Mordred

No he should be using the Newton approximation for observers on Earth. Though that won't help him solve beyond Hubble limit without including an expanding volume. The Newton solution and cosmological redshift corrections are previously shown on this thread. Lol very few people are aware the cosmological redshift formula isn't accurate beyond Hubble horizon. Here is the workup starting with the FLRW ds^2 line element. The last equation is the corrected redshift formula when recessive velocity exceeds c The FLRW metric derives from the Newton approximation then adds volume change.

Neither do I lol br doesn't work lol

The other problem is neither the OPs equation. Nor the Schwartzchild equation can be used when the recessive velocities are greater than c. One should be able to calculate velocity of said object with the time dilation formulas. the limit is the Hubble horizon for those formulas. Yet we measure recessive velocity up to 3.2 c at redshift 1100. You can't derive that redshift via the Schwartzchild metric. Even the cosmological redshift formula which includes an expanding volume requires corrections above Hubble horizon.

Don't feel bad Robin. Lots of people have difficulty with what is termed Spacetime curvature. In GR space is your x,z,z coordinates. Nothing more... time is just an added coordinate. It is simply geometric relations between events that is curved. Though if you add a multiparticle distribution the density distribution will also be curved in density values. At no point does GR require some spacetime "fabric" to curve. The curvature is geometric relations. The stress tensor in GR tells space how to curve. That stress tensor includes changes in density/pressure,temperature etc.

if there is no time. The BB couldn't happen in the first place. You need time to have a change... The singularity problem of the BB can be solved by avoiding the infinite values with a Planck length cutoff point. Or on temperature the Planck temperature ( which is often suggested as the maximum temperature.) Numerous BB models in particular LQC use this cutoff to deal with the singularity problem.

No I'm discussing basic math. Which you evidentally got wrong on the time dilation formula. Unfortunately you wrote the entire 88 page article based on this math error....

Your obviously using the time dilation formula incorrect if you have this conclusion... "Using the time dilation formula, the difference in rates decreases with distance. This means time is slowing over distance. until it again = 1 s/s of our inertial frame at infinity. Going slower than what? From where? The top of our heads? It can't slow from 1 s/s to become 1 s/s." The formula does not give 1 second/second compared by the at rest clock at infinity. This is where you are wrong. See the graph I posted. When v equals c time essentailly stops. This is what the formula shows. [latex]\acute{t}=\frac {t}{\sqrt {1-v^2/c^2}}[/latex] set v=c. You will get 1-1 under the denominator. Which is equal to zero. This will give a divide by zero. Time becomes infinitely slowed down. Divide any number by zero. You won't get a value of one. Secondly where do you see distance in that formula???? Distance doesn't affect time. Yes the gravitational potential decreases with distance but you only account for the difference in gravitational potential between observers. If we place two observers onto a uniform homogeneous and isotropic mass distribution. It doesn't matter how close or far those two observers are. There is no time dilation in this case. If one of the observers is in a stronger gravitational potential. While the other is in the GP of the background space. You only calculate the change between the two reference frames. The GP from the mass source will become essentially identical to the background GP at a certain distance. This background gravitational potential will stay constant as distance increases or until it hits another anistropy. I think you better study the basic formulas again. Your making serious math errors.

good point on required precision. A 10 km sample would be extremely difficult to measure the amount of curvature.

That graph is meaningless. Go ahead devide by infinity. Why do you think infinity has 1 s/s in that graph? as you approach infinite redshift time gets slower and slower. It doesn't jump back to being in the same frame as frame zero. That is 100% incorrect.... a massless particle essentially doesn't experience time nor have a length. This tells us this isn't a valid reference frame. Using the time dilation formulas... That formula certainly doesn't give the same reference frame as your (at rest observer)... https://en.m.wikipedia.org/wiki/File:Time_dilation.svg from wiki. Try and draw your graph in the same axis assignment. You will end up with a completely different curve in your graph with [latex]\gamma=\infty=1 second [/latex]

"Let me ask this another way...... How can time be going faster with altitude but slower with distance so it equals 1 s/s at infinity? I think I explain that......" Really not sure how you drew this conclusion from the time dilation formula. Yes time runs slower in a stronger gravitational potential. However time dilation has nothing to do with seperation distance, except length of time for a signal between events to reach each other Nor do I understand why you ignored the length contraction that goes hand in hand with gamma. You seem to have missed the difference between the spatial seperation components and the time component. Precisely why I asked you to work with the ds^2 line elements. Here is the problem with the above quoted line. Which observer? If I'm an observer time is not dilated in my own reference frame. T_0=T_1. I will always see my own time as the fastest. I will also see my own length as the longest. As gamma approaches infinity you get infinite redshift. This is true but infinite gamma isn't a valid reference frame. All of our math regarding motion in space uses units of time, m/s, for instance, to describe the forward evolution in space over so many seconds. m/s is a unit of velocity. Not a unit of time. Unit for time is seconds. Page 2... the opposite, s/m: so many seconds evolution in time for each meter of evolution of space into the future. this statement makes absolutely no sense...4d coordinates is (t,x,y,z) assign each event (observer/emitter) to those coordinates. The difference between the two events transforms as [latex]t=\acute{t}\gamma,x=\acute{x}/\gamma,y=\acute{y},z=\acute{z}[/latex]

Seriously 4 extremely basic formulas support this claim... "This is a grand unification theory" or the claim that mass emerges from time. "We see time dilation as a result of mass, but when we look at the processes in time, we see that mass is the result of time dilation" How about this claim? "where time dilation fields are irregular in shape and where Relativity fails to accurately describe gravity," Thats only the first page.... Do you honestly believe your 4 extremely simplistic formulas define the above????

oh my... This paper is so full of errors I don't even know where to begin.... Why would you publish something before having it looked over first? Anyways still going through it, but its clearly not a paper anyone would take seriously as written.( not trying to be offending, but you are making grandiose claims with simplistic formulas) (guess I placed my expectations too high, considering the discussions we had on this thread.)

Some interesting work on examining the data presented. I got curious on your comment "Gaussian beam divergence". Atmospheric optics isn't my strong suit. However I do recall collimation correlations with atmospheric turbulance via Gaussian Schell model beam. Though never really studied it in detail.

Yes I'm familiar with some of Wolframs work. Though certainly not in great detail. Ok so you are simulating Newton gravity along x axis distance. Judging from above. This shows x axis, but what about the y and z axis? I look through your links I'm unclear which is your work or others. you may find these articles helpful. Cell Automata and Physics. http://www.google.ca/url?sa=t&source=web&cd=1&ved=0ahUKEwi0js7IrpzPAhUGy2MKHefsA-8QFggbMAA&url=https%3A%2F%2Farxiv.org%2Fpdf%2Fphysics%2F9907013&usg=AFQjCNHja_3J6NFDSGI3PzKbHvDALS-3mQ&sig2=ymSvYw3QO-umfbRFt5yLKA And "What are the hidden Quantum laws behind Newtons laws" http://www.google.ca/url?sa=t&source=web&cd=2&ved=0ahUKEwi0js7IrpzPAhUGy2MKHefsA-8QFgggMAE&url=http%3A%2F%2Farxiv.org%2Fpdf%2Fphysics%2F9904036&usg=AFQjCNGiDpIcBEmWePTYr-qmDmD_O8qx-g&sig2=n2oIRg0Qj90JeDaINLgbKw both articles gives some excellent examples in Newton gravity. particularly in the 3d regime with CA having 26 neighbors. 2D only 8 ( see second article)

Ok look forward to seeing to it. At least you understand the importance of the math apects in your modelling. Even wrong directions teach (generality, not aimed at you). You may have manipulated the variant quantities. (observer aspects) but will also need to include your invariant quantites. Ideally by using a ds^2 line element, to show the departures.

Probably because as posted its too difficult to follow accurately. You need to find a more detailed way to explain the above. That is easily readable. People lose patience with difficult to read posts. "this post takes too much effort to translate. Let someone else worry about it" The quoted section is probably the typical response...

Understood GR is tricky to learn. I caught the cross post aspect. However just learning the tensor usages without knowing how to use tensors can give clues. ie anytime you see [latex]\eta [/latex] just remember Minkowskii geometry.

I wouldn't know,its too tricky to try and read your last post. You don't need every decimal place. That why we invented scientific notation. Secondly the above is pointless, it doesn't tell us the formula you used. Coincidence on a few numbers isn't substantial proof your formulas is correct. Particularly since you still ignore the thermodynamics in the FLRW. (you completely missed the details of what changes and why.. in the different line elements I posted earlier. (the volume changes, not the time aspects, in terms of dilation. In the FLRW metric) You claim to understand these line elements but keep chasing a garden path... Rather amusing actually, considering I showed the departures of redshift formulas beyond the Hubble limit... The other aspect you ignored is in those three line elements. Geodesic light paths follow completely different relations. These deviations alone should tell you the difference between gravitational redshift and cosmological redshift. The two formulas are not direct matches as they are derived from two seperate line elements. The first is time dilation relations. The second volume change. Again you chose to ignore this to chase your garden path... most importantly the standard time dilation formula does not work, beyond Hubble limit due to apparent velocity greater than c. I gave you those corrections. You assume the numbers above are correct as you do not accept current distance values. However you can't simply compare numbers. We must compare the formulas and see if those formulas match known physics. Derivable with known physics.

Ok mathematically I have no problem with using math to describe reality. This is essentially done with physics. Without having to search your links is there specific formulas you want to look at? The Newton limit we can already derive using math. So without having to search your links. Can you post the math in your solution? The extension of the Bohr model should also be looked at.

Excellent. Now the formulas you tend to see for GW waves is for an observer away from a BH in an Newton approximated geometry. (An observer on Earth). A GW wave polarizes in the x and y axis. The direction of propogation is the z axis. It doesn't alter the mass term per se, but it does induce pressure changes. So in this manner a GW wave through the energy/mass relation. Can induce additional gravity via the stress tensor. In the formula above the stress tensor changes will be included under the "h" tensor. (I think of the h tensor as the permutation tensor)

Newtonian gravity can be derived from GR. Its a special treatment where the effects of gravity is significantly low. Mainly no time dilation. Once you start having time dilation you depart from Newtonian gravity approximation. Does that help or did it confuse ? [math]g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}[/math] The [latex]\eta [/latex] specifies an approximately Euclidean geometry. More specifically Minkowskii geometry. This doesn't hold true for geometry near a blackhole

Most likely the evaperation duct. The average height for the temperature range was roughly 2 metres. Assuming I ran the calcs correct. The effect is that the light path curvature would be less than the curvature of the Earth. This causes signal entrapment and skipping. Either way it indicated conditions not favorable to the test. On the interest of the next test. It is difficult to guage how much those involved learned. Both from previous test and discussion. I recommend we look first at methodology. Please describe how you plan to undertake the next test. Break it down to each stage. From there we can look to improve this stage first. Then look at addressing human error corrections etc. As Studiot mentioned include your control points.

1) methodology 2) human error 3) instrument error 4) refraction in order. Every experiment has the same sequence. The corrective measures not with standing

excellent post MrMaker +1

I got about as far as the first ten minutes. Then I recalled a lesson. Systematic errors get increasingly worse at later measurement points and increased distance in this case. After seeing the uncertainties in the first two points that was enough for me. Hopefully the next attempt takes and applies the advice given. Its a common mistake to overly trust a laser. One may be aware of atmospheric effects but not aware of how much a tiny variation increases over distance in angles. As well as other optical effects. (simply calculate how much a 1% change in angle will change the height measured over 100 metres let alone 1 km.) Most surveyer handbooks I've looked over including their equipment manuals recommend breaking down your total distance to increments of less than 100 metres. (coincidentally refraction is the primary reason). At least on the ones including level correction. That a lot of measurement points and time over a 7 km lake let alone a 10 km survey.