Is the Hubble Shift a relativistic illusion?

[captcass]

I explain the mirror gradients in the revised paper I just put up on Vixra. It is too long to go into here.

 

Let me ask this.....If galaxies farther away from us appear to be moving apart from each other, and us, at greater speeds, then shouldn't galactic densities seem sparser at distance? Yet they do not. Galactic distribution seems to be uniform at all distances.

This is a serious question. In the BB view, how is this resolved? The "raisins in a rising loaf" analogy does not work to explain this. Even in a rising loaf, the more distant the raisins, the greater the separation and sparser the raisins near the edge of the loaf.

[Mordred]

Your confusing conditions then as opposed to conditions now. Expansion is time independent. Meaning it doesn't involve time dilation.

 

Your trying to apply a time dependancy into it.

 

This becomes apparent when you compare the changes to the ds^2 line elements.

 

The FLRW metric is a history of change over a period of proper times.

 

The Scwartzchild child metric compares proper time vs coordinate time at a particular moment in proper time.

 

Not a history of proper times.

 

Anyways expansion follows ideal gas laws. We don't need relativity to describe how a gas can expand or contract over time by density changes. I already provided the related formulas and resources to learn cosmology thermodynamics.

 

However those same ideal gas laws also dictate how time dilation works via the stress tensor.

 

The problem is the Schwartzchild metric assumes the background density is zero...

 

Its not precisely zero just close to it... more importantly though it only models Localized anistropy, its not designed for a homogeneous and isotropic background. It specifically models a preferred direction and location. The Centre of the BH... one with an extreme curvature locally...

 

The Newton approximation is closer to a homogeneous and isotropic background.

but the time dilation is still gravitational potential vs background metric mass density.

 

Essentially one observers frame of reference is the global background at a moment in time, while the other is time deviation from the previous frame of reference due to localized density change.

 

NOT GLOBAL the FLRW metric is density change over proper time. (at rest observer...called a fundamental observer. A fundamental observer is essentailly at rest to the global density)

Edited September 22, 2016 by Mordred

[captcass]

I understand that. The sharp curve is very evident in the dRt's as one nears the energy density. I see this as a lensing effect and tried to use that in my original derivations but failed because I was using a compound effect, when it is a point of origin effect, as per my revision.

But this doesn't really answer my question.

We are seeing more distant bodies moving away from each other and us at higher and higher speeds with distance based upon the red shift. The farther away they are, the more distant back in time the shift occurred. Whether due to to pressure expansion of just velocity through space, higher velocity = greater distance. It really doesn't matter "when" we are looking at. Higher velocity = greater distance. Thus it seems we should see a sparser density with distance. We do not. We see a uniform galactic density, regardless of distance and relative apparent velocity. How does the BB and pressure expansion explain that difference.

[Mordred]

Don't confuse recessive velocity as a real velocity. Its a consequence of the formula used. The rate of expansion is roughly 70 km/s/Mpc. So depending on how many times you multiply 70 km by Mpc will be exponential.

 

Try this. Take a ruler each unit 1 for one. draw 1 unit line. Now next second double the ratio so one unit is 2 of the previous. Then for the third second you will have 4 to 1 previous.

 

You now have accelerating seperation distance. However the rate of expansion was constant per Mpc.

 

This is funny because the "Rate of Expansion is currently getting lower per Mpc." however the seperation distance is accelerating...

 

POP media articles never truly detail that. This is probably one of the better papers, the Author is a Ph.d philosophies of Cosmology. He specializes in inflation studies. Numerous arxiv articles.

 

http://tangentspace.info/docs/horizon.pdf :Inflation and the Cosmological Horizon by Brian Powell

 

He wrote this targetting forums and typical forum questions.

 

think of it this way. thermodynamics determine the rate of expansion, not the seperation distance/recessive velocity. That changes per observer. rate of expansion doesn't

 

food for thought. Matter collecting into Blackholes, galaxies, stars etc.

 

Actually causes a universe to expand...all by its little ole lonesome...

The reason being is the global density distribution of matter gets lower as matter falls into localized distribution...The very moment two particles collect or pool together. Expansion occurs.... 👹

Edited September 22, 2016 by Mordred

[captcass]

I have been through this before but am mis-remembering about what I thought at the time. Sorry, senior moment. You are correct, it appears the same to any observer.

 

At the time I thought it was faulty because it put us each at the center of the universe and didn't allow for the singularity, which I do understand is a highly compressed energy density, etc.

 

My thinking was that If it did originate in a singularity, then there has to be an origin point, and edges, Edges on the infinite really bother me.

 

Also, for us to be experiencing inflation that always appears to put us at the center, without being able to discern any difference at all in the direction of the singularity, then we are much too far from the origin point for the proposed age and size of the universe. The origin point is much too distant, it seems to me.

 

I have no problem with us seeming to be at the center of the universe, because that is what I see. We are each at the center of our own universe. Our individual universes are harmonized so they make mutual sense to us. The universe is evolving around each of us for us, otherwise my hand wouldn't end up where i want to move it.

 

In an eternal universe, I see black holes re-emitting the energy they absorb. The same is true of quanta. Time vortices generate viable energy. Two ends of a cycle. Time vortices form quanta that form particles of increasing size until we get a massive time vortice in the black hole which changes the form of the energy. Possibly just as potential energy in the fabric of space/time, or the unknown Hawking radiation......

 

As per my theory, I also have no problem with the universe appearing to expand at an accelerating rate. I'm simply trying to express why it appears that way in terms of time and the way time is perceived to change over distance so we don't end up with a cold void.

 

"thermodynamics determine the rate of expansion, not the seperation distance/recessive velocity. That changes per observer. rate of expansion doesn't

food for thought. Matter collecting into Blackholes, galaxies, stars etc.

Actually causes a universe to expand...all by its little ole lonesome...
The reason being is the global density distribution of matter gets lower as matter falls into localized distribution...The very moment two particles collect or pool together. Expansion occurs...."

 

Could you say then that energy contraction, or concentration, creates the impression of expansion by lowering overall energy density distribution in the vacuum? Could such a contraction cause the reverse perception of expansion?

I was just thinking and, really, I also have no problem with the thermodynamics, only some of the parts that are theoretical and devised to fit the overall theory, like Guth's inflation.

 

From my primary point of view, the spiritual reinforced by the quantum point of view, the science itself is part of the illusion. Spiritually speaking, the universe appears to be logical so we have the faith to try to manipulate it, and that faith allows us to direct the direction of evolution of the continuum to suit our needs. It passes eternal time in a constructive way that pleases itself through us.

 

There is divine power in faith. This I know to be a fact from lifelong personal experience. I learned to wash my hands in acid without harm when I was 22 and a pretty angry atheist. The circumstances gave me the faith. I also did it with doubt the next day under different circumstances and it was like liquid fire that took off about four layers of skin. And so on throughout my life. So I m firmly based in that perspective.

 

What are the odds that a universe that is so unlikely to even exist, would produce intelligent parts that could manipulate events within it to serve the needs of those intelligent parts of itself?

 

How could such a thing expire in a cold dark void?

 

The fact is we will never know what lies beyond the wall. Perhaps what we can see is the limit of what is. Beyond that the only thing that exists are quantum possibilities and probabilities. This is in accord with quantum theory.

 

I'm thinking a lot about the section of yours I put in parenthesis. It really is elegant.

[Mordred]

While your at it. Think on this problem. You wish to model a stable universe that is eternal neither contracting nor expanding. Very well lets do just that...

 

Line element of a static homogeneous and isotropic Uniform universe.

 

[latex]ds^2=-c^2dt^2+dl^2[/latex]

 

uh oh we have a problem Houston.... How can you have gravitational redshift or cosmological redshift in a static and uniform universe. That line element only uses proper time. There is no coordinate time needed as the average density of the universe WOULD NOT EVOLVE>>>>

 

So how can you possibly get time dilation if the observer is in the same frame as the global metric (fundamental observer)

 

Quite simply you can't.

 

This is the impossibility aspect of your proposed model. Time dilation requires mass density change, or velocity difference. If you have neither then you have no time dilation. Not to repeat that the FLRW metric is time independent where the Schwartzchild solution is time dependant.

 

 

So answer this question. In your model you have a static universe....no density change

 

How can you possibly have time dilation to an observer sitting in free space away from any localized anistropy? (fundamental observer). The very minute you tried to model the cosmological redshift as gravitational redshift. You induce an evolving background metric. As the metric we require is a fundamental observer, the only valid solution is an expanding volume. The spatial components evolve over proper time. (time independent)

Edited September 25, 2016 by Mordred

[captcass]

I want to post a graphic here. Does anyone know how to do that? Perhaps a file type? It won't let me use the image extension.

[imatfaal]

I am not changing my tune. This is what I have been saying all along, though not clearly enough here obviously.

 

My only objective is to show the red shift can be explained in terms of a non-expanding universe. The mirror gradients accomplish this.

 

This is the most basic of derivations that doesn't include rotation or motion or the presence of other bodies. It is meant merely to show how the effect can be generated.

 

Don't know what else to say........If you want to understand it, you have to put the BB and the accelerating universe aside and just consider the basics of a non-expanding, most likely eternal, universe.

 

I know this is difficult as everything has been developed over the last hundred years assuming the shift is due to the Hubble effect. I fully agree all of that seems to make nearly perfect sense.......except for the conclusions of a singularity, BB and accelerating expanding universe that eventually goes cold.

 

By-the-by, I am certainly not the only one who does not agree with the BB, et al. Lots of folks are looking for other answers to the effects we see.

 

The first equation in your paper is flat out wrong and you refuse to give a derivation for it. Forget not agreeing with the BB and mirror gradiants etc. Your paper includes this line

 

time dilation for a stationary, non-rotating body, To/ Tr=√((1-( Ro/R))

 

and

 

For a non-rotating stationary Earth, To/ Tr=√((1-(Ro/R)), where To/Tr is the ratio between times on the surface, To, and at distance R, Tr, and Ro is the Schwarzschild radius of the Earth

 

Please provide a derivation for this equation - IT IS NOT THE ONE IN WIKIPEDIA

---

 

FYG - we know Newton's Gravitational Constant to about 5 parts in 100,000 - any equation in which you are multiplying by Newton's Gravitational constant is going to have at least this error. Providing 60 decimal places is just nonsense. In fact anything that relies on a greater accuracy than that of G is something you need to be very careful in handling

I want to post a graphic here. Does anyone know how to do that? Perhaps a file type? It won't let me use the image extension.

 

try a simple jpeg - they normally work. Or upload to image hosting site and use the image tags 11th icon on bottom row of reply options

[michel123456]

I want to post a graphic here. Does anyone know how to do that? Perhaps a file type? It won't let me use the image extension.

Go to the "more reply options" in the bottom right corner of the post. It will give you the ability to upload an image file and add it to your post.

[imatfaal]

I want to post a graphic here. Does anyone know how to do that? Perhaps a file type? It won't let me use the image extension.

 

 

Here you can find a hand-written scan that I wrote to explain uploading - and the next post in that thread is Michel's explaining how he uses an alternative method

 

http://www.scienceforums.net/topic/73369-uploading-images/#entry732878

 

nb they seem to have renamed the "Choose..." button to "Browse..."

[captcass]

Thanks folks. Also, how do you folks do those pretty formulas here? How do I do math symbols?

Are copying and pasting?

[Mordred]

You use latex commands. Google latex symbols for a decent list.

 

Then type [l@tex]\frac{1}{2}[/latex]

 

I intentionally replaced a with @ in the first command so you can see the structure

 

Another hint hit quote on posts that have latex done. You can see the command structure that way.

 

[latex]\frac{1}{2}[/latex]

Edited September 23, 2016 by Mordred

[Strange]

There is a handy interactive editor which can help you test/learn latex: http://www.codecogs.com/latex/eqneditor.php

[captcass]

Trying to sort out the confusion over the formula. This is the formula from Wikipedia.

 

To = Tf * √((1 – (Rs/r))

 

To = the proper time between events A and B for a slow-ticking observer within the gravitational field, I am placing the slow ticker observer at Frame 1, which is 1 Rs from the center of the mass (energy density).

Tf = the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object.

r = the radial coordinate of the observer. I think this is where the confusion comes in. The observer here is the observer at the fast ticking coordinates, not the observer at 1 Rs. Thus r = the distance from the observer at Frame 1 to the coordinates of the fast ticker.

 

Therefore:

If r = 1 Rs, then To = 0 and the formula implies that time stops at the Rs, which is the event horizon of a black hole. This is in accordance with current assumptions. But Tf does not equal 0. Tf still depends on distance. At infinity the rate of time is 1 s/s. Thus the dRt relative to infinity is 1 s/s, as follows.

 

If we solve for To/Tf between any two frames, we get the ratio of the difference in rates, At 1 Rs this also equates to 0. There is 0 difference in the rates. This is also in accordance with current assumptions. 1 s/s = 1 s/s.

 

If we move the fast ticker farther away, we get a ratio, To/Tf = 0.999999whatever.

1 - that ratio equals the difference in rates of time per s/s between observers, the dRt.

 

Using this at 1 Rs, we get 1 - 0 = 1, a 1 s/s difference in the rates of time at the Rs. This is also in accordance with current assumptions that have time stopping, so the difference between 0 at the Rs and 1 at infinity is 1 s/s.

 

As r approaches infinity Rs/r approaches 0 (we can never get to infinity) and To/Tf approaches 1.

 

The dRt therefore equals 1 - 1 = 0, again in accordance with current assumptions that 1 s/s = 1 s/s at both ends of the gradient.

 

The thing is, we are using Frame 1, which would be the event horizon of a black hole if the energy density was one, and not the center of the energy density, Frame 0. The rate of time has to continue to slow beyond Frame 1 and so the dRt to infinity must increase. Frame 1 is our personal frame of perception, our inertial frame. We are an energy density with an Ro. This means the dRt has to continue to increase within our energy density as time continues to slow.

 

I am saying in my theory that time does not stop at the Rs, even at a black hole event horizon. As per my main theory, when the update impinges on itself as it approaches the bottom of a gravity well, it goes into a spin, a time vortex that is a quantum. In the Fundamental Particles section I quantize the quanta in terms of space. The smallest radius that gives us whole number multiples of 2 constants (pi and Planck length) for the dimensions is 1 Planck length. As the quanta are time vortices, like black holes, this is the radius to the event horizon of the quanta, their Rs.

 

First: We can never get to infinity. So from our perspective, the difference in the rates of time, dRt, continues to decrease towards 0, but never reaches 0 as we approach infinity.

 

Within us this dRt continues to grow as the distance to the Rs' of our quantum diminishes. until the difference between infinity and our "insides" nearly reaches 2 s/s, but it can never get to that, just as we can't get to infinity at the other end of the gradient.

 

As the update is shifting into us, it is ultimately shifting into the quanta that make us up, which are the update impinging on itself from all directions, creating time vortices, which are the quanta. In the vortex, the update is nearly instantaneously re-updating the same frame over and over again. As per my theory, time evolves forward at C in any inertial frame and the update shifts down the gradient at C. The dRt to infinity within us continues to grow until the update is forced into the spin when the update impinges on itself, where the nearly instantaneous repetition of the update creates a nearly 2 s/s rate of time at the event horizon of the quantum: at our energy density's end of the gradient relative to infinity. I also note that the dRt drops off dramatically in a spin.

 

The dRt in the inertial frame of the quantum itself is 4-16*10^-65 s/s, as per my main theory.

 

Meanwhile at the other end, approaching infinity, the dRt also continues to decrease. When it gets to 4-16*10^-65 s/s, it equals the dRt in the inertial frames of our quanta. I haven't worked out the distance required for that dRt, yet, my bad, but it is extremely large: most likely infinitely.......

 

If we have a nearly 2 s/s rate of time difference just outside the quantum time vortices at our end, we also have that at infinity relative to us. Thus I attribute a 2 s/s difference between the two.

 

Time vortices attract each other and combine to form larger and larger complex vortices until a critical mass is achieved and the individual vortices of the composite particles collapse into one giant time vortex, a black hole.

 

I'm still working on the graph thing.

[imatfaal]

Trying to sort out the confusion over the formula. This is the formula from Wikipedia.

 

To = Tf * √((1 – (Rs/r))

 

To = the proper time between events A and B for a slow-ticking observer within the gravitational field, I am placing the slow ticker observer at Frame 1, which is 1 Rs from the center of the mass (energy density).

Tf = the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object.

r = the radial coordinate of the observer. I think this is where the confusion comes in. The observer here is the observer at the fast ticking coordinates, not the observer at 1 Rs. Thus r = the distance from the observer at Frame 1 to the coordinates of the fast ticker.

 

 

This is incorrect. T_f is the time for fast ticker at infinite distance at zero gravitational potential - it is not a variable which can be calculated by changing r. T_f is coordinate time - you do not get multiple coordinate times through manipulating this equation.

 

[latex]\frac{t_0}{t_f}=\sqrt{1-\frac{r_s}{r}}[/latex]

 

Around a given black hole (for which mass is the only variable) you get this equation

 

[latex]\frac{t_0}{t_f}=\sqrt{1-\frac{2GM}{c^2r_0}}[/latex]

 

You have two variables and the rest are constants a/o set by the conditions. (I have bolded just for ease of reading)

G and c are constants

M the mass of the black hole is set by conditions

t_f is coordinate time at infinite distance / zero gravitational potential. This is non-negotiable - S'child Metric defines it so; you cannot vary this part. I will now refer to this as the "fastest ticker" - as it is not just fast it is the fastest any clock goes

 

t_0 the time at position of observer - ie proper time

r_0 (I have subscripted this to make it obvious)

 

The two variables subscripted 0 are those which vary - you set one and get the other

 

To get the timing difference between two points in a gravity well you have to compare both points separately against the fastest-ticker.

 

1. I am sorry but there is no doubt that you have been and continue to use one of the most basic equations in this area incorrectly.

 

2. The equation would not apply anyway as the schwartzchild metric is a massive simplification

 

3. Even if it did you need to take on board the criticism by Mordred - which is at a much more fundamental level.

 

Please please please - before you come back and claim I am misunderstanding or that you actually mean something slightly different (you will note you have already resiled from the position in your paper) could you just work out the time dilation of the GPS satellites

[captcass]

 

OK, I'm tryijng to follow and will work out the GPS bit sometime today.

But I need some clarification here. In the above equation, what are the variables?

 

 

 

I see this equation as the same as

 

T_o/T_{f = √}((1-(R_s/R_s)) and T_o/T_f = 0

Would you say that Is correct?

[imatfaal]

 

OK, I'm tryijng to follow and will work out the GPS bit sometime today.

But I need some clarification here. In the above equation, what are the variables?

 

 

 

I see this equation as the same as

 

T_o/T_{f = √}((1-(R_s/R_s)) and T_o/T_f = 0

Would you say that Is correct?

 

In the top equation the only variable inputs are t_0 and r. ie proper time of observer and position of observer

 

The two equations are not the same as r_0 is the position of the observer (the radial distance from Centre of Mass or more properly the radial schwartzchild coordinate) and not the schwartzchild radius. I subscripted it 0 to make it clear that t_0 and r_0 were a pair; the radial distance of the observer and the rate of proper time of the observer

 

 

Measurements at the event horizon are subject to a mathematical singularity when using scwartzchild coordinates - you just cannot do it; it doesnt mean time stops, it means you have to use a coordinate system that doesn't break at the event horizon (eddington finkelstein?)

[captcass]

Position of the observer from the center of the mass?

Also, what would be the fastest time at infinity? Infinitely fast?

[imatfaal]

Position of the observer from the center of the mass?

Also, what would be the fastest time at infinity? Infinitely fast?

 

The radial coordinate - r (I have more recently called it r_0 to link it to t_0 ) is simplisitically the distance from the centre of mass of the black hole. Remember these are vacuum solutions to the EFE and thus are not immediately interchangeable into real word situations - but the Schild Solution (around a non-rotating black hole) is very close to describing test masses around a central planet or sun. So in these more real world approximations r is the distance of the observer from the centre of the sun/earth/etc

 

The fastest time is the coordinate time - which is proper time / clock time for a different observer who is at zero gravitational potential. This is technically at infinity - but in real world terms it is far enough from the central mass that gravity becomes unimportant. It is not infinite by any means - some poor sucker stuck on a floating laboratory way past the oort cloud will be very close (but not exactly there), an even more lonesome lab-rat stuck outside the milky way will be even closer, and some super-loner in an intercluster void will be as close as anyone gets.

[captcass]

OK. I see what you are saying. This is what I originally thought but then came upon an edu site that said the rate of time reduced to 1 s of our time at infinity. This has caused me to conflate. I still end up with a 2 s/s difference at infinity, but I need to rework what I am saying. It is actually better for me as I do not have to make such a reach to get the 2 s/s difference....I think. I need to spend some time looking at it again.

Please look at the diagram on the bottom right of the Wiki page:

https://en.wikipedia.org/wiki/Gravitational_time_dilation#/media/File:Orbit_times.svg

 

The green gravity speed up is the effect I see myself as describing and it plots out similar though I haven't compared the two to scale. Time goes faster with altitude, but the rate of change of the dRt halves with a doubling of the distance. Since we never get to infinity the rate of change never = 0 so time keeps going faster.

Likewise it keeps going slower towards the center of the mass, in what I am saying are the time vortices of our quanta.

 

This has been driving me nuts for over a month. I was researching all this and ran across an edu site that said the difference in rates decreased to 0 at infinity, That started me applying what is the difference in the rate of change per frame with the difference in the rates.....I think.

 

I won't comment on the rest of what was said above until I re-evaluate my work.

 

Thanks for your time and input.

[imatfaal]

...

https://en.wikipedia.org/wiki/Gravitational_time_dilation#/media/File:Orbit_times.svg

 

The green gravity speed up is the effect I see myself as describing and it plots out similar though I haven't compared the two to scale. Time goes faster with altitude, but the rate of change of the dRt halves with a doubling of the distance. Since we never get to infinity the rate of change never = 0 so time keeps going faster.

Likewise it keeps going slower towards the center of the mass, in what I am saying are the time vortices of our quanta.

...

 

[latex] \frac{t_0}{t_f}=\sqrt{1-\frac{r_s}{r_0}} [/latex]

 

Remember t_0 is the proper time of observer at position r_0

 

[latex]\frac{d}{dr_0} (t_0/t_f) = \frac{1}{r_0^2 \cdot \sqrt{\frac{-r_s + r_0}{r_0}}}[/latex]

 

I am not sure what you mean by dRt - but the rate of change of t_o/t_f wrto r_0 is given above - it is not a simple inverse relationship.

 

Perhaps someone can check my differentiation

Thanks for your time and input.

 

No problem - a pleasure so far

[Mordred]

I don't see any mistakes in the differentation.

[captcass]

Thanks guys, You've been great and very patient. Can't believe I fell for the edu site. Should of known when I couldn't find it again. That is the effect in the how the difference in the rates changes. The rate of change decreases by half as the distance doubles (doing what I was doing). How I let myself get twisted I do not know. Too much wine?

 

By dRt I mean the difference in the rates of time between 1 set of frames. From our inertial frame rate of 1 s/s, at a higher frame if To/Tr = .99999999whatever, then the difference in the rates in s/s between frames, is = 1 - .99999999whatever.

 

Back to go with the shift, it seems......

 

You said

"The radial coordinate - r (I have more recently called it r_0 to link it to t_0 ) is simplisitically the distance from the centre of mass of the black hole. Remember these are vacuum solutions to the EFE and thus are not immediately interchangeable into real word situations - but the Schild Solution (around a non-rotating black hole) is very close to describing test masses around a central planet or sun. So in these more real world approximations r is the distance of the observer from the centre of the sun/earth/etc"

 

This tells me it can be used to derive the difference at distance, at least for shorter distances. Or am I misunderstanding? If we relate r to distance from the center we can determine the difference at that distance?

Took a nice crow out of the freezer for dinner tonight.

[imatfaal]

By dRt I mean the difference in the rates of time between 1 set of frames. From our inertial frame rate of 1 s/s, at a higher frame if To/Tr = .99999999whatever, then the difference in the rates in s/s between frames, is = 1 - .99999999whatever.

..

 

You will get better reception if your terminology is standard - if you mean a change then use capital Delta ∆, if you mean a derivative (ie infinitesimal change) use d, and if it is a partial derivative use a curly delta ∂. And unless it is patently obvious also include what that change is in respect to - especially the first usage

You said

"The radial coordinate - r (I have more recently called it r_0 to link it to t_0 ) is simplisitically the distance from the centre of mass of the black hole. Remember these are vacuum solutions to the EFE and thus are not immediately interchangeable into real word situations - but the Schild Solution (around a non-rotating black hole) is very close to describing test masses around a central planet or sun. So in these more real world approximations r is the distance of the observer from the centre of the sun/earth/etc"

 

This tells me it can be used to derive the difference at distance, at least for shorter distances. Or am I misunderstanding? If we relate r to distance from the center we can determine the difference at that distance?

 

I am not sure what you mean - but you can run this equation

 

[latex] \frac{t_0}{t_f}=\sqrt{1-\frac{r_s}{r_0}} [/latex]

 

with as many different r_0 as you wish (call them r_1, r_2 etc for convenience here) . This will get you the lots of ratios of t_0/t_f - fairly simple maths can then get you ratios between different observational frames

 

[latex]\left( \frac{t_0}{t_f}\right) \cdot \left( \frac{t_1}{t_f}\right)^{-1} = \left( \frac{t_0}{t_1}\right)[/latex]

Took a nice crow out of the freezer for dinner tonight.

 

+1 Well said.

[Mordred]

I agree well said. I've always found though that one often learns more from mistakes than correct answers. Provided one keeps at it.

A side note, when I first started my studies, I was much like many that post in Speculations. Coming up with fixes that made sense to me at the time.

After a while I began to truly see how interconnected the various models truly were and how much detail and research went into the simplest of formulas.

Don't get me wrong, trying your own models is good practice. It works best with study and practice.

I originally first started with the FLRW metric, then GR, Qm then particle physics.

That sequence worked for me but each person is different.

 

one recommendation when your writing your articles. Stick to what the math shows. When you start departing from that. People start thinking crackpot. Its ok to suggest potentials that a model has. However declaring that it does more than it shows without the mathematical proof is highly questionable.

Edited September 25, 2016 by Mordred