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."

Comments

direction(s) of time

[bcrowell]

I admit I haven't read every word of his two massive sets of lecture slides. He seems to be trying to make the case that various anomalies in astronomical and geodetic data point to something wrong with general relativity. That would be cool, but extraordinary claims require extraordinary evidence, and although we know that general relativity is not the correct theory of gravity at the Planck scale, there's every reason to believe that it's correct at the classical scale. If you want to read about tests of classical general relativity, check out the book Was Einstein Right? by Clifford Will. He discusses various alternatives to general relativity and how they've been tested.

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.

Lecture2Signed, page 25

[Sunlighter]

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.

Re:Point(s) of interest

[ZombieWomble]

0.999999999999999999999.... is always going to be the smallest possible difference from 1 in reality.

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.