Bill Ryan

Geordief - I see that - sorry

Curved time doesn't make a whole lot of sense. It's a scalar. How does it curve? Responding in two parts: 1.) Regarding the "scalar" point - good question. Are x, y and z scalars? In any case if you are arguing that the space components of space-time may be curved but time is just along for the ride, I think that's a problem. Maybe it's THE problem. Space-time in its totality and its parts is geometry. 2.) With respect to "how does it curve?" we are ships passing in the night. My last several posts comprise a description of its curvature and the mechanism by which this results in the totality of gravitational attraction in every day circumstances. The marker for its curvature is time dilation along the z axis. The mechanism by which passage across the time gradient results in "attraction" is equivalent to refraction. Let me now say it in a different way and you tell me what is wrong with this. Imagine normalizing time by converting it into a synthetic negative space dimension - multiplying by -c. As a result we now have "the world" - a four dimensional geometry warped by the presence of mass (among other things). And in this world the time gradient has been remodeled as a spatial distortion equivalent to the spatial distortion in the space dimensions. Applying parallel transport to geodesics we document curvature - all four dimensions contributing. (Except with the dropping apple viewed from a nearby picnic only one dimension's curvature shows up - that of time.) One might argue that this normalization of time is a trick in modeling, that it has questionable ontological standing and results in unfortunate artifacts, but most of us prefer to see Einstein and his contemporaries as heroically accomplishing Ahab's mission and "striking through the mask" thereby grasping a world more real than the phenomenal. In any case, this is the model. It is geometrical - all four dimensions. On July 8th above I quoted Einstein veering from this perspective (the quote repeated below). I think where you stand with respect to this quote goes to the heart of our dispute. In my estimation this is not the master at his best. You've invoked a spatial dimension here I have indeed. But if you are implying that I am therefore admitting that space curvature is a component of the cause of attraction in these limited circumstances - I am not. It's all time all day long. The significance of z here is entirely as to the disposition of the time gradient and therefore the direction of "attraction." I am essentially restating Einstein's 1911 argument quoted above on July 8th (including the z axis) and he was not offering up spatial curvature at the time.

Sorry for the crumby wording - what you said is what I was referring to (and have illustrated in several posts in this thread.)

Kip Thorne is not making this point to simplify the maths. To predict motion in the circumstances under discussion without wearing down a pencil just skip GR altogether. Thorne is pursuing this to illuminate the physics. As to pedagogy, sure, but I have a hard time untanglling that from an actual physics dispute. Bad pedagogy certainly contributes to the persistence of the disagreement. Every GR course addresses the Newtonian limit, but apparently many (not all) skip over what this physically means (time curvature cause of attraction) and quickly move to GR verification in clock discrepancies. Herbert Hamber's recorded course does describe it directly, but briefly. John Wheeler’s GR distillation applies to time here. “Matter tells space how to curve and space tells matter how to move.” (Let’s admit “space” is short for “spacetime.”) In the circumstances under discussion, the everyday experience of gravity on Earth (outside the source, low velocity, moderate field), Wheeler can be reasonably recapitulated as “Matter tells time how to curve and curved time tells matter how to move.” Curved time means a time rate gradient along the z axis. Passage through time is across this gradient and results in a deviation analogous to refraction which we call falling. This is spacetime curvature in this instance. The time component is no less geometric than the space component and it is the only significant component under these limited circumstances. How often do you read that gravity causes clocks to vary in speed according to height? This is a miserable formulation which buries Wheeler’s simple causal sequence in a sloppy anti-GR inversion. It’s as if there is a Newtonian force of attraction and the closer you are to its source the slower time goes. No. As we know, there is only mass shaping the metric field (in this case, varying rates of time flow) which in turn directs motion. Not only can the idea of spacetime withstand analysis – it is enhanced by looking at how its parts work. I understand the Einstein equation adds up to a universal picture true for all reference frames but Thorne is simply doing with words what Gμν does by pairing all the dimensions. The equation is an analytic as well as synthetic machine. I don’t think you advance GR by deploying “spacetime” as a gloss to resist Thorne’s physical intuition about time.

Several people on this thread have questioned Kip Thorne’s language by pointing out that space and time are not separate. True – but they are nevertheless distinguishable. As Thorne says, Einstein’s 1911 attempt to describe the effect of gravitation on light takes only time curvature into account. It produces a bending prediction that is off by half. When he later gets his math act together and models spacetime he subsumes the earlier model. He does not dump it. He complements time curvature with space curvature and nails the prediction. Also, in non-extreme gravity, such as Earth’s, and at non-relativistic speeds, space is essentially flat and the entirety of mass’s effect on motion (gravitational attraction) can be understood as the result of time curvature. The falling apple (and even the orbiting Earth) are simply not moving much in the space component of spacetime. (Time is made equivalent to space by the speed of light so as we sit here reading this in a chair or in an airplane or while skydiving, our progress through space is de minimis. But we and the apple are all going very fast – through time.) Under these conditions, with respect to motion, time dominates and GR reduces to Newton. Some others on the thread seem to believe that there is a critique of GR lurking here. All of the above is in support of GR and its author. It has been repeatedly described in its essentials by Einstein and many others since. As far as I can tell, it may appear exotic or even egregious because of a widespread pedagogical failure, but it is definitely part of GR. Here are some Einstein sources and excerpts that I think support the Kip Thorne case (quotes mark excerpts. My comments inside excerpts are in brackets): 1911 In 1911 Einstein published On the Influence of Gravitation on the Propagation of Light. He explains that light’s behavior in a gravitational field demonstrates that time flows slower near the gravitational source. The marker for this is an apparent variation in the speed of light. The show-stopper comes in the middle of page 107 as this is reprinted in the Dover paperback The Principle of Relativity. “From the proposition which has just been proved, that the velocity of light in the gravitational field is a function of the place, we may easily infer, by means of Huyghens’s principle, that light rays propagated across a gravitational field undergo deflexion.” This is followed by a little diagram showing the plane light-wave changing direction as a result of crossing a time gradient. This is equivalent to optical refraction where varying thickness of a retarding medium alters the path of light (which is why he has dragged in Huyghens.) Think of the wave as a group of ice skaters in chorus line formation, shoulder to shoulder and arms locked, all skating with equal effort. As you move from right to left on the line (as they are facing) the ice is increasingly slushy (they are skating across a temperature gradient), the slush retards each skater to a different degree and the line inexorably turns left. Time moves more slowly as you get closer to the surface of the sun. So the equivalent of turning left is to bend toward the sun – otherwise known as falling. Why are we watching the sausage being made? If the 1911 theory were thrown out in 1915 then this discussion might be a sterile curiosity. But that did not happen. It is absorbed into general relativity as the Newton limit. It was not a complete description of bending light because light is covering as much space as it is time so space curvature and time curvature play equivalent and reinforcing roles and Einstein had not yet gotten a grip on curved space. But re-contextualized, as a component of spacetime, time curvature remains an accurate explanation and predictor for the dropping apple. 1915 In The General Theory of Relativity section of The Meaning of Relativity – Fifth Edition MJF Books - Einstein presents the general relativity equation on page 79 for the “motion of a material particle, under the action only of inertia and gravitation” and then asks on page 80, “How are these [GR] equations connected with Newton’s equations of motion?” On page 81 he answers “Let the velocity of the material particles be very small compared to that of light…dx₁/ds , dx₂/ds, dx₃/ds [the curvature components of the three spatial dimensions] will vanish compared to dx₄/ds [time curvature]…This [resulting] equation is identical with Newton’s equation of motion for a material particle in a gravitational field…” In The Foundation of the General Theory of Relativity in a section titled Newton’s Theory as a First Approximation Einstein goes through a similar exercise and states on page 158,9 of The Principle of Relativity, “If we restrict ourselves to the case which almost exclusively offers itself to our experience, of v being small as compared with the velocity of light…What is remarkable in this result is that the component g₄₄ [the time component pf spacetime curvature (in modern notation: g₀₀)] of the fundamental tensor alone defines, to a first approximation, the motion of a material point.” My final piece of evidence is in Relativity The Special and General Theory, which he wrote (in contrast with the above sources) for mere civilians such as myself. In Appendix III The Experimental Confirmation of the General Theory of Relativity, he lays out on page 127 of the Crown Publishers paperback the confirmed angle of deflection of starlight around the sun and then, “It may be added that, according to the theory, half of this deflection is produced by the Newtonian field of attraction of the sun, and the other half by the geometrical modification (“curvature”) of space caused by the sun.” This unfortunate formulation (apparently in service of keeping it simple) gives the impression that GR might be something pasted on to Newton instead of subsuming it. It also gives the impression that geometrical considerations only apply to space as opposed to spacetime. It is only from the standpoint of the actual theory as indicated by the previous references that we can recapitulate Einstein by substituting “time curvature” for “Newtonian field of attraction.” I think this pedagogical misstep, and related ones since, are at the heart of the confusion about Kip Thorne’s idea. See this Physics Forum link for the trouble caused by the Einstein quote. https://www.physicsforums.com/threads/a-baffling-quote-from-einstein-badly-requiring-explanation.300849/

Time dilation does not cause gravity. But in a gravitational field, time dilation changes along the radius. And that change in value according to location (the gradient) causes gravitational attraction. I think the Thorne quote above justifies this interpretation. "Warp" here means curvature. Otherwise, the whimsical "everything likes to live where it will age the most slowly," wouldn't really apply. How would things get to live there if all available aging were at the same rate? Thorne's formula takes the data points of the gradient, not the slow rate as such. I think when he says"The greater the slowing of time, the stronger gravity's pull," this is true because stronger fields means steeper gradients (I would think generally at least.) So for your first counterexample, the formula works. Outside of a gravitational field, in my fast spaceship, I have two clocks. They may be slow with respect to the outside world but there is no "fractional difference in their ticking rates" between them: R= zero , g = 0c2/D = 0. I have now reached or surpassed my math ability so I can't use math in your second example. Maybe the answer above is worth something because your second counterexample is, as I understand it, also about special relativity.

Here is context for Kip Thorne quote from Chapter 4 of The Science of Interstellar (it includes from page 35 a chapter title and opening paragraph and then the sentence quoted above and then on pp 291-2 a technical note - bold emphasis mine and my annotations in brackets. The use of italics is Thorne's. If there are errors, it is my transcription.): Chapter 4 Warped Time and Space, and Tidal Gravity Einstein's Law of Time Warps [For those of you hoping that Thorne "comes to his senses" - by your lights - the fact that he has plopped this pithy moniker on what follows augurs badly.] Einstein struggled to understand gravity on and off from 1907 onward. Finally in 1912 he had a brilliant inspiration. Time , he realized, must be warped by the masses of heavy bodies such as the Earth or a black hole, and that warping is responsible for gravity. He embodied this insight in what I like to call "Einstein's law of time warps," a precise mathematical formula1 that I describe qualitatively this way: Everything likes to live where it will age the most slowly, and gravity pulls it there. The greater the slowing of time, the stronger gravity's pull. On Earth, ... [And here is the referenced technical note] The simplest, quantitative form of Einstein's law of time warps is this: Place two identical clocks near each other, and at rest with respect to each other, separated from each other along the direction of the gravitational pull that they feel. Denote by R the fractional difference in their ticking rates, by D the distance between them, and by g the acceleration of the gravity they feel (which points from the one that ages the fastest to the one that ages the slowest). Then Einstein's law says that g=Rc2 /D. For the Pound-Rebca experiment in the Harvard tower, R was 210 picoseconds in one day, which is 2.43 X 10-15 , and the tower height D was 73 feet (22.3 meters). Inserting these into Einstein's law, we deduce g= 9.8 meters/second2 , which indeed is the gravitational acceleration on Earth. [Admittedly, I did not check his math.]

Right - I see that. There is a possible contextual explanation. I'm guessing Kip Thorne is talking about the same thing I am going on about it but I don't know yet.

I think this might be the exception that proves the rule because it is not really time dilation that causes gravitational attraction - it's the gradient. In your example time is running slower but the gradient is the same in all directions - so no attraction. Not true standing on earth getting hit by a falling apple where time dilation changes along the vertical.

Sorry for joining a year late. I just joined this site. I was surprised Kip Thorne was so tentative in that video. On another site a similar conversation started with reference to this link: This is the best attempt I've seen to support a physical intuition of the causal relation between curved time and gravitational attraction. On Earth (modest gravity/ normal speeds) Earth's mass produces a time dilation gradient that is way more important than space curvature. Our progress through time is like light moving through a prism - the drag increases toward the thicker part of the prism and the light bends. I think this is in line with Bird11dog 2014 thread as far as I understood it. Excerpting from the other site, I said this: This is how I see the video. Everybody knows that when you are mowing the lawn and hit the sidewalk at an angle the difference in the resistance between grass and concrete makes the mower change direction towards the grass. Similarly, when light passes through a retarding medium with angled surfaces ( a prism) the right and left differences in the amount of glass as opposed to air makes the light change direction towards the thicker glass. Exotically, as an object is traveling through time in any gravitational field (for instance near the earth's surface) the modestly greater retardation in such progress that any object, even a point particle, experiences on its high and low flanks (as a result of gravitational time dilation) shifts the direction in space of its progress through time. Thus, if unsupported, it falls. Time dilation is responsible for what we experience as gravity in normal low velocity settings. But when something is traveling through space at a speed equivalent to how we are all progressing through time, (like light) then the curvature of space shows dramatically and the total effect, space plus time, is double what we normally experience. If Newton thought light had mass he would have predicted the same starlight curvature around the sun that Einstein mistakenly originally predicted before he figured out the double effect above. In this sense you can think of Newton gravity as the equivalent of time curvature without space curvature. I am without credentials so will now let the physicists have their way with me. Reference https://www.physicsforums.com/threads/does-gravitational-time-dilation-cause-gravitys-attraction.881449/ And then BepiIT (who sounds like he might be a physicist), said this: The GR metric for Newton's gravity is obtained from the Schwarzschild metric by assuming non relativistic velocities (v^2/c^2 << 1) and weak gravitational field (GM/Rc^2 << 1). In Cartesian coordinates It reads ds^2 = -(c dt)^2(1-2GM/rc^2) + (dx^2 + dy^2 + dz^2)(1+2GM/rc^2) so it does contain a time deformation term g_00 = (1-2GM/rc^2) (causing gravitational time dilation) as well as a space deformation term (1+2GM/rc^2). For non relativistic velocities, the time deformation is c^2 times larger than space curvature, because of the c^2 term in (c dt)^2. Therefore, to leading term Newtonian space is flat. And in fact the equation of Newtonian motion derived via a least action principle do not make use of the spatial term of the metric. Newton gravity originates from the g_00 term, as its spatial gradient (as Pervect wrote), and may be intuitively understood as a differential motions described by Bill Ryan (in fact gravitational force is the gradient of the potential, which in the above metric corresponds to the g_00 term). Space curvature is relevant for relativistic motions, e.g. by doubling the light deflection effect in the weak field limit (whereas for strong gravitational fields the space curvature term becomes dominant). Space curvature is also important for non relativistic motions if the measure is very accurate, e.g. by opening the orbit of planets and causing a precession like that measured for Mercury. Therefore the visual exemplification of a rubber sheet curved by a heavy ball (the Sun), with smaller marbles orbiting around due to space curvature, is essentially wrong, because Newtonian space is flat. Eugene Khutoryansky's video is thus correct as far as I understand. The problem is that no GR book discusses this explicitly, but leave the point rather implicit (see for example the discussion on Newtonian metric in Hartle's "Gravity"). Only exception I know is this book: http://www.relativity.li/en/epstein2/read/ by David Eckstein. Hope this helps a bit. Reference https://www.physicsforums.com/threads/does-gravitational-time-dilation-cause-gravitys-attraction.881449/