Trajectory, path, line segment, geodesic, wordline etc.......In calculations the motion of particle is defined invariably as a trajectory, then why do we make a reference to spacetime, area ? Area has nothing to do with the trajectory of a particle under Gravity. Packaging ?
Your claim as I said, has been totally lost in the bullshit red herrings and gutless attacks on newbies, simply because they tend to align with mainstream and sensibility. I don't believe you know what your claim is yourself...In your pompous pretentious nonsense, you have in your own mind, created a whole new 21st century cosmology; Except of course no one else knows about it, just us lucky few. Please Register or Log in to view the hidden image! Oh the pain of such delusions! Please Register or Log in to view the hidden image!
Again, take it to the world and reveal all this imaginary packaging........ It's troublesome for you I know, to accept that you are a no body. The truth is hard to face. That being of course that Spacetime is simple the geometric framework against which we calculate GR and in which we exist. It exists to show time as the fourth dimension and its relationship with space, both which we now know to be variable, dependent on one's Frame of reference. Space exists: It stops everything being together. Time exists; It stops everything from happening together. Therefor spacetime exists.
I see not much reason to refer to areas. And the spacetime is simply the GR name for the gravitational field, which influences the clock showings of all imaginable clocks.
Well, now we get to the real purpose of the thread, to insult 100+ years of science. Time to move this to pseudoscience.
Whats the hurry ? Many here are fighting tooth and nail (that includes you also possibly, as you have never countered Paddoboy) that spacetime is real and capable of getting warped bent etc.....If these people learn at the conclusion of this thread that spacetime is nothing but curves and graphs, and it has nothing to do with reality and it is not something...then whats the harm ? Discussing the objectionable aspect does not make it insulting.....the tone is among us only and has nothing to do with the merit of the topic....
Contd..... Now the Packaging Aspect..... I am of the opinion that GR is a nicely packaged (of course with some improvization) version of Newtonian Only. Its like this, We are looking at the motion from the road's perspective rather than from the perspective of vehicle. Obviously the presentation and the packaging will be different, but it hardly matters to the real motion. and this is confirmed by the following.. 1. We still use Newtonian Gravity in day to day observations. 2. We use newtonian for understanding orbital motions. 3. We do Newtonian / keplarian even for galaxy speed Distribution curves. 4. We still use newtonian for energy conservation calculations (KE + PE) 5. Newtonian is still used to calculate escape velocity even in GR. 6. Neutron star hydrostatic Equations use Newtonian Energy formula for inward pressure calculations. 7. Newtonian has no problem in multi body solution, GR gets stumped. 8. BH can be envisaged in newtonian also. So, lets understand further this curved spacetime (GR baby) and see if we can derive curved spacetime in Newtonian (like GR derives Newtonian)....This will be quite interesting and will prove that actually we are talking of same thing in different package....of course we will tackle something like mercury precession etc.
The reason I object to this thread is because "The God" is a liar. He lies about science. Then why does it make different predictions from Newtonian mechanics? Sure, because it's super accurate. It's just not as accurate as GR. Sure, because it's super accurate. It's just not as accurate as GR. Of course, the US Navy commissions scientists to work on GR in order to get the best navigation. Sure, because it's super accurate. It's just not as accurate as GR. So some people use Newtonian mechanics to demonstrate the need for dark matter. More accurate work is done with GR. Sure, because it's super accurate. It's just not as accurate as GR. Sure, because it's super accurate. It's just not as accurate as GR. GR is designed to reproduce Netwonian mechanics in certain circumstances. Sure, because it's super accurate. It's just not as accurate as GR. Multi-body solutions are always a problem. Sure. And the envisaging is radically different. Someone did this almost a hundred years ago. Because Newtonian mechanics is super accurate. It's just not as accurate as GR.
If the universe repeatedly behaves as if certain of the weirder furniture of physics is actual (in the context of tests, experiments, technological exploitation, etc) then that's good enough for basic scientific realism minus the dogmatic boot thumping. Any brand of "the way things truly are beyond the appearances and interpretations outputted by mind or psychological activity" runs up against that impassable wall of consciousness / reflective thought. That if the conceptual and perceptual representations of such are [imaginatively] left behind, then there's no thinking agent and world manifested anymore for studying and poking _X_ (like in the aftermath of death, periods of clinical dreamless non-awareness, etc, where the empirical and intellectual evidence of an existence disappear). So the qualifying limit for"warranted belief" in a theoretical item of physics being "real" or inter-subjectively demonstrable is, again, that the universe demonstrates time and again that it conforms to that idea. The everyday world prescribes belief in itself by humans in similar fashion via its sensed regularities. No less strange physics entities which scientific interrogations uphold long-term via the regularities in its contexts. Ancient philosophical claims that reason and arguments of necessity can detour around the barrier of experience related affairs and inferences grounded to them -- that pure rationalism possesses a special hotline to both details and "proof" of what is or is not the case regarding a metaphenomenal realm -- fell out of favor in the 18th century. A mindless or "non-presentation" version of be-ing, by its very defined nature, would lack psychological affairs like reasoning as much as the visual, aural, tactile "showings". Thus why absence or oblivion follows cessation of consciousness, when brain functioning ceases and dissolves back into the conventional, generic nature of what matter is to itself minus the emergent psychological representations of biological organisms (this label of "matter" also being the mindless substance / monistic principle boasted by a popular abstract, metaphysical view like physicalism). Dan Lloyd -- In the [Descartes] demon's thrall, we are deluded about everything, and all the time -- a terrible fate, but one whose terrors are only hypothetical, since systematic demonic delusion is without practical consequences. In practice, an uncontradicted delusion is as good as a truth. --Popping The Thought Balloon
What you or your apparently new trolling friend think, is neither here nor there, and makes no difference to what the real experts think and know. You and your apparent new trolling friend are pissing into the wind.
As do most agenda laden anti science nuts, particularly the religiously driven ones [as is our divine friend] and their closeted supporters. Please Register or Log in to view the hidden image!
And Newton doesn't predict a strong field. Perfectly understandable considering the information he had to start with. For these cranks it's the strong field analysis which messes up ther uninformed mental process. They think of spacetime curvature as some huge thing. It must be huge since they weigh 10 times their mass on the surface of the earth. They don't have any understanding of what constitutes the natural path in relativistic physics. Geodesic paths and how they would terminate on the surface of the earth. Or what would happen if the earth suddenly disappeared. They didn't learn anything when they fell off the roof of their family abode.
Your opinions as amateurish as they are, count for nil in the greater scheme of things. The only packaging that is obvious, is your own god inspired agenda laden rants re 21st century cosmology. Please Register or Log in to view the hidden image! Why would we use anything else? We reside in a sub relativistic arena on Earth. shesh! Please Register or Log in to view the hidden image!See previous answer. Yep, that's all we need to obtain required results. The difficulty and precision in GR, makes it complicated to unnecessarily use. Hence why your ignorance sky rockets when you broach the subject. Wow!!You are certainly fabricating any thing you can scrap together to attempt to invalidate GR. All we use is the comparison in terminology. Please check previous answers. Totally false. Again, totally false, which highlights your ignorance of not only GR, but also Newtonian. Newtonian predicts and allows for what we call "Dark Stars" as derived by John Michell in the late 1700's. Dark Stars simply exist when compression in a star sees the surface escape velocity equal "c". It does not predict total compulsory collapse as does GR and GR BH's. There are many reputable links, many University papers and arXiv papers that explains what you are mangling in simple precise terminology, without any agenda or inflated ego problem. What you claim makes no difference at all in the greater scheme of things: As a distributor of 21st century cosmological knowledge, you I'm afraid are a registered no body.
You should do some initial reading on the subject to insure you can ask a meaningful question. It makes sense. For Einstein's theoretical model matter tells spacetime how to curve and spacetime curvature, gravity, determines the geodesic path. For the local proper frame the geodesic path is straight. This is because the local spacetime curvature is an infinitesimal, very very very small, over all local geodesic paths. GR is a theory that models geodesic paths, the natural freefall paths, through the universe. That's what it's all about. It models the local paths and remote coordinate paths which are frame dependent and sum the local spacetime curvature over the entire global path of the geodesic. GR is a local theory of gravity. None of this is strange as evidenced by how we observe the frame we live in. The local proper frame. This frame is almost identical for Newton and Einstein. The only differnence is accounting for the infinitesimal local spacetime curvature when it would make a difference during empirical analysis. Very seldom do we need to account for the local spacetime curvature, gravity, during empirical analysis, conducted in the local proper 'laboratory' frame since it won't make any meaningful difference to the empirical results. Experimental analysis where this infinitesimal difference needs to be accounted for is the GPS and Gravity Probe B experiments which are a test for GR. This has been kinda long winded but I just wanted to give you some info on how GR works. All the tests of GR require accounting for spacetime curvature. A famous one is deriving the natural precession of Einstein orbits. Famous empirical test is to determine the natural precession of Mercury's orbit. Newton says the rate of radial oscillation and angular velocity is M/r^3. This is a close approximation to GR but not close enough to answer the question. Even in the weak field. Derive the natural precession rate of Einstein orbits. All Einstein orbits naturally precess. Start with the Schwarzschild metric, in geometric units, setting theta at 0. dTau^2 = (1-2M/r)dt^2 - dr^2/(1-2M/r) - r^2(dphi)^2 Substituting constants of geodesic motion E/m and L/m for dt and dphi dt = [(E/m)/(1-2M/r)]dTau dphi = [(L/m)/r^2]dTau The solution relates squared values for radial motion (dr/dTau)^2, energy per unit mass (E/m)^2, and the effective potential per unit mass (V/m)^2 = (1-2M/r)(1+[(L/m)^2/r^2]). (dr/dTau)^2 = +/- (E/m)^2 - (1-2M/r)(1+[(L/m)^2/r^2]) Taking some license for the weak field and multiplying through by 1/2 after multiplying out the squared effective potential. 1/2(dr/dTau)^2 = 1/2(E/m)^2 - [1/2 - M/r + (L/m)^2/2r^2 - M(L/m)^2/r^3] setting (V/m)^2 = U/m U/m = 1/2 - M/r + (L/m)^2/2r^2 - M(L/m)^2/r^3 1st derivative d(U/m)/dr = M/r^2 - (L/m)^2/r^3 + 3M(L/m)^2/r^4 2nd derivative d'2(U/m)/dr'2 = rate of radial oscillation = w^2_r w^2_r = M(r-6M)/r^3(r-3M) Without writing down details the rate of angular velocity becomes w^2_phi ~ (dphi/dTau)^2 = M/r^2(r-3M) The difference. w^2_phi - w^2_r = 6M^2/r^3(r-3M) We can find a factor * M/r^3 which closely approximates 6M^2/r^3(r-3M) That factor is 6M/r (6M/r)(M/r^3) = 6M^2/r^4 The last step is further weak field approximation (6M/r)^1/2 ~ 1/2(6M/r) = 3M/r So a very close approximation for the rate of orbital precession, in the weak field is 3M/r. You can plug in numbers and get an answer that matches observation. 3M_Sun = 4431mr_mean Mercury = 5.8x10^10 meters, 415.1539069 times Mercury orbits the Sun in 100 Earth years, 360 degrees per year, 3600 arcseconds per degree...etc I find stuff like this instructive, further amateur analysis, LOL. The predicted geodesic path, including natural precession, over the orbit of Mercury is defined by 3M/r while the predicted deviation for the geodesic path of light is 4M/r. Both are geodesic paths. The first is the path of an object with mass and the second is the path of light. The way we define these geodesic paths is they follow the path of extremal aging. Extremal is either the maximum time between the origin and termination of the geodesic or minimum for the geodesic path of light [stuff with no mass].
Note for Xelasnave below the derivation. Derive the natural precession rate of Einstein orbits. All Einstein orbits naturally precess. Start with the Schwarzschild metric, in geometric units, setting theta at 0. dTau^2 = (1-2M/r)dt^2 - dr^2/(1-2M/r) - r^2(dphi)^2 Substituting constants of geodesic motion E/m and L/m for dt and dphi dt = [(E/m)/(1-2M/r)]dTau dphi = [(L/m)/r^2]dTau The solution relates squared values for radial motion (dr/dTau)^2, energy per unit mass (E/m)^2, and the effective potential per unit mass (V/m)^2 = (1-2M/r)(1+[(L/m)^2/r^2]). (dr/dTau)^2 = +/- (E/m)^2 - (1-2M/r)(1+[(L/m)^2/r^2]) Taking some license for the weak field and multiplying through by 1/2 after multiplying out the squared effective potential. 1/2(dr/dTau)^2 = 1/2(E/m)^2 - [1/2 - M/r + (L/m)^2/2r^2 - M(L/m)^2/r^3] setting (V/m)^2 = U/m U/m = 1/2 - M/r + (L/m)^2/2r^2 - M(L/m)^2/r^3 1st derivative d(U/m)/dr = M/r^2 - (L/m)^2/r^3 + 3M(L/m)^2/r^4 2nd derivative d'2(U/m)/dr'2 = rate of radial oscillation = w^2_r w^2_r = M(r-6M)/r^3(r-3M) Without writing down details the rate of angular velocity becomes w^2_phi ~ (dphi/dTau)^2 = M/r^2(r-3M) The difference. w^2_phi - w^2_r = 6M^2/r^3(r-3M) We can find a factor * M/r^3 which closely approximates 6M^2/r^3(r-3M) That factor is 6M/r (6M/r)(M/r^3) = 6M^2/r^4 The last step is further weak field approximation (6M/r)^1/2 ~ 1/2(6M/r) = 3M/r So a very close approximation for the rate of orbital precession, in the weak field! is 3M/r. You can plug in numbers and get an answer that matches observation. 3M_Sun = 4431meter, r_mean Mercury = 5.8x10^10 meters, 415.1539069 times Mercury orbits the Sun in 100 Earth years, 360 degrees per year, 3600 arcseconds per degree...etc Note to Xelasnave. This is another example of how the physics is derived from a metric equation. There's good examples that only require a simple understanding of algebra. That would be to derive the local speed of light from the Minkowski metric and remote radial coordinate speed of light from the Schwarzschild metric. Since these metric solutions, other than Minkowski, are derived from a solution to Einstein's field equations they provide an avenue to understanding Einstein's model. A way to help somebody like me recognize what's going on with a knowledge of the principle of extremal aging [Noether's theorem], algebra, the quadratic equation for finding limits, weak field approximation techniques [simple stuff], and most importantly basic calculus. That's it. I better say trigonometry or rpenner will think I'm nuts. This should be interesting for you. Choose Chapter 1 Speeding. The metric they introduce is a very simplified version of the Minkowski metric. In Chapter 2 they introduce the Schwarzschild metric. The theme of this book is to introduce undergraduate students to GR. That includes you and I as far as Professor Taylor concludes. http://www.eftaylor.com/download.html#general_relativity
I fixed a couple of writing mistakes 3M_sun = 4431 meter r_mean Mercury = 5.8E10 meters This thing were the IPad changes what you write based on it's complete lack of understanding scientific terms gets on my nerves.
