# Mordred

Resident Experts

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7

1. ## What is Space made of?

FAQ article development, feel free to ask questions or make suggestions. (I'm still working on the Einstein field equation section. Probably keep that portion seperate to minimize length) This question is amongst one of the most commonly asked questions in relativity. Numerous articles both in pop media and peer reviewed articles refer to terms such as space time fabric, space time curvature. This leads the new learners with a common misconception that space has some mysterious fabric or material like property. To answer this properly we need to describe a few principles. A) gravity influences mass B) energy is a property of particles, or physical configurations such as feilds. Energy does not exist on its own. C) space is defined as a volume only. That volume contains the standard model particles and feilds. It is not something form of ether. In GR space is mapped in an arbitrary coordinate system. Without the time component the coordinates are in 3d. D) spacetime is any metric that includes the time component as a vector. This is the 4th dimension, in GR the time component is treated in coordinate form. E) General relativity is a coordinate system metric. This coordinate system makes use of manifolds. Which is a topological space that is resembles Euclidean space at beach point. For example a Euclidean space (flat space), can undergo a homeomorphism to curved space via relativistic effects such as inertia and mass to an observer. The rubber sheet example is one such homeomorphism. http://theory.uwinnipeg.ca/users/gabor/black_holes/slide5.html A good YouTube video is http://m.youtube.com/watch?v=MTY1Kje0yLg Keep in mind the rubber sheet analogy is just that. An analogy, it was never intended to state that space time is a materialistic fabric or ether. A classical example of a homeomorphism is the coordinate change from Cartesian coordinates (Euclidean flat space) to polar coordinates. (Curved, spherical geometry) https://www.mathsisfun.com/polar-cartesian-coordinates.html http://en.m.wikipedia.org/wiki/Manifold http://en.m.wikipedia.org/wiki/Homeomorphic Now with those in mind, we find that spacetime curvature is a geometric coordinate relation of how the strength of gravity influences the particles that reside in the volume of space. In short it is a geometric description of how gravity influences particles not the volume of space. The terms fabric, curvature, sretches are misleading. They are analogies used to explain the change in geometric relations. 2) How is space time created? The volume of space simply increases, space itself is just volume filled with the standard model particles.
2. ## Cosmological Principle

In my spare time I will be writing a series of useful articles to help answer common questions. As these are being designed for forum reference I feel strongly on cooperative review. Here is the first. Please look over and feel free to make suggestions. Any solid contributions will be accorded credit at the end of the final product. (Key note all articles MUST comply with textbook descriptives, they are being designed as teaching aids) $\textbf{The Cosmological principle}$ is defined as "at sufficiently large scales, the universe appears as homogeneous and isotropic." $\underline{Homogenous}$ is oft defined as " no preferred location" $\underline{Isotropic}$ is oft defined as "no preferred direction" Obviously at smaller localized scales we can see numerous examples of systems that are inhomogeneous and anisotropic (planets, stars galaxies and large scale structures). However if you increase the radius of measurements sufficient enough those non uniform regions essentially become negligible or more accurately averages out. A good analogy is look at the surface of a lake. At small scales you can discern waves and ripples. As you increase in height or distance from the lake those non uniform regions become a uniform appearing surface. The cosmological principle works the same way. The scale commonly used is 100 Mpc mega parsecs. Speed of light in a vacuum: $c\ =\ 2.99792458\ \times\ 10^{8}\ m\ s^{-1}$ The parsec (symbol: pc) is a unit of length used in astronomy, equal to about 30.9 trillion kilometers (19.2 trillion miles). In astronomical terms, it is equal to 3.26 light-years, and in scientific terms it is equal to 3.09×1013 kilometers The cosmological principle has an added reward in that complex systems can be modelled as good approximations with far less complicated mathematics. However it should be noted that if measurements and observations disagree with the cosmological principle those metrics become invalid. We're lucky though as the body of evidence fully support the cosmological principle. A commonly referred to example being the CMB. Cosmic microwave background. Although the temperature images look chaotic, the difference in temperature of the blue regions and red regions are roughly 1/1000 of a degree. Certainly supports the cosmological principle. The cosmological principle is of importance in telling us that the Universe did not have an origin point nor is the result of an explosion. This is of primary importance in regards to expansion and inflation. Lets detail this a bit further. Take any number of points, three or more. As the volume of space increases, the same ratio of change will occur between any two points and the angles between those points also do not change. This mathematically is only possible via a uniform change regardless of location. A good analogy is the balloon analogy or the raisin bread analogy. http://www.phinds.com/balloonanalogy/: A thorough write up on the balloon analogy used to describe expansion http://tangentspace.info/docs/horizon.pdf:Inflation and the Cosmological Horizon by Brian Powell The other consequence of the cosmological principle is that the universe cannot have a rotation. All rotating bodies have a center of rotation and rotation imparts a preferred direction.
3. ## Curvature of spacetime by gravity and the flat universe?

As Beecee mentioned the curvature term isn't directly related to a physical shape as per se, but is a descriptive of how the density terms affect the light paths (worldlines). A flat universe means the wordlines remain parallel, while the curvature terms will either cause two worldlines to either converge or diverge.
4. ## Photons & Cosmic Expansion

Answering asked questions is never annoying, dealing with false assertions is. edit: lets qualify that slightly it can get annoying to repeat/repeat/repeat.... the same answers to the same person who makes no effort to learn from those answers. lol not to indicate yourself but in general.
5. ## Photons & Cosmic Expansion

Well your right in so far as photons do contribute to expansion, it is part of the current radiation density term. It simply isn't a major contributor in our current universe time slice. Every particle species contributes to a certain degree, albeit some species less than others. The dominant contributor however in our current time slice is $\Lambda$. However as explained in previous threads the standard model of particles contribution will continuously reduce as the volume increases, while $\Lambda$ stays constant to the point where any deviational evidence isn't sufficient to show a variation due to volume change. Hence as the universe expands $\Lambda$ becomes more and more the driving contributor to expansion. Eventually reaching the point where it will be the only contributor where it can be determined.
6. ## DARK ENERGY IN A NEW LIGHT

Only for the first part of the speculation with regards to the DE portion similarities to a quantum fluctuation process. However once the OP started into trying to connect this to gravity and time, that generosity is lost. Coincidentally Swansont has quoted the relevant section above. Though the OP has several aspects that need correcting in that portion. Anyways parts of that portion can be described by employing the spin 0 propagator Langrangian however I wouldn't expect the OP to have any ability to know of the formula. For the first portion of the quoted section by Swansont one can replace any descriptive of VP with the creation and annihilation field operators of QFT. $A^\dagger A$ for the creation operator and $B^\dagger B$ for the annihilation operator. However this is far too advanced for the OP. I cannot ignore that there is a reasonable starting point to apply some valid mathematics to that portion of the speculation. Now these operators themselves are not particles, they are employed to define quantized states. They are however employed to correlate when field conditions give rise to particle production. ie they connect to how particles pop in and out of existence due to field conditions. For the OP to meet a minimal standard of applying some testable mathematics to support the speculations I would start by first defining your geometry. As a stating point the FLRW metric itself provides a good starting point. $d{s^2}=-{c^2}d{t^2}+a({t^2})(d{r^2}+{S,k}{(r)^2}d\Omega^2)$ $S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}$ You want to include the Hubble and scale factor relation $H=\frac{\dot{a}}{a}$ Then I would look for a good formula that describes a scalar field with the relevant equation of state. $w=\frac{\frac{1}{2}\dot{\phi}^2-V\phi}{\frac{1}{2}\dot{\phi}^2+V\phi}$ https://en.wikipedia.org/wiki/Equation_of_state_(cosmology) the numerator portion correlates to the pressure terms the denominator to the density terms so it matches $w=\frac{P}{\rho}$ However to match the cosmological constant term you must meet the condition w=-1. Now thus far we have not identified any process that causes this scalar field however we have defined a scalar spin zero field under an applicable geometry and provided a relevant equation of state that matches observational evidence. Now I myself can readily apply those operators above to develop possible causes of that scalar field, however this has been done in numerous models already in existence so would really be simply looking at different models in existence. For example the universe from nothing model itself is a good example. Or the zero energy universe https://arxiv.org/pdf/gr-qc/0605063.pdf To the OP I have provided the above to give you a direction to properly develop your model, and to help meet the minimal standards of model development. How your model deviates from those already out there and previously proposed is up to you however you will require the mathematics in order for any chance of success or testability. The above are relevant formulas to get you started. The stage of how that scalar field arises will require further mathematics.
7. ## DARK ENERGY IN A NEW LIGHT

Sounds close enough to the inflaton of chaotic eternal inflation that it has a similar enough viability. Particle production typically comes in particle/antiparticle pairs so you got that part correct (this is true for the inflaton as well). You need not have a higher production in regions of open space vs a higher gravitational potential. As mentioned other processes such as gravity will overpower the cosmological constant. This is advantageous as you can simply model the process you described as a scalar field. This also preserves a homogeneous and isotropic distribution.
8. ## Gravitation constant or not

Here is a clear example see this educators guide to the Gravity probe. Please note the following equation $\Omega=\underbrace{\frac{3GM}{2c^2 R^3}(R*v)}_{geodesic precession}+\underbrace{\frac{GI}{c^2 R^3}[\frac{3R}{r^2}(\omega\cdot R)-\omega]}_{frame dragging precession}$ If G varied as a result of distance then you can bet this would have deviations from the predictions of GR. http://einstein.stanford.edu/content/education/GP-B_T-Guide4-2008.pdf simply because a test does not directly test for specifically G does not mean it doesn't indirectly test G in other related dynamics such as the example above.
9. ## DARK ENERGY IN A NEW LIGHT

Yes the stochastic background is the GW waves that would be relevant to the pre CMB, The BAO B-Modes will result from this background noise and in theory leave a temperature imprint. Bicep2 once thought they had found the B-mode but later research showed that was a misinterpretation.
10. ## Gravitation constant or not

Your formula gives the wrong dimensions so is useless if you cannot get the units right on the LHS and RHS of the equal sign under dimensional analysis then it doesn't matter what the formula is meant to describe. It is automatically invalid. That is a serious mistake also as it is your theory that G varies the onus is up to you to correct not expect some physicist to come along and make your corrections for you. Ignoring the fact that all our astronomy models rely on G being constant in making calculations for spacecraft, orbits etc and correctly predicting those orbits (example location of stable orbits etc) is evidence that G is constant. Yet you have provided none in your model support that this is wrong. agreed huh ??? I agree with Swansont on this one...regardless it still means your equation is invalid.
11. ## DARK ENERGY IN A NEW LIGHT

talk about taking a few tangents lmao, however as mentioned (attempting to provide some tools to alleviate some of challenges faced nowadays with layman understanding cosmology) math in reading articles is always a big challenge. Feel free to ask questions on any of the above I didn't go into any great details but provided useful aids to help understand a very complex topic to fully understand.
12. ## DARK ENERGY IN A NEW LIGHT

To CJWILLI1. Here is a little trick that will help you better understand cosmology in general. Now I will have to skip a huge amount of details however I will explain the FLRW metric advantage over other field treatments. ( Beecee was correct in his earlier assessment of this thread , you have shown every sign of here to learn rather than assert.) The math and numerous models is incredibly daunting when you first start so I will describe a way to simplify cosmology mathematics in general. The first trick is to understand all physics formulas and models rely on what you can graph or plot. This can always apply to a coordinate basis. You asked in an earlier thread where to start well in terms of modelling done by someone in the know how they would start with a coordinate system where one can identify the invariant to observer quantities. However one must be ready for gauge group symmetries to understand that mouthful lol. So lets simplify that first we choose a coordinate basis, well I learned starting from the FLRW metric of the BB model. (granted a few decades ago lmao). A huge advantage of this stage is that it applies (and I cannot stress this enough without shouting) RATIOS. It is not the values that are so important as the ratio of change in graph form. For example a graph with a line regardless of the quantities used to describe the x and y axis will follow the relation y=mx+b. (Lmao you have no idea how many questions I correctly answered by cross multiply and divide when ever given a question of a linear relation within 3 for the four terms are provided when I couldn't recall the correct formula but knew it was linear) On a more complex note the light cone graph for hyperbola functions will follow the graph $\frac{c^2}{g^4}$ see contour plot as per https://www.wolframalpha.com/input/?i=plot+c^2%2Fg^4 anything in the red is faster than light. Now note that wolfram alpha employed the limit of each axis at value 1. The numbers don't matter they are tools to describe the ratio of change of the graph. Simply changing the powers change the graph. see example https://www.wolframalpha.com/input/?i=plot+c^3%2Fg^4 it is the ratios of change that a formula typically encapsulates.((((STRONG HINT symmetries in ratios of change as applied to symmetries to invariant quantities )))) Now notice that in each case we limit that graph to value 1. Any vector quantity we can NATURALIZE to unitary value 1 is a naturalized unit. The actual number we can convert later...so lets use an example under the FLRW metric this metric uses Naturalized units (set graph maximal to unitary value 1) (which requires some correlation to a v ector of length) for example time we give length by interval ct fundamental to under stand GR and SR... this is the 4d coordinate where time is given units of length by the relation ct. so the graph has naturalized units(unitary 1) $c=g=\hbar=1$ these represent the maximal at value 1. (it is the ratio of change that matters. conversions come later) so reread http://cosmology101.wikidot.com/geometry-flrw-metric/ which describes the FLRW metric coordinate system in naturalized units, then (and I will later step you through this as required) however here is the FRW advantage. take the final equation. $d{s^2}=-{c^2}d{t^2}+a({t^2})(d{r^2}+{S,k}{(r)^2}d\Omega^2)$ $S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}$ if you remove the scale factor a then the equations are identical in GR. (note this also applies under that basis the Stretch term S ) the dimensionless value "a" scale factor denotes the conditions of volume from observer now compared to conditions of observer set at group of values then. ThE expansion represented using COMOVING COORDINATES via ratio of change between spacetime event/observer NOW and spacetime observer then. (at time of past measurement) so for Hubble an example is $H=\frac{H_0}{H}=\frac{\dot{a}}{a}$ where the overdot denotes now, so if $a=0.5$ then H is 1/2 the value of today. In the comso calculator graph I posted earlier this is the $H/H_0$ column. This advantage is made possible by ratios of natural units under graph. I can 100% guarantee this will apply in every physics theory you can ever possible study. When you get practiced enough one can start to visualize equations in terms of graphs for many of commonly used equations. Regardless of what each axis represents. (RATIOS) follow this back and the SR Lorentz transformation laws also uses a Ratio of change methodology through the $\gamma$ observer dependent corrections. (The FLRW metric alters the coordinates axis (x,y,z) SR alters coordinate axis of x and time interval= vector coordinate length (ct). the $\gamma$ dimensionless ratio is similar to the scale factor $a$ see Galilean relativity tranformation https://en.wikipedia.org/wiki/Galilean_transformation then look at where $\gamma$ applies under Lorentz invariance commutations (transformation laws). https://en.wikipedia.org/wiki/Lorentz_transformation in all these cases the ratios is what matters under ability to treat and describe under graph.
13. ## DARK ENERGY IN A NEW LIGHT

I've been contemplating such a tutorial, some of my current studies relate in terms of looking at the early universe from the angle of different models. It is the early universe physics which drives my studies into the high energy particle physics regime. (I've been doing a bit of work as I have time in line with this just need to actually formalize how I want to put it together). The trick is connecting the equations of state with correlations to the thermodynamic laws with regards to symmetry breaking processes with the Higg's field. In essence a descriptive of nucleosynthesis As far as detection for GW waves from this era (pre CMB) the corresponding wavelengths are currently beyond our sensitivity range however ALIGO has a remote possibility of catching some signals depending on the wavelengths involved. Were still in the prediction range until we can fine tune by catching a signal. The more GW signals we get the more accurate we can fine tune on them regardless of event. That being said I am still waiting to see if any papers correlate the recent GW findings to fine tune the range of frequencies for B mode polarizations in the baryon acoustic oscillations of the CMB. This would be a huge finding for inflation model fine tuning. Once we can find and confirm the B-mode in CMB data LOL predicting how easily we can go off tangent
14. ## DARK ENERGY IN A NEW LIGHT

No worries I probably would have stated :There is evidence for and against inflation contained in the CMB. Competitive models always abound and inflation isn't conclusive.
15. ## Great article about the 2017 neutron star merger

Anyone have a really big vacuum cleaner with a really long hose lol nice overview its decently done what is really cool is the added details from all the additional detection. I can see this event being studied with a swath of papers and related studies resulting from the data it found in its added details.
16. ## The Robustness of Einstein’s General Theory of Relativity at Cosmological Scales.

Here is the arxiv copy https://arxiv.org/abs/1809.09019
17. ## DARK ENERGY IN A NEW LIGHT

No problem for the learning of the OP here is a relevant paper on how the CMB is being probed for inflationary models. As per inflation article, this is one of the primary questions that originally led to thee concept of seeking inflation. The question is How come the universe is so uniform in mass and temperature distribution. This is the Horizon problem https://en.wikipedia.org/wiki/Horizon_problem here is a quick detail on the flatness problem http://www.astronomynotes.com/cosmolgy/s12.htm Ok so lets break this down and speed up the process. I will run through a quick step by step history of our universe. First we start at $10^{-43} seconds$ we have infinities occurring in our mathematics prior to this, (mathematical singularity conditions) Now so I don't have to describe all the processes involved here is a quick breakdown https://en.wikipedia.org/wiki/Chronology_of_the_universe study this link, I will add to this link that the Higgs field is what provides the mass term to the gauge bosons of the strong and weak field (this is what leads to the Higg's field inflationary model) where inflation is a result of adding the mass terms to the quarks/leptons, W+ and W- bosons. In essence inflation is a phase transition of the electroweak symmetry breaking process. (according to Higg's inflation). Here is a secret, to understand how the universe expands and has evolved the process deeply involves our thermodynamic laws. Our universe history is largely based upon thermodynamic processes as they pertain to each particle contributor. Hence we have equations of state for groups of particles. https://en.wikipedia.org/wiki/Equation_of_state_(cosmology) (needless to say I am being quick in this explanation I could literally go on for hours and hours on what I have learned about the processes prior to the CMB) I don't want to overly confuse you at this stage.)
18. ## Three Dimensional Expansion of everything in the Universe.

Flat Earthers should try dropping two test weights from a sufficient height and distance from each other to measure how those dropped objects approach each other when they fall. If the Earth was indeed flat those same objects would remain parallel. Google gravitational tidal forces there is no point of reconciling with flat Earthers, they are simply plain wrong you are better off ignoring them. Here is another related question why is the Earth and other planets round instead of random shapes ? the answer is it is the most conserved configuration of a multi particle object is round. Once a body gains sufficient mass the gravitational force will cause it to become round.
19. ## Photons & Cosmic Expansion

We account for radiation pressure due to photons in the FLRW equations, as mentioned its density falls off as a function of volume. The ratio its density reduces follows the relation to the scale factor of $\rho\propto a^{-4}$. In the early universe the radiation pressure was sufficient to be the dominant contributor to expansion (this includes all particles whose momentum greatly exceeds its rest mass) such as neutrinos however as the volume increases they simply dilute to the point where they can no longer counter the gravitational terms. The next stage is matter dominant which is harder to explain how it can contribute to expansion but a simple explanation is that as matter starts to form structures its average density decreases so gravity has less of a hold in the regions away from the structure formations. The stage were at now is the Lambda dominant (DE or cosmological constant). see here for more details https://en.wikipedia.org/wiki/Equation_of_state_(cosmology)
20. ## Gravitation constant or not

And yet it has proven to be so incredibly accurate that it is still applicable today with extreme accuracy right up until you get into requiring relativistic corrections. Yet you claim it is not constant despite its incredible successes with numerous mistakes in much of your mathematics. Many of those mistakes have already been pointed out. Even if you had correct mathematics, you still require measurement support. In the mainstream methods the fact that it has been so successful in predicting planetary motion and satellite orbits etc tells a completely different story than your claim. precisely if G was not constant this alone would have reflected in errors in these applications. For example it would have applied in fuel consumption of all those spacecraft. Not to mention determining the correct stable orbits...
21. ## DARK ENERGY IN A NEW LIGHT

There is evidence for inflationary processes contained in the CMB its one of the fundamental reasons its primarily used to determine which inflationary model is more accurate. Granted it is based on indirect evidence as opposed to direct but it is still evidence.
22. ## Gravitation constant or not

You do realize there is a difference between g and the constant G right ? That last link shows the $1/r^2$ relation for g not G. The constant G is kept constant in every calculation in that paper. The mass terms however may vary such as above the mountain example or the equator. The variations in mass distribution affect the mass terms not the constant G.
23. ## DARK ENERGY IN A NEW LIGHT

Let me ask you a question, If you have an expansion force strong enough to cause matter to expand (as I think your implying here) How can stars ,galaxies and planets form ? Yes there is strong evidence that inflation occurred, however there is also some models that argue against inflation.
24. ## Trigger happy mods?

One of the primary reasons I endeavour to be an informative and accurate as possible in my responses. +1
25. ## What are you watching?

same qualities I enjoyed in the Firefly series