Mordred

No apology needed it was an excellent question and thanks Eise for the Nitpick lol They are invaluable in understanding the higher physics, helps keep one from travelling endless garden paths

Yes you can find an SR solution in all the examples of that article, however that is under the restrictions mentioned by Markus. If you can keep each reference frame approximately Euclid... ie at rest example is under the Schwartzchild example the key clue is in the term Proper acceleration this correlates to proper as opposed to coordinate time. Proper time is a clock that follows the world-line. See here on proper time and note the statement https://en.wikipedia.org/wiki/Proper_time In the SR example for Schwartzchild on this link they also mention you can see the requirement of maintaining a rest frame is preserved. However that is a different situation than say comparing two coordinate times to one another. https://en.wikipedia.org/wiki/Coordinate_time

The photon is an invalid frame of reference to begin with. The separation distance will correspond to no time passing [latex] ds^2=0[/latex] we know this is incorrect as it must take time to travel from A to B. So we call this a null geodesic. The photon can never be set as the observer due to this null result of the separation distance between event and observer. The null term specifies that the particle has no valid observer frame and only observers with mass can determine its spacetime path. A massless object's observer point of view would correspond to being everywhere at once. That is obviously invalid as a reference frame.

Yet time must pass in order for the photon to come into existence. So must mass for that matter. As mass is simply resistance to inertia change by physics definition it is a property of a state not an object or substance. the formula that equates mass should be the clue f=ma... this applies in all physics theories GR, string theory QFT etc etc...The definition never changes. It is a garden path to nowhere to think of time as anything other than a measure of rate of change or duration. It is also a property. The property that corresponds to rate of change

Once you measure a state that state is no longer in superposition which a is probability term of all possible states. Take a coin, the coin has two states heads or tails. You flip the coin the probability of either heads or tails landing is in superposition. Once you measure the coin you have determined the result it is no longer in a superposition state but a determined state. This can be applied to the polarity of the possible states of the entangled particles either spin up or spin down in the same mannerism as the coin flip. The entanglement event determines the range of possible states along with the particles quantum numbers. By measuring one particle of the pair you automatically know the other particles state. Another common example is two coloured balls one red, one blue if you place one of each in two separate bags they are in superposition as to the possibility of being either red or blue in a particular bag. Once you open one bag then you know the result in the other bag. The balls are no longer in superposition but are now determined

This can get a bit tricky to explain. One of the key distinctions of SR to GR is the rest frame. The rest frame is a Euclidean frame of reference in which within the bounds of that frame of reference the Galilean transformations apply. In essence our Newton laws of inertia as well as Pythagoras theory. This is point 1 Markus makes in the above. One must be able to define within a frame of reference of the event or observer that is approximately Euclid. Point two is the symmetry relations between the observer and emitter. A change in observer or reversal of vector direction amounts to a change in sign between the spatial and temporal coordinates. This is easy under constant velocity however tricky to maintain under acceleration. However it can be done by performing a hyperbolic rotation or transformation instead of the linear transform of the Lorentz group. In essence it amounts to a rotation of the Lorentz group. One can find examples of how to apply SR to a constant acceleration of which I will provide here. http://www.physik.uni-leipzig.de/~schiller/ed10/Uniform relativistic acceleration.pdf It doesn't get into the groups themselves however gives the transforms which will make it easier to understand rather than trying to explain how its shown in gauge groups. Point three is well described in Markus post. Now where GR handles better than SR is in terms of curvature. It has no requirement of a rest frame that approximates a Euclidean geometry. So in a given volume of strong curvature it is a better tool. However one can restrict the volume of the rest frame under SR to a tight enough region that can approximate the Euclid frame. So SR can be used in much the same way as GR to the same results, however when dealing with curvature it is better to use GR for the reasons above for large regions in particular. One way to see this is to look at the following. [latex] g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}[/latex] this is a GR class of solution called the weak field limit or Newton limit. Under this SR will work fine. It will handle the vast majority of astronomical events such as freefall towards planets and stars etc. As you can see it applies the Minkowskii tensor that is used in SR. Now a situation such as the strong field [latex] g_{\mu\nu}=g_{\mu\nu}+h_{\mu\nu}[/latex] notice we have no Minkowskii tensor this is a situation where it is not reasonable to approximate a Euclid rest frame due to extreme curvature such as outside the event horizon of a BH as one example. On an aside not this is one of the reasons why QFT and String theory uses SR primarily in terms of the Feymann diagrams one has a rest mass for the particle and its locality is easily handled via a Euclid frame. However when dealing with a multi-particle system it oft becomes more convenient to step into the GR methodologies. In essence GR handles variations in spacetime geometries better than SR

One further detail, if the surrounding blackbody temperature outside the BH is hotter than the blackbody temperature of the EH. Then the BH will gain mass. This lends itself to the rate a BH will lose mass, as a smaller EH surface area is hotter it will lose at a rate faster rate with a given surrounding blackbody temperature. CMB temperature today being 2.73 Kelvin it would be highly unlikely any BH larger than the mass of the moon if memory serves correct on the calculations will radiate Hawking radiation at todays CMB temperature. Going from memory on the BH mass, so might be a bit off.

Well I had hope we weren't going down the Eather path but apparently it is the main aspect of your hypothesis. Unfortunately this idea is common to the Speculation forum LMAO. Ah well lets get at it. I will state that experiments looking for eather have been performed, science never takes the word of any physicist at verbatim and this includes Einstein. An eather has an effect in so far as it will create a drag effect. This is part and parcel of the 1 way tests on the speed of light. It doesn't matter if the eather is luminiferous or some other form. The drag effect would be measurable by comparing the symmetry of light travel times in different directions. All known tests have shown a null result. One of the solutions to the Einstein field equations, is the vacuum solutions. This is a state where one removes all forms of particles. We know that one can have quantum fluctuations for this state however this isn't much of a problem in large scales. The term spacetime fabric is a misnomer in so far as spacetime is simply just a geometry.

Well I'm going to ignore the flat Earther statement I hope others do as well as it isn't relevant to the thread topic. I will also consider that your descriptive lacks the terminology to more accurately describe your hypothesis. So lets try this to confirm. A better way to describe your eather term is to use the term field. A field is a collection of values, functions, coordinates, events etc on a coordinate basis. Now your correct GR doesn't get too detailed on the quantum level, however QFT does and it uses relativity. Your spring analogy is a common descriptive of the Heisenburg Uncertainty Principle, this is also already incorporated into the QFT treatments. Many people do not realize that a field is also affected by the uncertainty Principle as well as the particle being measured. So what you are describing in terms of spacetime and geodesics has an influence at the quantum level however this effect is largely washed out on the macroscale. Atempts have been made unsuccessfully to measure the granularity of spacetime however this may simply means we haven't an adequate test. An unsuccessful result does not necessarily mean the theory of spacetime granularity isn't present but it does place additional doubts as to the scale of the granularity based on the HUP calculations.

Perhaps the mathematics will help understand the quoted portion. This calculator uses a specific formula that correlates how matter, radiation and DE [latex]\Lambda[/latex] evolves in terms of mass/ density as the universe expands and then applies their equations of state to calculate how the universe has expanded in the past and how it will expand far into the future. I only did 20 steps and set it to use the Planck 2013 dataset for the matter/radiation content. [latex]{\small\begin{array}{|c|c|c|c|c|c|}\hline T_{Ho} (Gy) & T_{H\infty} (Gy) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}[/latex] [latex]{\small\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&z&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)&V_{gen}/c&V_{now}/c&V_{then}/c&H/Ho \\ \hline 0.001&1090.000&1089.000&0.000373&0.000628&45.331596&0.041589&0.056714&0.000856&21.023&3.148&66.182&22915.263\\ \hline 0.002&608.566&607.566&0.000979&0.001594&44.853035&0.073703&0.100794&0.002319&14.843&3.115&46.232&9032.833\\ \hline 0.003&339.773&338.773&0.002496&0.003956&44.183524&0.130038&0.178562&0.006124&10.712&3.068&32.869&3639.803\\ \hline 0.005&189.701&188.701&0.006228&0.009680&43.263304&0.228060&0.314971&0.015819&7.842&3.004&23.561&1487.678\\ \hline 0.009&105.913&104.913&0.015309&0.023478&42.012463&0.396668&0.552333&0.040144&5.791&2.918&16.895&613.344\\ \hline 0.017&59.133&58.133&0.037266&0.056657&40.323472&0.681908&0.960718&0.100464&4.298&2.800&12.036&254.163\\ \hline 0.030&33.015&32.015&0.090158&0.136321&38.051665&1.152552&1.651928&0.248752&3.200&2.642&8.455&105.633\\ \hline 0.054&18.433&17.433&0.217283&0.327417&35.002842&1.898930&2.793361&0.610939&2.386&2.431&5.800&43.981\\ \hline 0.097&10.291&9.291&0.522342&0.785104&30.917756&3.004225&4.606237&1.491191&1.782&2.147&3.827&18.342\\ \hline 0.174&5.746&4.746&1.252327&1.874042&25.458852&4.430801&7.300157&3.620922&1.337&1.768&2.364&7.684\\ \hline 0.312&3.208&2.208&2.977691&4.373615&18.247534&5.688090&10.827382&8.733318&1.026&1.267&1.301&3.292\\ \hline 0.558&1.791&0.791&6.817286&9.184553&9.242569&5.160286&14.365254&20.669840&0.875&0.642&0.562&1.568\\ \hline 1.000&1.000&0.000&13.787206&14.399932&0.000000&0.000000&16.472274&46.278944&1.000&0.000&0.000&1.000\\ \hline 1.791&0.558&-0.442&22.979870&16.668843&6.932899&12.417487&17.112278&95.281180&1.547&0.481&0.745&0.864\\ \hline 2.961&0.338&-0.662&31.510659&17.154169&10.671781&31.602098&17.220415&168.603314&2.486&0.741&1.842&0.839\\ \hline 4.896&0.204&-0.796&40.170941&17.267296&12.969607&63.498868&17.267296&290.007398&4.083&0.901&3.677&0.834\\ \hline 8.095&0.124&-0.876&48.860612&17.292739&14.364429&116.275356&17.292739&490.769217&6.741&0.998&6.724&0.833\\ \hline 13.383&0.075&-0.925&57.557046&17.298283&15.208769&203.541746&17.298283&822.704529&11.141&1.056&11.767&0.832\\ \hline 22.127&0.045&-0.955&66.254768&17.299620&15.719539&347.823873&17.299620&1371.505677&18.418&1.092&20.106&0.832\\ \hline 36.583&0.027&-0.973&74.952986&17.299815&16.028491&586.370846&17.299815&2278.857001&30.451&1.113&33.895&0.832\\ \hline 60.484&0.017&-0.983&83.651102&17.299968&16.215356&980.768127&17.299968&3779.010092&50.345&1.126&56.692&0.832\\ \hline 100.000&0.010&-0.990&92.349407&17.299900&16.328381&1632.838131&17.299900&6259.261851&83.237&1.134&94.384&0.832\\ \hline \end{array}}[/latex] From this I can give you the rate of expansion at any redshift value, the time signal was sent from that redshift in proper distance, the temperature at that location and time the distance to the various horizons etc. This calculator uses the formulas on this page http://cosmocalc.wikidot.com/advanced-user The [latex] H/H_0[/latex] relation is the rate of expansion then compared to rate at a particular then. The formula is on the previous link and uses the matter, radiation and DE content. The term stretch is simply the inverse of the scale factor a, coincidently the average temperature is also estimated via the inverse of the scale factor. Forgot to add Stretch 1 column is today. S=1090 is time of the CMB though the calculator can go further back in time, However not as far back as [latex] 10^{-43} [/latex] a limit was placed due to the inflationary period. Here is as far back as it will go [latex]{\small\begin{array}{|c|c|c|c|c|c|}\hline T_{Ho} (Gy) & T_{H\infty} (Gy) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}[/latex] [latex]{\small\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{gen}/c&H/Ho \\ \hline 20000.000&0.000001873&0.000004&46.176564&0.002309&0.003133&205.563&4111262.687\\ \hline 4859.562&0.000026708&0.000049&45.978633&0.009461&0.012854&60.203&292559.510\\ \hline 1180.767&0.000326239&0.000552&45.385041&0.038437&0.052400&22.101&26096.200\\ \hline 286.901&0.003260744&0.005135&43.945393&0.153173&0.210639&9.774&2804.152\\ \hline 69.711&0.029010535&0.044197&40.852331&0.586028&0.822534&4.674&325.817\\ \hline 16.938&0.246807722&0.371763&34.481457&2.035729&3.009093&2.287&38.734\\ \hline 4.116&2.060351110&3.061435&21.564722&5.239755&9.245731&1.143&4.704\\ \hline 1.000&13.787205857&14.399932&0.000000&0.000000&16.472274&1.000&1.000\\ \hline 0.243&37.174601593&17.245130&12.301284&50.627128&17.245130&3.437&0.835\\ \hline 0.084&55.554649839&17.297731&15.050146&179.402832&17.297731&9.923&0.832\\ \hline 0.029&73.951681546&17.299856&16.000313&552.424303&17.299856&28.739&0.832\\ \hline 0.010&92.349406808&17.299900&16.328381&1632.838131&17.299900&83.237&0.832\\ \hline \end{array}}[/latex] see time in Gy column S=20,000

That part is fine in the sense of gathering information as to the behavior of expansion. However none of those listed items can be the cause of the initial expansion prior to their existence Obviously another process must have existed if expansion occurs before stars existed. Lets recap and start with the term smallest possible denominator of some volume. Lets start with a cm and set 1 cm at value one. [latex]\frac{1}{10^{\infty -1}}[/latex] does this qualify ? What fraction of 1 cm is the smallest possible portion ? The other question that can be asked is How many dots does it take to cause a measurable displacement ? A Planck length is the theoretical smallest measurable quantity how many dots to cause a 1 Planck length of displacement ? (be easier if I use the correct term Action) Which is the reason behind the Planck unit 1 unit of action see here https://en.wikipedia.org/wiki/Planck_constant Also read here and how it can relate to the spacetime geometry. https://en.wikipedia.org/wiki/Action_(physics)

That makes no sense when you start with a universe prior to any stars, cities, people etc etc existing yet expansion occurs prior to any of the above list.

The smallest common denominator is meaningless. What makes the dot itself the smallest possible denominator ? other than mere say so ? What makes it smaller than any other point-like particle with indiscernible volume ? How do you define the limits of this supposed dot in terms of a region ? How fast can it change location ? What causes more dots to form ? Why do the dots cause expansion ? I can go on forever as you haven't described a dot as anything other than the lowest common denominator

Well unfortunately this is your model. So we cannot define this dot for you. This is your visualization and we have nothing to work from in terms of your descriptive. For example the first question is What distinquishes this dot from a particle ? A quasi particle such as the Inflaton used in Chaotic eternal inflation or a curvaton, soliton or quantum spin foam in QFT ? Each of the above has mathematically defined characteristics that correlates what they interact with, how they behave when they interact with other fields etc etc. They have been defined in some relative mathematical way in order for the model to apply them.

Then you will never be able to develop a model with mathematics to apply any formula that uses these dots to show expansion. You must define a dot in some way to build a model from them

What size ,volume, mass, energy does this dot possess? That is what I mean by mathematically defining a dot. What forms the dot ? What is it comprised of Pixie dust?

Let me point out a simple detail. I will always stress proper terminology and correct misconceptions in any post regardless of how long a poster has been a member. I would do so even if that poster is a PH.D. It is fun to toy model however there are rules required by this forum when doing so. See the guidelines on the pinned threads at thee top of the Speculation forum page. Your model still does not address the problems I mentioned even with the added descriptives. The simple fact is that you have a preferred direction to expansion/inflation. This does not match observational evidence, with which is in very strong agreement as to its accuracy in the professional scientific community. This evidence is supported by the Planck CMB datasets. Now one aspect you completely missed is the formula I provided does precisely what you were looking for (its also the formula that the majority of all inflationary theories work from) It does correlate how a mass/energy field can expand or contract. However it still won't do you much good as you have not shown any means of defining what a dot or a pixel is in terms of mass/energy etc. You haven't mathematically defined either object. You can find numerous variations of that formula throughout this article detailing studies on inflation and the comparisons to observational evidence of the major different inflationary models. https://arxiv.org/abs/1303.3787

I lost count long ago on how many posts I've seen claim their model as fact. The most annoying part is that physics itself never claims any theory as fact. They only claim to the best of our current understanding. I'm actually going to use the OP's pixel descriptive to provide an accurate analogy to explain what the observational evidence of expansion supports in terms of the Cosmological Principle. First step lets define a Pixel as simply a geometric volume (amount of space with a given unit of measure). Lets set an arbritary value that each Pixel represents 1cubic parsec which is a standard unit under cosmology. Lets then set the number of Pixels as [latex] 10^10[/latex] on each coordinate axis. ( completely arbitrary numbers...). Now then this represents the size of the universe as we measure it today. Now instead of changing the number of Pixels. (keep the number precisely the same) simply decrease the size of each Pixel as you approach T=0 backwards in time. Do not change the coordinate location of any Pixel on graph but simply recognize that the volume of each Pixel is decreasing in length scale on the X, Y,Z coordinate axis. Now this will represent a Homogeneous and Isotropic expansion that has no preferred direction or origin point (preferred location) If you pick any number of arbritary pixel. The angles will not change between any two or more Pixels. This is what we observe with expansion, a changing volume THAT DOES NOT CHANGE THE ANGLE between any number of reference points. An expansion of a volume that radiates outward from a central point will not preserve the angle between reference points and the way the angles change will provide a point of origin. Now take this a step further within each Pixel we have N number of particles that are interfering with each other. They are doing so in random directions where the average direction sums to zero. No preferred direction of the pixel volume of gas, Much like Brownian motion. It would be a natural consequence that this type of multi-particle interaction will naturally lead to an expansion of that gas. The tendency for particles to remain bound to one another will fight this volume change ie if the binding potential exceeds the average motion of the gas, then the volume will collapse. Now lets define the binding potential energy as gravity and this can be described as the gravitational field potential energy. The particle motion of matter as the kinetic energy term. We have no referred location according to observation so we can then describe this as a charge-less scalar field. A charge is a vector quantity. Why surprise surprise we already have a formula that describes this. see the scalar field model formula on this link https://en.wikipedia.org/wiki/Equation_of_state_(cosmology) Please note that I just described how a matter only universe without dark energy or radiation can expand or contract while preserving a homogeneous and isotropic expansion with no preferred direction that also correlates to zero pressure per mass density. equation of state w=0. As per the link above...

Correct the mean free particle path of the photon prior to the surface of last scattering (CMB) due to the opacity of free electrons prior to stable formation of atoms is roughly [latex] 10^{-33}[/latex] metres. Once stable atoms formed the mean free path of photons becomes infinite in possible extend. Space is a term that literally means the amount of volume. Look up the definition of space. Space is not a medium. Motion is not a requirement of time. I can measure the amount of time a rock stays a rock without changing its composition or location. Motion is a vector quantity and temperature can change in value in a given time frame at the precise same location. Temperature is a scalar quantity. Energy is not a fabric or any other form of substance. It is a property of any field, object etc to perform work. Ignoring the proper physics definitions will not allow your model to progress far. Note to other readers, OP has reached his 5 post first day limit. Which after today will no longer apply.

Ok last response confirms that you have an inhomogeneous expansion ( a preferred directional component) with expansion radiating outward from a central point. I can promise you that this will not match any observational evidence of how expansion occurs.

This thread is in essence a duplicate of another thread I have already moved from the mainstream QM section to the Speculation forum.

tAlright first off there is no accurate facts in any of the above descriptive. For starters non of the terminology usage is accurate to the scientific definitions of those terms. So lets address this first. Space is simply volume, it in itself is not a medium. Energy is the ability to perform work it is a property of a system not a substance. Dimension under physics and mathematics is any independent variable for example under 3 dimensions each coordinate axis is an independent variable. One can change location on the x axis without changing the coordinate value of the Y or Z axis. Now terminology and poor descriptive aside, from what you describe above it sounds like you visualize an expansion radiating out from a central point. The point of the singularity with your energy waves radiating outward. However this will not match the measured observation of how expansion occurs. Expansion follows the cosmological principle with strong observational support. See here for a brief descriptive of the Cosmological Principle. Also motion is not required for time to pass. Time is also a measure of an objects duration in the same state and not just a measure of rate of change.

Well I seriously doubt total accuracy in any analogy is ever possible lol. However in any scattering event the mass energy conservation applies. This includes the invariant (rest mass) and particle momentum terms. Total mass/energy in = total mass/energy out. This conservation law as well as those others such as charge conservation, flavor, lepton, isospin etc is what determines what possible particle decays can occur.

! Moderator Note This thread with the very little detail and highly speculative nature certainly does not qualify under the Mainstream QM section. Model conjectures and personal theorem is more appropriate to the Speculations forum provided they follow the guidelines of such. Please review https://www.scienceforums.net/topic/86720-guidelines-for-participating-in-speculations-discussions/ Please note a Higher ranking member of the Moderator staff may decide upon additional measures

Your welcome a rule of thumb is never listen to pop media based articles. They will invariably confuse you as to the true nature of a theory. The language of physics is mathematics. The best way to understand any physics theory or model is to study mathematics. In particular Calculus, Differential and linear geometry. So for example in your opening post time is one dimension particularly if its assigned as a coordinate axis such as in GR. Space is a volume so typically 3 dimensions. Matter however is tricky. The common technique is to describe how matter interacts, charge is one example so the dimensions will correspond to a term called the effective degrees of freedom. However in field theory these degrees of freedom will correspond to the number of possible quantum numbers a particle can have. For example a qluon can have a spin, for one degree of freedom, a color degree of freedom, and 8 degrees of freedom under the SU(3) symmetry group. Each degree of freedom is an independent variable. ie a dimension. Now lets look at another common term. Compact dimensions, mathematically when you compactify you have some variable that has an infinite range, well any infinite quantity has a finite portion. When you compactify a variable your specifying a limit to a infinite quantity and restricting this to a finite portion to avoid the singularity conditions associated with infinite quantities. Hope this helps with your studies its more for an FYI to yourself and other readers that commonly get confused by the terminology associated with dimensions. Edit: probably one of the easiest ways to understand degrees of freedom is the number of independent ways any object (physical) or mathematical which includes any number, set , matrix, tensor, scalar, and vector etc ( An object in mathematics can be construed as any representation ) can move or vary without affecting any other object. With the above you should see the connection to the term dimension.