Slashdot Mirror
Physicist Claims Time Has a Geometry
sciencenews writes to tell us that a physicist at Stanford has just recently published a peer review website for several physics lectures focusing on a single underlying idea that "time is not a single dimension of spacetime but rather a local geometric distinction in spacetime." The science is presented quite clearly and originally uses GPS systems as a point of focus. From the article: "Not too long ago, people thought the Earth was flat, which meant they thought that gravity pointed in the same direction everywhere. Today, we think of that as a silly idea, but at the same time, most people today (including most scientists) still think of spacetime as if it were a big box with 3 space dimensions and 1 time dimension. So, like gravity for a flat Earth, the single time dimension for the 'big box universe' points in one direction, from the Big-Bang into the future. A lot of lip service is given to the idea of "curved spacetime", but the simplistic 3+1 'box' remains the dominant concept of what cosmic spacetime is like."
Is available at the author's website, timecube.com.
I always knew my high school geometry teacher came from another dimension.
I suggest you read Slashdot
I agree that there aren't a lot of people who intuitively reach to the Lorentz transform to explain the progression of time, but there are plenty of obvious reasons for that. Not sure it takes a Stanford physics prof. to make what is essentially a epistemological point though.
For kicks, check out one way to visualize the spacetime wheel.
http://tinyurl.com/4ny52
Robert Heinlein used this as the central idea of his book "Then Number of the Beast" in 1986 The Number of the Beats
You are in a maze of twisted little posts, all alike.
Perhaps someone should tell him that general relativity has already been invented. Physicists know that time has geometry---it is, after all, a part of spacetime, which has geometry. With regard to his claim that GPS has unexplained anomalies, he may be right. However, GPS is based on the Schwarzschild metric, which assumes a non-spinning, point-like mass. The earth is neither of these. Accordingly, there will be small corrections due to the combined effect of earth's spin and its density profile. At present, we are unable to calculate those corrections (we've only solved some important special cases, because the math is so hard), but they almost certainly explain the GPS deviations.
The novel idea that there are an infinite number of time dimensions in the Universe revolutionizes gravitational theory and much of modern science with it. A number of outstanding scientific mysteries are definitively solved, including observations that lead to the concepts of 'dark energy' and 'dark matter'.
A number of outstanding scientific mysteries are also solved with my new unpublished theory that 1+1 = 2. Doesn't mean that the idea holds water, though.
I think that many problems in academia are because of "publish or perish" advancement. I think this is an example in point.
If time has many dimensions then I wonder why we perceive it to go forward only (though at different relative rates depending on relative speed). The reason why we perceived gravity to point down only was just a matter of not being able to see the big picture, although I would have thought more people would have noticed the Earth is round sooner, the curve is clearly visible from most mountaintops. So what's the big picture we need to see in order to see more dimensions to time? How do we step back and notice the slight curve in the horizon?
It sure seems like time goes forward only, from my own day to day observations. My mind can't even comprehend what going another direction (except for "backwards") would even mean as a concept.
"Time is an illusion. Lunchtime, doubly so."
Not meaning to troll or anything but this has quite a few of the silly science traits. Not saying its junk but a healthy skeptical approach is necessary here.
Basically if it was the genuine article, I would expect the website to list his position with Standford (he appears not be facutly) and his previous work. I didnt see that. The power point presentation has all the signs such as lots of pretty graphs and pictures which "prove" this (although admittedly this is better than most) and a lot of big words. What I would expect to see is a bit of hard maths and maybe one example, he's coming on far too eager. Also he focuses on what it fixes, what does it break? I want some predictions for experiments to measure. Its easy to explain one or two effects with a theory, the real test is what does it predict. I would also expect a link to a preprint explaining this and its abstract. I would go so far that any serious scientist would post a preprint on xxx.lanl.gov as the first step of going public.
I'm very doubious about any werid and wonderfull theory coming from somebody who is outside the world of science, as theres a lot of chafe out there. Just go the poster session of the APS annual meeting to see what I mean. Okay its helpfull to keep an open mind, Einstein came from the outside with his really werid seemly crackpot theories but that happens rarely.
Now just to point out I'm not saying its junk, I havnt read it yet, just saying it appears to raise of a few of the warning flags.
In my experience, scientists who work with such issues are quite clear on this point (and, so far as I can tell, have been for eighty some years).
But for other sorts of scientists (e.g. biologists), engineers, and the rest of us, who only need to calculate things to five or ten decimal places or so, assuming that the time points in the same direction throughout the area of interest (and generally that space is flat and such) is reasonable--so reasonable, in fact, that we'd be nuts not to work with that as an assumption.
If I'm tracking the migration of some sort of beetle or planning a system of trusses to support a load or deciding if I should walk or drive to the store for milk, I would have to be mad to start out treating spacetime as a fine-grained network of plank-scale events with information flow between them determining the local geometry of space time (and thus the direction of time). Likewise with the effects of nearby astronomical bodies--if they were big enough and close enough to seriously distort spacetime I'd have a lot bigger problems to worry about. On average, to the level I'd ever need to deal with in these sorts of cases, it is now and the future is coming up later and the past is what already happened.
--MarkusQ
"Not too long ago, people thought the Earth was flat" It's a common misconception and almost modern myth that people in the recent past believed the earth was flat. The truth is that it was generally accepted by most learned people that the earth was spherical from the 1st century onwards and many argued so much earlier. You can read more about this here: http://en.wikipedia.org/wiki/Flat_earth
Reading his paper/presentation it seems like he is throwing out the theory of relativity, and most of modern astrophysics.
I am a bit skeptical towards those who make revolutionary claims like this and publish it to the general public instead of in scientific journals.
Tor
Multidimensional representations of time do not get you to Oz. "Pantheistic solipsism" does, according to the book. The central idea of that book was that the world was all myth, and as such there's no reason you can't hop from myth to myth, as long as your particular myth was written by someone who will script you to do it. The parallel universes were only parallel in that they were all represented in works of fiction.
REM Old programmers don't die. They just GOSUB without RETURN.
Only Time will tell...
teehee~ (sorry.)
"I'm a Laver, not a Phyto[plankton]"
http://www.bede.org.uk/flatearth.htm -- This is one myth that really needs to die! Even more so than that Betsy Ross was involved with the American Flag.
There is definitely a good case to be made that the past-versus-future arrow of time is not fundamental. Basically our psychological sense that the past is different from the future comes from the direction of the thermodynamic arrow of time, but the second law of thermodynamics doesn't come from the basic laws of physics (which are essentially time-reversal symmetric) but from the boundary conditions of the universe: for some reason unknown to us, we had a low-entropy big bang. The meaning of "past" is really "that way to the big bang."
It's also probably true that in a complete theory of quantum gravity, the picture of three space dimensions plus one time dimension (3+1) would break down completely at small scales. The whole idea of distance and dimensionality is probably a large-scale approximation that loses its validity at small scales. There is a strong argument to be made that for fundamental reasons, spacetime must be discrete, not continuous, at the Planck scale. The only people seriously trying to construct discrete theories of quantum gravity right now seem to be the people doing loop quantum gravity (not string theory, which uses a flat 3+1 background of spacetime). For a good popular-level account of this kind of stuff, see Smolen's Three Roads to Quantum Gravity. In loop quantum gravity, they are able to construct an infinite set of possible universes (each one is a type of knot), but the problem is that none of them can be proved to resemble flat 3+1 spacetime, even asymptotically. In other words, there's no way you can even take this tangle of events and figure out whether it has anything like time and space that you can define on it. It's like being a flea living in a world that consists of threads woven together. On your scale, can't be sure whether it's a one-dimensional piece of yarn, a two-dimensional piece of fabric, or a three-dimensional wad of wool.
Find free books.
...people never thought the world was flat. For millenia, we've noticed that you see the top of a ship in the horizon before the rest of it, which was attributed to the world's spherical shape. One of the great Greek mathematicians also accurately determined the circumference of the Earth within a couple of miles, if I recall.
When this story gets duped, I'll be looking for this exact same comment.
And my response to it.
Unless you're editing a movie, it really doesn't make sense considering time as a an axis. It's almost as if time is a cohesion of forces expressed cumulatively across all forces in the universe. As objects move, the relative difference in forces expresses a change. That is time.
So perhaps time would be best understood not as a straight line, but as water sloshing around in a bathtub.
Another aspect of space-time may be a non-uniform fabric. We understand gravity as a curvature of space time. Perhaps there are multiple space times expressed via the three of the fundamental forces. Different fundamental particles are either affected or immune via these overlapping space-times. Particles affect one another via strong nuclear forces. These particles in turn affects the behavior of the whole as expressed across the three space times: gravity, electro-magnetism and weak nuclear.
Those were my thoughts.
-------- -------- Support Wesley Clark for president!!!
Spacetime perceives time as a one dimensional vector that is orthogonal to all other vectors. Because relativistic equations for time, distance, mass, etc, use a sqare root function, you get imaginary distances and imaginary time when an object exceeds C. Usually, an imaginary quantity means that you're looking at the wrong axis.
(Trivial case in point: when solving a quadratic equation, if the parabola doesn't intersect the X axis, you will get a complex number. If you break that down into real and imaginary components, the imaginary components correspond to the displacement in the Y axis for that solution's real component value in the X axis.)
Ergo, if a tachyon exists, it would experience a spacial axis as "time" and the time axis as space, UNLESS "time" is not a single axis, in which case all bets are off.
In consequence of not having a telephone-number IQ, I can only speculate wildly, but I'm going to guess that the relativistic equations do indeed refer to some measure of bleeding between space and time and that no further dimensions are required - for GPS or for any other phenomena governed by relativity. (Superstrings being about the only exception I can think of.)
I personally think that part of the problem is that time IS regarded as "special", whereas perhaps it would be better if it were regarded as special "only as far as absolutely necessary". To the extent that specialness is an extra parameter, you want to eliminate all extra parameters as far as possible (and no further).
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
I was brought up in a conservative, FSM-fearing family. All my life I believed that the FSM was the one and only divine creator, and that only through His Word I could reach salvation (stripper factory and beer volcano)
/. for leading me to the path of enlightenment.
Yet, today, as I read the teachings of Dr. Gene Ray for the first time, I finally saw the TRUTH. I have been lied to all my life but my anger only feeds my love for the Cube. We are all sinn^H^H^H^H stupid and only through the glorious Time Cube can we reach the ultimate, 4-corner, polar smartness.
Thank you
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Well I read the article and went through the power point presentation using Open Office :-)
I must admit, I'm convinced that time is different depending on where a person is. I know it for a fact 'cause where I'm sitting it took FOREVER to work through that presentation! Ugggghhhhh....
The race isn't always to the swift... but that's the way to bet!
...that's like saying ther's no "up" separate from "east". The real question is if they are orthogonal.
I have discovered a truly remarkable sig which this 120 chars is too small to contain.
This might work in theory, but I've never observed it.
What? You've never experienced deja-vu? That's what happens when you see the same cat twice, or something like that.
What? You've never experienced deja-vu? That's what happens when you see the same cat twice, or something like that.
Thought I saw it on an old bottle of soap.
Faster! Faster! Faster would be better!
Jump to page 25 of the second set of slides, where the author shows two time vectors at an angle to each other. If you have two observers, one with each time vector, then each observer thinks that the other is slowed down. Each sees redshifted light from the other.
This angle between time vectors can be caused by gravity or by the curvature of the universe.
In the gravity case, it is used to explain discrepancies in all sorts of measurements, from the Pioneer spacecraft, to the changes in the orbits of various celestial bodies, to discrepancies in the GPS, to the apparency that a U.S. atomic clock and a French one will each think the other is ticking slower. This is what most of the first slide show is about.
In the cosmological case, the idea is that the universe is round (see page 28 of the second presentation) and that the redshift that we think is due to the expansion of the unverse is actually due to the curvature of the universe, i.e., a galaxy around the universe from us will appear to have slower time, because its time vector is going in a different direction than ours. A galaxy ninety degrees around would appear to have time completely stopped, so it would be invisible to us (frequency of zero). Galaxies further away than that would be going backwards in time from our perspective, but we can't see them.
This is an idea I have not seen before. It seems really neat to me. It seems plausible but then (a) I can't personally verify the observations that he claims validate his theory; he could have produced fake graphs and they would fool me, but I would think it would be easy for him to get caught at that, and (b) even though I've had calculus up to differential equations, I never had non-Euclidean geometry or higher-dimensional stuff, so I can't actually follow his calculations very well. Then again, I didn't try very hard.
We shall soon see if he has made a significant error. The numbers and the observations will tell the story; either they work out, or they don't.
Sunlit World Scheme. Weird and different.
that the Timecube is *not* a Flying Spaghetti Monster. Most likely, Timecube is the 4th dimensional manifestation of FSM (or other way around. I wonder if hyperstring ... eh, hyperspaghetti theory has to do with it)
Can I get a research grant now? Kthx.
If you look at his colleagues,
i ng.html
http://www.scu.edu/spo/spring_03_2.htmhttp://www.stanford.edu/dept/physics/people/visit
then cross-reference a few of them:
http://www.gf.org/lfellow.html
Douglas N. C. Lin, Professor of Astronomy and Astrophysics, University of California, Santa Cruz: 1991
If you look him up he is all over about Astrophysics and applied mathematics.
Betty Young, Santa Clara:
Now if you research Betty you find this:
u ng.cfm
http://www.scu.edu/cas/physics/facultyandstaff/yo
Now whatever becomes of this Alex Mayer and his credentials are yet to be determined. However, I doubt Stanford would even allow him web space under the Physics department if he didn't have the credentials to back it up.
Something just doesn't seem right about that power point presentation. The part that raised my red flag, was that this guy claims that he's trying to "get the word out" to a general audience, yet he uses terminology that goes WAY over my head. That's when I know I'm getting bamboozled.
Authority questions you. Return the favor.
No they didn't. Find me one reference - other than the satirical Flat Earth Society - for that. If he can't even get his blurb right, what hope for his science?
If you were blocking sigs, you wouldn't have to read this.
"Einstein's relativity theory still remains a THEORY, seeing as how no one has actually tested the limits of it."
What has testing got to do with it? It will always be a theory, because that's all science can produce. If you want something definate you want mathematical theorems - those are known to be true. Theories never will be - they can just be very reliable at predicting things, nothing more.
Now, as to his claims, there are many. Most, if not all, seem to me to rely on his concept of "gravitational transverse redshift" GTR, which in turn (he claims) follows from "a simple thought experiment" on slide 6 of his first lecture, "A Correction to the Gravitational Model". A little though shows his conclusions on slides 6 and 7 to be incorrect. If A sees B's clock running slowly and B sees A's clock running slowly this leads inevitably to a contradiction - an inescapable paradox.
Say both A and B set their clocks simultaneously to zero, according to an observer at rest at a point O, halfway between A and B, while the spacecraft is at rest. The observer at O also sets their clock to zero at the same time. At this point both Mayer and Einstein would say that all three clocks are observed by A, B and O to be running at the same rate.
Let the spacecraft accelerate at rate g for t seconds according to the clock at O, which continues to be halfway between A and B. Then let the spacecraft coast - becoming an inertial frame again. Now all three clocks are again observed to be running at the same rate. According to Mayer though, O sees the clocks at both A and B to be lagging the clock at O, A sees the clocks at O and B to be lagging the clock at A, B sees the clocks at O and A to be lagging the clock at A.
We now move the observers and clocks at A and B to the location of O, taking great care to do so completely symmetrically, so that there is no reason to distinguish between A and B. Here is the paradox - according to Mayer, A continues to see B's clock lagging A, and B continues to see A's clock lagging B.
This is not the same as the twins paradox. According to O, who has been sitting in the middle all this time, the movement of A and B has been completely symmetrical and there is no reason to favour one over the other.
Since the rest of Mayer's argument, especially GTR, seems to me to depend on this thought experiment, and since his conclusions from the thought experiment are wrong, his remaining theoretical arguments will fall, unless they follow from other principles.
He's going beyond special relativity by allowing both special relativity, but also the unions among geometries which, with their relativistic delays and apparencies (e.g. red shifts), explain a lot:
1) time is non-linear within the same object, when the object is accelerating (and all objects are accelerating at all times; there is no restful object in the universe--relativistically), so measurements that were thought to be predictable through redshifts are not in fact predictable through the means we've been using and
2) these new domains of time can be thought of not as time-coherency but rather non-red shift, individual object domains. Calculating domains then becomes possible, as newly defined 'red shifts among red shifts' rather than the simplistic comparison from Einstein's equations. Einstein's equations were right, but didn't consider all objects can have their own relativistic differentials in time; hence the new 'geometric' concept. I like the idea, and will mosh it through my Mathematica constructs to see what happens.
---- Teach Peace. It's Cheaper Than War.
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Math theorems don't necessarily have to apply to the physical universe. The axioms on which the theorems are built are explicitly part of the theorems, leading to a logically self-consistent system. That is, you define the particular 'universe' you want to study by setting down axioms, then you prove things which you know are true about that universe because you've derived them in a logical fashion from those axioms you've set down.
Not strictly true. The "bede.org" page is right that flat earth cosmology was never, ever accepted by any Christian intellectuals. But pre-scientific belief in the ancient world (for example, in Greece before the 6th or 7th century bc) the idea that the earth was flat was very common, because the things that make the sphericity of the earth apparent weren't yet obvious to them (beginning with the shadow the earth casts on the moon during a lunar eclipse). This was a time when "astronomers" had a hard time understanding that "the morning star" (Phosphoros) and "the evening star" (Hesperos) were actually the same astronomical body.
What is this 'reality' you speak of?
Mathematics isn't constrained by our perceptions of what it 'should' be or what feels right. It's constrained by the axioms and principles we build it from. And in this case, 0.9 recurring is exactly equal to one. As you demonstrated, there are countless proofs of it (the one you selected being one of the less rigorous ones), and since the proofs are not incorrect, it means that their conclusion is wholly true, from a mathematical point of view.
Strictly speaking, math is every bit as empirical as physics. People have less confidence in physical theorems than math theorems because physics relies on math, and because physics has a heavy dependence on observations. But the basic validity of math also depends on observations. In particular, where mathematical systems can be interpreted as describing themselves, it is no longer safe to think of "math reality" versus "physical reality" as being complety distinct. One example that comes to mind is the Axiom of Choice; you can take it to be true or false, and in both cases you get a logically consistent mathematics (like euclidean vs noneuclidean geometry). But despite this empirical status, the Axiom of Choice has major consequences for abstract mathematical "truth".
Also, from philosophy standpoint, math relies on lots of nontrivial physical observations that humans take for granted (e.g. of paper, of mental states, etc). This concern goes beyond mere speculations about pathological situations (what if I'm insane? what if my life is a conspiracy like in the Matrix?). A key result of the 20th Century is that it's entirely possible that study of arithmetic will one day lead us to conclude that our basic model of arithmetic is logically inconsistent. In fact, Kurt Godel showed that proving the consistency of arithmetic is actually impossible in any conventional mathematical/metamathematical system.
-Gonz
You know when you fall down? Well, the part when your head hits the ground, you know that part, that comes after you're mostly done falling? Well, that part confuses me. And there's some kind of relationship to distance, because the further I fall, the more confused I get when my head hits the ground. I have verified this through empirical testing, although lately, I've been unable to commit all the resulting data thus obtained to long term storage.
Well, uh, I am interested in your ideas and would like to subscribe to your newletter.
I've fallen off your lawn, and I can't get up.
Please stop harping about Lorenz and time.
In his paper "On the Cause of Geodetic Satellite Accelerations and Other Correlated Unmodeled Phenomena", via the American Geophysical Union in December 2005, he outlined specific modifications to general relativity. The paper's Abstract begins:
"An oversight in the development of the Einstein field equations requires a well-defined amendment to general relativity that very slightly modifies the weak-field Schwarzschild geometry yielding unambiguous new predictions of gravitational relativistic phenomena."
The result of this amendment is an additional relativistic effect. As you may know, in general relativity, the velocity of light is a constant. Thus one's velocity relative to a photon can result in a shift of measured frequency, i.e. the red-shift, or blue-shift of spectra. Also, since the theory claims that accelerated reference frames are identical, this shift is also observed due to gravitational acceleration.
The author claims that gravitationally induced red-shifting is also dependent on the angle through which a photon travels in a gravitational field. In addition, the theory discusses gravity and angular momentum. An accelerating electric charge emits electromagnetic energy. Though long theorized, a similar gravity wave has never been observed. The author suggests that angular momentum, e.g. spinning and orbiting masses emit electromagnetic energy as well. Thus, orbits even in a perfect vacuum will decay. As a spinning body slows, or orbital momentum decays, this energy will be balanced by radiation in the microwave range.
The additional source relativistic red shift, and the additional changes with respect to conservation of momentum, have profound cosmological import, if true. The theory passes the simplicity and beauty tests admirably. What I particularly like about his presentation has to do with testability.
He discusses numerous problems with the GPS and geodetic satellite systems, various puzzling data from several deep space missions, the orbits of planets and moons, and show how his equations account for the discrepancies in the data. He also proposes a number of simple experiments which could prove or disprove his theory. He predicts what to look for in terrestrial microwave radiation, and suggests experiments that could be run using existing satellites which could prove or disprove his theory. He also suggest that other scientist look at data which has already been collected but which he has never seen, and predicts what patterns might confirm the theory.
From the ground up, the ideas are well reasoned, and his approach seems scientifically sound.
Time gets into the mix, because the broader ramifications of the theory are large. Imagine a space ship under constant acceleration. On the floor (aft bulkhead) place two clocks communicating via pulses of light. He shows how each clock (even though they share the same acceleration reference frame) will each view the other as slow. By virtue of general relativity, pairs of clocks on earth should likewise each view the ticks of another clock as slow. Thus, there is no common, universal time. The rate of time is a local attribute at each location.
The cosmological implications if this theory are also impressive.
There is no need to posit dark matter or dark energy. They are discussed only to account for missing matter and the expansion of the universe. However, if this theory is true, the universe is not expanding, thus removing the need to postulate dark energy. The matter needed to keep galaxies from flying apart is no longer needed. Rotating galaxies are radiating microwaves and slowing down, not being gripped by dark matter. The universe finite and unbounded. It is neither expanding nor contracting.
No big bang would have happened. Remember the history of the theory? It was attempting to account for red shifted stellar spectra and for the microwave background. If the red shift is a relativistic phenomenon (not the result of unive
hi,
...
[disclaimer: i am an experimental high-energy physicist -- i am not an "expert" on GR but it's a sucker bet that i know more about GR than most of y'all do]
i've gone through the lengthy lecture presentations and mayer meets the (or at least my) criteria for good science from a theorist -- he makes specific predictions which can be tested against empirically obtained datasets -- however, i didn't do the nasty integrals required to be done to see if he was simply lying and i will have to take him at his word that he has done them
essentially, the kernel of his hypothesis is contained at page 32 of his "lecture 1" pdf -- it is a small correction (in the weak-field approximation if i grok correctly) of the underlying metric which is the differential element which is used in standard GR calculations
*everything* in GR depends on the metric -- if mayer's metric can be empirically (or theoretically) motivated and, while using the differential geometry/GR mathematical machinery accrued over the last century or so, it can provide a more close approximation to empirical results than standard GR, then it is valid and more than worthy of further consideration
mayer provides a *very* long list of predictions about phenomena where standard GR predictions have failed to match the data and each of his predictions seems more or less rigorously derived from his singular assumption -- whether he has published or not (and a spires search did not yield any publications), and whether he is a post-doc, professor, grad student or invertebrate, he makes no appeal to authority (as i somewhat do in this posting) -- he only asks that his predictions be tested against unbiasedly observed reality
yo, gotta go --- i see it's super bowl time, chips and beer are waiting
cheers,
kevin
Given that caveat, I found Mayer worth a serious look. He's got a number of references showing measurements that GR does not explain. The most convincing stuff is from GPS satellite measurements which show an unexplained sawtooth pattern with a period of two cycles per day and an amplitude of several feet (or nanoseconds). GPS satellites and ground stations explicitly correct for the general relativistic effects of the earth's gravity well, so any anomalies would be very interesting. But he's also got anomalies in measurements of hydrogen 21 cm radiation and in the effect of Ganymede on signals sent from the Galileo spacecraft.
If Mayer faked the anomalies (but I believe they're real), he would be shot down in no time. Assuming the anomalies are real, then any theory that can explain them in addition to the rest of the effects explained by GR (precession of Mercury's orbit, redshift of a gravity well, etc) deserves a serious look.
One other point. In grad school, when we students complained about the many annoyances involved in writing and publishing our work, my advisor would say "50% of science is communication." There's alot of wisdom in that. There are plenty of cranks (or not so cranky folk) out there tugging on physicists' sleeves and saying "Einstein was wrong and I have a notebook full of equations to prove it!" I know such a fellow myself, but it would take weeks to examine his equations and maybe months to explain his errors. What he and his ilk lack is the ability to communicate like a scientist. Anyway, where I'm going with all this is that Mayer suffers no such lack. His 'Lecture 1' document is much better than average writing by a scientist. While this doesn't prove his equations are better than Einstein's, it is further reason why he deserves a serious look.
--- Often in error; never in doubt!