Mordred

Only half I thought it would be higher 😆

Good advertising though lol. Give too much technical detail and no one will hear about it.

Well I must admit you have some very impressive work here. Far better than one typically comes across on a forum.+1 for that. It will take me a bit to look over. You mentioned above your dataset is roughly 50 pages is that correct? Anyways finding a connection between gravities spacetime and its influence on the electromagnetic field is a topic under study. So there really isn't any issue with looking for one. The question being whether or not your in fact finding such a link. You may be interested in this paper as it is one such study. If anything the formulas involved in the link will help progress your modelling. Other studies can be found under gravitoelectromsgnetism. https://www.google.ca/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/1602.01492&ved=0ahUKEwj1l8L5rrvUAhVE3GMKHQGdAkMQFggiMAE&usg=AFQjCNEnq7MLzlt11hIoZG4yZz4a7AS4KA&sig2=S7wTMAHLbOh91NiVdwvOxA

Which is difficult enough to detect.

Our detectors wouldn't be sensitive enough. The arm lengths determine what frequency range we can detect. For example our solar system produces GW waves but the frequency is far too low to detect. LIGO has a decent practical range of detectable frequencies. However does have its limits. Assuming a schotastic GW background exists the frequency range would be extremely low. The one paper I linked mentions an upper range.

Alright lets try this angle shall we. Equivalence principle m_i=m_g. Now explicitly show this. Under SR and GR all forms of mass energy contribute to curvature. Via the equation [latex]e^2=(m_oc^2)^2+(pc^2)^2[/latex] Well good so does GR. though it does not require any additional terms if you use the correct formula. WHY do you think I keep mentioning it? Umm the momentum term of the above equation and the invariant mass of the above equation when applied to your four momentum determines your spacetime curvature. You have already accounted for potential vs kinetic energy in terms of how total mass-energy density via the stress tensor curves spacetime. (at least in terms of energy equivalent contributions go.) so my question is why do you think you need any adfitional kinetic energy terms? If you used the correct equation I posted above this is unnecessaryShall I continue ? [latex] e=pc^2[/latex] also happens to the the energy due to momentum of specifically all massless particles. (this technically includes kinetic energy, as energy is a property) In essence [latex]e^2=(m_oc^2)^2+(pc^2)^2[/latex] includes BOTH the invariant and variant mass that you claim needed adding to SR. Your further statement of trying to account for changes in mass due to acceleration ie in an acceleration frame is already interconnected via SR and GR. in essence you ignored a key equation that accounts for the kinetic energy term then tried to add that term in the above equation you provided by replacing p with [latex]pc^2\rightarrow\frac{d\tau}{dt}c^2[/latex] in the last quoted section As per my first reply when I hit this equation from your article [latex] e_t=ymc^2-mc^2[/latex] Why two observers for the same coordinates? if you model potential vs kinetic energy seperately then apply them together you have an embedded geometry with two fields overlapping. So where does the two observers come from???? An observer is an EVENT.....not a state an event is in essence a spacetime coordinate that is defined by total energy contributions via [latex]e^2=(m_oc^2)^2+(pc^2)^2[/latex] However as your in [latex]\mathbb{R}^4[/latex] you need to apply that to a multiparticle field under the four momentum and three velocity. The rest of your article does not get any better.... Now back to this goofy equation [latex] E_t= \frac{d\tau}{dt}mc^2-mc^2[/latex] Great what about massless particles that definetely has kinetic energy but no invariant mass? How does that equation work in a system of massless particles where you have no invariant mass? Brings us right back to that replacement I mentioned above. Except you also flipped the sign so you are no longer adding two forms of energy for total energy. You are subtracting one from the other via your very OWN equations ???????? You have already defined [latex] E_a=mc^2[/latex] you are subtracting from total energy. Why? Oh right to correspond to your negative acceleration. Let's get back to that later. Under R^4 field treatment =not good I assume you have rewritten the groups under Noether's theory in its definition of conservation of energy/momentum ? in R^4 ? Is not your purpose to treat kinetic energy as the gamma factor ? If you did the derivitaves correct you should have gotten [latex] E_t=\gamma m_oc^2[/latex] Not this [latex] E_t= \frac{d\tau}{dt}mc^2-mc^2[/latex] Here study it for yourself. https://www.google.ca/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/1604.02651&ved=0ahUKEwiNq4-LpLrUAhVCwmMKHauqCew4ChAWCCMwAg&usg=AFQjCNEyL1NsYSdoH8evMNTVYjwRJO2ZPg&sig2=PV1eCsO8V5ctiLlNX1oqtQ Start at section D and work down to equation 29. I have no idea how you got this goofy equation. [latex] E_t= \frac{d\tau}{dt}mc^2-mc^2[/latex]

I asked you specifically to define what the discrepancy is that you are trying to improve in the standard model. You gave values that did not match. Yet you are altering a key aspect kinetic energy term that makes up the above degree of accuracy then claim it doesn't affect the accuracy of GR. I do not require lessons on what the standard model states. I need a detailed analysis that your model approximates the standard model in particular the freefall rate itself as per the standard model then the comaprison to your model. Which quite frankly should have been in your paper to begin with. Any good paper does a detailed comparison. Key word DETAILED. That has been what I have been trying to get you to include. For instance when you claim your model shows negative acceleration as opposed to the increasing acceleration of the standard model. Then lay the claim that this does not conflict you better have some very strong evidence. I do not see that reflected in your posts nor your paper as you have not done a detailed standard model series of tests to compare against. I will not merely take your word on it. I will not struggle with the lack of latex in your article. A good article should be written in a clear and precise format that is easily read. I do not have issue with understanding any complex mathematics. I am the reader it is up to you to provide a detailed analysis to sell me on your idea. A good article will be written for a target audience. If your target audience is the professional peer review standard then your well below the required details as per the suggestions I placed above. I am more than well aware of how GR determines freefall geodesics. I can derive such under GR. Regardless of the particle contributors. I specifically asked you to do the same USING your model and not merely posting the formula. And for bloody sakes start applying the CORRECT energy momentum equation. E=mc^2 is strictly the invariant mass under GR. IT DOES NOT include momentum. The equation I posted above does.

Well considering the weak equivalence principle has been tested numerous times to a degree of accuracy to 1 part in [latex]10^{18}[/latex] Which is far finer than the numbers you just posted. I would state that the experimental data doesn't reflect the discrepancy values you just posted. As I stated you have your work cut out for you. Though you still haven't recognized that the quality of your article needs a huge overhaul as per the items I mentioned above. You have better details posted here than in your article where those details belong. The error of margins you posted is several degrees of error greater than the experimental data. Answer a simple question does this discrepancy show up under your model? or does it show up using the standard model? Sounds like your model where it shows up. Which tells me something is wrong in your model. As the standard model is far more accurate than the numbers you posted. I would be a far more accurate match to experimental data using the standard model as opposed to using your model. In other words you haven't improved anything but instead added a greater margin of error.

A negative acceleration great when all the datasets show an incredible degree of accuracy under the standard equations I provided. ie an increasing acceleration term as you approach a higher mass. You really have your work cut out for you. First you need to show precisely what discrepancies your referring to under the standard equations. GR does have an incredibly high degree of accuracy so which discrepancies are you referring to? Little side note an added kinetic term would have temperature effects but lets skip by that for now. though by your descriptive a reduced temp.

Right then Count up the graph locations of every single blue pixel in that graph. As it is already in hertz on the vertical. You average each data point frequency to the time. Accuracy will depend on interpreted points via that graph and number of sample points. This degree of accuracy will increase in error margin at each stage of calculations ( extra number of samples helps reduce) After all it is already hertz over time get to it. Don't forget to denote the ones in the + or - 20 hertz range. We don't have the recorded data files 😉 We don't have telemetary so we can't use transverse doppler for corrections. You can bulldoze your way through using the first doppler equation on the above then average them. Of course it won't be accurate either lol.

Yeeah its been done for good reason. Sheer complexity on number of calculations to get an accurate mean average. In case you haven't noticed every single paper we posted. References some piece of simulation software....

Your right I can't you require a computer program designed to do so. That has been the point all along. Its not as simple as plug in single point values but a time average of values for some mean baseline depending on the fourier transformations of the graph/plot you are dealing with. However I am aware of the types of equations involved. Which I took the time to find decent references to them to show the complexity involved. see section 50 that is the best answer I can give you. The thing is when you are trying to establish a mean average of a waveform your stepping into a whole series of calcs. (corresponding to the number of sample points) Not just a simple application such as the basic Dopplers I posted above.

recall the reference I mentioned above section 50. Your formulas are there. Recall the paper where got the graph above from. Specific quote. "The presence of diurnal and seasonal variations in the residuals has also been reported by Anderson et al. (Anderson et al., 2002). It has to be noted that these specific periods are unlikely to be due to anything related to the spacecraft or its environment." That is the paper I stated see section 50 for the related formulas. In other words the paper you got that graph from references the paper I provided. https://arxiv.org/abs/gr-qc/0104064 on laptop now may as well link the arxiv link

Roflmao I particularly like equation 3 for [latex] i [/latex]th planetary bodies in system. The article has a decent list of relevant studies. No fault to the posting the topic, not many would pick up the detail "schotastic acceleration" for [latex] a_p[/latex] As a side note any estimates based on the transverse formula over time we could make. Without a decent range of datasets would most likely be more in error than the error margin were to calculate lol. As schotastic accelerations would be involved. Here is a decent study on orbital Schotastic doppler. https://www.google.ca/url?sa=t&source=web&rct=j&url=https://ipnpr.jpl.nasa.gov/progress_report/42-146/146D.pdf&ved=0ahUKEwijyJb8nrfUAhWQ0YMKHRASC1UQFggrMAQ&usg=AFQjCNGBCCEmknQOV54gyyX4W2pi8rcDlA&sig2=cTNGu-a4pz-cdcIk82pzRA It has a good coverage of how to determine [latex]a_p[/latex] It should illustrate the complexity involved under Schotastic treatment. Come to think of it of these treatmemts could come in handy for my notes. I always like tracking different derivitaves and their causes and mathematical methods to compensate involving all three types of redshift.

You really are missing the point. I've read these in your paper. They do not include the metrics I am referring to. Ok start with the Newton approximation and model under GR. Get your paper to apply Noethers theorem under SO(1.3) Lorentz group as well as the Poisson group. Establish your geometry and symmetry relations. Start there. You need to properly model each state with the particle contributors modelled under their kinetic energy contributions via their equations of state. Yes kinetic energy and potential energy are describing specific states what of it ? You need to apply the relations of those states under some geometry. In this case you can describe each state (using your terminology) as a seperate geometry. Yet they overlap. So do so. Blooming bugger at least apply the correct equation with regards to the kinetic energy contributions. Which is also referred to as the energy momentum equation. [latex] e^2=(pc^2)+(m_oc^2)^2[/latex] where [latex]m_o[/latex] is your rest (invariant) mass under [latex]e=mc^2[/latex] Establish a coordinate system (included in your article). [latex] ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}[/latex] [latex]\eta=\begin{pmatrix}-c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/latex] describe in under the above geometry or some similar established metric the Principle of least action in the Standard view Then apply where your proposal differentiates. Include the energy momentum tensor under GR [latex] T_{\mu\nu}[/latex] define the four velocity. [latex]u^\mu[/latex] [latex]u^\mu=\frac{dx^\mu}{dt}=(c\frac{dt}{d\tau},\frac{dx}{d\tau},\frac{dy}{d\tau},\frac{dz}{d\tau})[/latex] this gives in the SR limit [latex]\eta u^\mu u^\nu=u^\mu u_\mu=-c^2[/latex] the four velocity has constant length. [latex]d/d\tau(u^\mu u_\mu)=0=2\dot{u}^\mu u_\mu[/latex] the acceleration four vector [latex]a^\mu=\dot{u}^\mu[/latex] [latex]\eta_{\mu\nu}a^\mu u^\nu=a^\mu u_\mu=0[/latex] so the acceleration and velocity four vectors are [latex]c \frac{dt}{d\tau}=u^0[/latex] [latex]\frac{dx^1}{d\tau}=u^1[/latex] [latex]\frac{du^0}{d\tau}=a^0[/latex] [latex]\frac{du^1}{d\tau}=a^1[/latex] Now your establishing the metric under SR for the lay person readers. Professionalism is also being established. As your mentioning QM apply the QFT treatments. Use the metrics and describe how the Principle of least action falls under it. Which will Include your potential and kinetic energy terms. (the following will give a list of the equations under QFT.) This is the type of details you need. That is if you want your paper to go anywhere. Secondly energy does not exist on its own.... So you need to detail the particle contributors and their hydrodynamic contributions to the average kinetic energy. For scalar models. Use the equation [latex]w=\frac{\frac{1}{2}\dot{\phi}^2-V\phi}{\frac{1}{2}\dot{\phi}^2+V\phi}[/latex] where the numerator is your potential energy and the denominator your potential energy term. As you can see we already describe systems via strictly kinetic to potential energy clearly define where your model differentiates from the metrics already existing.... In the QFT Langrene above [latex]L=\frac{1}{2}m\dot{x}^2-V{x}[/latex] To the right of the- sign is potential energy to the left is the kinetic energy Why would I need your model for something already available?????

If you have rotation you will have a non uniform mass distribution. The universe would measure as inhomogeneous and anistropic regardless of how slow the rotation. Godel universe is one such hypothetical model. Our universe has a homogenous and isotropic distribution.

Gompothere https://en.m.wikipedia.org/wiki/Gomphothere surprise surprise a 4 tusked elephant like mammal did exist 😀

The problem is you need the relevant angles for the transverse. You were already provided the mean average frequency for the a_p value above. Which is [latex] 5.99*10^{-9}[/latex] hertz/s. Perhaps you need to see the formula for the diurnal velocity error margin. Let me dig it up. Here see section 50 but note all acceleration values are weighted average values as mentioned numerous times in this article. https://www.google.ca/url?sa=t&source=web&rct=j&url=https://arxiv.org/abs/gr-qc/0104064&ved=0ahUKEwia5Y2Uy7bUAhUC6GMKHW4pBNwQFggdMAA&usg=AFQjCNEs949Tk1b1iYg4EEXv_ChHnPTRtA&sig2=3XHWC131R8ZIgTDvsaq3Ew I had to track this paper down via the citations from other articles. As far as I can tell it has highest citations specific to the diurnal variations. (hopefully you will see just how complex the averaging gets in these types of datasets) particularly many of the values you see in most papers are under schotastic treatments. Your going to need some very serious computing power to come up with better than already researched on the last few decades of extensive research. (lol hope you plan on dedicating a decade or so of your time to this problem)

Read my last reply you literally asked a question in your OP that is impossible to answer on a forum. On any forum as we simply do not know the location of the satelite when you wish to calculate the frequency from the cm/s value. It will not stay consistent but will literally be a wavefunction over time. Do not pretend to know what you are talking about when you already admitted you have never worked with the Doppler formulas. Take some time and practice some calcs you will see precisely what I mean. Those values above are mean averages

K that is where the problem lies. Unfortunately it is also a highly complex topic unto itself. (Far more complex than most laymen realize) When you have two objects moving relative to one another, signals sent to one another experience a doppler shift relative to their motion to each other. There is three BASIC equations Unfortunately none of these three will work directly as written below. Doppler (non relativistic) [latex]f=\frac{c+v_r}{c+v_s}f_o[/latex] Gravitational redshift [latex]\frac{\lambda}{\lambda_o}=\frac{1}{\sqrt{(1 - \frac{2GM}{r c^2})}}[/latex] Cosmological (expansion contraction of space volume) [latex]1+Z=\frac{\lambda}{\lambda_o} or 1+Z=\frac{\lambda-\lambda_o}{\lambda_o}[/latex] Now the one we need the most is the first equation as we do not have relativistic velocities involved it will be to good approximation (though not exact, all equations are to best approximation) for the system state they are describing. Now all the above equations are along the x axis. In other words directly moving toward or away from the detector. For the Pioneer we need a far more complex equation called the transerve Doppler formula. [latex] f_o=\frac{f_s}{\gamma(1+\frac{v}{c}cos\theta_o)}[/latex] this equation includes relativistic effects via gamma So when you get a velocity value relative to instruments on Earth (which is at a higher gravitational potential) we need two equations (transverse doppler and gravitational redshift) in order to get your redshift/blueshift frequency values. Now asked for the frequency in your original post. You gave one value when requested from your first paper. (velocity) which is great but what is the satellite trajectory relative to Earth to convert to frequency? we don't know which is why were stuck doing precisely what your doing (looking for the appropriate datasets ) that has the sidereal and diurnal values in hertz specifically as we have no idea what the applicable trajectories will be to apply the correct formulas. See the problem? Hence the only answer we can apply is datasets that might help. However any frequency calculation will be at a Specific location and moment in time and not constant the most constant value will be the velocity not the frequency. Which is precisely why the value is given in cm/s.

We have replied perhaps your not understanding the replies. Have you ever worked with the Doppler formulas? I ask this because the manner of your posts indicate to me your not particularly familiar with them.

After reading your paper in your attempts to describe quantum processes and gravitational wave influences. Why do you not have any of the pertinant equations of the two influences mentioned above? Don't you think actually applying the equations would be important? You haven't defined how a GW wave causes action nor how the quantum influences may be involved in terms of your creation/annihilation operators. Sorry but that is incredibly lacking in the required details. When you mention a process is involved. One must show how it is involved via the appropriate equations. You mention the higher equations but do not present them nor even apply them why? You don't even have the Einstein field equations mentioned in your paper. as a reader this comes across as knowing they exist but not knowing how they work or applies. it does not give any confidence you have attempted to fully apply the various standard models you mentioned. May I also suggest you use an editor where you can properly latex your math. If anything your subscripts and superscript will be more presentable.

Then your going to need a very strong case to support that. Particularly since you had difficulties in applying the Doppler shift formula to the cm/s value above. The value in hertz/s is converted from the first value. Are you confident you have the required skill set to take any dataset and extract the data your looking for? (assuming its contained somewhere not obvious in the dataset) Not trying to be insulting but far too often posters try to solve complex problems without having the needed skills. (Quite frankly I would wonder if even I would have the right skill mix in this case) let alone access to the right data. Lets take the last paper for example. With better data they found that the anamoly is decreasing over time. Which means it must be from an internal source as the dynamics of our solar system would be relatively constant over the flight time. (with solar seasonal variations accounted for) After all the scientists at NASA certainly have the datasets to account for solar seasonal variations. Far greater than what is readily available on the internet. Lets look at the key difference between your article and the one I just posted. The problem here is the first article shows the anomoly as constant over time where the later and recovered datasets shows decreasing over time. Fundamentally the lack of availability of the correct datasets led to a huge mountain of incorrect interpretations. I won't go over all the alternative models far too many to list them all. From your paper "In its present status, the data analysis does not take into account the detailed thermal models of the spacecraft, currently under study by different groups. These models are expected to produce a slowly evoluting radiation force due to heat dissipation from the Radioisotope Thermoelectric Generators (RTG); this force should appear as a part of the anomalous secular acceleration to be found below" So they even admit the influence of the paper I posted but did not have that data to account for in your paper. As it was still being studied at the time.

Definetely not. It is a very specific synchronization procedure (Einstein synchronization). In all the time you have been posting on this forum on trying to rewrite relativity. Have you spent any of that time studying the subject you are trying to rewrite? I mean intensive study.

Nah us geeks often have to look up new things. Otherwise we would get bored without new items to geek over.