Mordred

what benefit ? nothing you have here is of any level to be beneficial. To get others to listen to any theory you need to be able to show you, yourself understand a given theory and have sufficient references, and that you understand your theory at a level where others can come directly to you and not some program for answers otherwise what is the point ?

Self adjoint ODEs \[\acute{p_0}(x)=p_1(x)\] \[\mathcal{L}=\frac{d}{dx}[p_o{x}\frac{d}{dx}]+p_2(x)\] \[\mathcal{L}u=\acute{(p_o \acute{u})}+p_2u\] integration by parts \[\int^b_a=v^\ast(x)\mathcal{L}u(x)dx=\int^b_a[v^\ast\acute{(p_o\acute{u})}+v^\ast p_2 u]dx\] \[=v\ast p_o\acute{u}]^b_a+\int^b_a[-(v^\ast)p_o\acute{u}+v^\ast p_2 u]dx\] second integration to be continued. self reminder of goal Dirichlet and Neumann boundary conditions applicability to Chebyshev differential equation first and second order polynomials. (via Sturm-Luiville)

that amounts to a handwave for I don't want to take the effort to perform my own research and seek the answers myself. How does that help you ? You can search every post I have ever made on this forum. Not once will you find me starting a thread asking a question in regards to physics. At most I ask if anyone has come across a good article on a topic. I know how to perform my own research and know how to find the answers to any question I may have for any particular research interest I have ever had. I never rely on others for any study.

You would have a very hard time convincing me of that. For that matter we also have very rules involving ChatGPT on this forum. However that is irrelevant The person that should become the expert in your theory is you. Yourself not some computer generated response. How do you plan to do that if you rely on others including ChatGPT

quite frankly ChatGP will lead you down so many garden paths its next to useless. If you want to rely on that. That is your choice. I for one rely on hard work and actual studies than some computer generated response. Its the only true way to understand any topic. A good example of the number of tradespersons I have met that have such a reliance on calculators they don't even know how to add fractions or divide fractions. I've lost count on the number of times I've run across that

They are examples you asked where mathematics can be applied. another method being correlation functions involving statistical mean averages on other case studies. It is quite possible to employ professional grade examinations on any study if you understand the techniques even philosophy.

You might want to look into examples such as https://psicoterapia-palermo.it/PDFS/Studio sulla Coscienza di Hameroff e Penrose.PDF they have quite a bit of literature involving quantum mind. There is one example. Its not a line of research I follow but I have read some of their papers and they do employ mathematics where its potentially applicable. Boltzmann brain is another example this example follows more on probability statistics and the standard model of particles. Its not the same approach your looking for but it is examples where mathematics can be employed with regards to consciousness, awareness and physics. https://en.wikipedia.org/wiki/Boltzmann_brain these are simply examples of different approaches and should provide clues on how to move past speculative conjectures

It can be I even recommended a useful set of mathematics You can employ above. That onus however is in your court as I can honestly state I'm horrible at philosophical based arguments

That's the first statement you made I agree with

Even with strictly philosophical examinations one can still employ examinations involving mathematics by examining statistical based studies done in regards to any research involving the mind

Thought you were leaving ? Quite frankly I would not be surprised if the majority of this conversation gets split off to the trash can. I actually recommend that to happen.

Considering I already reported this conversation for moderator review I will see if I'm correct. For the record that rank is simply due to reputation rankings. It's meaningless beyond that

That would certainly establish the finite space constraints

Goodbye No bet I already came to that conclusion.

Unlikely had you been willing to listen I would have been able to explain how every single equation in both articles work in accordance to standard cosmology.

Well I chose to add further details in the hopes you might actually learn something however your mind is already closed so it was a waste of time.

Every statement you have so far is 100 percent incorrect. You haven't made a single accurate statement. Your basic logic chose to ignore what it chose to ignore so is absolutely meaningless because you choose to ignore Any detail that runs counter to your way of thinking. Literally every single physicist that has ever looked at cosmology would disagree with you.

No that's where the equations of state come into play were dealing with the mass distributions of a multi particle field distribution. All of this being contained in the sections you chose to ignore. Here is a little for thought. COBE, WMAP and Planck all looked for specific signatures to define and determine the universe curvature term using the CMB. They looked for distortions that would result from the multiparticle distributions over the expansion history due specifically to how those distortions would result from expansion /contraction of that multiparticle field.

Wrong our universe does in fact have a slight curvature term. It only approximated as flat. However that curvature term specifies a relation called the critical density formula. Which isn't quite the same as a GR curvature term. All in the papers being discussed. Expansion and contraction does in fact alter the null geodesic paths of massless particles such as photons. Gr curvature typically involve a center of mass hence it only assists the FLRW metric ( the FLRW metric is a specific class of solution that applies GR ) however the k curvature term itself for the FLRW metric directly involves the critical density relationship. If the actual density precisely matches the critical density term then and only then is our universe critically flat.

That's your hangup then as you refuse to understand why the authors state what they do. The key difference between SR and GR. Is that SR does not account for the spacetime curvature terms. Where as GR is specifically dealing with the spacetime curvature terms. The FLRW metric is a very specific coordinate system. That coordinate system is not accounted for strictly by the equations you posted. By ignoring the rest of the paper your understanding and conclusion is in error.

Here is the complete dissertation paper https://people.smp.uq.edu.au/TamaraDavis/papers/thesis_complete.pdf No you must understand the entirety of a paper before judging it in error.

There is no errors in the Lineweaver and Davies article. If their was it would have been pointed out when the dissertation paper was examined in order for the authors to recieve their Ph.D. It also one reference often mentioned as a reliable reference. You must understand how GR and SR applies in a commoving volume with curvature terms and not just focus on the SR equations and assume thats sufficient. Secondly mainstream physics section require answers that are mainstream concordance answers. It is not the place to post personal theories we have a separate forum for that. Focusing on just the equations you copy pasted is literally ignoring the rest of the article

All I'm interested is something with actual physics practicality.

\[ ct,x,y,z\] Done there is your 4 spatial components using interval for time. Is there some way you can think of to make that statement more intuitive ? Normalize the units \[c=\hbar=g=k=1\] and the majority of your equations are far easier to work with.

Your really are not grasping the time component. It is not a spatial dimension. We use an interval to measure the rate of signals between observer and emitter via (ct) which gives dimensionality equivalence to length but time itself has no spatial dimension. So modelling time using a tesseract or any other 3d object with an secondary object that can shift is not the same thing as time. Yes you can use 4 dimensions to describe the tesseract but it's simply 2 3d objects with a degree of movement of the secondary object that is independent of the main 3d object. That has nothing to do with time which is a property describing rate of change.