Mordred

In all the years I have watched your posts. This is one of the best replies I have seen. Highly accurate +1. ( Not to say your replies have been inaccurate. I particularly like the ramifications of this simple but profound reply) Fields for example is an abstract descriptive for a group of mathematical objects (scalars, vectors, spinors, tensors) under a geometric basis. In the QFT formalism which the Hobbs paper supports the field has probability path integrals (Feymann path integrals) Wavefunctions of the Schrodinger equation involves probability functions. The pointllike attributes can be described by the DeBroglie or Compton wavelength. In all the three dynamics they break down to descriptives. The OP is correct in that an elementary particle has no corspuscular (matter like ) constituents ie not little billiard balls. However particles can be described as field excitations which has both point like and wave like characteristics(side note another descriptive I have seen you often state. Physics doesn't describe reality) is also very apt. Physics describes what we can observe. Though it also speculated on the unobservable for example virtual particles.

Sigh no have you never done dimensional analysis on an equation ? Do you understand what I mean when I state the word " unit" On the left hand side your unit is seconds in SI units. How many units are on the right hand side of the equal sign in the first equation ? This is a basic mathematics skill to ensure the units on the left hand or right side of an equal sign match up in the same equation. Let's put it bluntly you cannot claim Seconds= kg times meters times seconds as an example your first equation does something highly similar . You have seconds on the left hand side but on the right hand side you have meters and kg along with seconds. Invalid The first equation is fine little g is equivalent to force which has SI units . Kg time mass/seconds^2 Those units are on the right hand side of the equal sign. Please identify them. [math] F=\frac{GM}{r^2}[/math]

Sigh no the SI units for G is [math] m^3\cdot kg^{-1}\cdot s^{-2}[/math] The SI unit for mass is kg. Radius obviously has units of length Those threeunits are on the RHS of the equal sign in formula one. On the left hand side you have the SI unit for time. Guess what it's seconds.( A single unit) So how can the left hand as side equal the right hand side when the units do not match regardless of value ? I have kg on the right hand side and units of length Yet on the left hand side I only have units of time. The right hand side does not cancel our the kg of meter units to leave only seconds. Please study the link I posted on dimensional analysis.

No how are you cancelling for example Kg in the first equation. You have no kg on the LHS. That's just one of the terms. Follow the procedures as per https://www.google.com/url?sa=t&source=web&rct=j&url=http://web.mit.edu/2.25/www/pdf/DA_unified.pdf&ved=2ahUKEwi6ybXastfpAhWTsJ4KHVrVCP8QFjAAegQIChAB&usg=AOvVaw3hTYBubBOwEQX7596gEKFR Easiest to convert to SI units.

These equations are invalid. If you perform a dimensional analysis you will find the LHS and RHS do not match.

Good discussion on wave particle duality. The main point is all particles exhibits point like (particle like) and wavelike characteristics.

Div operator is a short hand but you got the point. +1 An off topic side note the mass distribution is also how a matter only universe can expand. Which is a very tricky concept to understand. One would think a matter only universe would collapse. If you think about my last post one can see that as anistropies develop ie LSS and galaxy formation the density of the void regions decrease. In essence local gravitational anistropies aid expansion. However that's off topic...and involves the term and formula for critical density...

The Div operator is a vector. If you have a uniform matter field with no anistropies then you have no curvature and no gravity. Strange as this may be to understand but the term gravity is rather misleading. Marcus mentioned tidal forces. So let's add some detail. Take that uniform distribution. Now in that uniform distribution place two massive particles in free fall with an initial velocity or in this case momentum can be used ( momentum is the rest mass multiplied by the velocity) the two terms are not equal. The paths of those two particles do not change nor do they accelerate due to gravity. The field is uniform in distribution. Now take a region with spacetime curvature such as a planet. Drop the same two objects. The paths will converge toward the center of mass. So to understand the origin of gravity one can only answer the local anistropy regions of the mass distribution. The very term gravity is replaced by spacetime curvature. With EM the potential difference (voltage) induces current flow. The resistance restricts the current. Mass is resistance to inertia change or resistance to acceleration. So you can see the similarity. Photons do not couple with any field they interact with so have no invariant (rest mass). Though they do not couple they still interact with other particles in a region. We describe this interaction via the path of least action which a good study source would be Feymann path integrals. (The Feymann path integrals are also curved paths). Though gravity is not involved in the latter case. Another way to look at a uniform field of mass. (Which can be gained through all other fields in a multi particle system) Is take a multiparticle system uniformly distributed. You can arbitrarily choose any test particle in that field a the centre of mass then apply the shell theorem. However as any particle can be chosen with no difference you effectively have a scalar field. Gravity is at minimal treatment a vector field. (Attraction)

I think part of your confusion lies in that the Einstein field equations including the stress energy momentum tensor. Don't just describe spacetime curvature (gravity) but also describes how particles move in spacetime. The trick is the metric and Ricci tensor can both modify the stress energy tensor and vise versa. Remember the expression I gave mass tells spacetime how to curve spacetime tells matter/ particles how to move. The Einstein field equations cover both statements.

Since when provide a citation from. A peer reviewed source.

Lol I often come across equations that are so fustrating to latex it takes me several hours. So I can well imagine.

As opposed to 50 lines of mathematics lol. ( I recently came across an SM Langrangian that was three pages long...) Would take me several days to latex lmao. Speaking of cross checks a few times Markus caught me on mixing the metric tensor with the Einstein tensor...

So this details a question. When does one consider another a crackpot ? Not an easy term to define, the best estimate I have ever come up with is a poster who refuses to accept any counter evidence against his own views. It is understandable a poster would not be current with modern research. Just as it is the lack of mathematics ( takes a certain degree of desire to predictive desire). My experience has been a lack of desire to accept counter arguments. (Once you assign a label you have closed the book) surprisingly that expression oft applies to OP and commenter.

Now there is a theorem I had forgotten about my thanks for the reminder.

I would concur on the dark matter not being a significant factor. The images strike me as being a solid application of density wave theorem. Which coincides with the more probable theorem explaining the rings of Saturn as well as the formation of spiral galaxies. In so far as the Spiral action is strikingly similar to Limblad resonances. I would not be surprised if the density wave theorem is a viable model of the dynamics in the images above. I would love to see a spectrograph image to see if different specific gravity of elements are being layered. The mass to luminosity ratios I can see in the images seem to support such layering.

I have never seen any reason for an apology from any of your posts. In point of detail I recognize your skill as a check to ensure I am accurate in my responses to other forum members and fully welcome any corrections or instances where clarification is needed. You need not worry if you find yourself at odds with any of my posts. This is a discussion forum and all viable opinions are welcome. Ps to all the kudos from yourself and others I am thankful. I am also positive you have knowledge of certain physics disciplines that exceed my own or Markus. The field of physics is a huge topic in applications.

Recommendation on steps apply the FLRW metric without the cosmological constant. Then apply the changes to the expansion rate due to the constant. Specifically describe which of the cosmological constant problems you are describing. Show previous other person solutions to the problem as reference such as the Unruh paper for comparison Then describe your solution in comparison to the solutions you discussed in this thread. Treat this as a full paper. ! Moderator Note Request has been sent.

Work on your finalized form and I will get approval from the other moderator staff. Then PM you once approval is gained.

Then I suggest you go through this lengthy thread and plan a finalized form to debate in a separate thread. This would cut short a lot of the training steps for other readers.

After 10 pages of modification and corrections over nearly a year. Easily done. To be honest I lost track and I am one of your most active guide as well as participant.

Equation 34 gives an example of the gravitational action. https://www.google.ca/url?sa=t&source=web&rct=j&url=http://www.math.toronto.edu/mccann/assignments/426/DeGiuli.pdf&ved=2ahUKEwi_oLKjpcrpAhWEop4KHT1DAZMQFjACegQIAhAB&usg=AOvVaw15IQoP61wefGJ5yTd0oMlc I don't believe the OP is ready for the Langrangian at this time. However the article here provides some details.

Excellent reply +1. I don't have much too add as of yet.

A couple of points to add to the excellent post above. A scalar is rank 0. A vector is rank 1. A vector has both magnitude and direction. You need a higher rank when you require two vectors. Such as the example given by Markus. If I recall correctly the Kronecker delta function is also rank two. If I'm correct then hermitean groups would also be rank 2 but that's just a side note. The Poincare group is SO(3.1) which GR falls under. Which is a double cover [math]SU(2)\otimes SU(2)/\mathbb{Z}^2[/math] . So even in tensor ranks you require a minimal rank 2. Just to provide a tensor example. (Each of those groups is a tensor. The SO(3.1) is a 4×4 while each SU(2) is a 2×2 The Z parity operator is also 2×2. The proofs I have come across on rank 2 requirement were tensor related proofs. Which I looking for a more understandable example as they tend to be too complex for the average poster. Edit I did a quick search and I am correct the Kronecker delta function is a rank two tensor. https://mathworld.wolfram.com/KroneckerDelta.html So even a Cartesian space which uses the Kronecker delta function would be rank 2. The link above provides the differential geometry form using Euler angles. This link will show how Euler angles are employed and will understand their usage for different observers under different rotations. https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.weizmann.ac.il/sci-tea/benari/sites/sci-tea.benari/files/uploads/softwareAndLearningMaterials/quaternion-tutorial-2-0-1.pdf&ved=2ahUKEwid-fT1msrpAhU1KX0KHeAkDXQQFjABegQIAhAB&usg=AOvVaw07DuN5EIV2sfGXU19NMjbO It will also be a valuable tool to better understand rotations of the tensors. Such an example of tensor rotations is when you must rotate the Minkowskii or Lorentz tensor to describe acceleration (rapidity requires a rotation) or boost (A boost is also a type of rotation). Brian Crowell gave examples of each in that SR textbook I previously linked and provides some greater detail. A little side note the best tool to master GR is to study differential geometry. Once you understand differential geometry for Euclidean and curved geometries understanding GR8 becomes incredibly easy. (You won't even require Tensors ) they are a tool to handle multiple unknowns in essence an organization tool to keep track of multiple unknowns)

Unfortunately it's clear you don't have a good understanding of the current models of relativity, the LCDM (big bang model) or particle physics. So let's start with some basic terminology. First energy does not exist on its own. It is the ability to perform work and is a property of a system or state. Mass is resistance to inertia change. Quite frankly particle physics does an excellent job explaining mass with its coupling constants. Even going so far as to being able to predict the mass of numerous particles prior to detecting those particles. A good example is the predictions for the mass of the Higgs boson. I have no idea why you believe transverse mass differs from longitudinal mass. The primary forms of mass is invariant mass (rest mass) and variant mass ( inertial mass) so please provide a citation on the transerve and longitudinal mass. Occam's razer only applies if a simpler model can perform the same degree of predictive and falsifiable accuracy. Your hypothesis is nowhere near that point.

I know the OP probably won't understand this however it's informative. Here is how the metric tensor would look as a rotation of reference frames S and [math]\acute{S}[/math] around their common z axis in cylindrical coordinates. [latex]\eta=\begin{pmatrix}-(1-\frac{\omega^2r^2}{c^2})&0&\frac{\omega r^2}{c^2}&0\\0&1&0&0\\\frac{\omega r^2}{c^2}&0&r^2&0\\0&0&0&1\end{pmatrix}[/latex] Anyways this will give the time relation between proper time and coordinate time of [math]d\tau=\sqrt{1-\frac{\omega r^2}{c^2}dt}[/math] where [math]\tau[/math] is proper time. I too recall such a proof, if I can remember the source I will post it.