Howard Landman

Oops, sorry, I see that it was actually Bird11dog. How do I edit to fix that? There doesn't seem to be any edit button. Also I apparently neglected to remove some terms from the later equations ... typical "copy paste and forget to change" error. The last 2 should be ds2 = -c2dt2 + dr2 + r2dΩ2 + (2GM/r)c2dt2 + (2GM/r)dr2 and ds2 = -c2dt2 + dr2 + r2dΩ2 + (2GM/r)c2dt2 respectively.

The gravity that we (as slow moving objects) experience here one the Earth (far away from any black holes) is almost entirely due to "curvature of time", i.e. the time dilation field around the Earth. The easiest way to see this is to assume a spherical non-rotating Earth, so we can use the Schwarzschild metric: ds2 = -(1 - 2GM/r)c2dt2 + (1 - 2GM/r)-1dr2 + r2dΩ2 In the weak-field limit where GM/r is small (i.e. far from any black holes, r >> rs = 2GM/c2) this is approximately: ds2 = -c2dt2 + (1 - 2GM/r)-1dr2 + r2dΩ2 + (2GM/r)c2dt2 + (2GM/r)dr2 The 2nd and 3rd terms together are just dx2 + dy2 + dz2 (in polar coordinates); they give the length of flat Euclidean space. The first 3 terms together give flat Minkowski spacetime, which has no gravity. For particles that are slow (v = dr/dt << c), dr << cdt so we can ignore the last term which corresponds to the space curvature, and get simply: ds2 = -c2dt2 + (1 - 2GM/r)-1dr2 + r2dΩ2 + (2GM/r)c2dt2 = flat_spacetime + time_dilation This tells us that space is extremely flat near the Earth, and almost ALL the gravity is coming from the time term, which merely describes the time dilation field. In fact the geodesics of this metric give Newtonian gravity; note that GM/r = Φ(r) = the Newtonian gravitational potential. "The reason that your ass is being pressed into your seat is that time is moving faster at your head than at your feet." - Landman's Mantra (As a curious aside, chapter 12 of Misner-Thorne-Wheeler Gravitation states that it is IMPOSSIBLE to have a metric for Newtonian gravity, but their proof makes assumptions that don't apply to this metric, so their conclusion is false despite the fact that the proof is perfectly valid. See their Exercise 12.10 for more details.) Swansont Bird11dog asks "do we have proof that matter warps space?" Yes we do. The bending of light by the Sun is twice as great as predicted by Newtonian gravity. The time dilation term gives the Newtonian prediction, and the other half comes from the space term which we ignored for slow-moving objects. Light is not slow-moving, so we can't ignore that term for light. To light, time and space appear about equally curved by the Sun. GR also predicts that space will be severely warped near a black hole event horizon, but we may need to wait a few years before we can test that directly. In the mean time, gravitational waves might tell us something. Swansont Bird11dog also asks how time can bend light. The effect is similar to a graded index of refraction (GRIN) lens. If time is flowing faster at the top than at the bottom of a wave packet moving right, then then the speed of light is different, and a wave packet that starts out like ||||||||||| will eventually start to look like /////////// and the packet will be traveling slightly downward. Machapungo complains that "[nothing] has ever shown that time is a physical reality", but certainly many experiments have shown that time dilation is a physical reality, so I'm not sure what his point is. It's kind of like quantum phase; absolute phase may or may not be real, but phase frequency = energy and certainly is real. Similarly, absolute time is probably meaningless since you can set T0 to be anywhere you want; but the passage of time is demonstrably real and measurable.

On June 13 I ran an indirect test of (my understanding of) quantum time dilation inside the giant Van De Graaff generator at Museum Of Science in Boston. It got a null result at up to + and - 1 MV, which seems to imply that gauge invariance with respect to electrostatic potential is valid. I still need to go through the reasoning that predicted an effect and figure out where and why it is wrong. The experiment was looking for change in the charge/mass ratio of an electron at potential. Since QM tells us a change in potential gives a change in phase frequency, and the de Broglie mass-frequency formula equates frequency (in rest frame) with (rest) mass, this seemed like a reasonable thing to try. No such change was detected within the 5% or so resolution of the equipment. Since a potential of -1 MV should roughly triple the phase frequency of an electron, and tripling the mass of the electrons should have produced a huge effect, it appears that either (1) no frequency shift actually occurred, or (2) the mass-frequency formula is simply wrong in this case, or (3) something else is going on that hides the effect (e.g. perhaps the charge and mass of the electrons changed by the same amount). This does not necessarily completely eliminate QTD, but it seems to imply that van Holten's view (that only fields, and not potentials, cause dilation) might be the most reasonable interpretation at this time. Even if that's not what the equations seem to say. Even if that's not at all how it works for gravity. I am very proud that, with help from MOS and borrowed equipment from CSU, the entire experiment cost less than US$1000 to perform. And that includes round-trip airfare from Denver to Boston. I also want to thank Southwest Airlines for letting me hand-carry the fragile electron tube both ways, and to the TSA official with a BS in physics who recognized the device on X-ray and waved me through without opening the box. I have a direct test involving muon lifetimes in the planning stages. If I can coax the TeachSpin muon detector into doing what I want, it may be feasible by late this year.

OK, I've read van Holten's 1991 and 1993 papers. His theory gets the same time dilation as mine (and Apsel's), since the equations in both papers essentially say deltaE/E = deltaT/T, which is the right formula at least for deltaE << E. (Not surprising: it's the only answer consistent with h nu = E = mc^2.) The really odd thing is that, despite him commenting absolutely correctly that "It is quite clear from this formula, that any quantity which contributes to the energy E in an observable way, also contributes to the time dilation", he seems completely fixated on strong external fields and completely blind to the possibility of dilation by a field-free potential. To see how silly this is, he gives an example of a spin-down muon in a magnetic field of 5 GT, when the same energy shift (and hence dilation) can be caused by putting the muon in an electric potential of a few kV. It's a lot easier to generate a potential of a few kV than a field of a few billion Tesla. The nice thing of course is that this makes the theory testable with "educational" grade equipment. Some of the first experiments I proposed involved things like 25 ton toroidal NdFeB permanent magnets. My latest require under US$5K of total equipment, and I got a tour of the physics storage room at CSU this week and practically everything I need is already there. So I plan to run experiments starting in a few weeks. After a year of theorizing, it feels good to be putting the question to nature, who will tell me whether I am smoking crack, in line for a Nobel prize, or more likely, somewhere on the long continuum in between with a lot of work still ahead of me.

First I would like to thank Jarek for directing me to this discussion. The latest version (1.2) of my paper is at http://www.riverrock.org/~howard/QuantumTime12.pdf (or .tex). I disagree with the notion that time dilation is inherently an effect of motion. As I show, the stationary gravitational time dilation in GR is identical to the change in rate of phase oscillation in QM for stationary solutions to the Schrodinger equation, so it is entirely possible to discuss TD in stationary or static contexts, and in fact easier to see the deep link between GR and QM in that way. In fact gravitational time dilation can be derived from Newtonian mechanics and the de Broglie relation, and so can be viewed as fundamentally quantum-mechanical in nature. Special relativity and the Maxwell equations really have nothing to do with it. (They do, of course, have a lot to do with EM TD.)