Mordred

Well I certainly never bothered too much with block universe conjectures. Either way the original block universe model didn't model reality too well. Is the evolving block universe model any better.? You tell me its incredibly difficult to find decent papers on the subject that has the math formulization. Words only go so far. I certainly have no adherence to the block universe. I already pointed out the problems of the block universe. Which you weren't aware of. Nor were you aware that the block universe was replaced by the evolving block universe. spacetime is also a generic term that includes the SM particles within its volume. How do you think the stress tensor causes the spacetime geometry to change without having a source of mass ie particles etc? It can't you cannot seperate the stress tensor from the metric tensor or the Einstein tensor. What affects one affects them all. Just like pressure affects temperature and density. They are properties that rely on each other. Spacetime geometry relies on the stress tensor. The stress tensor relies on the thermodynamics of the SM particles. You can model each seperately but they will affect each other.

Yes I read those posts before. You only included two physical interpretations. I'm not going to restrict my discussion to two problematic models simply so you can apply a physical aspect to a model that already details all the physical aspects. The physical aspects of GR is inherent in the thermodynamics of the standard model of particles. Nothing more. No ether. No block. No preferred frame. The math above is right on target from the GR view. You seem to want to restrict yourself to SR historical arguments. However SR (Lorentz,Minskowskii) has a strong reliance on simultaneous events and observers at rest. The Einstein field equations is where you should be looking to describe the physical hydrodynamic aspects of spacetime. mass is only one aspect of the stress tensor, you also have flux and vorticity. Your four momentum and 4 vectors are described by the stress tensor. It is the stress tensor that determines the spacetime geometry. With the proper applications. One can calculate how every particle species behaves or moves from the EFE. You can calculate nearly every physical characteristic you want. Temperature, pressure, entropy density, chemical potential, wavelength, mass, energy etc What other physical characteristics are you specifically seeking that isn't included in the above? I certainly don't require some mythical ether nor block universe to describe how spacetime affected the motion of freefalling particles.

You've named the key problem. "deterministic" However deterministic events is also reversible. These type of events the block universe describes rather well. Essentially the block universe can be described by the following. At any particular moment in time, past or future events can be determined by the time reversible hamiltons. Now what about the events that aren't deterministic? good example QM and superposition? The uncertainty principle, quantum fluctuations etc. Now one might argue that this averages out on the macro scale and it does. Right until you include inflation. Anyways describing our universe evolution by strictly deterministic events was too limited an approach. In steps the evolving block universe. a simple few sentences can describe this. The past is already determined and fixed. The future cannot be determined due to quantum fluctuations. All change occurs in the present. The papers I've read on the subject. (I still study alternative models. You can often find interesting modelling techniques) tend to get heavily into trying to define presentist, eternalist and probalistic observers. Which becomes quite messy....

Technically no. Permanent magnets can demagnetize via temperature, impacts or being realigned in some fashion. For example an external magnetic field can demagnetize a permanent magnet

Who said anything about SM particles involvement in the stress tensor being an alternative view to GR.? That is precisely what GR describes... As far as block universes. There is two main models. "block universe" and "evolving block universe". The first is problematic as it requires reversible processes. The second fixes this using tangent bundle worldlines. However you still run into the "presentism vs eternal arguments". the block universe models would just serve to add distraction. I really don't understand why people can't see the stress tensor involvement in the Einstein field equations. How the stress tensor correlates pressure/mass density to determine the metric tensor. The Lorentz group SO(3.1) includes all the SM particles under SO(2)×U (1). So all dynamics not involving supersymmetric particles and the Higgs field is described under the SO(3)×SO(2)×U (1). This includes their thermodynamic influences via their corresponding equations of state. However this is probably best done by a worked example. To save some time I'll post an example of just matter with an equation of state w=0. pressureless. Radiation and lambda have different pressure relations. As I mentioned equations of state... here is another workup I did on another thread. What the above correlates to is particle degrees of freedom. One can calculate how much influence any particle with known properties influence the temperature... pressure... expansion relations. Provided one knows the correct correlations to the Einstein field equations. (the above can and does affect geodesic equations. Which in turn can and does affect redshift to distance calculations) So to that end a sample of how to define a geodesic may be handy. For that Im going to cheat again and use a previous post... in the presence of matter or when matter is not too distant physical distances between two points change. For example an approximately static distribution of matter in region D. Can be replaced by the equivalent mass [latex]M=\int_Dd^3x\rho(\overrightarrow{x})[/latex] concentrated at a point [latex]\overrightarrow{x}_0=M^{-1}\int_Dd^3x\overrightarrow{x}\rho(\overrightarrow{x})[/latex] Which we can choose to be at the origin [latex]\overrightarrow{x}=\overrightarrow{0}[/latex] Sources outside region D the following Newton potential at [latex]\overrightarrow{x}[/latex] [latex]\phi_N(\overrightarrow{x})=-G_N\frac{M}{r}[/latex] Where [latex] G_n=6.673*10^{-11}m^3/KG s^2[/latex] and [latex]r\equiv||\overrightarrow{x}||[/latex] According to Einsteins theory the physical distance of objects in the gravitational field of this mass distribution is described by the line element. [latex]ds^2=c^2(1+\frac{2\phi_N}{c^2})-\frac{dr^2}{1+2\phi_N/c^2}-r^2d\Omega^2[/latex] Where [latex]d\Omega^2=d\theta^2+sin^2(\theta)d\varphi^2[/latex] denotes the volume element of a 2d sphere [latex]\theta\in(0,\pi)[/latex] and [latex]\varphi\in(0,\pi)[/latex] are the two angles fully covering the sphere. The general relativistic form is. [latex]ds^2=g_{\mu\nu}(x)dx^\mu x^\nu[/latex] By comparing the last two equations we can find the static mass distribution in spherical coordinates. [latex](r,\theta\varphi)[/latex] [latex]G_{\mu\nu}=\begin{pmatrix}1+2\phi_N/c^2&0&0&0\\0&-(1+2\phi_N/c^2)^{-1}&0&0\\0&0&-r^2&0\\0&0&0&-r^2sin^2(\theta)\end{pmatrix}[/latex] Now that we have defined our static multi particle field. Our next step is to define the geodesic to include the principle of equivalence. Followed by General Covariance. Ok so now the Principle of Equivalence. You can google that term for more detail but in the same format as above [latex]m_i=m_g...m_i\frac{d^2\overrightarrow{x}}{dt^2}=m_g\overrightarrow{g}[/latex] [latex]\overrightarrow{g}-\bigtriangledown\phi_N[/latex] Denotes the gravitational field above. Now General Covariance. Which use the ds^2 line elements above and the Einstein tensor it follows that the line element above is invariant under general coordinate transformation(diffeomorphism) [latex]x\mu\rightarrow\tilde{x}^\mu(x)[/latex] Provided ds^2 is invariant [latex]ds^2=d\tilde{s}^2[/latex] an infinitesimal coordinate transformation [latex]d\tilde{x}^\mu=\frac{\partial\tilde{x}^\mu}{\partial x^\alpha}dx^\alpha[/latex] With the line element invariance [latex]\tilde{g}_{\mu\nu}(\tilde{x})=\frac{\partial\tilde{x}^\mu \partial\tilde{x}^\nu}{\partial x^\alpha\partial x^\beta} g_{\alpha\beta}x[/latex] The inverse of the metric tensor transforms as [latex]\tilde{g}^{\mu\nu}(\tilde{x})=\frac{\partial\tilde{x}^\mu \partial\tilde{x}^\nu}{\partial x^\alpha\partial x^\beta} g^{\alpha\beta}x[/latex] In GR one introduces the notion of covariant vectors [latex]A_\mu[/latex] and contravariant [latex]A^\mu[/latex] which is related as [latex]A_\mu=G_{\mu\nu} A^\nu[/latex] conversely the inverse is [latex]A^\mu=G^{\mu\nu} A_\nu[/latex] the metric tensor can be defined as [latex]g^{\mu\rho}g_{\rho\nu}=\delta^\mu_\mu[/latex] where [latex]\delta^\mu_nu[/latex]=diag(1,1,1,1) which denotes the Kronecker delta. Finally we can start to look at geodesics. Let us consider a free falling observer. O who erects a special coordinate system such that particles move along trajectories [latex]\xi^\mu=\xi^\mu (t)=(\xi^0,x^i)[/latex] Specified by a non accelerated motion. Described as [latex]\frac{d^2\xi^\mu}{ds^2}[/latex] Where the line element ds=cdt such that [latex]ds^2=c^2dt^2=\eta_{\mu\nu}d\xi^\mu d\xi^\nu[/latex] Now assunme that the motion of O changes in such a way that it can be described by a coordinate transformation. [latex]d\xi^\mu=\frac{\partial\xi^\mu}{\partial x^\alpha}dx^\alpha, x^\mu=(ct,x^0)[/latex] This and the previous non accelerated equation imply that the observer O, will percieve an accelerated motion of particles governed by the Geodesic equation. [latex]\frac{d^2x^\mu}{ds^2}+\Gamma^\mu_{\alpha\beta}(x)\frac{dx^\alpha}{ds}\frac{dx^\beta}{ds}=0[/latex] Where the new line element is given by [latex]ds^2=g_{\mu\nu}(x)dx^\mu dx^\nu[/latex] and [latex] g_{\mu\nu}=\frac{\partial\xi^\alpha}{\partial\xi x^\mu}\frac{\partial\xi^\beta}{\partial x^\nu}\eta_{\alpha\beta}[/latex] and [latex]\Gamma^\mu_{\alpha\beta}=\frac{\partial x^\mu}{\partial\eta^\nu}\frac{\partial^2\xi^\nu}{\partial x^\alpha\partial x^\beta}[/latex] Denote the metric tensor and the affine Levi-Civita connection respectively. To put bluntly I just described freefall of two particles above a typical planet or star. That description did not require an Ether. Nor did it require force... The quoted section details the individual EoS. The portion after is freefall matter. What did I cover... 1) principle of equivalence 2) principle of covariance 3) spacetime geodesic in Newton limit. 4) The equation of state of matter and radiation 5) Levi-Civita_connection 6) parallel transport and its usage to map curvature. yet the only particle I needed to describe that is motionless baryonic matter.... I did not need a block universe conjecture nor an Eather. The medium already exists (just at extremely low density. ie 10^-29 grams/m^3...) and greater. What that medium is comprised of requires factoring in the Equations of state and the added degrees of freedom. Though it is your standard model of particles. Different equations of state influence the stress tensor which influences the metric tensor. No Ether... If you wish to do the above in QFT style treatments switch to action vs momentum vectors. of course if you do that. Using the above you can arrive at the principle of least action . I simply included the principle above without any details. In simplistic form the principle of least action can be expressed as. [latex]Action=S=\int_{t_0}^{t_1}[\frac{1}{2}m (\frac{dx}{dt})^2+-mgx]dt [/latex] Between events t_0 and T_1 there is millions of possible paths. Starting and ending at those points. The correct path is the one where the sum of kinetic energy (LHS of the + sign) and potential energy (rhs of the + sign) is lowest. You can correlate the EoS influence upon the KE term... edit:::forgot to add an important formula involving the stress tensor [latex]T^{\mu\nu}=(\rho+p)U^{\mu}U^{\nu}+p\eta^{\mu\nu}[/latex] Now I realize none of the above is easy to understand. However trying to describe the above in terms of an Eather or block universe would only cause additional problems. Trying to learn GR using ether or block universes will not aid in the above. Your better off simply sticking within GR (albiet the field equations include thermodynamics) lol from personal experience trying to understand the above using alternative models etc cost me several years. Once I stayed focussed on just GR....

Along with generating enough gamma rays to wipe out the planet you leave and arrive at. I'll see if I still have the arxiv Alcubierre drive paper correlating the gamma ray aspects. located it. http://www.google.ca/url?sa=t&source=web&cd=3&ved=0ahUKEwjvlqC-8bLPAhVK7GMKHUutAjAQFggfMAI&url=https%3A%2F%2Farxiv.org%2Fpdf%2F1202.5708&usg=AFQjCNHjTF6Xb8C0z-xXv6nqIAL1sNJLsA&sig2=CAAP4G_fAX8isctE934MTg

In order to be plausible it must obeys the laws of physics. You have not shown plausibility. One can counter a model as implausible long before testing by applying the well tested laws of physics. You have not done so. The law of physics your ignoring is the conservation of energy laws. Which in itself invalidates free energy...

the biggest problem with block universe is irreversible processes. Thermodynamics itself argues against block universe. Hence the development of the evolving block universe model. Which is a seperate model. I'm not what the logic here is. Why would we try to teach relativity using models outside of what relativity describes. If your going to teach a model. Stick to just that model. Adding other models just adds unnecessary complexity. For example lack of drag (medium characteristics in eather ) For block universe the complexity of reversible vs irreversible processes in the numerous block universe models. (which hasn't been shown to work at all measurement scales. In particular QM.) Stick to just GR. Use the energy density to pressure aspects of the stress tensor. After all it is the stress tensor itself that tells space how to curve... You don't require an absolute frame, this is one of the greatest contributions to science. Why throw it away?. How can you possibly teach relativity if you require an absolute frame to compare to? Quite frankly one should be able to transform between any frames. Quite frankly relativity becomes easier to comprehend when you detail how thermodynamics work within GR. The medium can be accurately described as a field or just use the intergalactic medium of standard model particles. Fundamentally the last approach will better equip the reader to handle GR and cosmology combined...

Not sure I will ever understand why people that think time requires motion. Always forget time is also a measure of duration. How long does "a" stay in the same state..? A doesn't move yet we still measure that it didn't move in time "x"

I know of no treatment that allows "From the perspective of the photon" or more specifically "rest frame of photon. Even under GR. However we can still handle the wordline apects of the photon path. Specifically light like intervals. This would fall under null geodesic relations. One of the easiest ways to describe this... If we include the rest frame of the photon we are stating v equals zero. However v=c for a photon it is invariant. We can't have two simultaneous speeds for the photon. So this frame is invalid as a rest frame. More importantly it provides a convenient boundary between spacelike and time like intervals. Which will correspond to causally connected and causally disconnected paths. edit another problem with the photon (invalid frame) is that you lose coordinates. 4d coordinates reduce ie coordinate time being zero. So no I don't know of any treatment under coordinate change which can solve this to validate the photon frame as valid for an observation frame.

While calculus is handy. Another practical study is differential geometry. This will greatly assist in understanding of GR. Photon frame isn't considered a valid inertial frame in GR.

No I wouldn't try to place a measurable boundary to our universe. The thing is science cannot prove or disprove a multiverse. Nor has science been able to determine whether our universe is finite or infinite. A multiverse doesn't preclude the possibility of an infinite universe. You can possibly have an infinite number of infinite universes. As science can neither prove nor disprove these mathematically accurate possibilities. The best we can say is its plausible. Beyond that its sheer wild guesses.

I noticed the accidental double post. I'll flag the extra to avoid cross posts. Ok not sure what your implying by space created at speed of light. Space by definition is the volume. GR uses it this way as well. GR doesn't state space is created. This is usually a pop media hindrance of trying to describe geometric volume relations between events as space being created, curved, folded etc. Yet its really describing is the differential geometry relations. Not some fabric or other materilistic property.

Thats not as popular an idea as pop media may lead you to believe. I would suggest more feel that the cyclic models are more likely. The problem universe from nothing models fail to adequately adress is that it takes energy for virtual particles to form. The zero energy universe uses a balancing act to accomodate this. However uses psuodo tensors to describe curvature. Many frown upon this. Out of the numerous "universe from nothing" models this is probably one of the more sucessful in popularity. Though Lawrence Krauss's model may seem more popular the zero energy model was more widely accepted Funny I find something existing for infinity more unlikely. Good thing science doesn't rely on personal feelings

Have you tried googling Geoid? The process Studiot is describing has a decent article on wiki. https://en.m.wikipedia.org/wiki/Geoid

your welcome. Lol I just noticed I missed the exponent on the line element in post 181. I applied the correction. Will make more sense now. 👌 Corrected form... [latex]ds^2=-c^2dt^2+dl^2[/latex]

I agree well said. I've always found though that one often learns more from mistakes than correct answers. Provided one keeps at it. A side note, when I first started my studies, I was much like many that post in Speculations. Coming up with fixes that made sense to me at the time. After a while I began to truly see how interconnected the various models truly were and how much detail and research went into the simplest of formulas. Don't get me wrong, trying your own models is good practice. It works best with study and practice. I originally first started with the FLRW metric, then GR, Qm then particle physics. That sequence worked for me but each person is different. one recommendation when your writing your articles. Stick to what the math shows. When you start departing from that. People start thinking crackpot. Its ok to suggest potentials that a model has. However declaring that it does more than it shows without the mathematical proof is highly questionable.

I don't see any mistakes in the differentation.

photon sphere of a Bh just outside the event horizon can cause circular looped spacetime null geodesics

Great we can all run around in circles yelling " My Frame,My Frame.."

You use latex commands. Google latex symbols for a decent list. Then type [l@tex]\frac{1}{2}[/latex] I intentionally replaced a with @ in the first command so you can see the structure Another hint hit quote on posts that have latex done. You can see the command structure that way. [latex]\frac{1}{2}[/latex]

While your at it. Think on this problem. You wish to model a stable universe that is eternal neither contracting nor expanding. Very well lets do just that... Line element of a static homogeneous and isotropic Uniform universe. [latex]ds^2=-c^2dt^2+dl^2[/latex] uh oh we have a problem Houston.... How can you have gravitational redshift or cosmological redshift in a static and uniform universe. That line element only uses proper time. There is no coordinate time needed as the average density of the universe WOULD NOT EVOLVE>>>> So how can you possibly get time dilation if the observer is in the same frame as the global metric (fundamental observer) Quite simply you can't. This is the impossibility aspect of your proposed model. Time dilation requires mass density change, or velocity difference. If you have neither then you have no time dilation. Not to repeat that the FLRW metric is time independent where the Schwartzchild solution is time dependant. So answer this question. In your model you have a static universe....no density change How can you possibly have time dilation to an observer sitting in free space away from any localized anistropy? (fundamental observer). The very minute you tried to model the cosmological redshift as gravitational redshift. You induce an evolving background metric. As the metric we require is a fundamental observer, the only valid solution is an expanding volume. The spatial components evolve over proper time. (time independent)

Don't confuse recessive velocity as a real velocity. Its a consequence of the formula used. The rate of expansion is roughly 70 km/s/Mpc. So depending on how many times you multiply 70 km by Mpc will be exponential. Try this. Take a ruler each unit 1 for one. draw 1 unit line. Now next second double the ratio so one unit is 2 of the previous. Then for the third second you will have 4 to 1 previous. You now have accelerating seperation distance. However the rate of expansion was constant per Mpc. This is funny because the "Rate of Expansion is currently getting lower per Mpc." however the seperation distance is accelerating... POP media articles never truly detail that. This is probably one of the better papers, the Author is a Ph.d philosophies of Cosmology. He specializes in inflation studies. Numerous arxiv articles. http://tangentspace.info/docs/horizon.pdf :Inflation and the Cosmological Horizon by Brian Powell He wrote this targetting forums and typical forum questions. think of it this way. thermodynamics determine the rate of expansion, not the seperation distance/recessive velocity. That changes per observer. rate of expansion doesn't food for thought. Matter collecting into Blackholes, galaxies, stars etc. Actually causes a universe to expand...all by its little ole lonesome... The reason being is the global density distribution of matter gets lower as matter falls into localized distribution...The very moment two particles collect or pool together. Expansion occurs.... 👹

Your confusing conditions then as opposed to conditions now. Expansion is time independent. Meaning it doesn't involve time dilation. Your trying to apply a time dependancy into it. This becomes apparent when you compare the changes to the ds^2 line elements. The FLRW metric is a history of change over a period of proper times. The Scwartzchild child metric compares proper time vs coordinate time at a particular moment in proper time. Not a history of proper times. Anyways expansion follows ideal gas laws. We don't need relativity to describe how a gas can expand or contract over time by density changes. I already provided the related formulas and resources to learn cosmology thermodynamics. However those same ideal gas laws also dictate how time dilation works via the stress tensor. The problem is the Schwartzchild metric assumes the background density is zero... Its not precisely zero just close to it... more importantly though it only models Localized anistropy, its not designed for a homogeneous and isotropic background. It specifically models a preferred direction and location. The Centre of the BH... one with an extreme curvature locally... The Newton approximation is closer to a homogeneous and isotropic background. but the time dilation is still gravitational potential vs background metric mass density. Essentially one observers frame of reference is the global background at a moment in time, while the other is time deviation from the previous frame of reference due to localized density change. NOT GLOBAL the FLRW metric is density change over proper time. (at rest observer...called a fundamental observer. A fundamental observer is essentailly at rest to the global density)

what in the world is a mirror gradient ? Were dealing with the basic math issues here...atm let alone the rest of your paper