Mordred

Ok enough of this. Its obvious you need a good textbook or two and ample time to properly study them. Luckily I can help there. Though your video had some. http://www.lightandmatter.com/sr/ http://www.blau.itp.unibe.ch/newlecturesGR.pdf "Lecture Notes on General Relativity" Matthias Blau The first will provide a decent coverage of SR. Study it first

Here is how spacetime curvature replaces Force. 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 tve 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. There I just provided all the formulas to map and describe spacetime curvature. Did you understand it? of course not it requires intensive study but it does show how Newtonian gravity is replaced.

Via the principle of least action. I could post the higher mathematics to show how it works and will do so but it won't make much sense without intensive study.

Physics is the lanquage of mathematics. No physics theory exists without the mathematics. How can any model make a prediction without the mathematics?

Ok lets explain spacetime curvature. It is not space is curved. What it really describes is a set of mathematical relations in terms of differential geometry. The mathematical relations it is mapping is freefall motion. After all GR is all about kinematic motion. Lets try a different tact. Take a thermometers and measure the rise in temperature of water as you heat it. With the exception of the phase changes you have a linear relation. Spacetime curvature is just that. A set of relations done in terms of geometry. Another example is universe curvature in Cosmology. It is not saying that the universe is flat in terms of its volume. It is specifically describibg the density evolution of the universe over time. Physics is based upon math, 90% of its descriptions are mathematical in nature spacetime curvature is no exception.

I found it an excellent collection of theories with a basic coverage of each including a helpful mathematical coverage of each. In many ways its akin to "Elements in astrophysics" which I find incredibly useful for similar reasons. Penrose often finds ways to explain mathematical complexity involved in many of the theories he discusses in a manner that makes sense. So yes I find it is a handy reference. It however isn't as good as a textbook dedicated to a particular subject as those textbooks are dedicated to that particular subject. Probably the most useful tool in my repertoire is "Mathematics methods for Physicists" https://www.amazon.com/Mathematical-Methods-Physicists-Seventh-Comprehensive/dp/0123846544 It details all the higher mathematics in a well organized model independant manner. That works with all types of physic theories including QM/relativity/group theory etc.

Like I said forget eather think in terms of fields and their interactions and you will be able to make sense of relativity. All fields contribute to mass. When you fully comprehend it Spacetime curvature is simply the sum of all field interactions. Electromagnetic/strong/weak/Higgs etc.

Yes two light beams can interfere with each other. A strong enough light beam can also generate gravity. All forms of energy can. Your definition of spacetime will get you into problems. Space is simply volume spacetime is any metric of space that includes time as a coordinate. When you map spacetime you are generating a map of goedesics called worldlines that equate to freefall motion. This mapping technique replaces the need to treat freefall via force. However its appropriate as mass is resistance to inertia change. The principle you need to study is the "Principle of least action"

correct hence no rest mass all particles are field excitations not bullet like objects. The photon is no exception. A field can and does have medium like properties but is not a medium. By the way how can the thermodynamic laws be too early to prove your model that is trying to overturn estsablished and well tested physics? GR takes the thermodynamic laws and utilizes them in its field equations? ie the stress/momentum tensor

Light has no rest mass it still has inertial mass All of the above can be answered if you stop to think. Take an electric field for example. Have you ever heard the term "propogation delay" ie you can slow down signals via an electromagnetic field? Mass is "resistance to inertia change" Spacetime is a geometry that describes freefall motion. Fields can and do interact and interfere with kinematic motion via their respective coupling constants

For one thing its obvious from that video you absolutely no idea how time dilation works. If you did understand it then you would realize it makes perfect sense. The problem is you refuse to take the time to understand how it works within field theory. Start with mass give the proper definition of mass? Forget all this garbage about an ether and replace ether with fields. Now setup a global field metric using mass density (you can use the Einstein field equations for this setup) then setup your mass distribution, fire lasers through different mass density regions will that laser travel the same rate? absolutely not. Secondly it is impossible to have a static Eather in a vacuum that is dragged by the Earth without being detectable via redshift. Or for that matter having zero thermodynamic temperature influence aka friction itself. Basic physics if you move any body through any static medium you create differential pressure regions. The high pressure zone at the front with low pressure following. Pressure affects temperature. I just proved your theory wrong. Though if you studied the subjects and tests everyone pointed out to you. You would have learned that those tests were testing for that behavior I just described and those results came back null.

And I shouldn't have to load some questionable video that may or may not be hazardous to my computer. Especially one where you quickly move your camera across the pertinant text from some book. Take it from a professional cosmologist all your video does is show how little you understand. Not trying to be insulting but if you wish to prove Eather of any form and Einstein wrong this video doesn't even come close and yes I watched it all

insufficient post your formulas and calcs here. I should not need to go outside this forum to get answers on a speculation model

How about simply following the criteria of our forum rules in speculations on mathematical rigor? http://www.scienceforums.net/topic/86720-guidelines-for-participating-in-speculations-discussions/#entry839842 as a Cosmologist I certainly won't bother listening or watching some video telling me physics is wrong without substantial mathematical rigor and a comprehensive mathematical proof. Videos are a waste of time without showing extensive calculations that a measly 10 minute video cannot possibly cover.

Your in essence correct there are causally disconnected regions beyond the Cosmological event horizon. Those causally disconnected regions will never become causally connected on the future unless they were causally connected at one time in the past. Inflation in solving the horizon problem connected previously disconnected regions but this is an extreme example that runs counter to the above. So unless we have another inflationary scale event its unlikely to connect to further causal disconnected regions afiak. Sometime in the future galaxies we see today will become causally disconnected never to be seen again. The other problem is that we can now see the surface of last scattering which is the furthest we will ever see until we can measure the cosmic neutrino background. This then will be the new and furthest possible extent we will ever see. The neutrino background will allow us to see past the opaque fog prior to recombination.

Lol I love that book

Its as low math as feasible to be informative. However I will answer you last question. Metric expansion is not limitted by the speed limit of GR as it does not involve velocity change or inertia. (its strictly a volume change not kinematic motion)

I have a better article which covers this. It was written specifically with forum members as the target audience http://tangentspace.info/docs/horizon.pdf :Inflation and the Cosmological Horizon by Brian Powell Now lets look specifically why no inertia is imparted. Inertia change requires work or force to be done to cause the inertia change ie f=ma. The regions surrounding galaxies are homogeneous and isotropic so in essence uniform. (Cosmological principle) So the force due to pressure surrounding every galaxy is uniform. How can that galaxy gain inertia due to expansion if there is no differences in the amount of pressure on any facing? The answer is its impossible, instead the metric changes

There is no difference both observers will still measure the same dilation to each other. Though the amount of that dilation will change in the two circumstances. The Lorentz transforms are symmetric Also keep in mind the equivalence principle. So it is possible for one observer to use gravitational potential to match an inertial observer. In essence they can establish the same Inertial frame of reference

Expansion doesn't run counter to GR in fact the FLRW metric works beautifully with the Einstein field equations to such an extent one can choose to use either to equal accuracy. The recessive velocity exceeding c is a commonly misunderstood result of a particular formula involving extreme seperation distance to the observer. Hubbles law The greater the distance the greater the recessive velocity [latex] v_{recessive}=H_Od [/latex] This is not a true inertial based velocity but a calculation based upon mere seperation distance. Those galaxies beyond Hubble horizon with recessive velocity greater than c are not in actuality moving greater than c. It is a consequence of seperation distance not inertia which GR details. Hence their is no competition as those galaxies gain no inertia due to expansion. Now as far as GR goes our current formulas are continuosly improved when it is needed. We have taken GR to heights never imagined by Einstein but laypersons tend to get focussed on the basic equations in SR that they fail to see the later developments. I will post a 998 page texbook on GR just to illustrate this point. The article shows solutions to many of the paradoxes that plaqued GR in its earlier stages and details numerous different coordinate systems that were developed later than Einstein, Lorentz, Minkowskii etc. They supplied the stepping stones. Modern physics took those stepping stones and built a road. http://www.blau.itp.unibe.ch/newlecturesGR.pdf "Lecture Notes on General Relativity" Matthias Blau The reason you still see the formulas from Lorentz and Einstein is we proved there is no need to change them as they are incredibly accurate. If a modern day test showed them wrong. Believe me they will be replaced. However that isn't likely to happen as they are so incredibly accurate. edit I should add the later chapters cover the FLRW metric and shows some of the pertinent details of how it ties to GR and the Einstein field equations.

Lol I liked that one too

We haven't got an exact science on planetary migration. Each system will vary depending on factors such as density and size of the protoplanetary disk, mass of star, composition of the disk, other planetary influence etc. So answering your last set of questions requires considerable research on the factors I mentioned as well as other possible influences

Start with your height 9.8 metres calculate the time for an object to fall 9.8 metres. It will not be 1 second. [latex] t=\sqrt{\frac{2h}{g}}[/latex] [latex]v=\sqrt{2gh}[/latex] Use the first formula to calculate time of fall the second formula the final velocity. There is a difference between acceleration and velocity that you are overlooking. acceleration is 9.8 m/s^2 not 9.8 metres per second. The mistake was assuming the object will drop 9.8 metres in 1 second. If you use the formulas above you will find it takes longer than 1 second. Think about the meaning of acceleration. Then consider your objects starts at zero velocity. If it helps recall that just like your car you don't instantly go from 0 to 9.8 metres per second. It takes a falling object 1 second to accelerate to a velocity of 9.8 metres/sec. it does not mean the falling object travelled 9.8 metres in the first second.

The confusion is the sheer seperation distance between observer and emitter. take the formula [latex]v_{recessive}=H_o d[/latex] now each Mpc add the rate of expansion 70 km/s/Mpc. For example 1 Mpc =70 2Mpc=140 3Mpc=210 ... Eventually you will reach a distance where the recessive velocity exceeds c. However that only to a far distant observer. Roughly 4400 Mpc away from the object being measured. It is a apparent velocity based upon the recessive velocity formula above. Not an actual inertial velocity which relativity uses. Here read this as it covers the above http://tangentspace.info/docs/horizon.pdf The main trick to grasp is that expansion doesn't give inertia to any galaxies. The volume of space between galaxies are simply increasing but this doesn't impart any inertia to any object. The true velocity of those galaxies is their normal drift ie for Milky way 631 km/s relative to CMB.

Yes I'm sure number 4 isn't based on curvature. Read your link carefully k is an inertial frame. [latex] k=(ct,x,yz) \acute{k}=(\acute{ct},\acute{x},\acute{y},\acute{z})[/latex] " consider a composition of transformations from the inertial frame K to inertial frame K′" As you can see from the quoted statement k is an assigned designation for your primed and unprimed inertial frames with the coordinates I supplied. This is the problem I am referring to. You have jumped ahead into group theory symmetry relations instead of focussing on the basic transformations. The wikipage covers literal chapters in a good GR texbook without really explaining each topic in any great detail. It is in essence telling you that it doesn't matter if your travelling toward or away from an emitter. All observers will measure the speed of light as c. (invariant) For the purpose of this thread this should be the only formulas you should focus on. https://en.m.wikipedia.org/wiki/Lorentz_transformation as well as the velocity addition formula https://en.m.wikipedia.org/wiki/Velocity-addition_formula