Mordred

Absolutely GR allows for virtual particle production. That's all covered under the behavior the standard model. Explain how your standing waves are different from the normal field excitations. As I stated your first paper is absolutely NOT credible. You keep handwaving that explanation away. Along with the numerous other counter arguments I and others have presented. As it stands your first paper and model is a violation of the conservation of energy. Or more accurately a violation of the four momentum. Virtual particle production follows conservation rules. They dont pop in and out for no reason. Guage bosons being an example. They mediate specific interactions within the standard model. You haven't shown any interaction details on your magical origin field. I will stress once again GR does not state that spacetime itself is its own materialistic type entity. Space is simply a geometric volume. Spacetime is any metric of that volume that includes time as a coordinate vector. The standard model of particlesvl that reside in that volume is what causes the virtual particle production. NOT SPACETIME.

Most definetely you also need to explain how your non homogeneous and isotropic fluid flow does not affect the homogeneous and isotropic flat cosmology we accurately detect today. This is in regards to your first paper. As Ajb mentioned there isnt much substance on your rotation curve article to discuss. Not without adressing your personal theory in the first paper. Which quite frankly is insufficient. Unfortunately you think this first paper is accurate. Yet it doesn't address the key issues I just mentioned. Nor any of the key issues adressed by others on this thread. Nor do you offer any tests or refer to any tests of a medium like substance of spacetime itself outside the thermodynamics of the standard model of particles. It is the thermodynamic equations of state of those standard model which the Einstein field equations utilizes in the stress momentum term. Quite frankly your usage of the term spacetime flow tells me you have a serious misunderstanding if the definition and meaning of spacetime. Which is simply a geometrical volume where time is treated as a coordinate. Spacetime curvature simply describes the geometry changes due to the presence of mass density. However those geometry changes is due to the mass density distribution influences upon the stress momentum tensor. Which quite frankly is the term that dictates how spacetime will curve. As mentioned though it involves the thermodynamic pressure influences of the standard model of particles. NOT ITS OWN unique particles. Here is a heuristic mathematical detail that is contained in Andrew Liddle's Introductory to Cosmology. This involves both kinetic and potential energy for gravity and expansion. We start with a homogeneous and isotropic distribution. For this we can detail using Newtons laws. [latex] F=\frac{GMm}{r^2}[/latex] Mass density we will use [latex]\rho[/latex] which is the mass per unit volume. Now assume a field of test particles. Motion and mass currently unimportant. One of the aspects of the shell theorem in Newtons laws is the test particle will only notice a force from the center of mass. In a homogeneous and isotropic distribution any test particle or CoM can be used. As we're dealing with test particles we just need the mass relation. [latex]M=\frac{4\pi\rho^3}{3}[/latex] So [latex]E_p=-\frac{GMm}{r^2}=-\frac{4\pi G\rho^3 m}{3}[/latex] Kinetic energy is [latex]E_k=1/2m\dot{r}^2[/latex] [latex]U=E_k+E_p[/latex] U is just a dimensionless constant to equate total energy must be set as a constant value. So the above translates to [latex]U=\frac{1}{2}m\dot{r}^2-\frac{GMm}{r^2}=-\frac{4\pi G\rho^3 m}{3}[/latex] Now with the vector relation of the radius to length we can denote the scale factor. [latex]\overrightarrow{r}=a(t)\overrightarrow{x}[/latex] Where a is a function of time. This leads to [latex]U=\frac{1}{2}m\dot{a}^2x^2-\frac{4\pi}{3}G\rho a^2x^2 m[/latex] Multiply each side by [latex]2/ma^2x^2[/latex] Leads to [latex](\frac{\dot{a}}{a})^2=\frac{8\pi G}{3}\rho-\frac{kc^2}{a^2}[/latex] [latex]kc^2=-2U/mx^2[/latex] [latex]k=-2U/mc^2x^2[/latex] K is the curvature constant

Its becoming apparent to me that your understanding of the spacetime is incorrect. As well as your understanding of the Einstein field equations. First off all GR requires no medium or eather like properties. This is something you have added without explaining where this mysterious source comes from. Lets look at the stress tensor for GR. [latex]T^{\mu\nu}=(\rho+p)U^{\mu}U^{\nu}+p\eta^{\mu\nu}[/latex] [latex]\rho[/latex] being the energy density The energy density and pressure terms in the above equation uses the equations of state for the mass density distribution of the standard model particles. It does not state spacetime generates its own particles medium or standing wave.

First point, you need to match the 21cm hydrogen line curve. Otherwise you shouldn't claim your model matches the rotation curve. A comparison on other galaxies with known rotation curves to luminosity data is also recommended. Secondly If you wish to model spacetime itself as moving. Then your going to need to show those metric changes in the [latex]G_{\mu\nu}[/latex] tensors. Naturally your going to need to look at the Ricci tensor and stress momentum tensor. We do have a profile that does an excellent job of matching galaxy rotations curves. It is the Navarro Frenk white profile. Yes it uses dark matter but the important part is the how the formula handles the mass distribution.

Ive looked over your papers. Truthfull the questions being asked are valid ones. Particularly since your attributing properties to spacetime that dont exist under GR. At least not under SO(1.3) Lorentz group. The equations thus far presented don't properly define how your value a comes about. Either way It still apears to be Keplarian still. As added energy in GR adds to mass curvature. This is different in the NFW profile and I don't see a comparison to the 21cm line. As I don't see those details within the paper...

Lol no prob. I'm going to add one other concept to think about. Take neutrinos which are weakly interactive. Neutrinos can travel through a thousand light years of solid lead without a single interaction. Now the lead certainly counts as a medium but to the neutrino that medium essentially doesnt exist. Same thing applies to fields. If a particle doesn't interact to type of force. Example the neutrino which doesn't interact with the electromagnetic force. The electromagnetic field doesn't exist to the neutrino. A field is an interaction map

Cross posted see my last reply. However lets add statement to hopefully help on guage bosons. First we will use the magnet as the source of the field you mapped. You mapped the interaction strength at each field coordinate. That interaction is mediated by a transmitted guage boson. Now replace the Newtonian scale magnet with some object that doesnt interact with magnets. In this last example there is no interaction. This means that no guage bosons are being transmitted from source to measuring reciever. The field you mapped on the previous example now has a zero value at each point. See the danger in thinking of tbe field itself as a medium?

In the magnet example source is the magnet in the center. The magnet your measuring the interaction is the reciever. Between those two magnets the interaction is mediated by the transmition of guage photons. Your field is the mapping of the interaction influence. In this exampke the amount of transmitted force. Which if you do it correctly can be assigned a vector value at each measurement coordinate.

The strength of the field from source to reciever is transmitted by virtual guage photons in units of quanta. For electromagnetic force or any electromagnetic interaction. Here this wiki will help https://en.m.wikipedia.org/wiki/Gauge_boson

So here is a home experiment for you. Take a graph paper. Assign a coordinate system to said graph. Now take a magnet place it at the center of that graph. Take another magnet attached to a Newtonian scale. At each coordinate assign the amount of force between the two magnets at each coordinate. Youve just modelled the magnetic field Yes you keep thinking the influence from a to b requires a medium to travel to. This incorrect. This is precisely what Relativity taught us as being incorrect. Particles can travel from a to b without any medium or fluid.

No spacetime curvature isnt describing the electromagnetic field. As per se. Though the electromagnetic field as well all other fields are influenced by spacetime curvature. One thing to clarify here on the scale of the universe the electromagnet field is considered neutral. Its influence on average is insignificant and neglibible. I can see this is still going over top your head. Lets try this angle. Lets say I want to describe and model amount of influence of some random influence has without naming that influence. The first step is to find some way to describe the geometry of that influence. So I assign points of reference or coordinates at points in a given volume. Now that we have a baseline map we can add the influence. A handy tool is a vector field. So prior to adding the influence we assign a baseline vector component to our assigned coordinates. The influence we add will affect each of those vectors. The strength of influence will most likely be strongest closer you get to interaction source. Any field involving force can be modelled via a vector field. Temperature in a given volume however is more convenient to use a scalar field. This should make it clear that a field is more akin to a map. The particles that interact with that field map is your medium. Not the map itself

It seems to me you tend to think objects instead of relations. When you measure field strength at any particular point your not measuring a field as per some object. What your measuring is how much influence that field has upon objects or particles. Lets take for example spacetime curvature. Many people get confused into thinking this is shape of spacetime near a mass. However it is a descriptive of relations between the stress energy tensor vs geometric change due to time dilation and length contraction. I've watched your posts for quite some time. The dependancy you have on visual objects tends to extremely limit your comprehension. Unfortunately the only way to truly understand field theory is to understand what relations are being mathematically modelled and how differential geometry models those relations into a coordinate system. Or in the case of tensors a coordinate independent system. For example the term topography doesn't necessarily describe some physical object. It can and does describe physical relations and interactions

If your dealing primarily with adder circuits there is another methodology. In binary devide and multiply by two operations can performed with fewer clock cycles by bit shift left or right instructions. This requires less clock cycles than multiply or devide operations. Though for the exponent value you asked about you will need to significantly need to add registers

The flowchart you posted is excellent Studiot

Yes density data is a vital piece of information. We can utilize the ideal gas laws to help determine the density at a particular time period via the average blackhody temperature at that time period. That being said there are other supportive pieces of data that are also involved. One being tbe cosmological redshift. The problem with using redshift however is knowing the emitter frequency. Without a known emitter frequency we cannot calculate the amount of redshift. Thankfully various elements such as the most abundant element hydrogen has unique spectral frequency bands. We have excellent data on using spectronomy on all known element's and can readily identify those elements via spectrography. The frequency bands will be redshifted when looking at those elements at far distances. Another tool is luminosity to mass relations. (Formula in the luminosity section on the redshift article) Unfortunately no single method is usable to determine distance. Through considerable experimentation and research scientists today have numerous tools that work extremely well to fine tuning distance measures. These are under the category the Cosmic distance ladder. This wiki link has a decent coverage https://en.m.wikipedia.org/wiki/Cosmic_distance_ladder

You seem to have the wrong notion of time dilation. Time dilation isnt merely some mechanical clock slow down. It doesnt matter what type of clock you use and has nothing to do with the particles or components that make up the clock. For example the Earth surfaces is bombarded with muons. Those muons have too short a mean lifetime to be able to reach the Earths surface. The only possible way they can do so is time dilation which has nothing to do with how we measure it. It is something that will occur regardless if there is an observer or not. This is one example of the reality of time dilation. Another aspect is measurable gravitational redshift. The twin paradox itself is an artifact of the coordinate system used in the paradox. It is solvable using a different coordinate system. The age of both twins are effected. The solution is in this article which details numerous poorly misunderstandings in GR due to various coordinate system artifacts. http://www.blau.itp.unibe.ch/newlecturesGR.pdf "Lecture Notes on General Relativity" Matthias Blau Curvature as mentioned is measurable. We even have a satellite doing just that near Earth. https://en.m.wikipedia.org/wiki/Gravity_Probe_B https://en.m.wikipedia.org/wiki/Time_dilation_of_moving_particles The last link details several experiments on how time dilation affects the mean lifetimes of particles

Actually because EM radiation falls off in strength the universe and even most galaxies are considered electromagnetically neutral. Even a magnetars electromagnetic influence isnt felt at any significant stellar distance. How galaxies form into its stellar formation is a combination of gravity, rotation and whats called density waves. The spiral arms are in a sense misleading. Those are simply regions where the stars are brighter than the stars between the arms which are extremely difficult to see. The stars inside the arms are typically younger stars. For an analogy we will simplify how density waves work. You do this at home. Take a tub of water. Place in that tub semi buoyant particles doesnt matter what you use. Now start stirring the water in the same continous direction (circular). The water will form a whirlpool. The particles will flatten out and follow the whirlpool path. The same density waves work on both galaxy rotation for spiral galaxies as well as tbe rings of Saturn. https://en.m.wikipedia.org/wiki/Density_wave_theory

No in actuality we can calculate the proper distance when the object first started emitting light and the proper distance today of any stellar object. Granted the distance today requires assumptions that nothing out of the ordinary occured. The universe doesnt appear larger in the past. You can't see an edge of the observable universe at any point in time. That isnt how it works. The furthest back we can see is shortly after the dark ages at the surface of last scattering. That CMB surrounds us today. No matter which direction you look in or how far you look you will see the universe around you. Your merely at the center of the observable universe due to your current location. You never have a god like view of the full universe in a particular direction as were inside the universe. You can only calculate the size of that observable portion based upon observation and redshift data with other methods such as the Sache Wolfe effect and stellar parallax. With that data we extrapolate the proper distances. The FLRW metric initially uses commoving distances ( in the past we used conformal distances prior to the cosmological constant). These in turn allow to calculate the proper distance then and today. The calculator in my signature does precisely that. As far as the observable universe it will always be a sphere. When they state the universe is flat. They are not describing its shape. They are describing its actual density compared to its critical density. This is in actuality a thermodynamic relationship that affects light paths. A perfectly flat universe without the cosmological constant is one that is static. Yet this is in itself unstable. Our universe is extremely close to flat with a cosmological constant so will continue to expand. I suggest reading these two articles I wrote a few years back they will help. http://cosmology101.wikidot.com/redshift-and-expansion http://cosmology101.wikidot.com/universe-geometry Page two of the last article details the Flrw metric and how curvature affects light paths (in effect the null geodesics on a universal scale GR) Here is page two on the geometry article. http://cosmology101.wikidot.com/geometry-flrw-metric/ I broke this section down to the 2d 3d and 4d metrics on all three curvatures. Positive,negative and flat cosmologies. The formulas on this page is the calculations for commoving distances.

Incorrect. You can see light from further than the age of the universe. This is due to expansion. This is tricky for many to understand how light can reach us at distances greater than the age of the universe. What happens is that the light has already travelled part of the way. Yet during the light path the distances on the path already travelled and ahead of the light path continues to expand. Locally though that expansion per Mpc is miniscule so light will continue to make headway. The observable universe is significantly larger than 13.7 Gly in radius. This expansion affects the light path wavelength causing cosmological redshift

Thats understandable. While you think on that we can do other types of fields. For example we can alternately assign each point in space a vector value or a scalar value ( temperature for example). The vector value is commonly used in force type fields. Ie electromagnetic. Or even just mapping the amount of force at any given location The above should help understand why differential geometry is so important in physics

Good question to answer I'll take a textbook description of the electromagnetic field. Assign every point in space a virtual photon. (Sometimes called a photon field) For each field you use the guage boson in the same manner. Gluons for the strong force. Higgs boson for the Higgs field etc. For gravity we usually just use test particles. Each virtual photon is assigned a coordinate. When you add an influence you cause a change in coodinate distribution. Example curved spacetime

Think of topography as a set of coordinates. In Euclidean geometry coordinates are Cartesian much like a flat map. Now think of coordinates that curve around a sphere. (Polar coordinates). Those are two of the more common. String theory however doesn't stop there. In some of their dimensions the coordinates can be distributed in a rotational or even a tightly curled fashion. Mathematically the number of dimensions to describe an object or interaction completely is indicative of the number of coordinates to describe each location. This is the topography baseline when you add a particle influence you alter from the topography baseline. Your little bumps lol. Everything in physics can be described in geometry which is why differential geometry is so important

Not bad I wouldnt personally think of a field as a medium. However thats more a semantic reasoning. The field itself is more a topography map if you will. For example if the field has zero energy the field is still there but you will have no medium influence. One of the difficulties many people have is the tendency to think in terms of matter and solids. In actuality what constitutes matter is only fermionic particles. Yet these particles are essentially excitations. When you get down to it a particles wavefunction is far more an accurate descriptive. For example the term mass gives many people a great deal of grief. So lets look at it. We all know the equation f=ma. However most fail to recognize the meaning and definition of mass. "Which is resistance to inertia change." So what does this have to do with fields? Lets take an arbitrary particle. Lets first assume that particle has no rest mass. (Invariant mass). Example being the photon. Although the photon mediates the electromagnetic force. It doesnt directly interact with the electromagnetic field in terms of binding energy. A binding energy would create resistance. However the photon does interact with the electromagnetic force. Now lets look at a massive particle. For simplicity this particle only binds to one field. This binding causes a resistance to inertia change. Some particles interact with several fields and gain invariant mass from each field interaction. So in the above thinking a field can have medium like characteristics. However as energy is a property and doesnt exist on its own its more accurate to state that the particles that mediate and interact with the field topography form the medium. Ps I will give +1 lol

Thats a possibility. Well done in noting that by the way +1

Not quite true, there is some conjecture we are still in a lower false vacuum state. In particular in regards to the non zero vacuum component of the Higgs field. As far as modelling the cosmological constant or Higgs field another method is the scalar equations of state.