Miles Mathis' Charge Field
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The Cause of Gravity - the next major chapter

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Vexman
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Post by Nevyn Fri Apr 05, 2019 7:02 pm

The larger percentage for Jupiter and Saturn also show Miles point about the solar system being out of order. Those big planets need to move outwards, and they will move out to where their charge-pauses are within 1%.
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Post by LongtimeAirman Fri Apr 05, 2019 9:06 pm

.
Just a quick update. Mostly confused.

Nevyn wrote. Yes, I believe the moon's field is stronger than the earth's, at least close to the moon. I'm not sure how far it reaches from the surface. The Moon Gives Up a Secret paper mentions the moon's field being larger than the earth's. Well, I should say that it is stronger, it is not necessarily larger, and I can't remember if that is only when measured at the moon or if it means at the same distance from each body. That is, if we measured at 10,000km from the earth and 10,000km from the moon. I would think that it only refers to a single position close to the moon, because the smaller size of the moon has a larger curvature, so it will dissipate much quicker.

Nevyn wrote. So the moon's charge-pause should be near 16 moon radii from its center. That's about 7% of the distance to the earth.

Airman. I am mentally wrapped around the radius of the newly identified, moon’s earth-pause, and the moon’s extraordinary strength in that regard, thank you very much. I suppose the relative charge field diagram absolutely needs a modification of some sort - something that indicates the field's fall-off rate. An idea does occur to me. I can replace each current individual infinitely long radial with a series or train of radials, from longer to shorter, ending at the object's Kuiper limit.  

Jared wrote. What I'm getting at is that I think this bounce-charge has been severely underestimated in the maths and concepts. Without it, even the proton cannot work per the theory. For any charge to enter ANY pole of any body, it must be moving parallel to the poles to some extent or other at the time it enters, which is perpendicular to (say) solar emission. In general orbits, we have charge moving perpendicular to the poles almost entirely.

The Cause of Gravity - the next major chapter - Page 7 Satura10
Airman. I agree, bounce-charge is present. It increases the charge density and effective charge receiving width about the planet. Looking at the Saturn/Uranus/Neptune inclinations. I believe Miles considers it a circuit diagram. From our previous discussion, the direct radial charge emission contribution we’ve been considering is the primary component of the Sun/planet circuit. The planet is also recycling charge. The charge field includes larger charged particles. These particles are massed over the planetary poles. They get their primary charge from the planet’s poles or the sun. Emissions from the larger charge helps extend and direct more photons into the planetary poles.  

I believe the diagram shows the equilibrium tilts that result from adding both the direct charge and recycling secondary charge. A proton aligns it's pole to the planet, but the charge mix the planet receives makes that direct (sun/planet pole) alignment impossible - although Uranus gets pretty close.  
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Post by Jared Magneson Sat Apr 06, 2019 2:32 am

Nevyn wrote: Maybe that implies that the Moon is actually too big to be a moon of the Earth at its proper distance. If it gets far enough away, we may lose it and the Moon becomes another planet. Unfortunately, we will all be long gone before that happens, so we may never know if my prediction is correct.

But wouldn't it just slowly "suck" back in, due to gravity, at some eventuality? You know, the ol' ping-pong ball held underwater analogy?

I guess that's a bit naive considering it's NOT a 3-body problem, but rather an every-body problem. Even so, since Luna and the Earth are both orbiting the sun, the moon can hardly propel itself into a higher or lower orbit. It would require some force that would trump the Earth's gravity field, it seems like, to pull it faster or slower and thus change orbits, but it would have to change orbits enough to escape the Earth's gravity, which seems pretty farfetched to me.

That said, it needn't change orbits outright, but perhaps would "tail" the Earth like the C-orbit horseshoe asteroids do?

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Post by Nevyn Sat Apr 06, 2019 3:44 pm

I've found that the reason my app does't find the charge-pause at extreme distances is because of the tolerance value. At those distances, the charge fields of the bodies are so weak that they are already below the tolerance. Setting the tolerance to 0 makes it work. I might remove the tolerance. I thought it would be needed to avoid looping forever.
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Post by Nevyn Sat Apr 06, 2019 4:05 pm

I can't get Jupiter's charge-pause below 1.77%, even at 7786e+78km between it and the Sun. At 7786e+79km they are too far apart. So maybe these percentages don't mean as much as I first thought.
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Post by Russ T Mon Apr 08, 2019 8:31 am

Blimey! You guy's have been busy. I have some catching up to do.

I notice someone mentioned this dual property of the charge field i.e. gravity and charge pressure (?).
I haven't read the last 11 blog pages so need some time to absorb...but...in the meantime, is this duality/dual field a bit like the dual field in electrical circuits? The E & B fields, electric and magnetic? The charge photons being charge anyway. Moving charge/moving photons creating a magnetic field? Aren't they all properties of the same field i.e. electric charge, magnetism, gravity, heat, all describing different properties of the charge field?
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Post by Jared Magneson Mon Apr 08, 2019 1:06 pm

Russ T wrote: Aren't they all properties of the same field i.e. electric charge, magnetism, gravity, heat, all describing different properties of the charge field?

Yes indeed, they are. The problem we're having with charge-binding gravity (the one I'm having so far) is that it's hard to get that huge vector DOWN out of it. But it's a work in progress and we'll see where it leads. Miles has emailed me about it and he's trying to flesh it out as the muses allow, but there's a lot of great questions and issues here that the theory can confront down the road too. I'm not expecting him to drop every damn thing and just cater to us here. This is just the best place for such discussions, with the best team around on the task at hand. Read up. Maybe you'll see something we missed?

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Post by LongtimeAirman Mon Apr 08, 2019 2:35 pm

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Russ T wrote. I notice someone mentioned this dual property of the charge field i.e. gravity and charge pressure (?).
Airman. Hi Russ T. There is only the charge field. Before this thread, Miles described the charge field as a real exclusionary emission field in opposition to gravity; now, gravity is an aspect of charge. Most everyone - I know I am - is having difficulties fitting charge binding in with the rest of their own charge field understanding.

Russ T  wrote. ... is this duality/dual field a bit like the dual field in electrical circuits? The E & B fields, electric and magnetic? The charge photons being charge anyway. Moving charge/moving photons creating a magnetic field?
Airman. According to my understanding, both B and E fields are the effects of the charge field observed at the electron scale or larger. All charge photons spin and travel at light speed. The E field is the result of charge photons pushing electrons or ions in the forward direction, at a resulting velocity indicating momentum or energy. The B field is the amount of spin coherency imparted on the electrons and ions by the spinning of those same charge field photons.

Russ T  wrote. Aren't they all properties of the same field i.e. electric charge, magnetism, gravity, heat, all describing different properties of the charge field?
Airman. Absolutely, yes Sir, I agree, although I must admit, the charge gravity explanation of electromagnetism is a bit beyond me at present.
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Post by Jared Magneson Mon Apr 08, 2019 4:10 pm

LongtimeAirman wrote:Airman. Absolutely, yes Sir, I agree, although I must admit, the charge gravity explanation of electromagnetism is a bit beyond me at present.

It's actually mildly comforting that I'm not the only one struggling here. That said, I do have a bit of faith that Miles will either make sense of it all or jettison it. I don't see him chasing a theory too hard if it turns out to have more problems than it fixes, just because it was his. He's corrected himself before but at the same time I'd love for him to be RIGHT too, so we could source gravity once and for all! Or once and for now, anyway!

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Post by Chromium6 Sun Jul 16, 2023 4:52 am

Notes on "Gravity" affecting photons and a mostly classical explanation for it. Miles has rewritten some of this below in his UFT-Gravity papers. The site link has full equations:
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https://profoundphysics.com/how-are-photons-affected-by-gravity-if-they-have-no-mass/

How Gravity Affects Photons: The Physics Explained

We know that photons have no mass  Question and we like to think that gravity only affects things that have a mass. However, photons still get deflected by the Sun and can even orbit around a black hole. How exactly are photons being affected by gravity then?

Photons have no mass, but they are nonetheless affected by gravity due to the bending of spacetime itself. In the presence of gravity, photons travel along geodesics. Geodesics depend on the geometry of spacetime and photons moving along a curved geodesic will appear to be affected by gravity.

In this article, we’ll look at how Newton didn’t quite get it right with gravity, what gravity really is, how general relativity describes gravity and how this all relates to tell us how massless photons are affected by gravity.

If you’re wondering why exactly photons do not have mass in the first place, I have a full article covering that here. I also cover why photons still have momentum, even though they have zero mass in this article.


Does Newtonian Gravity Affect Photons?

The first and longest standing theory of gravity was Newton’s theory. This comes nicely within the framework of Newton’s laws,

Law 1: A body stays at rest, or travels in a straight line at constant speed, unless acted on by a force.
Law 2: Force equals mass times acceleration F = ma.
Law 3: Every action has an equal and opposite reaction.
Newton’s theory of gravity fits on the left-hand side of the equation in his second law. This is the formula telling us the force of gravity due to a body of mass M on a second body of mass m that are separated by some distance r:

F=-G\frac{Mm}{r^2}
Here G is the gravitational constant – a number fundamental to the universe that tells us how strong gravity is.

The minus sign is a bit of mathematical convention that tells us that the force is attractive!
Let’s put this force to action with a body such as a star with mass M and a photon with mass m. Starting with what we know, photons have mass m=0, so let’s plug that in here:

F=-G\frac{M\cdot0}{r^2}=0
Here we’ve arrived at Newton’s interpretation of how light is affected by gravity – it isn’t! No massive object will affect a photon according to Newtonian gravity!

We can apply all of Newton’s laws here – his third law tells us that the photon also doesn’t exert a force on the star and his first law tells us that since there is no force of gravity acting on the photon, the photon travels in a straight line!


These laws seemed infallible for a long time – they described everything we saw on Earth well for a long time. An issue came up with the orbit of Mercury.

The technical term for this is orbital precession but we’ll get on to what that exactly means in a moment. First, we just need to know one fact: orbits in Newtonian gravity are ellipses – they look like squashed circles.

These ellipses slowly rotate over time as the planet orbits – this is orbital precession and is predicted in Newtonian gravity. However, the amount Mercury should precess according to Newtonian gravity versus how much astronomers saw did not agree.

This was one of the first hints that Newtonian gravity were not complete!

However, Newton’s laws stood the test of time until Einstein came along with a new perspective on gravity known as the theory of general relativity.

Why Gravity Affects Photons In General Relativity
Next, we’ll look at how Einstein’s theory of general relativity, a more accurate description of gravity, explains why photons indeed are affected by gravity like all other forms of matter.

Specifically, we’ll discover that:

In general relativity, photons always travel along geodesics.

Geodesics can be thought of as the shortest paths between two points.

In general relativity, the shortest path between two points might not always be a straight line.
Sometimes the shortest distance a photon can take between two points may actually be along a curved path, in which case it would appear to us that gravity has an effect on the photon’s path.

It may be funny to think that the shortest distance between two points could possibly be anything other than a straight line, but in general relativity, it indeed can. This is one of the many peculiarities of the theory.
Now, what determines the shortest distance between two points? In general relativity, it is the curvature of spacetime. The geodesics of photons appear as different paths depending on how spacetime is curved.

Einstein formulated the concept of “spacetime”, meaning that we look at space and time equally as one greater concept, rather than as time being some universal ticking clock.

Einstein’s theory of relativity does away with the idea that gravity is a force and replaces it with the idea that gravity is the bending of spacetime due to matter! This can be summarized as:

“Spacetime tells matter how to move, matter tells spacetime how to bend.”

Einstein’s theory has to be a geometric theory in order to talk about the shape of spacetime so it is all described in a new mathematical language.

To truly understand how and why gravity affects photons, we need to dive into the mathematics of general relativity a little bit and see how exactly Einstein predicted the bending of light and the trajectories of photons.

If general relativity is something you'd be interested to learn more about, I have a full introductory article called General Relativity For Dummies: An Intuitive Introduction. The article gives you a full overview of what general relativity is about and teaches you the most important concepts in an intuitive sense.

I also have a full guide on learning general relativity on your own, if that's something you're interested in doing.

A Brief Introduction To The Mathematics of General Relativity

In Newtonian physics, we can talk about how things change with time, we can talk about, say, the position of a car at time t = 0, t = 1, t = 10 etc. We would write this position x(t) as x(0), x(1), x(10). Time is special and can “parameterize” the path that the car takes.

In general relativity, time is no longer special and is put on an equal footing with spatial coordinates. We describe everything using the concept of spacetime, which means that paths need to also be parameterized in a different way than by using time.

Paths in spacetime are called worldlines and we write them as xµ(λ). The upper µ labels four coordinates
µ = 0,1,2,3 and can be represented as a vector (called a four-vector):

x^{\mu}\left(\lambda\right)=\begin{pmatrix}
x^0\left(\lambda\right)\\
x^1\left(\lambda\right)\\
x^2\left(\lambda\right)\\
x^3\left(\lambda\right)
\end{pmatrix}

We’ve now seen the notation xµ(λ) or x(t) but what does this mean? We treat the coordinates like functions. In these two cases they are either functions of λ or of t, time!

This means that if you plug in some number for time or the “parameter variable”, the function will give you what xµ or x is at that time or parameter value.

Using a general path parameter λ in general relativity is just a mathematical tool to allow us to parameterize paths of particles in a similar way as in Newtonian physics, where time does this for us.

Now, most of us have heard of Pythagoras’ theorem; this relates two sides of a right angled triangle to its hypotenuse, most famously as a2+b2=c2.

What this is secretly telling us is that the diagonal line between any two points is the shortest distance between those two points (mathematically, this follows from the fact that for two positive numbers a and b, √(a2+b2)
The maths of general relativity uses ideas exactly like this. If we want to talk about the surface of a shape, we think about how the shape changes on very small length scales – this is the same intuition as what derivatives are!

Since we’ve identified c2 as the squared size of the hypotenuse, this is our “line element“, which we’ll call ds2.

We can then treat a and b as being some small distances on an (x,y)-plane. Small changes are often written with the letter d in from of them (representing differentials), like dx and dy.

With this in mind, Pythagoras’ theorem would read:

ds^2=dx^2+dy^2

This is what we call the line element in Euclidean geometry. This extends (like Pythagoras’ theorem) to three dimensions as ds2=dx2+dy2+dz2.

This line element describes a small distance in space. However, in general relativity, we model everything by describing not only space, but spacetime.

In space, we can walk forwards, backwards, turn to the side, and jump – we have motion that we can control in our three spatial dimensions. However, time acts differently. To model this, we write time slightly different in our line element as:

ds^2=-dt^2+dx^2+dy^2+dz^2

This is what we call the Minkowski spacetime line element. This describes a small distance in flat spacetime. The Minkowski line element resembles a “straight line” in spacetime, meaning that there is no curvature.

If you’d like to read an intuitive introduction to special relativity, you’ll find one here. The article covers everything discussed here, but in much more detail.

The important thing for us is that the line element encodes all the information about gravity in general relativity. Minkowski spacetime is the special case where there is no gravity in our spacetime!

Much like how we economically write xµ for coordinates (worldlines), we often write the line element in a slightly different way as:

ds^2=g_{\mu\nu}dx^{\mu}dx^{\nu}
The nice thing about this form of the line element is that it is completely general; we can write all line elements (even in curved spacetime) in this form.

This is also an example of index notation and Einstein’s summation convention. The rules are as follows:

Greek letters represent the numbers 0, 1, 2, 3.
Roman letters represent the numbers 1, 2, 3.
If an index appears the same in an upper and lower position, we sum over all values of the index (according to rules 1 and 2).
Before we see an example of this, let’s talk about this gµν that we introduced. This is called the metric tensor. For most purposes, this is a 4×4 symmetric matrix.

The metric tensor tells us the coefficients of our small distances dxµ. The metric also describes how distances are measured in spacetime; if the spacetime is curved, the shortest distance between two points may not be a “straight” line anymore and this is all encoded in the metric!

In the Minkowski line element above, we use the special letter gµν = ηµν with:

\eta_{\mu\nu}=\begin{pmatrix}
\eta_{00}&\eta_{01}&\eta_{02}&\eta_{03}\\
\eta_{10}&\eta_{11}&\eta_{12}&\eta_{13}\\
\eta_{20}&\eta_{21}&\eta_{22}&\eta_{23}\\
\eta_{30}&\eta_{31}&\eta_{32}&\eta_{33}
\end{pmatrix}=\begin{pmatrix}
-1&0&0&0\\
0&1&0&0\\
0&0&1&0\\
0&0&0&1
\end{pmatrix}
In the vocabulary of linear algebra, we say that this is a diagonal matrix and many metrics that are interesting to study are diagonal. The indices µ and ν label each entry in this matrix. Since it is diagonal, the non-zero entries are η00=-1, η11=1, η22=1 and η33=1.
Example: Flat Spacetime Minkowski Line Element
Whilst having no gravity in a spacetime is the simplest case, that is not the question at hand; We want to see what happens to light in the presence of gravity!

Perhaps the most widely known spacetime with gravity (which also describes the bending of light near a star, for example) is called Schwarzschild spacetime. The Schwarzschild solution to general relativity describes how spacetime reacts to a massive, spherical object such as a star!

Before we see that, let’s recap spherical coordinates as these will be used throughout this article (and everywhere else in physics). This is the last thing we need to go over before looking at photons specifically.

Quick tip: Spherical coordinates are one of the many important things used in physics that I cover in my Advanced Math For Physics: A Complete Self-Study Course (link to the course page). In fact, vector calculus is one of most important topics you should learn for understanding relativity, electromagnetism or even just mechanics. This course will teach you that, along with giving you all the tools you need for applying everything in practice.

We can describe the position of something in space by three coordinates (x,y,z) which are great in general but become difficult if we want to think about things that are symmetric under rotations, such as a sphere (which has a radius of √(x2+y2+z2) which is often difficult to work with!).

Instead, we use spherical coordinates (r, θ, φ) which describes a radius r and two angles of rotation:


Essentially, we describe a point in space by specifying two angles and a radial coordinate (distance from the center).

In this way, spherical coordinates cover all the same space as (x, y, z) do and are equivalent but sometimes much easier to work with!

The three dimensional line element in spherical coordinates is written as:

ds^2=dr^2+r^2d\theta^2+r^2\sin^2\theta d\varphi^2
In fact, this line element is equal to ds2=dx2+dy2+dz2. This signifies the fact that all distances (line elements) are the same regardless of which coordinates we describe them in; physics doesn’t care about your coordinate system!

This looks a little more complicated but despite its appearance, is much easier to work with in the case of a spherical star and in many other gravitational spacetimes as well!

Now, the line element in a Schwarzschild spacetime (which describes all distances near a gravitating spherical star) looks somewhat similar to this, but is written as:

ds^2=-\left(1-\frac{2M}{r}\right)dt^2+\frac{1}{1-\frac{2M}{r}}dr^2+r^2d\theta^2+r^2\sin^2\theta d\varphi^2

M here is the mass of our star and all physical stars will have r > 2M since we look outside the star. This is relevant because 1−2Mr is zero at r = 2M. If we were modelling a non-rotating, uncharged black hole, this would correspond to the event horizon of a black hole.
The last term terms are exactly the same as the Minkowski (flat or non-gravitational spacetime) line element – this tells us that in terms of gravity, it doesn’t matter how we rotate the star, only the distance from it does.

There’s now a prefactor in front of the time portion of the line element – this is telling us that time acts differently due to gravity.

This gives us amazing features such as gravitational time dilation; we can see that the coefficient in front of dt2 gets smaller the closer we get to r = 2M, we interpret this as time slowing down!

For an interesting example on why exactly time slows down near a black hole, I have an entire article on that, which you’ll find here.

In the same manner, gravity also affects distances in the Schwarzschild spacetime. It turns out that the shortest paths for photons in Schwarzschild spacetime are actually curved trajectories, leading to the deflection of light around a star.

With line elements, metrics, and worldlines safely under our belts, we can tackle the question at hand: How does gravity affect matter? And most importantly for us, how does gravity affect photons if they have no mass?

How Does Gravity Affect The Path of a Photon?
We’ll start with one important fact: The universe is lazy. Everything – planets, photons, everything – travels on the shortest path it can.

If we consider only gravity, we want to consider the paths or worldlines that all matter follows without any external forces (since gravity is no longer a force in general relativity).

These paths have special names – geodesics! They can be assigned three different types: timelike, null and spacelike.

Timelike geodesics are for matter that has mass and travels slower than the speed of light.
Null geodesics are for matter without mass (such as photons) which travels at the speed of light.
Spacelike geodesics are for matter which travels faster than the speed of light (hypothetical particles known as tachyons).

To tell us about these paths, we define the line element in a specific way since this is telling us intimate details about the geometry of our spacetime. By convention, we say:


The important thing is that light travels on a null geodesic – We can now understand how gravity affects a photon by looking at these null geodesics in any given spacetime with gravity.

Let’s think about this physically for a moment: we said before that ds2 is like a distance in spacetime, so a null geodesic means that light travels on paths that have zero spacetime distance.

This sounds funny but in general relativity, this is indeed possible; a photon can still move through space without moving in spacetime (this is because of the minus sign we saw earlier in front of the dt-part of the line element).

So essentially, photons travel along the shortest paths through spacetime and at the same time, these paths always have zero spacetime length. In this sense, it doesn’t make sense to talk about a “shortest distance” in spacetime for a photon, since the spacetime distance is always zero.

In any case, photons move along null geodesics in spacetime. The shape and form of these geodesics depends on the spacetime we’re in.


Now, how do we actually find the geodesics of photons? The simplest and most brute force approach to get the trajectory is via the geodesic equation:

\frac{d^2x^{\alpha}\left(\lambda\right)}{d\lambda^2}+\Gamma_{\mu\nu}^{\alpha}\frac{dx^{\mu}\left(\lambda\right)}{d\lambda}\frac{dx^{\nu}\left(\lambda\right)}{d\lambda}=0
We can see the parameterized worldlines xα(λ) in this equation that we discussed earlier appearing in three places here; the purpose of the geodesic equation is to solve for these to get the spacetime trajectories.

The first and second derivatives of the wordlines are taken in the above – these derivatives describe how the wordlines xα(λ) change as we vary the path parameter λ.

Finally, we have the Christoffel symbols, denoted by Γ. In short, these encode any changes in coordinates if we look at our system from different perspectives – just like when we changed from Cartesian (x,y,z) coordinates to spherical coordinates earlier!

For those who are interested, the Christoffel symbols are mathematically given by:

\Gamma_{\mu\nu}^{\alpha}=\frac{1}{2}g^{\alpha\beta}\left(\frac{\partial g_{\nu\beta}}{\partial x^{\mu}}+\frac{\partial g_{\mu\beta}}{\partial x^{\nu}}-\frac{\partial g_{\mu\nu}}{\partial x^{\beta}}\right)
The main part we see is the metric tensor that describes our spacetime as well as its derivatives.

The Christoffel symbols give rise to phenomena such as artificial or fictitious forces like the centrifugal force when rotating something – this arises effectively from changing a coordinate system to another.

I actually have a full guide on Christoffel symbols, which you’ll find here. It covers everything from the physical and geometric meanings of the Christoffel symbols all the way up to how to actually calculate and use them in practice.

In case you’re interested to see where the geodesic equation really comes from, you’ll find its full derivation below. This uses some advanced concepts, which are presented as intuitively as possible.

Where Does The Geodesic Equation Come From? (Full Derivation)

Now, in flat or Minkowski spacetime, the geodesics of photons are straight lines, just like Newton’s laws would predict. You’ll see how this comes about down below.

However, things change greatly when we consider other, more complicated spacetimes and metrics, which correspond to spacetimes in which gravity is present.

In these cases, a photon may not travel in a straight line anymore, differing from the predictions of Newtonian gravity.

The most extreme case of this may be for a photon orbiting around a black hole. I have a full article explaining how this happens, in case you’re interested.

Example: Geodesics In Flat Spacetime

As we’ve seen, the geodesic equation in specific circumstances can tell us all about Newtonian physics but it can do much more.

For any spacetime, if you can write down its metric, you can plug it into the geodesic equation and find the equations of motion for any particle! However, that doesn’t mean the equation is always necessarily solvable, but if it is, then you can find the trajectories of a photon (or any other particle) under gravity.

Mathematically, a more elegant approach is to take the metric, look at its geodesic Lagrangian (explained earlier), calculate its Euler-Lagrange equations, and combine this with the fact that we are looking at null geodesics for light!

We can easily get the geodesic Lagrangian by taking the line element, replacing any variable (such as dt, dr, dx etc.) by the same variable with a dot over it (ṫ, ṙ, ẋ etc.), representing a derivative with respect to λ and putting a half in front of the whole thing!

For example, in the Schwarzschild spacetime we briefly looked at earlier, we have (see the similarity between the line element and the geodesic Lagrangian?):

ds^2=-\left(1-\frac{2M}{r}\right)dt^2+\frac{1}{1-\frac{2M}{r}}dr^2+r^2d\theta^2+r^2\sin^2\theta d\varphi^2
L=-\frac{1}{2}\left(1-\frac{2M}{r}\right)\dot{t}^2+\frac{1}{2}\frac{1}{1-\frac{2M}{r}}\dot{r}^2+\frac{1}{2}r^2\dot{\theta}^2+\frac{1}{2}r^2\sin^2\theta\dot{\varphi}^2
In fact, this can also be used as an efficient method for calculating Christoffel symbols. I cover this “trick” in this article.

Now, to answer the main question: if photons are massless, how are they affected by gravity – under the influence of gravity, photons travel on null geodesics (ds2 = 0) and geodesics are described by the Euler-Lagrange equations of their geodesic Lagrangian (or equivalently by the geodesic equation; both describe the same thing).

The equations we get are determined by the metric gµν and in general relativity, gravity is the curving of spacetime rather than a force so all the effects of gravity are wrapped up in the metric.

Photons, like all matter, want to follow a geodesic because of the laziness of the universe and the easiest path to take is to follow how matter has bent and curved spacetime, causing gravity.

The point is that it doesn’t matter whether the photons are massless or not; they still travel along geodesics and IF the metric describes a curved spacetime (in which gravity is present), then the photons will inevitably move along curved paths as well. This is how gravity affects photons!

The only place where the fact that photons are massless actually matters is that the geodesics of photons are null (ds2 = 0), which is different in the case for massive particles (with ds2 = -1 instead).

This doesn’t change the fact that photons are still affected by gravity, it simply causes the paths of photons and massive particles to look slightly different.

For example, light can orbit a black hole at only one possible distance, while a massive particle could have two different orbits. You can read more about orbits of light around a black hole in this article.

With all this theory, let’s see it altogether fully in an example spacetime!

How Gravity Affects Photons Near a Star

We have seen already that in the presence of no external forces and without gravity, all matter travels in straight lines. If we introduce gravity, that is no longer true – think about planetary orbits!

Let’s look at what happens to a photon (light) when it passes a perfectly spherical star. In Newtonian gravity, we would expect for the photons to keep moving in a straight line, as gravity does not affect them.

In general relativity, this is not true – the key result is that a ray of light passing a star gets deflected by an angle:

\delta=\frac{4GM}{c^2D}
G is the gravitational constant, c is the speed of light, M is the mass of the star, and D is the smallest distance radially that the light gets to the star.
Essentially, this deflection angle describes how much a light ray would get bent as it passes near a star. In other words, how much the path of the photon differs from being a straight line.

This can be observed by looking at light rays (photons) coming from a distant star – since the light rays get deflected as they pass the Sun, for us, the distant star would appear to be in a different position in the sky compared to where we would expect it to be.


For some context, if we consider light just grazing the sun, this gives a measurement of 1.75 arcseconds – Arthur Eddington verified this empirically in 1919 and it was a key result in verifying general relativity experimentally!

The deflection angle δ is typically very small. For scale, an arcsecond is 1/3600th of a degree – so the result is very very small as expected – but crucially it is not zero as we would expect in Newtonian gravity!

This shows directly how a massless photon is affected by gravity – it must follow the natural bending of spacetime due to matter!

Now, where does this result come from? Let’s get down to the details – the key ingredient is geometry!

Essentially, we will discover that the geodesic of a photon as it passes by a star, is described by the following equation:

r\left(\varphi\right)=\frac{D^2}{M}\frac{1}{1+C\cos\varphi+\frac{D}{M}\sin\varphi+\cos^2\varphi}
Note; this is in units where G=c=1. In case you’re familiar with standard orbital mechanics, this may look somewhat similar to Kepler’s orbit equation describing, for example, the elliptical orbits of planets. In a sense, this is a more complicated “orbit equation” that describes the orbit of a photon.
This describes the distance r of the photon to the star as a function of the angle φ in polar coordinates (see picture below).


From this, we can derive the deflection angle δ=4GM/c2D. You’ll see the full derivation of this below.

Derivation of Photon Geodesics & Deflection Angle Near a Star
More importantly than the actual result of deflection, this is an example that directly shows that photons are indeed affected by gravity – how they are affected by gravity will depend on the particular spacetime we look at.

In Minkowski spacetime, we saw that photons travel in straight lines. This corresponds to the case with no gravity and is consistent with what we expect in Newtonian physics!

However, in Schwarzschild spacetime (under the gravity of a spherical mass), a photon will travel in a curved path and get deflected. In this case, the photon will be affected by gravity.

In other spacetimes, photons will also generally be affected by gravity but in different ways – near a rotating black hole (described by the so-called Kerr spacetime), for example, a photon’s trajectory may look incredibly complicated.


Ville Hirvonen

I'm the founder of Profound Physics, a website I created to help especially those trying to self-study physics as that is what I'm passionate about doing myself. I like to explain what I've learned in an understandable and laid-back way and I'll keep doing so as I learn more about the wonders of physics.

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Post by Jared Magneson Sun Jul 16, 2023 1:55 pm

Newton’s theory of gravity fits on the left-hand side of the equation in his second law.

False. Gravity is not the F, gravity is the a (acceleration).

Also space-time was falsified absolutely by Miles in a series of papers.

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Post by LongtimeAirman Mon Jul 17, 2023 12:24 pm

.
Cr6, thanks for bringing up this old thread, maybe this site’s most liveliest. I don’t think we resolved Miles’ "gravity as charge idea", but I certainly enjoyed the discussion at the time, as well as in re-reading some of it yesterday.

Hi Jared! Happy to hear from you, was thinking about you just yesterday. You made some great animations, do you still make them?

How Gravity Affects Photons: The Physics Explained
https://profoundphysics.com/how-are-photons-affected-by-gravity-if-they-have-no-mass/
Of course I disagree with the article’s main assertions: 1. Photons have no mass; and 2. Mass curves spacetime. Profoundphysics does a good job providing and explaining the mainstream math involved and how to use it.

Back to the discussion.
LongtimeAirman wrote:...nuclear matter will align its main n/s axis with the local dominant charge source. Objects in the dominant emission (gravitational) field will acquire energy and acceleration in the downward direction.
Jared wrote. I'm fine with the first statement at the atomic level anyway, but the second statement contradicts it and itself.

"dominant emission" in this case would be the Earth, correct? So if it's emitting UP, how does this cause an acceleration DOWN? ...
Airman. Yes, the “dominant emission" in this case would be the Earth. The proton aligns its n/s spin axis to the Earth directly below.

The proton will feel a net downward force not from the photons it receives and mainly channels as through-charge upward from the earth. The proton is accelerated downward by photons it receives from space, and incoming charge spiraling downward entering the topside of the proton.
.

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Post by LongtimeAirman Wed Jul 19, 2023 12:33 pm

.
26 February 2019 at 3:00 pm. Jared wrote. I'm actually stuck on this one, myself. I keep thinking back to what Nevyn said in his first response here, about the orbits of planets.

While I can kinda see how charge might "create" or cause gravity at, say, a planet's surface as the binding energy for matter, I don't yet see how this could apply to the planetary orbits around the sun. They aren't at the surface. They are very, very far away from it - so it seems like any binding energy should be long lost by the time it could reach a planet, even Mercury. What would cause Mercury then to move towards the sun?
Airman. There is no binding energy, gravity is not a “force of attraction”. Objects within the Sun’s gravitational field are pushed toward the Sun by charge approaching the Sun from the rest of the galaxy. The Sun provides some charge resistance to any large proton matter objects simply falling within its gravitational field, emitted solar charge will not stop that object from striking the Sun’s surface. Gravity keeps us on the Earth's surface. So far this sounds a lot like the old Push gravity idea.

The charge field has something the old Push gravity ideas lacked - lift.* As we know, objects traveling with a velocity orthogonal to the Sun’s center, constantly break the charge channels between the object and the Sun, re-directing the solar charge received outward creating lift.  
Mercury’s orbit is in balance between the Sun’s emission field and galactic charge headed toward the Sun, based on Mercury’s size and distance from the Sun, etc.

*
264a. Lift on a Wing. http://milesmathis.com/lift.pdf Plus extended comments on buoyancy and on the raindrop problem. 14pp.
264b. The Magnus Effect, Lift, and Charge. http://milesmathis.com/magnus.pdf Where we learn more about bending soccer balls as well as about lift on a wing. 3pp.
http://milesmathis.com/index.html
.

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Post by LongtimeAirman Wed Jul 19, 2023 9:01 pm

.
Jared, Please don’t think I’m trying to pick a fight with you, I'm not. You started this thread. If I’m trying to argue with anyone, it would be Miles.

I’ve re-read Miles’ paper, “The Cause of Gravity, the Next Chapter”. I didn’t understand it then and I don’t understand it now. I didn’t get the impression anyone else here understood "magnetic resonance" either.

Miles wrote.  I suppose it bears repeating that this theory is not a variant of push gravity. About the only thing Le Sage got right was proposing a field of corpuscles (photons). He was completely right there. Well, to be honest, he also got some other things right, such as that gravity is not a pull and that the mainstream was wrong. So in general he was on the right track. But the theory of blocking was far too naïve to answer data, which is why his theory never made much headway. However, the current mainstream theory of gravity (Newton's) is also far too naïve to answer data, and they have known that for centuries. As a field theory, it is nearly as oversimplified as Le Sage's.

Dismissing Le Sage’s push theory on the basis of it being too naïve is a bit rash. In my opinion the addition of charge field's  ‘Lift’ makes push gravity work perfectly. A clear explanation of Gravity as a function of charge. Much easier to understand than “magnetic resonance”.

My apologies everyone. I'll keep trying. I'll re-read More on Gravity again too.

NEW PAPER, added 2/20/19, http://milesmathis.com/grav3.pdf The Cause of Gravity, the Next Chapter. Possibly the most important paper I have published in several years.

NEW PAPER, added 3/3/19, http://milesmathis.com/grav4.pdf More on Gravity. This may clarify for some readers.
.

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Post by Jared Magneson Wed Jul 19, 2023 9:53 pm

LongtimeAirman wrote:
Jared, Please don’t think I’m trying to pick a fight with you, I'm not. You started this thread. If I’m trying to argue with anyone, it would be Miles.


I feel no animosity here at all, only genuine curiosity and desire to understand!

It just occurred to me as well that if we have charge "pushing" down and charge pushing up (from the Earth, for example), there would be some level of stasis or balance between the two net forces.

But if charge-gravity pushing down was caused by photons, why would it be so consistent? How could it stay at a near-constant 9.8m/s², all across the land and see, where different charge emissions FROM the Earth would affect that stasis/balance ratio?

And what about when the Earth is receiving more insolation, such as when we're closest to the sun (in January), or less insolation, in June? Wouldn't that affect gravity as well?

As far as I know, objects don't weigh more or less in January or June. I imagine such a variance would be detectable. But all that said, one might argue that if the Earth were receiving more insolation, it would also be receiving more through-charge as well, and offset that difference.

I just don't know. Kinda spit-balling, here.

And to answer your other question, I haven't done any new animations in quite some time. But I still CAN! It was the photon stacked-spin stuff that kinda... Broke me. It's so complex, and I wasn't able to script any of it really. Not in my program, Maya.

The last things I did were generate an actual gravity/charge balanced "orbit" and then illustrate the solution to the 3-Body Problem (charge, obviously). Neither of which are using charge-gravity, but here they are:

Orbit:
https://vimeo.com/538340408

3-Body Problem:
https://vimeo.com/327650447

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Post by LongtimeAirman Sun Jul 23, 2023 6:27 pm

.
Well I certainly needed and sure enough enjoyed, the review.  

After re-reading “The Cause of Gravity, the Next Chapter” and, “More on Gravity” I also re-read “Why Gravity is not a Function of Charge” *. Then I re-read them again. I’m over my confusion and embarrassment and feeling much better. Don’t know why my mind latched onto push gravity.  

During charge recycling, the Earth’s emission field has been split, compressed and reversed compared to downward, incoming solar charge. Gravity is a measure of binding force due to matter’s spin augmentation occurring where the emission and incoming charge fields meet, which falls off above the Earth surface according to gravity’s inverse square gradient. Or something like that.

Glad the only charge field change Lift needs is in explaining lift as a loss of charge binding with the Earth below, which sounds like breaking vertical charge channels to me.

Jared, Thanks for kindly stepping in.
I enjoyed your latest animations as well as some of your older ones including:
PhotonCharge_X2-spin Infrared_paths
Planetary Spin - Charge Dynamics
Alpha Particle - Charge Channels (Helium) v5
I've been thinking a lot about Helium and proton stacks too lately, wondering how binding energy, or gravity as charge, might effect them.

182b. Why Gravity is not a Function of Charge. http://milesmathis.com/gravmag.pdf  A short paper, explaining why I have unified gravity and charge, but not resolved them into one field. 3pp.
http://milesmathis.com/index.html
.

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Post by Jared Magneson Sun Jul 30, 2023 9:39 pm

Thank you so much for your patience and persistence, Airman. I too re-read all those papers and it does make sense to me now. I'm not sure I completely agree (not that it matters), but I can see where Miles is coming from a LOT better after some time and distance and a fresh look at it all.

I can't quite put my finger on my primary rebuttal, though. He definitely answered many of them, but I need to go back and re-read all of Nevyn's replies here to feel it out, again. It's good stuff, all around!

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Post by Chromium6 Sat Aug 12, 2023 2:43 am

Found this that might be kind of interesting to look at from 2013. Keep in mind Miles' Pyramid papers. They use LIDAR with oil/gas discovery which can give hints of what gravity is doing on the surface:

LIDAR for geospatial discoveries:
LIDAR
https://www.degruyter.com/document/doi/10.1515/geo-2020-0257/html?lang=en
Performance comparison of the wavenumber and spatial domain techniques for mapping basement reliefs from gravity data
https://www.degruyter.com/document/doi/10.1515/geo-2020-0321/html
https://www.bluefalconaerial.com/from-exploration-to-refining-lidars-impact-on-oil-and-gas-operations/

Salt Dome Gravity for changes...they use above and subsurface to find O/G:

MULTIDISCIPLINARY INVESTIGATION OF SURFACE
DEFORMATION ABOVE SALT DOMES IN HOUSTON, TEXAS

https://uh-ir.tdl.org/bitstream/handle/10657/636/Zheng%20Huang%20MS%20Thesis%20Geology.pdf?sequence=1
Abstract
Surface deformation has been an ongoing problem in the Houston Metropolitan
area because of the city’s location in a passive margin where faulting and subsidence are
common. According to previous studies the causes of the surface deformation are
typically attributed to anthropogenic activities, mainly the subsurface withdrawals of oil,
gas, and groundwater. However, the majority of the studies done have not accounted for
the vast amount of salt underneath the Houston area and its role in the surface
deformation. The objective of this study was to identify areas of surface deformation in
the greater Houston area and their possible relationship with subsurface salt movements.
To accomplish this, I integrated three kinds of data:
1) GPS,
2) LiDAR (Airborne and TLS), and
3) Gravity. GPS data revealed subsidence and uplift in Harris County. DEMs
generated from airborne LiDAR revealed changes between salt domes and their
surrounding areas. TLS data collected over the Pierce Junction site, chosen for
accessibility and depth, revealed vertical changes over the surface above the salt dome.
Gravity data acquired over Pierce Junction salt dome also revealed changes in the
subsurface. Groundwater withdrawal may be a large influence in the surface deformation
of the Houston area, but salt-related surface deformation should be more closely studied
to quantify its influence.

https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/grl.50838
Geophysical Research Letters

New ultrahigh-resolution picture of Earth's gravity field


Christian Hirt, Sten Claessens, Thomas Fecher, Michael Kuhn, Roland Pail, Moritz Rexer
First published: 12 August 2013 https://doi.org/10.1002/grl.50838Citations: 146
2 Data and Methods

[4] Our ultrahigh resolution picture of Earth's gravity field is a combined solution based on the three key constituents GOCE/GRACE satellite gravity (providing the spatial scales of ~10,000 down to ~100 km), EGM2008 (~100 to ~10 km), and topographic gravity, i.e., the gravitational effect implied by a high-pass filtered terrain model (scales of ~10 km to ~250 m).

[5] Regarding the satellite component, we use the latest satellite-measured gravity data (release GOCE-TIM4) from the European Space Agency's GOCE satellite [Drinkwater et al., 2003; Pail et al., 2011], parameterized as coefficients of a spherical harmonic series expansion, that currently provides the highest-resolution picture of Earth's gravity ever obtained from a space gravity sensor. Resolving gravity field features at spatial scales as short as 80–100 km, GOCE confers new gravity field knowledge, most notably over poorly surveyed regions of Africa, South America, and Asia [Pail et al., 2011].

[6] Compared to pure GOCE models, complementary GRACE satellite gravity [Mayer-Gürr et al., 2010] is superior in the spectral range up to degrees 70–80 [Pail et al., 2010]. Therefore, first, a combined satellite-only solution based on full normal equations of GRACE (up to degree 180) and GOCE (up to degree 250) is computed [see, e.g., Pail et al., 2010]. The GRACE/GOCE combination is then merged with EGM2008 [Pavlis et al., 2012] using the EGM2008 coefficients as pseudo-observations. Since for EGM2008 only the error variances are available, the corresponding normal equations have diagonal structure. In our combination, GRACE/GOCE data have dominant influence in the spectral band of harmonic degrees 0 to 180 with EGM2008 information taking over in the spectral range 200 to 2190, leaving the main spectral range of transition from GRACE/GOCE to EGM2008 in spectral band of degrees 181 to 200. The relative contributions of EGM2008 and GRACE/GOCE satellite gravity are shown in Figure 1.

Details are in the caption following the image
Figure 1
The Cause of Gravity - the next major chapter - Page 7 Grl50838-fig-0001-m

Relative contribution of GOCE/GRACE data per spherical harmonic coefficient in the combination with EGM2008 data (in percent) for the degrees 0 to 250.
[7] The spherical harmonic coefficients of the combined GRACE/GOCE/EGM2008 (GGE) gravity model were used in the spectral band of degrees 2 to 2190 to synthesize a range of frequently used gravity field functionals at the Earth's surface. For accurate spherical harmonic synthesis at the Earth's surface, as represented through the Shuttle Radar Topography Mission (SRTM) topography, the gradient approach to fifth order [Hirt, 2012] was applied. This numerically efficient evaluation technique takes into account the effect of gravity attenuation with height. Applying the gradient approach as described in Hirt [2012] yielded numerical estimates for radial derivatives (gravity disturbances) and horizontal derivatives (deflections of the vertical) of the disturbing potential and quasi-geoid heights from the GGE data set at 7.2 arc sec resolution (about 3 billion surface points) within the SRTM data coverage.

[8] For the Mount Everest region, Figure 2 exemplifies the associated resolution of GOCE/GRACE satellite gravity (a) and their combination with EGM2008 gravity (b). The spatial resolution of the GGE gravity field functionals is limited to about ~10 km (or harmonic degree of 2190) which leaves the problem of modeling the field structures at short scales, down to few 100 m resolution at any of the surface points.

Details are in the caption following the image
Figure 2
Open in figure viewer
PowerPoint
Gravity field at different levels of resolution over Mount Everest area. (a) Satellite-only (free-air) gravity from GOCE and GRACE satellites, (b) GGE gravity (satellite gravity combined with EGM2008 gravity), and (c) GGMplus as composite of satellite gravity, EGM2008, and topographic gravity. Shown is the radial component of the gravity field over a ~400 × 400 km area covering parts of the Southern Himalayas including the Mount Everest summit area (marked), units in 10−5 m s−2. The spatial resolution of the gravity modeling increases from ~100 km, ~10 km to ultra-fine ~200 m spatial scales.

[9] Because ground gravity measurements at a spatial density commensurate with our model resolution do not exist over most parts of Earth [e.g., Sansò and Sideris, 2013]—and will not become available in the foreseeable future—alternative solutions are required to estimate the gravity field signals at scales shorter than 10 km. High-resolution topography data is widely considered the key to ultrahigh-resolution gravity modeling and used successfully as effective means to estimate short-scale gravity effects [Sansò and Sideris, 2013; Tziavos and Sideris, 2013; Pavlis et al., 2012; Forsberg and Tscherning, 1981]. This is because the short-scale gravity field is dominated by the constituents generated by the visible topographic masses [Forsberg and Tscherning, 1981]. However, forward estimation of the short-scale gravity field constituents from elevation models near-globally at ultrahigh (few 100 meters) resolution is computationally demanding. Yet we have accomplished this challenge for the first time through advanced computational resources.

[10] Massive parallelization and the use of Western Australia's iVEC/Epic supercomputing facility allowed us to convert topography from the Shuttle Radar Topography Mission (SRTM) [cf. Jarvis et al., 2008]—along with bathymetric information along coastlines [Becker et al., 2009]—to topographic gravity at 7.2 arc sec resolution everywhere on Earth between ±60° latitude with SRTM data available. Based on nonparallelized standard computation techniques, the calculation of topographic gravity effects would have taken an estimated 20 years, which is why previous efforts were restricted to regional areas [Kuhn et al., 2009; Hirt, 2012].

[11] The conversion of topography to topographic gravity is based on the residual terrain modeling technique [Forsberg, 1984], with the topography high-pass filtered through subtraction of a spherical harmonic reference surface (of degree and order 2160) prior to the forward modeling. We treated the ocean water masses and those of the major inland water bodies (Great Lakes, Baikal, Caspian Sea) using a combination of residual terrain modeling with the concept of rock-equivalent topography [Hirt, 2013], whereby the water masses were “compressed” to layers equivalent to topographic rock. These procedures yield short-scale topographic gravity that is suitable for augmentation of degree 2190 spherical harmonic gravity models beyond their associated 10 km resolution [cf. Hirt, 2010, 2013]. The topographic gravity is based on a mass-density assumption of 2670 kg m−3 and provides the spatial scales of ~10 to ~250 m, which is complementary to the GGE gravity (spatial scales from ~10,000 km to ~10 km).

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