Gravity waves and the aether

[ajb]

But What is Generating or Causing the Fields to exist ?

You are falling into a deep well called philosophy. I hope you don't get trapped by metaphysics!

[Strange]

But What is Generating or Causing the Fields to exist ?

 

I am.

[Mike Smith Cosmos]

Nothing. It is just part of nature.

You can't just say that ! Surely ?

 

That's like waving a majic wand , ' there ! And nature with fields exist !

 

Mike

[swansont]

But What is Generating or Causing the Fields to exist ?

 

 

I just answered that.

[StringJunky]

You can't just say that ! Surely ?

 

That's like waving a majic wand , ' there ! And nature with fields exist !

 

Mike

Why must everything be infinitely irreducible? Once you reach the fundamental, as far as we know, that's it.

Edited June 20, 2016 by StringJunky

[ajb]

That's like waving a majic wand , ' there ! And nature with fields exist !

 

It is based on what we see, or at least on what our mathematical models tell us. Trying to get into the details of what 'exists' and so on is metaphysics. The best we can really tell you is that our Universe is well described by a model that is based on the notion of space-time equipped with several fields on it. The nature of these fields depends on the models in question and the classical and quantum pictures are very different.

[Strange]

You can't just say that ! Surely ?

 

That's like waving a majic wand , ' there ! And nature with fields exist !

 

Mike

 

 

OK. Let's say that we have a new theory and in this theory, the fields exist because of something I shall call X (because we don't know what it is yet).

 

So we have moved on from fields being fundamental to X being fundamental.

 

Now, your question becomes: what causes X.

 

To put it another way: as far as we know currently, the fields are a fundamental aspect of the way the universe is. We may have more information one day, but there will always be something we consider fundamental. (And you will never be satisfied.)

[Markus Hanke]

To put it another way: as far as we know currently, the fields are a fundamental aspect of the way the universe is.

 

 

Actually, there is more going on here than immediately meets the eye. The field itself isn't fundamental, it arises from a more fundamental entity called the electromagnetic 4-potential A via exterior differentiation : F=dA. Stoke's theorem then implies that, for the boundary of a small volume V :

 

[latex]\displaystyle{\int_{\partial V}F=\int_{\partial V}dA=\int_{\partial \partial V}A\equiv 0}[/latex]

 

Or, written more succinctly : dF=ddA=0. Physically this means that magnetic field lines have no boundary, meaning they do not end anywhere and can thus only form closed loops; in other words, there are no magnetic charges. That is precisely the "magnetic" part of Maxwell's equations.

 

In the above expression, the last integral identically vanishes because of a very fundamental principle of topology called "the boundary of a boundary is zero". Therefore, the structure of electromagnetism as a model is not just some arbitrary ad-hoc construct that someone came up with, but it is actually based on powerful and very elementary topological principles which at first seem to have nothing to do at all with physics. The electromagnetic 4-potential itself then arises due to a symmetry breaking process from whatever it is that will enable us to eventually unify all the fundamental forces - in that context it is important to remember that the Standard Model as it stands is only an effective field theory, and by no means the last word.

 

P.S. It may be interesting to mention that the same topological principle ( "the boundary of a boundary is zero" ) also underlies the theory of General Relativity, though it is less obvious and requires more complicated maths to demonstrate.

[Strange]

Which almost implies that the universe is the way it is because it couldn't really be any other way...

[ajb]

I don't think any of us has been careful in what we mean by the electromagnatic field. But I would take it to be the connection one-form associated with a principle U(1)-bundle - essentially the A in the above.

 

F = dA is then the field strength, which is the curvature two-form of the connection. People do not usually mean the field strength when they speak of the electromagnetic field. But none of us have been careful so far.

[Markus Hanke]

People do not usually mean the field strength when they speak of the electromagnetic field.

 

 

I think that is a matter of convention rather than physics, but to me, the "electromagnetic field" is the Faraday tensor field, and I think a lot of texts follow that nomenclature - probably for historic reasons. But I guess one could make a case for the connection form to be regarded as "the field". Ultimately though the maths are clear and unambiguous; I only mentioned these things to point out that Maxwell's theory ( or even QED for that matter ) is not just some ad-hoc invention, but based on fundamental principles of nature.

[Mike Smith Cosmos]

Which almost implies that the universe is the way it is because it couldn't really be any other way...

I think that is a matter of convention rather than physics, but to me, the "electromagnetic field" is the Faraday tensor field, and I think a lot of texts follow that nomenclature - probably for historic reasons. But I guess one could make a case for the connection form to be regarded as "the field". Ultimately though the maths are clear and unambiguous; I only mentioned these things to point out that Maxwell's theory ( or even QED for that matter ) is not just some ad-hoc invention, but based on fundamental principles of nature.

 

.

I really want to understand this , but am having a little bit of a tough time , getting my head around what you are saying .

It sounds right , but I do not quite understand everything you are saying .

 

You appear to be saying that maxwells equations , linking electricity and magnetism are more that just a manipulation of terms to perform a calculation/ calculations . But somehow carry within them ( maxwells equations ) MORE ? Namely they are stating a profound truth as to the very (nature of electro magnetism ) ?.

 

Let's take that bit first .

 

(A). Rather than just a mathematical operator(s) , even though he is using a mathmatical operator (s), he is relaying , somehow more . He is embodying the nature of the physics of electricity and its production of a magnetic field ? ( and visa versa ) .

 

Can I get that bit straight first ?

 

Mike

Edited June 20, 2016 by Mike Smith Cosmos

[ajb]

... and I think a lot of texts follow that nomenclature - probably for historic reasons.

I disagree, but then it will simply depend on the books we read

[Mike Smith Cosmos]

I think .........Maxwell's theory......is not just some ad-hoc invention, but based on fundamental principles of nature.

 

.

 

Exactly What / which principle of nature was he mainly saying ?

 

And what principle is " a border of a border is zero "

 

Mike

Edited June 20, 2016 by Mike Smith Cosmos

[Markus Hanke]

He is embodying the nature of the physics of electricity and its production of a magnetic field ? ( and visa versa ) .

 

 

Not quite, or at least that depends on what you mean by "nature". Basically, what I was attempting to point out is that - given the very fact that electromagnetism exists - the general form of the laws that govern the structure and evolution of electromagnetic fields follows from fundamental principles of topology. Now, topology ( being the study of shapes and transformations thereof ) seems at first glance to have very little to do with anything in physics, so this fact is quite surprising. Maxwell himself would not have been aware of this, as the necessary formalism to reveal those relationships was not developed until after his death. What's more, it turns out that Einstein's General Relativity ( the theory of gravity ) is also based on that very same topological principle.

 

I would say that this principle constraints the form that the laws governing those concepts can take, rather than the nature of the concepts themselves. Since we do not yet have a model that can describe both fundamental particles and the microscopic structure of spacetime under one common umbrella, I don't think that the question as to the fundamental nature of electromagnetism can be properly answered. But of course that does not mean that we don't understand how these fields behave.

 

 

 

And what principle is " a border of a border is zero

 

Suppose you have a ball - the boundary of a ball is its surface, which we call a sphere. What is the boundary of a sphere ? Right - it doesn't have one, it is a continuous manifold wherever you go.

The boundary of a boundary of the ball is zero, i.e. it doesn't exist.

 

Suppose you have a pyramid. What is the boundary of the pyramid ? It's the four triangles making up its surface area. What is the boundary of that surface ? Again, it doesn't exist - the surface of the pyramid does not end anywhere since the four triangles are seamlessly joined together into a continuous surface, you can take a pen and start drawing a line, and keep going into all eternity without ever having to lift the pen off that surface.

The boundary of the boundary of the pyramid is zero. It doesn't exist.

 

And so on. I think you get the general idea. That is the principle in topology that "the boundary of a boundary is zero". The above are both very simple examples, but the principle can be generalised to more complex scenarios in arbitrarily many dimensions, and can be made mathematically precise so long as certain conditions hold. It then makes an appearance in algebraic form, in that if you have two boundary operators on an integral, or two exterior derivative operators together, the result will always be identically zero. This is what I used in post #133.

​

I disagree, but then it will simply depend on the books we read

 

I am not sure I follow you here. Do I understand you correctly in that you would not identify the term "electromagnetic field" with the Faraday tensor / 2-form F and its dual *F, but rather with the electromagnetic 4-potential / 1-form A ?

Edited June 20, 2016 by Markus Hanke

[swansont]

A Medium , necessary for EM propagation. --------- No medium , no propagation . -----------

 

 

Is the earth moving through this medium, or are we stationary with respect to it? How would we test this?

[Mike Smith Cosmos]

Is the earth moving through this medium, or are we stationary with respect to it? How would we test this?

.

At this moment I do not know , as I have only just been getting near to understanding , that :-

 

The medium is likely to consist mainly of this Electro Magnetic field , which permeates all space ( is space).

 

If I have started to understand what all you guys have been saying over the last few pages of discussion .

 

I have asked , where it emanates from , but so far I have , I believe been told " it's just there" . I am latching on to this field as being the medium ( or part of it at least) , being space itself .

 

So in answer to your question . I am not sure . This idea is very new to me, that a field exists throughout all space, in fact is space . And it is an electromagnetic field , the best as I can glean .

 

So it seems light and radio ElectroMagnetic waves can and do travel through this medium at the speed of light . Also gravity waves can travel through this medium . And this medium which in fact is space itself gets curved under the influence of mass . If I understand, what I am currently being advised, (assuming I am understanding things correctly.)

 

IF I am not understanding things correctly , I am sure someone will say so.

 

I must say , I am finding this quite exciting .

 

Mike

Edited June 20, 2016 by Mike Smith Cosmos

[Strange]

I have asked , where it emanates from , but so far I have , I believe been told " it's just there" . I am latching on to this field as being the medium ( or part of it at least) , being space itself .

 

 

You can regard it as the medium for electromagnetic radiation, but it is not "space itself". The distance between tow points (you and your beer glass, for example) is "space". It is just a measurement. You don't need a field for that.

 

 

 

This idea is very new to me, that a field exists throughout all space, in fact is space . And it is an electromagnetic field , the best as I can glean .

 

I am a little surprised that, as an engineer, you have not come across the electromagnetic field before.

 

Also, there are multiple fields that permeate all of space. There is one for each type of fundamental particle and interaction. The electron field, the Higgs field, etc.

 

 

 

Also gravity waves can travel through this medium .

 

No, gravitational waves do not travel through the electromagnetic field. They travel through space-time. Which can be treated as another field.

[swansont]

 

So it seems light and radio ElectroMagnetic waves can and do travel through this medium at the speed of light . Also gravity waves can travel through this medium . And this medium which in fact is space itself gets curved under the influence of mass . If I understand, what I am currently being advised, (assuming I am understanding things correctly.)

 

 

How is it that light travels at c, even from a moving source, if it's traveling through this medium?

 

How does the speed of light depend on the density (strength) of this medium? This is a dependence that other waves in media have.

 

Why would gravity, which is not electromagnetic, require an EM field in order to propagate?

[Moontanman]

Damn, eight pages for a simple question!

[MigL]

You see what you started ?

[ajb]

Do I understand you correctly in that you would not identify the term "electromagnetic field" with the Faraday tensor / 2-form F and its dual *F, but rather with the electromagnetic 4-potential / 1-form A ?

Yes, but it is not really an issue here.

[Markus Hanke]

Yes, but it is not really an issue here.

 

 

Ok no worries, I was just curious My own background is mostly in General Relativity, so the focus is almost always on the electromagnetic field tensor rather than the A field, but I can see your point.

[Mike Smith Cosmos]

You can regard it as the medium for electromagnetic radiation, but it is not "space itself".

 

.

.o.k. So this medium for electromagnetic radiation is in space .

 

I still can not see what is producing it . ( this electro magnetic field , permeating all space ? ) . And my brain does not want to accept , that it's just there !

 

I used to think that it was the photon of energy produced by the transmitter , be that light or radio waves , somehow took along its own electro magnetic field , in a sort of photon wave packet . Buzzing along its own trajectory at the speed of light . Although I did not like this image , I never needed to change it . However , now I am trying to understand things in retrospect for intellectual purposes, I am more happier with this field ( EM FIELD ) existing throughout space and a wave packet ( as a photon of energy ) moving through the electromagnetic field ( which I am viewing as the medium ) .

 

Now I have a new problem , what is providing and sustaining the humongous Electro Magnetic Field , throughout all of space . That is a Very Very Very Large Field , makes Tesla experiments look like a pin prick in an Ocean ?

 

Like is it ( EXUDED ) by all the other stuff in space , ( like dust, point charges, Higgs, gravitational field, or whatever ? ) This I don't understand . I think you just want me to just accept that it is there .

 

 

I can't . It's mental agony to do that .

 

Mike

Edited June 21, 2016 by Mike Smith Cosmos

[Daecon]

Is there any connection to the cosmic microwave background radiation?