/ analogy . Then it does illustrate some interesting similarities!

 

For instance

A) with a rubber sheet , taught, no mass on it , anywhere to be seen immediately thereabouts. Then what . It exists only in two dimensions ,( so no 3 d space time ) if

B) you place a mass of some sort in the middle , you do get a displacement into a third dimension . This thing has mass , matter . The bigger the mass of matter the bigger the indentation .

If you were a massless particle , no dent . ( not sure of consequences of that ? )

 

C) second mass will receive an attraction to the first mass .in the model as well as reality . No avoidance . Unless you are massless!

D) if you creat a wave near the colliding masses , the rubber sheet will vibrate a while into the distance

 

Mike

Edited August 18, 2016 by Mike Smith Cosmos

[Strange]

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A) with a rubber sheet , taught, no mass on it , anywhere to be seen immediately thereabouts. Then what . It exists only in two dimensions ,( so no 3 d space time ) if

B) you place a mass of some sort in the middle , you do get a displacement into a third dimension .

 

 

That "extra dimension" is one of the ways that this analogy is misleading.

 

However, as you seem hooked on it, you might like this demo of someone showing how gravitational waves can spread across such a sheet.

http://nerdist.com/gravitational-waves-are-made-simple-in-this-easy-to-understand-demonstration/

[Mike Smith Cosmos]

That "extra dimension" is one of the ways that this analogy is misleading.

 

However, as you seem hooked on it, you might like this demo of someone showing how gravitational waves can spread across such a sheet.

http://nerdist.com/gravitational-waves-are-made-simple-in-this-easy-to-understand-demonstration/

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Yes ! , very good . I think ,demos, models , analogies are very educational. Obviously one has to keep a reserve, as

Only the real thing , can demonstrate perfectly the real thing. But equally it can throw in for free , things one might not have though of ?

 

I must say I always wondered a bit about the rubber sheet and things falling inward having anomalies in it , however perhaps without these analogies 'we might be lost ' sometimes .

 

I liked his ' speed limit ' comment ! I had always thought of light being the driver here , when in fact ( if what he says is correct ). Light only goes that fast , BECAUSE. It , light has hit the speed limit of ( space time ) .

 

That would infer that is the nature of ( space-time) as a medium that dictates the limit of anything within it . It cannot go any faster ( speed limit) . So one assumes , that IF. the NATURE of SPACE-TIME was different ( say thinner or more elastic or some other quality) and it imposed a higher speed limit . Then light would rise to meet the new limit . As opposed to the NATURE of LIGHT . ? Fixing its speed ? By the nature of light itself ?

 

Mike

Edited August 18, 2016 by Mike Smith Cosmos

[geordief]

I am not sure if the Permittivity of the vacuum is relevant the the speed of light (or just hangs off from it)

 

https://en.wikipedia.org/wiki/Vacuum_permittivity

 

Are these electrical and magnetic constants "just" mathematical concepts or is there any circumstance where they might be different from what they seem to have been measured to be?

Edited August 18, 2016 by geordief

[MigL]

So we've made Mike happy with...

'Space-time is the medium for gravitational waves'

and we can finally move on.

 

But space-time, or rather its curvature, IS gravity.

So Mike has finally agreed that the gravitational field IS the 'medium' for gravitational waves.

Just as he seems happy with the EM field is the 'medium' for EM waves.

 

IOW gravitational and EM waves are their 'own medium', or alternately, don't need a 'medium'.

Which for the rest of us ( less tenacious ) was established 35 pages ago

[geordief]

If I can party poop ,by that definition can the Gravitational Field also be seen as a medium for EM waves and so EM waves would have 2 mediums, the Gravitational Field as well as the EM field.?

 

Is the EM Field "inside" the Gravitational Field somewhat in the manner of a Russian doll?

[Mike Smith Cosmos]

If I can party poop ,by that definition can the Gravitational Field also be seen as a medium for EM waves and so EM waves would have 2 mediums, the Gravitational Field as well as the EM field.?

 

Is the EM Field "inside" the Gravitational Field somewhat in the manner of a Russian doll?

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That's a good question ! I hope someone could have a shot at it.

 

I beleive we are right at the fore front of modern physics research ?

Research , into the actual nature of SPACE-TIME and How it got here ?

 

Ref :- http://www.nature.com/news/theoretical-physics-the-origins-of-space-and-time-1.13613

 

Mike

Edited August 18, 2016 by Mike Smith Cosmos

[MigL]

EM waves have two mediums ?????

They don't even have one !

 

You didn't read that in my post.

Re-read it.

Otherwise, why would you jump to that conclusion ?

[ajb]

If I can party poop ,by that definition can the Gravitational Field also be seen as a medium for EM waves and so EM waves would have 2 mediums, the Gravitational Field as well as the EM field.?

Both the EM and gravitational field need space-time thought of as the underlying manifold of 'events'. But be careful here, gravity is really the local geometry of space-time and not 'just' space-time.

 

Gravitational waves are ripples in the local geometry of space-time - or really the frame bundle thereof - and electromagnetic waves are ripples in the local geometry of a U(1) principle bundle over space-time.

[Mike Smith Cosmos]

Both the EM and gravitational field need space-time thought of as the underlying manifold of 'events'. But be careful here, gravity is really the local geometry of space-time and not 'just' space-time.Gravitational waves are ripples in the local geometry of space-time - or really the frame bundle thereof - and electromagnetic waves are ripples in the local geometry of a U(1) principle bundle over space-time.

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It is much appreciated , AJB, your input to this issue.

Due to its importance , significance , help to all on their understanding , particularly mine !

 

Is it possible for you to translate your last ( clearly very significant ) comment about the nature of space-time and its ( medium style ) workings with em and gravity waves .

 

Could you speak it , as if you were talking to a ' gibbering idiot ' Ps . (not quite ) . Much appreciated .

 

Mike

Edited August 18, 2016 by Mike Smith Cosmos

[geordief]

EM waves have two mediums ?????

They don't even have one !

 

You didn't read that in my post.

Re-read it.

Otherwise, why would you jump to that conclusion ?

Here is the quote from your post (which I have re read)

 

"Just as he seems happy with the EM field is the 'medium' for EM waves"

 

I didn't say I agreed that "the EM field is the 'medium' for EM waves" (not competent to say) . I just asked whether "by that definition" EM waves could be said to need 2 mediums.

 

Not sure why you think I jumped to any conclusion. I thought it was a bizarre proposition but it seemed to follow from the premise you seemed to accord to Mike.

 

Maybe you were being sarcastic and I took your suggestion too seriously ?

Edited August 18, 2016 by geordief

[ajb]

Is it possible for you to translate your last ( clearly very significant ) comment about the nature of space-time and its ( medium style ) workings with em and gravity waves .

Space-time has 'two parts'

 

i) the structure of a smooth manifold of dimension 4 - meaning locally it looks like R^4.

ii) on that manifold we have a metric of signature (-1,1,1,1) (or (1,-1,-1,-1) depending on conventions)

 

The manifold structure we think of as the collection of all possible events - we don't dwell too much on what that means. The metric structure gives us a notion of the distence between two near by points, which we can also use to denfine the length of paths joint two points. This really encodes the causal structure.

 

Gravity we can think of in terms of this metric - the metric is like the gravitational potential found in Newtonian gravity. When there is no gravity the space-time is Minowski space-time, but when we have gravity the metric is different to the Minkowski metric.

 

Now, we like to measure how this is different. To do this we construct a connection - which gives us a way of moving vectors from one point to another near by point - and then we look at the curvature of this connection. We can think of the gravitational degree of freedom in terms of this connection rather than the metric.

 

We can do something similar in the case of EM, but we start with a connection (on a specific fibre bundle over the space-time) which we understand as the potential A. The field strength is the curvature of this connection (all mod possible plus or minus the complex unit).

[Mike Smith Cosmos]

Space-time has 'two parts'i) the structure of a smooth manifold of dimension 4 - meaning locally it looks like R^4.ii) on that manifold we have a metric of signature (-1,1,1,1) (or (1,-1,-1,-1) depending on conventions)The manifold structure we think of as the collection of all possible events - we don't dwell too much on what that means. The metric structure gives us a notion of the distence between two near by points, which we can also use to denfine the length of paths joint two points. This really encodes the causal structure.Gravity we can think of in terms of this metric - the metric is like the gravitational potential found in Newtonian gravity. When there is no gravity the space-time is Minowski space-time, but when we have gravity the metric is different to the Minkowski metric.Now, we like to measure how this is different. To do this we construct a connection - which gives us a way of moving vectors from one point to another near by point - and then we look at the curvature of this connection. We can think of the gravitational degree of freedom in terms of this connection rather than the metric.We can do something similar in the case of EM, but we start with a connection (on a specific fibre bundle over the space-time) which we understand as the potential A. The field strength is the curvature of this connection (all mod possible plus or minus the complex unit).

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I appreciate the effort you are going to, to help .

 

But could I dare to ask for another ' run at it ' . This time with the ' math speak ' turned down from level 7 to level 3 . Similarly the physics speak , turned down from 5 to 2 .

 

I will be thinking of the subject in hand to do with the composition of the Universe , both electro- magnetically ( light and other radiation ) and how Gravity , it's nature ,distribution and function throughout the universe , works .

 

Mike

[ajb]

I am not sure how much we can turn it down and still say something meaningful. If you really want to get to grips with what the EM field 'is' and what gravity 'is', then you will need to learn the maths. Or just be happy with what has been said - gravity is the local 'shape' of space-time and that electromagnetism can be understood in a similar, but different way.

Edited August 18, 2016 by ajb

[Mike Smith Cosmos]

I am not sure how much we can turn it down and still say something meaningful. If you really want to get to grips with what the EM field 'is' and what gravity 'is', then you will need to learn the maths. Or just be happy with what has been said - gravity is the local 'shape' of space-time and that electromagnetism can be understood in a similar, but different way.

.

 

No! Now you have ,overshot .

 

Is it asking too much for you to kindly , bring the intensity levels back up :-

A ) to 5/6 universal electro magnetic fields and

B) to 5/6. Universal gravitational fields.

 

I am sure you have something really interesting to say about the origins , interactions , and the general nature of these two fields .

And how they have shaped and are still shaping the universe we are barely seeing and understanding . If these two entities 1( mass with gravity ) and 2 ( electro- magnetism and light ) are the two major players in the development of the universe and contenders for the quantum - gravity, issue . Do we see any conclusion on their ultimate separateness or the understanding of their possible common origin ?

 

Sorry to 'go on ' a bit , but this subject is excruciatingly interesting as well as ground breaking .

 

As per the citation given previously :- http://www.nature.com/news/theoretical-physics-the-origins-of-space-and-time-1.13613

 

And :- http://www.tapir.caltech.edu/~teviet/Waves/gwave_spectrum.html

 

And :- background on interaction :- https://en.m.wikipedia.org/wiki/Fundamental_interaction

 

And :- gravitons :-

https://en.m.wikipedia.org/wiki/Graviton

 

Mike

Edited August 19, 2016 by Mike Smith Cosmos

[Strange]

Both the EM and gravitational field need space-time thought of as the underlying manifold of 'events'. But be careful here, gravity is really the local geometry of space-time and not 'just' space-time.

 

Gravitational waves are ripples in the local geometry of space-time - or really the frame bundle thereof - and electromagnetic waves are ripples in the local geometry of a U(1) principle bundle over space-time.

 

 

Any chance of a (relatively) lay explanation of what a bundle is, and how a fibre bundle differs from a frame bundle from a principle bundle?

[ajb]

Any chance of a (relatively) lay explanation of what a bundle is, and how a fibre bundle differs from a frame bundle from a principle bundle?

A fibre bundle is a manifold that locally looks like the product of two manifolds - but not globally. A trivial fibre buble is a fibre bundle that is globally a product. For example, the (finite) cylinder is a trivial bundle of the form IxS, where I is an interval and S is the circle. The Modius band is also a fibre bundle, but this is only locally of the form IxS as there is a twist - it is a non-trivial fibre bundle. You should think in terms of attaching an interval to each point on the circle and how many ways you can do this in a smooth way.

 

Another non-trivial (in general) example is the tangent bundle of a manifold. This is is made by building up all the tangent spaces of all the points on the manifold. In fact, this is an example of a vector bundle as each fibre - ie, each tangent space - is a vector space.

 

A principle bundle is a little more complicated, but again they are examples of fibre bundles. Locally principle bundles looks like XxG, where X is a manifold and G is a Lie group that acts on X.

 

The frame bundle of a manifold is the principle bundle associated with the tangent bundle. It consists of all the ordered bases of the tangent spaces and these come with a natural action of GL(n) - which is just a change of bases.

 

So, for general relativity, the mathematical setting can be understood as the frame bundle, which locally looks like MxGl(n) - though as we have a metric we can reduce the group structure here by picking just the othogonal bases.

 

For electromagnetism, we have a U(1) principle bundle, so this locally looks like MxU(1).

 

It may also be worth saying something about connections. A fibre bundle is a collection of 'fibres' - we have another space attached to each point of the 'base' manifold. Although these fibres are all 'the same' we don't have a canonical way of mapping the fibre at one point to the fibre at another near by point. This extra information that give or construct from other structures is a connection. I will just say that there are a few ways of understanding connections, but the most intuative is that connections connect near by fibres.

Edited August 19, 2016 by ajb

[Strange]

Thanks. I did get a little bit from that!

 

The Wikipedia page has a useful analogy:

 

A cylindrical hairbrush showing the intuition behind the term "fiber bundle". This hairbrush is like a fiber bundle in which the base space is a cylinder and the fibers (bristles) are line segments. The mapping π:E→B would take a point on any bristle and map it to its root on the cylinder.

https://en.wikipedia.org/wiki/Fiber_bundle

[Mike Smith Cosmos]

A fibre bundle is a manifold that locally looks like the product of two manifolds - but not globally. A trivial fibre buble is a fibre bundle that is globally a product. For example, the (finite) cylinder is a trivial bundle of the form IxS, where I is an interval and S is the circle. The Modius band is also a fibre bundle, but this is only locally of the form IxS as there is a twist - it is a non-trivial fibre bundle. You should think in terms of attaching an interval to each point on the circle and how many ways you can do this in a smooth way.Another non-trivial (in general) example is the tangent bundle of a manifold. This is is made by building up all the tangent spaces of all the points on the manifold. In fact, this is an example of a vector bundle as each fibre - ie, each tangent space - is a vector space.A principle bundle is a little more complicated, but again they are examples of fibre bundles. Locally principle bundles looks like XxG, where X is a manifold and G is a Lie group that acts on X.The frame bundle of a manifold is the principle bundle associated with the tangent bundle. It consists of all the ordered bases of the tangent spaces and these come with a natural action of GL(n) - which is just a change of bases.So, for general relativity, the mathematical setting can be understood as the frame bundle, which locally looks like MxGl(n) - though as we have a metric we can reduce the group structure here by picking just the othogonal bases.For electromagnetism, we have a U(1) principle bundle, so this locally looks like MxU(1).It may also be worth saying something about connections. A fibre bundle is a collection of 'fibres' - we have another space attached to each point of the 'base' manifold. Although these fibres are all 'the same' we don't have a canonical way of mapping the fibre at one point to the fibre at another near by point. This extra information that give or construct from other structures is a connection. I will just say that there are a few ways of understanding connections, but the most intuative is that connections connect near by fibres.

Is it possible to "SKETCH" in pencil ' roughly ' what all these things look like , ? I know you are talking in maths terms , but if you talk of a cylinder , with fibres clamped to the base , it conjures up a sort of image ? And if you talk of a Manifold , I have seen a weird sketch of a particular manifold . To me at this stage it does not matter if it is exactly right or even half right . I am finding it extremely difficult to build up a picture in my mind . ( you have probably gathered, I can only think in pictures) .

 

So one for Gravity field , and one for Electro-magnetism field .and sketches for the individual items you listed and described above . Please . I will be over the moon . Ecstatic , forever in your intellectual debt. Please don't say No , or you can't. Just sketch it on a scrap of paper , take a photo with your I pad , downsize to below 1 megabit and attach to the post .

 

Mike

Edited August 19, 2016 by Mike Smith Cosmos

[ajb]

Is it possible to "SKETCH" in pencil ' roughly ' what all these things look like , ? I

Think about the cylinder and the Mobius strip.

[MigL]

Keeping in mind that I haven't had my 'eureka' moment yet, where fibre bundles actually make sense to me...

 

In the example AJB gives.

If you consider a tube, and attach a 'fibre' at various points along the circumference, oriented towards the openings at each end of the tube, then you can transform the simple tube to a Mobius simply by flipping the fibres halfway around the circumference.

 

The 'fibres' are a convenient way to manipulate the action on a global topological manifold.

I wouldn't mind a new thread where AJB, if time permits as he must be extremely busy at the moment, could give us all a tutorial on the subject.

[Mike Smith Cosmos]

Now what is what :

 

Möbius : . .

 

Manifold :-

 

Cylinder and möbius :-

 

Where do the fibres go and what part is the Gravitational Field and Electro magnetic Field ?

 

Mike

Think about the cylinder and the Mobius strip.

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Bump mapped :-

Edited August 19, 2016 by Mike Smith Cosmos