Galaxy rotation rates explained without Dark Matter

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What has special relativity got to do with it?

Quite a lot as locally everything reduces to special relativity.

The observer on the planet's surface is stationary yet he measures the speed of light to be the same even....

Yes, he measures the local speed of light as c.

...though his time is running slowly.

As compared to other observers at different gravitational potential, yes.

If the speed of light was invariant then he would measure the speed of light to be higher than it should be.

But he does not... locally the speed of light is c and this is what all observers in free-fall measure - again locally.

As I have already said: light speed slows by the same amount as the observer's rate of time, thus all measurements he makes will still give the normal speed of light.

This is not the usual interpretation. You should show how this relates to the actual calculations.

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The question is what would an observer far outside the gravity well non-locally measure the speed of light to be deep inside the gravity well

Edited by granpa
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The question is what would an observer far outside the gravity well measure the speed of light to be non-locally

That is a different question and depends on the coordinates used.

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But it wouldn't be c

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But it wouldn't be c

Sure... if you use non-inertial coordinates then the speed of light will almost never be c.

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As I have already said: light speed slows by the same amount as the observer's rate of time, thus all measurements he makes will still give the normal speed of light.

Which is at odds with your claim that the measurement should be higher than this.

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If the speed of light was invariant then he would measure the speed of light to be higher than it should be.

You seem to be forgetting that gravity affects both time and space (in a way that keeps c invariant).

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To Swansont:

No, I was saying he would measure light speed as higher if light speed didn't slow by the same amount as the rate of time in his reference frame.

To Strange:

If you mean the size of the space in his reference frame increases so as to keep the speed of light invariant, then the observer would also increase in size by the same proportion and so he would still measure the speed of light to be higher than it should be as all his measuring rods would increase in size too.

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To Swansont:

No, I was saying he would measure light speed as higher if light speed didn't slow by the same amount as the rate of time in his reference frame.

Profound. If the laws of physics were different, then the laws would be different.

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No, the equations stay the same, but the Physical interpretation is different.

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No, the equations stay the same, but the Physical interpretation is different.

Show the equations as being unchanged then. Your papers have some command of latex within them. For this site its $demo[/late] replace  with x. Its one thing to assume the equations will remain the same. Its quite another to prove they will do so. Ive worked enough with EFE and FLRW metric to seriously doubt those equations will remain unchanged by your model. In point of detail I'm confident they won't. Which is why I supplied the articles I did covering the Schwartchild Newtonian connections. As well as recommending you study the geodesic equations. Edited by Mordred Link to comment Share on other sites I'm not sure which equation you are referring to, but if you have a 'c' you could replace it with [latex]c/gamma$

Where there is a 't' you could replace it with $gamma*t$

So a 'ct' would be invariant.

It may be necessary to 're-think' the equations from the new perspective and build them up based on that interpretation in order to be confident in the understanding and formulation.

I have done this in my Energy Field Theory paper for Time Dilation, Length Contraction, Mass Increase and Gravitational acceleration, however I have not tackled the GR wave equations/tensors, except for my suggested change to the Schwartzchild metric regarding flow into black holes.

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What if antimatter falls upward?

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Interestingly though, when I did this for Special Relativity - deriving the Lorentz factor - the equation came out of the analysis unchanged: 'c' still remained 'c' in the equation, although the Physical interpretation used to build the equation was different.

To an outside observer looking into a time dilated reference frame in regards to the Lorentz factor, he would change 'c' to 'c/gamma' and 'v' to v/gamma' - such that in the 'v^2/c^2' term the 'gammas' cancel, giving the original unchanged equation.

To Granpa:

I'm not sure how anti-matter falling upwards affects the current discussion, although if it did, a mechanism would need to be devised to account for it.

To Mordred:

Further to changes required to GR:

The GR wave equation essentially tells us how space curves with respect to mass/energy & the resulting effects on a test mass - Do I have this essentially correct?

As far as I can see, if we simply interpret the curvature as referring to the change in density of an energy field, rather than actual geometry changing, then we still have the same maths equations.

It is just the physical interpretation that has changed. The effect on the test particle is still the same.

I had a quick look through the book you suggested by Sean M Carroll. I don't have the time to work through the details at the moment - though it looks like a good text.

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There is an expression " matter tells geometry how to curve, while geometry tells matter how to move."

The stress-momentum monentum tensor tells spacetime how to curve. The geometry tells matter how to move.

In other words you cannot properly define the dynamics of the Einstein field equations with just the stress tensor. You need both sides of the equation.

In a sense they are two sides of the same coin. Much like energy and mass. Change one you change the other.

I'm glad to see your reading Sean Carrolls article. Keep in mind throughout this thread I've provided other resource aids. The lecture notes by Mathius Blau for example details nunerous misconceptions in GR due to artifacts of coordinates.

The second part of the basic particle physics has excellent Relativity coverage as well as that section is all Relativity.

Elements of Astrophysics has a huge collection of formulas with explanations used by any everyday astrophysicist. Including some detailed relations for galaxy rotation curves as well as GR.

Granted it will take a great deal of time to properly absorb it all.

To Mordred:

Further to changes required to GR:

The GR wave equation essentially tells us how space curves with respect to mass/energy & the resulting effects on a test mass - Do I have this essentially correct?

As far as I can see, if we simply interpret the curvature as referring to the change in density of an energy field, rather than actual geometry changing, then we still have the same maths equations.

It is just the physical interpretation that has changed. The effect on the test particle is still the same.

See above.

By the way +1 I'm glad to see your studying. Which puts you ahead of many of the crackpots we see in Speculations.

A couple of hints to help. The EFE includes the equivalence principle as well as conservation of energy/momentum. (Even though its debatable if energy is conserved in GR)

Pay close attention to the different geodesic equations for massive and massless particles.

Also any details on the Levi Civita connection.

https://en.m.wikipedia.org/wiki/Levi-Civita_connection

I'm not sure which equation you are referring to, but if you have a 'c' you could replace it with $\frac{c}{\gamma}$

Where there is a 't' you could replace it with $\gamma*t$

So a 'ct' would be invariant.

It may be necessary to 're-think' the equations from the new perspective and build them up based on that interpretation in order to be confident in the understanding and formulation.

I have done this in my Energy Field Theory paper for Time Dilation, Length Contraction, Mass Increase and Gravitational acceleration, however I have not tackled the GR wave equations/tensors, except for my suggested change to the Schwartzchild metric regarding flow into black holes.

I fixed the latex. If you quote this post you can see the corrections and how to latex symbols and fractions.

This will help a bit.

Coordinates in GR take the form (ct,x,y,z) this leads to a 4x4 matrix. For the moment we are ignoring everything but the exact specific real numbers the components of the metric take at a single point. Lets define a point as $x^\alpha$ and our new coordinate as $y^{\mu}$

$g_{\mu\nu}=g_{\alpha\beta}=\frac{dx^{\alpha}}{dy^{\mu}}\frac{dx^{\beta}}{dy^{\nu}}$

$dx^2=(dx^0)^2+(dx^1)^2+(dx^3)^2$

$G_{\mu\nu}=\begin{pmatrix}g_{0,0}&g_{0,1}&g_{0,2}&g_{0,3}\\g_{1,0}&g_{1,1}&g_{1,2}&g_{1,3}\\g_{2,0}&g_{2,1}&g_{2,2}&g_{2,3}\\g_{3,0}&g_{3,1}&g_{3,2}&g_{3,3}\end{pmatrix}=\begin{pmatrix}-1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}$

Which corresponds to

$\frac{dx^\alpha}{dy^{\mu}}=\frac{dx^\beta}{dy^{\nu}}=\begin{pmatrix}\frac{dx^0}{dy^0}&\frac{dx^1}{dy^0}&\frac{dx^2}{dy^0}&\frac{dx^3}{dy^0}\\\frac{dx^0}{dy^1}&\frac{dx^1}{dy^1}&\frac{dx^2}{dy^1}&\frac{dx^3}{dy^1}\\\frac{dx^0}{dy^2}&\frac{dx^1}{dy^2}&\frac{dx^2}{dy^2}&\frac{dx^3}{dy^2}\\\frac{dx^0}{dy^3}&\frac{dx^1}{dy^3}&\frac{dx^2}{dy^3}&\frac{dx^3}{dy^3}\end{pmatrix}$

The simplest transform is the Minkowskii metric, Euclidean space or flat space. This is denoted by $\eta[$

Flat space $\mathbb{R}^4$ with Coordinates (t,x,y,z) or alternatively (ct,x,y,z) flat space is done in Cartesian coordinates.

In this metric space time is defined as

$ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}$

$\eta=\begin{pmatrix}-c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}$

The sign convention can be confusing. In the above were using (-,+,+,+) so if you look at diagonal components of $G_{\mu\nu}$ (-1,1,1,1) were following the same sign convention. Some metrics use sign convention (+,+,+,-1).

(Well hopefully that helps rather than confuse)

Just in case here is a decent matrix algebra article.

Edited by Mordred
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I had a quick look through the book you suggested by Sean M Carroll. I don't have the time to work through the details at the moment - though it looks like a good text.

Carroll's notes are very good I really suggest you read them carefully.

That said, as you are working on a modification to general relativity, I find it strange that you are not already familiar with all the basic mathematics he writes about and most of the physics. I mean, it is like me trying to play a game of football without knowing any of the rules. For sure I can kick a ball, but is that really playing a game of football? Moreover, would anyone buy tickets to watch me do this?

Edited by ajb
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To Mordred: Thanks...

To ajb:

It is possible to understand Relativity without getting into the Tensor maths of GR - especially when you view it from the point of view of a space-filling energy field that determines the local speed of light and Time Dilation.

I hope you now understand that a space filling field with variable speed of light and Time Dilation is the only way to resolve the speed of light measuring problem by any observer.

It has other advantages too - the original topic of this discussion: Galaxy rotation rates due to this field being consumed by black holes...

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It is possible to understand Relativity without getting into the Tensor maths of GR

I would say that this is not really possible. In fact, not just for general relativity but physics as a whole.

- especially when you view it from the point of view of a space-filling energy field that determines the local speed of light and Time Dilation.

But this is not really general relativity - it seems to be your own made-up 'theory'.

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It is possible to understand Relativity without getting into the Tensor maths of GR - especially when you view it from the point of view of a space-filling energy field that determines the local speed of light and Time Dilation.

I am sure you would need a very firm grasp of the relevant mathematics to prove that your space-filling energy field produces the same results as GR.

I have heard many people over the years make the same claim about many different personal theories. They have all simply asserted this equivalence (for many different models from aether to push gravity to zero point energy). None have ever done the mathematics to prove this equivalence.

I am equally sceptical of your claim as I am of all the others.

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I am sure you would need a very firm grasp of the relevant mathematics to prove that your space-filling energy field produces the same results as GR.

In fact it is worse than that... you need a good grasp of mathematics to define this 'energy field' in the first place, before you actually try to do anything with it.

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You don't seem to understand that the precise curvature as defined by GR can be represented as a field with variable density. So the same equations apply just the physical interpretation is different. If you interpret curvature as meaning density then you *know* that the shape of the field will be the same.

It is a similar comparison between water waves and sound waves : vertical displacement versus air density. The Doppler shift equations are the same etc.

If you allow curvature to equal medium density and allow the speed of light and rate of time to follow the density, then the affect on test particles will be the same.

The kinematic equation x=vt reveals this to be true. You can optionally multiply x by some number or divide v by the same number - either one will give you the same value of t.

So speed and distance are complimentary - you can allow one or the other to change and you get the same type of result.

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You don't seem to understand that the precise curvature as defined by GR can be represented as a field with variable density.

i) You have a field - what values does this field take?

ii) Can you define the density carefully? (this infinitesimal density or are you integrating over a small region, or what?)

iii) There are several curvature tensors at play here, so which one are you refering to? (The Riemann curvature or the Einstein curvature, or something else?)

iv) From this field - i.e., a chosen section of the bundle that the field takes values in - you build one of these curvature tensors. How?

Please try to answer these questions caefully and mathematically. You can assume that some of us have some mathematical sophistication and can cope with some details.

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Ok, well I am not familiar enough with GR to represent it in tensor form, but the key point is that light will travel the same path in either the standard GR form or the medium with variable density form.

So in GR space is 'created' near a mass thereby causing light to take longer in traveling - leading to gravitational lensing to an outside observer. In the alternate interpretation the space remains fixed and the density of the field within in increases in the same proportion as the space size increases in the GR example. Thus light slows and lensing occurs for an outside observer in exactly the same fashion as in the GR example.

The equation for GR gravitational time dilation based on the gravitational potential gives the magnitude of the field density increase - thus causing light's speed to appear constant.

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Ok, well I am not familiar enough with GR to represent it in tensor form...

Meaning that you have nothing to back up your claim.

but the key point is that light will travel the same path in either the standard GR form or the medium with variable density form.

You can prove this?

So in GR space is 'created' near a mass thereby causing light to take longer in traveling - leading to gravitational lensing to an outside observer.

This is not well stated... you mean that the metric depends on location and is not just the Minkowski metric.

In the alternate interpretation the space remains fixed and the density of the field within in increases in the same proportion as the space size increases in the GR example.

I don't see that this is another interpretation. You will need to show us how the mathematics relates to your words.

An interpretation is a description of the mathematical framework and/or some description of a calculation therein.

Thus light slows and lensing occurs for an outside observer in exactly the same fashion as in the GR example.

You need to show this rather than just claim so.

Unless you can make some headway with my earlier questions you are just making stories up.

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Edit:

a) The claim was made by Declan that the problem of dark matter can be solved by using one of the well known classical equations of circular motion.

b) This was then changed to a claim that Declan actually has a gravity theory that is equivalent to general relativity.

d) The claim is now that Declan has a new interpretation of general relativity, however...

e) Declan admits he has no knowledge of the standard formulation of general relativity.

Edited by ajb
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a) Yes

b) Not changed, but this is the background work that lead me to (a)

c) No change to story, no change in position. Have maths showing the idea works, but not the Tensors you are looking for.

d) same as (b)

e) Not no knowledge, but am not too familiar with the maths to show it in Tensor form

And

f) If you give me a standard GR Tensor expressing the distribution of Gravitational Potential, then this is the same as the density of the energy field in my interpretation - no change required.