Gravity And Electromagnetism As Spacetime Structure Disturbances

[pogono]

Hi everybody :-)

 

I have just put on arXiv my 4th version of the article (after 2 reviews)

http://arxiv.org/abs/1301.2758

 

You my find there, that gravity and electromagnetism may be explained as two different consequences of one filed equation describing disturbances in spacetime structure.

 

If you would like to discuss the idea in real live - come to my seminars.

I was invited to give open speech at Moscov Lemonosov University (may 14th).

I also wait for confirmation of my speech at GR20 conference in Warsaw (July).

 

For those who are interested in my idea - I put news page at my webpage:

http://www.dilationasfield.net/eng

 

Regards

pogono

[Aethelwulf]

Interesting.

[pogono]

Hi,

I have prepared a presentation for one of my seminar that explains the article:

http://dilationasfield.net/Seminar.pdf

 

Take a look if you are curious how is it possible to:

- consider photon acceleration

- explain light as disturbances of spacetime structure

[CraigD]

This is interesting - and, if I may say so, pleasantly mind-boggling - work.

 

Unfortunately for me, even the condensed and nicely presented math in pogono’s (who I’m guessing is Piotr Ogonowski, one of its authors) webpages is more than my poor mathematical physics skills can make sense of in a brief reading, but the informal discussion, while challenging, makes great sense to me.

 

I’ve a giddy sense that this could be something big to come in physics.

[tetrahedron]

I wonder how this might translate to atomic quantum physics. Hmmmm...

 

Jess Tauber

[Lancewen]

Hi everybody :-)

 

I have just put on arXiv my 4th version of the article (after 2 reviews)

http://arxiv.org/abs/1301.2758

 

You my find there, that gravity and electromagnetism may be explained as two different consequences of one filed equation describing disturbances in spacetime structure.

 

If you would like to discuss the idea in real live - come to my seminars.

I was invited to give open speech at Moscov Lemonosov University (may 14th).

I also wait for confirmation of my speech at GR20 conference in Warsaw (July).

 

For those who are interested in my idea - I put news page at my webpage:

http://www.dilationasfield.net/eng

 

Regards

pogono

 

I like your idea a lot. I would like to follow your progress on this topic. [removed accidental site rules violation] If it's possible post any productive feedback you get on this subject. Your approach is novel and I really did appreciate your taking the time to explain it for those of us that are not physics majors.

[Lancewen]

I did find another forum you posted in, and it looks like nobody responded.

 

http://www.physicsgre.com/viewtopic.php?f=10&t=4786

[CraigD]

I did find another forum you posted in, and it looks like nobody responded.

Not too surprising, as that forum is specifically for people preparing for the Graduate Record Exam in Physics, a test usually taken by people completing an undergraduate degree and applying for admission to graduate school. The GRE is a test of educational achievement, not interest in unusual theories.

 

I’ve lots of thoughts about pogono’s “curving light creates mass” hypothesis (vs the usual “mass causes curving light” prediction), but unfortunately no time in the past week and approaching days to deeply think or post about them. Hopefully we can get some good conversation going in this thread (as a site rule, we encourage conversation in our forum, not others – though linking to other forums to further our own is OK) soon. I encourage everyone to follow the links and get a solid idea of what pogono’s proposing, being careful to distinguish it from existing theories and proto-theories, conventional or personal.

[LaurieAG]

Hi Pogono,

 

You my find there, that gravity and electromagnetism may be explained as two different consequences of one filed equation describing disturbances in spacetime structure.

Interesting paper. I noticed that your co author Piotr Skindzier was also a co author in another paper titled 'Do Spiral Galaxies Need So Much Dark Matter?'.

 

As you already have a paper out titled 'Time Dilation as Field' what are the cosmological consequences for dark matter according to your theory.

[pogono]

Hello,

thank you for your responses.

 

Excuse me for delayed reply - we had holidays this week in Poland.

 

Your approach is novel and I really did appreciate your taking the time to explain it for those of us that are not physics majors.

If some of you have any questions - I will be glad to answer.

 

I wonder how this might translate to atomic quantum physics. Hmmmm...

 

Yes! It is exactly what I am working about, now.

As you see in my article we obtain valid quanta for rest mass, photon, etc.

It also seems, that elementary particles rest mass values might be explained by some quasi-stable shapes of spinning spacetime disturbances. Or as you wish - self attracting photon.

 

Here is interesting reference that explains a bit how it could work:

http://www.nature.com/srep/2012/121025/srep00771/pdf/srep00771.pdf

 

I am working over it now.

 

Hi Pogono,

Interesting paper. I noticed that your co author Piotr Skindzier was also a co author in another paper titled 'Do Spiral Galaxies Need So Much Dark Matter?'.

As you already have a paper out titled 'Time Dilation as Field' what are the cosmological consequences for dark matter according to your theory.

 

Co-author of the article is a cosmologist. His research concentrates on cosmological aspects of our theory, mainly:

 

1. If corrected photon energy formula could help to explain inflation phase?

 

As you see we propose: [math]2E_P(\frac{1}{\sqrt{1-\frac{l_p}{r}}}-1)[/math] instead [math]h\nu[/math]

When we shrink spacetime to Planck scales, in our formula photon increase its energy rapidly up to infinity. If we reverse the film, we have something that looks like big-bang that rapidly decrease it energy in first phase what looks like inflation.

 

2. If our filed equations could explain spacetime expansion?

 

As you see in the article, we have found a way to show gravity as the consequence of the same field formula that explains electromagnetism. Maybe universe expansion could also be explained with the same universal field equation. Will see.

Edited May 3, 2013 by pogono

[Rade]

Dear Pogono...

 

There is already for many years now the theory of Kaluza-Klein that relates gravity and EM using a 5-D geometry approach:

 

http://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory

 

I see you do not make reference to Kaluza-Klein theory...is there a reason ?

[Aethelwulf]

 

1. If corrected photon energy formula could help to explain inflation phase?

 

As you see we propose: [math]2E_P(\frac{1}{\sqrt{1-\frac{l_p}{r}}}-1)[/math] instead [math]h\nu[/math]

When we shrink spacetime to Planck scales, in our formula photon increase its energy rapidly up to infinity. If we reverse the film, we have something that looks like big-bang that rapidly decrease it energy in first phase what looks like inflation.

 

 

 

Concerning what you are saying, one reason why energy would extend to infinity at Planck Scales would have to do with how much energy you are getting out of the uncertainty relationship [math]\Delta E \Delta t[/math]. Working at Planck Scales, energies like any system appear to be completely random and responsive to measurement.

[pogono]

Dear Pogono...

 

There is already for many years now the theory of Kaluza-Klein that relates gravity and EM using a 5-D geometry approach:

 

http://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory

 

I see you do not make reference to Kaluza-Klein theory...is there a reason ?

Hi Rade,

I agree, you are right. I will add reference to K-K.

 

Moreover,

as you see in my article I show, that imaginary time axis is just mathematical interpretation of some Euler helix for rotating field vector.

 

I will emphasis in the new version, that additional axis in K-K theory also may be just mathematical interpretation of spinning photons. All we need is modified K-K theory with imaginary axis, that is f.e. here: http://arxiv.org/abs/gr-qc/0110075

 

It probably also means, that additional axises in String theory and M-Theory are NOT REAL dimensions. They are just some mathematical tricks, to describe another rotations! We do not need to find for them anymore! :-D

 

Thank you Rade.

[Pmb]

This is interesting - and, if I may say so, pleasantly mind-boggling - work.

 

Unfortunately for me, even the condensed and nicely presented math in pogono’s (who I’m guessing is Piotr Ogonowski, one of its authors) webpages is more than my poor mathematical physics skills can make sense of in a brief reading, but the informal discussion, while challenging, makes great sense to me.

 

I’ve a giddy sense that this could be something big to come in physics.

There's something I don't understand. If you don't understand the math then why would you have any faith at all in the premise of the paper?

[pogono]

Ufff, generalization to General Relativity finished! :-)

In the way to arXiv.

 

I will appreciate your remarks and comments.

 

Title: Maxwell-like picture of General Relativity and its Planck limit

 

Abstract: We show that Geroch decomposition leads us to Maxwell-like representation of gravity in (3+1) metrics decomposition. For such decomposition we derive four-potential [math]V^\mu[/math] and gravitational field tensor [math]F^{\mu\nu}[/math] that may be associated with gravitational interaction. Next we introduce valid Lagrangian and equations of motion. Then we show that gravitational four-current [math]J^\mu[/math] derived for introduced four-potential produce energy-stress tensor and generalize main General Relativity formula. At the end we introduce new approach to quantization of gravity that results in proper quantum values and is open to further generalization.

 

File: http://arxiv.org/abs/1301.2758

 

 

I have also prepared brief explanation of DaF framework ended with General Relativity generalization.

 

Introduction

 

Thanks to Geroch's decomposition applied for Schwarzschild solution of the General Relativity one obtains metric in (3+1) decomposition (space + time). In this picture curved spacetime is equivalent to the flat space-like manifold minimally coupled to a scalar field [math]\Phi[/math], where [math]\Phi[/math] is equal to inversed gravitational time dilation factor.

 

In obtained picture gravity is described as regular field with Maxwell-like equations on flat spacetime as follows.

We define scalar fields as follows:

[math] \Phi=\frac{1}{\gamma_r}=\frac{d\tau_r}{dt}= \sqrt{1-\frac{r_s}{r}}[/math]

[math] \Theta= r \cdot \beta_r = r\sqrt{\frac{r_s}{r}} [/math]

where:

[math] t [/math] is the time coordinate (measured by a stationary clock located infinitely far from the massive body)

[math] \tau_r [/math] is the proper time of stationary observer located in distance r to the massive body

[math] r [/math] is the radial coordinate

[math] r_s [/math] is the Schwarzschild radius

 

As we know mass relation to Schwarzschild radius is:

[math]M=\frac{c^2r_s}{2G}[/math]

 

Therefore (assuming c=1) one may easy calculate that the gradient of the scalar field [math]\Phi[/math] is equal to proper gravitational acceleration "g" for Schwarzschild solution.

 

[math] \nabla \Phi = \frac{r_s}{2r^2} \gamma_r = \frac{GM}{r^2} \gamma_r =g[/math]

 

Above "g" acceleration is measured for the reference frame of the stationary observer located at distance "r" to the massive body.

 

Using introduced above scalar fields one defines vector fields as below (we assume c=1 and [math]\hat{e}[/math] as directional versors).

Vector field responsible for gravitational acceleration is denoted as “G”.

 

[math] \vec{T} = \Phi \cdot \hat{e}_y [/math]

[math] \vec{G} = -\nabla \Phi \times \hat{e}_y = -\nabla \times \vec{T}[/math]

[math] \vec{V} = \nabla \Theta \times \hat{e}_x [/math]

[math] \vec{B } = \nabla \times \vec{V} [/math]

 

Utilizing relations between above fields, one obtains Maxwell-like equations for gravitation:

[math] \nabla \cdot \vec{G} = 0 [/math]

[math] \nabla \cdot \vec{B} = 0 [/math]

[math] \nabla \times \vec{G} = \gamma_{r} \cdot \frac{\partial \vec{B }}{\partial t} [/math]

[math] \nabla \times \vec{B} = - \gamma_{r} \cdot \frac{\partial \vec{G}}{\partial t} [/math]

 

Therefore by analogy to electromagnetism we may introduce four-potential V in form of:

 

[math]V^\mu=(\Phi,\vec{V}) [/math]

 

and related gravitational field tensor:

 

[math]F_{\mu\nu}=\partial_\mu V_\nu - \partial_\nu V_\mu [/math]

 

After simple transformations one derives wave equation (d’Alembertian) as follows:

 

[math] \gamma^2_r \cdot \frac{\partial ^{ 2}\vec{G} }{ \partial t^{2}} - \nabla^2 \vec{G} = 0 [/math]

 

Above d’Alembertian describes the wave propagating in the flat spacetime with speed equal to:

 

[math]v_{light}=c/\gamma_r=c \cdot \sqrt{1-\frac{r_s}{r}} [/math]

 

In result, in considered case curved spacetime is physically equivalent to the flat spacetime with variable speed of light, where refracting index for light is equal to

 

[math]\eta=\frac{c}{v_{light}}=\gamma_r=\frac{1}{\sqrt{1-\frac{r_s}{r}}}[/math].

 

It should not surprise us, that in above picture, spacetime around the mass behaves as gravitational lens.

 

Lagrangian and Hamiltonian

 

Analyzing Einstein-Hilbert action for considered case one may derive proper Lagrangian and Hamiltonian for gravity on flat spacetime with refracting index for light speed.

 

For the stationary observer with rest mas 'm' that keeps his position against gravitation we obtain Lagrangian and Hamiltonian in the form of:

[math] \mathcal{L}= mc^2 \frac{1}{\gamma_r}[/math]

[math] \mathcal{H}= mc^2 \gamma_r [/math]

 

Thanks to superposition principle for some test body with rest mass 'm'' and four-velocity

 

[math]U^\mu=\gamma(c,\vec{v})[/math]

 

we obtain proper Lagrangian and Hamiltonian in form of:

 

[math] \mathcal{L}= mc^2 \frac {1}{\gamma_r} - mc^2 \frac {1}{\gamma} [/math]

[math] \mathcal{H}= mc^2 \gamma - mc^2 \gamma_r [/math]

 

To comply with the Newtonian approximation:

[math] \mathcal{H}= mc^2 (\gamma-1) - V ® [/math]

 

where

[math] V®=mc^2 (\gamma_r-1) [/math]

 

Classic Newtonian approximation we obtain using Maclaurin expansion of above Hamiltonian, the same way that we do it for Kinetic energy approximation:

 

[math] \mathcal{H}= mc^2 (\gamma-1) - mc^2 (\gamma_r-1) \approx mc^2 \frac{\beta^2}{2} - mc^2 \frac{\beta_r^2}{2} = \frac{mv^2}{2} - m \frac{c^2 r_s}{2r} = \frac{mv^2}{2} - G\frac{mM}{r} [/math]

 

If we consider above field V in the Planck limits, we obtain proper quanta equal to rest energy value.

For [math] r_s << l_{P}[/math] we calculate:

 

[math] \lim_{m \to m_P; r \to l_P} V® = m_{P}c^2 \left( \frac{1}{\sqrt{1-\frac{r_{s} }{l_P} } } -1\right) \approx m_{P} \cdot \frac{c^2 r_{s} }{2l_{P} } =\frac{c^{ 4}r_{s} }{2G}=Mc^2 [/math]

 

Obtained quanta may be treated as some rest energy (some rest mass M) related to given radius [math] r_s [/math]

(Schwarzschild radius).

 

 

Equations of motion and relation to Newton-Cartan theory

 

The introduced Lagrangian locally satisfies the Euler-Lagrange condition:

 

[math]\frac{d \frac{\partial \mathcal{L}}{\partial v}}{d\tau_r}= \frac{\partial \mathcal{L}}{\partial r}[/math]

 

what yields to:

 

[math]\frac{d (mv\gamma)}{d\tau_r}= mc^2 \cdot \frac{r_s}{2r^2} \gamma_r [/math]

 

where LHS is relativistic force and RHS is just equivalent to "gravitational force" in Schwarzschild solution.

Using introduced scalar field [math]\Phi[/math] we may rewrite it as:

 

[math] RHS = mc^2 \cdot \nabla \Phi [/math]

 

Considering above we see, that equations of motion should fulfill transitional condition (assuming c=1 to facilitate):

 

[math] \frac{d(v\gamma)}{d\tau_r}= \nabla \Phi [/math]

 

Therefore equations of motion for considered case are in the form of:

 

[math] \frac{d^2\vec{x}}{d\tau d\tau_r}= \nabla \Phi [/math]

 

where:

[math] \tau [/math] is the proper time of the test body

[math] \tau_r [/math] is the proper time of stationary observer located in distance r to the massive body

[math] \gamma=d\tau_r / d\tau [/math]

 

Above equations may be explained as relativistic form of Newton-Cartan theory equations of motion. In DaF, the proper times were taken in place of coordinate time "t".

 

The equations of motion in terms of four-velocity U and four-acceleration A may be rewritten for stationary observer reference frame as:

 

[math] \frac{d U^\mu}{d\tau_r}= \partial_\mu \Phi [/math]

 

and for the test body reference frame as just:

 

[math] A^\mu = \partial_\mu \Phi [/math]

 

 

General Relativity generalized for gravitational field

 

In the Lorentz gauge equation of motion may be rewritten as:

[math]A^\mu=\frac{\partial V^\mu}{\partial \tau}[/math]

 

Above formula says, that gravitational acceleration is equal to derivative of the gravitational four-potential. Reversed it also says, that any move is the source of gravitational acceleration. It means, that any body with four velocity [math]U^\mu[/math] is at the same time the source of gravitational potential [math]V^\mu[/math]:

 

[math]U^\mu=(\gamma,\gamma\vec{v}) \to V^\mu=(\frac{1}{\gamma},\vec{V})[/math]

 

Four-acceleration A

 

may be generalized to the tensor in the form of:

 

[math]A^{\mu\nu}=\partial_\nu V^\mu [/math]

 

showing it is equal to the first element of introduced gravitational field tensor:

 

[math]F_{\mu\nu}=\partial_\nu V_\mu - \partial_\mu V_\nu[/math]

 

where the second part is the acceleration for the other bodies.

 

If we introduce gravitation four-current by analogy to electromagnetism:

 

[math]J^\mu=\partial_\nu F^{\mu\nu}=\frac{2\pi r_s}{V}\cdot(\gamma_r,\gamma_r\vec{v_r})[/math]

 

and generalize to the tensor multiplying by four-velocity U of the source of gravity:

[math]J^{\mu\nu}=J^{\mu} \cdot U^{\nu} [/math]

 

we obtain stress-energy tensor T with respect to the constant

 

[math]J^{\mu\nu}=\frac{4 \pi G}{c^4} T^{\mu\nu}[/math]

 

what drives to General Relativity main formula in the form of:

 

[math]G_{\mu\nu}=2 \cdot J_{\mu\nu}[/math]

 

This way we have created General Relativity main equation equivalence as wave-based formulation that might help us with explaining the wave nature of mater.

Edited July 30, 2013 by pogono

[FrankM]

It is well known that the equations for Newtonian mechanics do not have a speed of gravity factor relative to distance, gravity has to be effectively instantaneous for solar system distances. Your arXiv article, 1301.2758v6.pdf, makes the conclusion, in Section 2,

We have just shown that in the Geroch decomposition for Schwarzschild metric we may obtain Maxwell-like picture of gravity that might let us to consider gravity as medium that changes the speed of light.

Are you inferring this gravity medium is responsible for instantaneous gravity in solar system distances?

[pogono]

It is well known that the equations for Newtonian mechanics do not have a speed of gravity factor relative to distance, gravity has to be effectively instantaneious for solar system distances.

Are you inferring this gravity medium is responsible for instantaneous gravity in solar system distances?

 

Great question!!! :-)

 

In Newtonian picture, gravity is interaction between bodies.

As you may read from the article, in our picture gravity is rather interaction with whole spacetime, or - as you wish - with light. By attracting the light, we make spacetime curved.

 

Curved spacetime means, that we have exactly the same result that Einstein did, what makes your question inappropriate.

But... just like you pointed, we have also shown physical analogy:

 

- curved spacetime with light speed = c

is equivalent

- flat spacetime with light speed = c\gamma

 

So, your question makes great sense in this second point of view, with flat spacetime!!

Give me a second. I will make some calculations and come back to this issue.