Mordred

Lol I predict that will be an absolute need

Griffiths books are excellent I have a copy of his Introductory to Quantum mechanics. 2nd edition. If I recall he also has a good example of even odd parity wavefunctions. (You may note you will want to change your symbology to avoid conflict with standardized symbols in QM) That will make it far easier for readers familiar with QM to avoid added confusion. +1 for dedicating yourself to learning the mainstream to properly test your own theory.

Then this is probably the best advise given this thread. I highly recommend it. This will give you an informed practical understanding of when and where different QM wavefunctions answer specific questions as well as the mathematics used to interpret those wavefunctions. One question often in an exam is "Draw a wavefunction (with given criteria example an electron in such and such orbital) at T=0. ? That question should highlight one of Swansonts relevant questions. (A very common mistake is taking classical understandings of waveforms and wavefunctions and believing they are treated the same in QM. While their are similarities there are are distinctive differences) Examples discrete energy levels, probability functions and weighted density of probability functions under graph. Another example of a typical wavefunction question. Given the wavefunction and the following potential well. With the infinite potential at such and such location. Give the probability of the particle (always has some details) escaping the potential well. (Quantum tunneling question) I also hope you that when the above advise you would recognize the need to be able to describe waveforms in different detector orientations ie spin in the Stern Gerlach detector.

How can you possibly use a gravitational lens for anything other than a lens ? Currently there is research on how to maximize their usage in different studies of cosmology and astrophysics.

One of the most important details you are consistently missing. How does your wavefunctions and symbology work with mainstream physics ? If I cannot apply standard formulas of QM/QFT to what you have. Then there is a problem I. Houston. A good workable theory would mean I could take any related formula beyond what you have applied and find accuracy. Thus far... Take your wavefunction graphs as one example. Where is the highest probability of a particle ? You have graphs that have a consistent rate of increase in amplitude from one waveform period to the next. Yet claim this is a probability function. Good luck on that

We take advantage of gravitational lensing today in many of the extreme deep field surveys. A gravitational lenses can be incredibly useful to extend the range of a telescope such as Hubble. I even recall some surveys using multiple lenses.

No the equation I gave is not natural units. The equation you have would give incorrect values. Try it and use the same mass and velocity for each equation.

Use the interval length as per GR. [math](ct,x,y,z)[/math] Why do you have e^2=p^2+m^2 ? That isn't the formula I gave you for energy momentum you need the full formula

E does not equal p. Have you corrected that ?

The post Studiot placed showing the eigenvalues for atomic orbitals. If your going to reinvent the wheel then you should at least apply the required quantum formulas. The energy momentum equation was one example. How many times have I mentioned mass and the need to be able to determine the particle mass from your waveforms ? If you cannot determine the mass then you cannot identify the particle the waveform represents. The mass term is part of the particles momentum term. This sets the possible values for the wave vector. (In QM it's k.)

Then you add the positive pressure region on the sail. The momentum is due to the pressure differential on one side of the sail compared to the other. Your correct though on the above.

Wrong mass is resistance to inertia change or acceleration. A point like object such as a particle can have mass. It has nothing to do with volume. Mass density yes but mass itself no. E=mc^2 does not mean mass and energy are equivalent. It means they are related but not equivalent. Energy as stated is the ability to perform work. Definition for mass is above. Neither energy or mass exists on it own they are both properties

Nonsense this statement makes literally no sense. Now here is some practical advise. Cosmology already factors in thermodynamics. It forms the fluid equations of the FLRW metric via the numerous equations of state. https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology)

Ok energy is simply the ability to perform work. A higher energy density will try to reach a lower energy density state. However this has nothing to do with force or gravity.

You should be basing your momentum of the particle by the energy momentum relation. [math]E^2=(pc)^2+(m_0c^2)^2[/math] If your not then you definitely have the wrong energy to mass and momentum relation. The above formula covers both massive and massless particles. Why is your frequency changing in your graphs if your looking for the particle wavefunction ? That in itself doesn't make sense. Take a close look at DeBroglie and Compton wavelength (including the mass term). Also look at the waveforms in Studiots post.

Lol good luck tracking every math theory on compactification.... You can nearly get PH.D on the topic

Ok thanks for a few more details. A couple of questions What do you mean by the statement "a particle with curvature " Secondly while I agree one can describe all dynamics of the universe mathematically. I wouldn't go so far as state were in a mathematical universe. Mathematics describe or represent not cause. Ok same challenge take any of your waveforms and calculate the mass and momentum. My point hasn't changed you need to be able to derive key particle properties from a wavefunction.

If want a more precise definition I would suggest adopting how Wolfram defines topological space. https://mathworld.wolfram.com/TopologicalSpace.html PS the points I gave was an example not a definition. A mathematical definition must be exact including the applicable axioms and lemmas.

The above could be considered incorrect. A topological space can a set of points with a line through it. However this example has no distance function. A metric space must have a distance function. A metric spaces are topological spaces but not all topological spaces are metric spaces. The term spacetime itself is erroneous one can topological spaces in Euclidean etc where there is no need for a time dimension or another example being a two dimensional phase space. A topological space used to be defined by four Hausdorff axioms. Whether that's still true or not I wouldn't know.

No problem take your time. Remember you should have enough detail that others can perform calculations that correlate to particle properties and be sufficient to identify the particle. The wavefunctions of a neutron or proton will be considerably different from each other or an electron even though all three are spin 1/2. (Every different particle type will have unique wavefunctions ) Here is you criteria for even odd parity. https://www.google.com/url?sa=t&source=web&rct=j&url=https://m.youtube.com/watch%3Fv%3DJxOi7q6xWSk&ved=2ahUKEwiLx_7UxpPpAhURsJ4KHUnUAIIQwqsBMAZ6BAgEEAk&usg=AOvVaw1Niks0rr1LOR2LAvFzqaqc Recall the Schrodinger animation. That animation showed a free particle with its DeBroglie wavelength and even parity. So you have a boson being the particle in that animation. ( The central peak being the highest probability region of particle location.)

Though I edited portions of your post I quoted the sections I like to highlight in full agreement. +1

Little side hint do not trust wiki graphics on parity. First you must determine the particles position. What can be mistaken for transient noise is just as important as the probability of location via [math]|\psi|^2 [/math] Just as multiparticle systems can lead to transient noise within the region of highest probability of neighboring particles.

I normally let others present their arguments and see how the OP respond on their own. However in this case I concur with Swansont. I have no greater understanding what those variables are than Swansont does. Here is the scary part both Swansont and I are both accredited Professional physicists. No an even parity graph must satisfy [math]|\psi(x)|^2=|\psi(-x)|^2[/math] for even parity. Your graphs do not. (Assigning x axis as direction of momentum of particle in lab frame) So here is a challenge. What is the formula for the condition of a wavefunction ? Second challenge How is charge identified identification in a waveform ? What formula can you apply ? Third question can you identify the helicity from a waveform ? And how would you do so ? Fourth question can you identify its spin with the above questions ? Far more complex can you determine the particles cross section ? Or mean lifetime ? Decay rate ? All these questions are determined from a particle wavefunction

You should be able to take a wavefunction and identify key properties directly from that wavefunction. The mass term of the particle has a direct affect on the wavefunction. That is one example parity and charge are others. Even helicity is identifiable. Unfortunately many of the details are extremely difficult to find in textbooks and articles on the web. Lol it's almost as difficult to identify a particle from LHC scattering experiments the shape of the curl, length etc are pieces of the puzzle to identify the particle. No one questions you can generate waveforms. What we question is whether or not they accurately represent a given particle beyond your declaration.

You obviously never looked at a DeBroglie wavelength formula. In one of those graphs Identify the particle including its mass term. Secondly none of your graphs exhibit even parity. I will get you a graph of even and odd parity later on. Thirdly you are ignoring interfere patterns. Instead of randomly declaring this is what such and such waveform represents. Calculate the mass and momentum of any given waveform a prove you can identify the particle.