space and time do not commute
June 27, 2009 6:54 PM   Subscribe

TOE breaking Lorentz invariance - "by treating space and time differently as well as separately, the infinities in the quantum mechanics equations vanish, and gravity behaves as it should." posted by kliuless (44 comments total) 24 users marked this as a favorite
So ... do I eat the red pill or the blue pill?
posted by ZenMasterThis at 7:05 PM on June 27, 2009

The universe is a weird place, with several large outstanding problems from our current point of view and innumerable smaller ones. However, while there are weird aspects to the universe, the idea that it might not be Lorentz invariance is really quite disturbingly weird. Some would say horrifically. And it's premature to declare it the correct explanation, to say the very least.
posted by edd at 7:09 PM on June 27, 2009

posted by edd at 7:09 PM on June 27, 2009

This stuff is way over my head. But I'm wondering if this new proposal explains Bell's Inequality.
posted by Chocolate Pickle at 7:16 PM on June 27, 2009

For some reason Wikipedia's Lorentz Invariance article redirects to Lorentz COvariance. I can't tell if they are supposed to be the same thing nor what the latter even is. From another link, it sounds like it might be a more mathematical version of galilean relativity? I'm not sure I'm ready to give that up yet....
posted by DU at 7:19 PM on June 27, 2009

That stuff is way over your head, but not Bell's Theorem?

Wow. I got a headache just skimming that article.
posted by mr_crash_davis mark II: Jazz Odyssey at 7:20 PM on June 27, 2009

Bell's Theorem is way over my head too. But what I do get from it is that it made testable predictions which, if confirmed, proved that the universe was non-local. And tests have been done, and they confirmed non-locality.
posted by Chocolate Pickle at 7:26 PM on June 27, 2009

Didja ever talk to a dog and notice how the dumb animal cocked his head and pricked up his ears and furrowed his brow in an attempt to make sense of what you were saying? Yeah, that's me reading these links.
posted by BitterOldPunk at 7:29 PM on June 27, 2009 [13 favorites]

Yes, Lorentz covariance is Lorentz invariance.

No, it's not going to 'fix' Bell's Inequality and the nonlocality of QM, at least as far as I'm aware.
posted by edd at 7:29 PM on June 27, 2009

Incomprehensible theory is incomprehensible.
posted by fnerg at 7:32 PM on June 27, 2009 [4 favorites]

Klammer and Steinacker posit that space and time do not commute
God also works from home; old bugger's been phoning it in since Genesis.
posted by Abiezer at 7:35 PM on June 27, 2009 [4 favorites]

From the wikipedia article on Lorentz Invariance:

Mathematically LQG is local gauge theory of the self-dual subgroup of the complexified Lorentz group, which is related to the action of the Lorentz group on Weyl spinors commonly used in elementary particle physics. This is partly a matter of mathematical convenience, as it results in a compact group SO(3) or SU(2) as gauge group, as opposed to the non-compact groups SO(3,1) or SL(2.C).

This is, to me, functionally the same as this (in)famous video about Rockwell Automation's Retroencabulator.
posted by Tomorrowful at 7:38 PM on June 27, 2009

Interesting idea. I think. The author does a remarkably poor job of explaining anything of actual note. He kinda-sorta explains Lorentz invariance, but then doesn't even start to explain where it's possibly wrong or why, or what it would actually mean to observers.

As far as I can see, he expresses almost no useful information himself. It's not a summary article. It's a vague, handwavy, half-assed description of papers that neither we nor the author understand.

Hopefully, someone will come along and give an actual summary. In the interim, I'd recommend skipping the article linked here. It's a lot of words without enough content to make reading them worthwhile.
posted by Malor at 7:45 PM on June 27, 2009

Hopefully, someone will come along and give an actual summary.

it's quite simple actually - the moon is no longer the north wind's cookie
posted by pyramid termite at 7:51 PM on June 27, 2009 [2 favorites]

Metafilter: vague, handwavy, half-assed description of papers that neither we nor the author understand.
posted by YoBananaBoy at 7:53 PM on June 27, 2009 [1 favorite]

it is simple in theory

But seriously, can this be explained in a classic Metafilter twelve paragraph comment? Or less?
posted by TwelveTwo at 7:53 PM on June 27, 2009 [1 favorite]

it's quite simple actually - the moon is no longer the north wind's cookie

No: wookie, not cookie.
posted by paladin at 7:56 PM on June 27, 2009

To summarize the reduction procedure, space and time are treated separately, which would normally cause all sorts of problems in quantum mechanics. However, by treating space and time differently as well as separately, the infinities in the quantum mechanics equations vanish, and gravity behaves as it should.
I thought that quantum mechanics already treated time 'separately'

As far as I can see, he expresses almost no useful information himself. It's not a summary article. It's a vague, handwavy, half-assed description of papers that neither we nor the author understand.

Yeah, that was my impression as well. There's not a single equation here.

Also, in relativity, time and space are not 'the same.' this article by Scott A. Aaronson explains the difference in a way that makes sense and appears (at least to me) to actually explain the math as far as it's relevant to the point he's making.
posted by delmoi at 8:04 PM on June 27, 2009

I'm still going sailing tomorrow, regardless of the (in)validity of the Lorentz Invariant.

This however, was well worth the link.
posted by Artful Codger at 8:13 PM on June 27, 2009 [1 favorite]

"They show that this sort of universe would naturally have an early inflationary period, and that the universe slips out of inflation nicely into the universe we observe."

Man, we printed so much money the *universe* is inflating!
posted by jamstigator at 8:42 PM on June 27, 2009

Anything that helps in understanding the workings of gravity and gets me that much closer to my Bladerunner flying car is progress in my book.
posted by QuestionableSwami at 8:48 PM on June 27, 2009

*randomly assaults someone with a skateboard*
posted by loquacious at 8:52 PM on June 27, 2009 [3 favorites]

Watson, my dear elementary.
posted by drhydro at 8:56 PM on June 27, 2009 [1 favorite]

Can we please get a summary for the stupid people?

Because when the stupid people get angry, we break things, and are too dumb to fix them.

Don't make us break space, or physics, or whatever.
posted by paisley henosis at 9:05 PM on June 27, 2009

I'm sorry, you know I love you, I just get so mad…
posted by paisley henosis at 9:08 PM on June 27, 2009

But does this mean there's a privileged frame?
posted by GuyZero at 9:08 PM on June 27, 2009

No, no, hold on everyone -- I understand it now! This picture from Wikipedia helps so much! I CAN SEE FOREVER
posted by Frobenius Twist at 9:18 PM on June 27, 2009 [1 favorite]

So... Do we get teleporters and FTL or what?
posted by Artw at 9:36 PM on June 27, 2009

No, no, hold on everyone -- I understand it now! This picture from Wikipedia helps so much! I CAN SEE FOREVER

That's one helluva die.
posted by TwelveTwo at 9:37 PM on June 27, 2009

Its so far over my head I couldn't hear the sonic boom as it passed.

The idea of space and time being commutable in the first place struck me as odd. I mean, we can slow down time (traveling fast) but we cant go backwards. Where we have the ability to move in all dimensions of space, backwards and forwards (from a coordinate grid perspective).
posted by SirOmega at 10:18 PM on June 27, 2009

Hm. I can't get access to the actual articles because I am far from my university at the moment. Here's my stab at Lorentz invariance from the perspective of a mathematician, knowing nothing about physics except what I learn from Wikipedia.

So let's say you are trying to draw a picture of gravity. You measure gravity at every point in the universe, and attach a little arrow to each point pointing in the direction that gravity pulls, and with length according to how strong gravity is at that point. So around earth, you have a bunch of arrows pointing down, but the further you are from the surface of the planet, the shorter the arrows get. That's a field. If you make a theory about it, it's called a field theory, and if you want more grant money to study your theory, you call it a quantum field theory. (And if you're batshitinsane, you call it a topological quantum field theory.)

Now, if you're a scientist trying to make general predictions about How Things Work, you would like to say that coordinates don't matter. So if I took the entire universe and moved everything in it, say, three feet to the left, then everything should still work exactly the same. Or If I rotated everything about some axis, or moved everything forward in time one hour; all the rules should still work the same way, because the relationships between the objects are the same after the transformation. This is what Lorentz Invariance is about. The Lorentz Group consists of all of the 'legal' ways you can move everything in the universe without fucking up the basic fabric of the universe in the process, and thus keep everything working as it should.

But if you watch too many Nova specials, you might have a problem with this. Let's try moving everything on earth three feet to the left. It makes sense to move my house three feet to the left, but if I try to move _everything_, then something strange will happen: I won't be able to do it. If everything moved to the East, for example, then the stuff at the North and South poles would be fixed, and wouldn't have moved the three feet I required them to. (And worse things would probably happen, too.) This is because the earth is curved, not flat: if the earth were flat, we could certainly move everything three feet east and not worry a bit.

Which brings us to those Nova specials, which tell us (along with relativity) that space-time has curvature, just like the earth does. It's tricky to get one's head around, though, because we can easily visualize the earth's curvature (it curves through a larger-dimensional space), but the space-time curvature isn't so easily seen: we can't jump out into whatever 84-dimensional space that the universe bends though and say, 'oh, yeah, it really is kinda curvy.' But we _can_ see this curvature in more subtle ways.

So then we see the problem with Lorentz Invariance: it doesn't really make sense to move everything three feet left, because the universe itself is curved, and if I tried to do this, then things would bunch up together at certain places and get too far spread out in other places, and wouldn't hold the same relationships to each other anymore. There's a bit of saving grace, though, because the curvature of the universe seems to be caused by the objects in the universe itself. So if you moved everything, then the curvature would move with the stuff.

That's just for the large scale, though; my understanding is that at the small scale, things are much more messy with respect to curvature. What can we do there?

Think of trying to make a sphere out of cloth. It's really hard to do with just one cut of fabric; you get all kinds of bunching up and stretching in order to make it look right. But what you can do instead is take a whole bunch of smaller pieces of flat cloth and stitch them together into something that is pretty curvy, but doesn't stretch the individual pieces of cloth too much. (Example.) So if I want to rebuild the universe out of flat bits, I should take lots and lots of flat pieces of space-time and try to stitch them together in a very fine way that emulates the curvature. These individual flat bits are called 'local coordinate systems.' The stitching is called a 'transition map,' and essentially tells you when you're in overlapping coordinates how to translate between the different coordinate systems.

So once we've given up on moving the whole universe three feet to the left because of this curvature problem, we can start looking at these local coordinates, and try to find ways to shift things around on that scale. And indeed, since the pieces are flat, I can move everything a little bit in one patch, and then look at the transitions to see how to move things in the next patch over, and so on and so forth until I've moved everything in the universe.

So this is my new, refined version of Lorentz Invariance: it's all the ways I can stitch together local transformations of the universe such that all of the physics stays the same. (I'm pretty sure this,or something close to it, is called a 'gauge theory,' for what its worth. You get a group of allowed local transformations at each point, and then a group of total transformations of the universe on the global scale.)

ok, that's enough for now... hopefully it's a little helpful.

Delmoi: It's worth remembering the Riemann's most pivotal work only had a single equation, which wasn't really all that memorable. I'll agree that equations are important for making things precise, but they aren't necessarily the best thing for explaining something to us plebs.
posted by kaibutsu at 10:35 PM on June 27, 2009 [57 favorites]

SirOmega: While the direction of time is incredibly obvious to us living in space and time, there's this annoying theme in physics in which it isn't at all obvious from the mathematics that time should prefer one direction over the other. See: The Arrow of Time. Building an arrow of time into a basic component of the physical theory in a meaningful way would be, from what I gather, a Big Deal.
posted by kaibutsu at 10:43 PM on June 27, 2009

First off, Chocolate Pickle isn't quite right about Bell's inequality; all bell's shows is that experiment is inconsistent with a local hidden variable theory. That is, quantum mechanics predicts results only statistically: the electron is going to be spin up or spin down, but I can't tell you which until you go test and find out. There would be a "hidden variable" if actually physics did somehow know before hand if the electron is spin up or spin down. A local hidden variable is a theory without "strange action at a distance" that somehow magically knows if the electron is spin up or down before you measure it. Bell's inequality and the experiments done to test it show that no such theory exists. So... you can either try to make a nonlocal hidden variable theory, or you can go in a another direction-- many worlds is a common interpretation.

I can't see how these new Lifshitz papers have anything whatsoever to do with Bell's inequality, however.

Unfortunately, it's also not clear that these papers describe a theory which is internally consistent, either. It certainly has (as it rightly should have) generated a large amount of interested in the theory community; the number of papers which have been posted on arxiv which have explored various consequences of the theory is quite large. A few of these papers are very critical however. The main criticism that I know of is that to be a viable theory that is a candidate for the world as we know it, Lorentz symmetry must be approximately true at lower energies (after all we have alot of evidence that relativity works pretty well-- up to a certain energy range). I have heard arguments on both sides of the issue and I don't think it's resolved yet.

Anyhow, boy do I get irritated when a few papers get a significant amount of press before the scientific community really has time to vet them. This work was published only this past fall (although it was being worked on for a year or two previous to that); it takes a while to see if such a new idea actually has useful results. This implementation of getting rid of Lorentz invariance is new and clearly of interest; however really not developed enough for the public light (and it's not personally clear to me that it ever will be).

But since it's out there, here's the super super short version:
1) Theories which are relativistic have the same units for space and time. (what? well the speed of light is a constant, just some number, that is the same everywhere and always; so that means i have a way to relate meters to seconds). Another way to think about this is that a "light year" is really a measure of distance. Just add the word "light" in front of any time and you get a distance measure and we all know what distance that is. IT's how far light goes in that time.
If I say 2 light years, you know that's twice as far (and the light had twice as long to get there).

2) Theories of the Lifshitz variety do not have the same units in different directions, in the same way that the length of a meter stick and the area of my floor do not have the same units. I can't describe the area of my floor in meters, only in a unit of area- like a square meter. or an acre. (Big floor!). So, in a lifshitz theory, the right way to describe a distance in terms of a time might be as a light square-root-year (or maybe a light (year^2)).

3) As to why this is useful, I'm just going to state a few facts. There are these annoying infinities that show up when you try to quantize various theories, but sometimes in a given dimension the infinities are manageable (we call this "renormalizeable"). For normal relativistic gravity, this dimension is two- one space, one time (this is why string theory seems like a good idea-- the objects you're talking about have one space dimension, along the string, and one time dimension). For the Lifshitz gravity that Horava proposes, I believe the dimension where these infinities magically go away is 3 space, 1 time. Which happens to be where we live, so that's pretty cool- except we live in a world where space and time *do* have roughly the same units (as in (1) above). That's a pretty big "except".
posted by nat at 10:44 PM on June 27, 2009 [6 favorites]

Chocolate Pickle: one interpretation of Bell's theorem illustrates a very odd sort of non-locality -- odd in the sense that quantum mechanics allows for events to have stronger correlations than allowed by local probabilistic theories, but while at the same time preserving causality in the special relativistic sense. If anything, the only confusion is that in principle there appears to be no reason why these correlations couldn't be stronger while still preserving causality, but there is no conflict between quantum mechanics and special relativity (i.e. quantum mechanics is perfectly compatible with special relativity ... so much so that there is a QM description of EM fields). The problem is trying to mesh QM with general relativity, which is the theory that says something about gravity as well.

Another interpretation doesn't say much about locality, but more about "reality", in the sense of whether physically observable properties have a definite value even when they are not measured. But that would be yet another tangent.

Moreover, the violation of Bell's inequalities in QM have not been verified experimentally in a satisfactory manner. There are two loopholes in the experiments performed so far: one due to proximity of the separate measurements which must be performed, and one due to how good the detectors used in the experiments are. While there are experiments which close each of the loopholes separately, there is none so far that cover both -- although it is widely expected that it will happen soon enough.
posted by TheyCallItPeace at 10:53 PM on June 27, 2009 [1 favorite]

Oh, and kaibatsu, or others who are interested-- I believe all of the listed papers are available in near-to-published form at arxiv:

The original paper which is wierdly not linked in the posted article

papers in the TEO article
Horava, Spectral Dim. paper
Klammer and Steinacker
posted by nat at 10:53 PM on June 27, 2009

I haven't read the technical papers here, but the idea that Lorentz invariance is only an approximate symmetry of the real universe is not completely outlandish.

The idea of using symmetry as a predictive tool was first used to make predictions by Einstein, in the formulation of special relativity. A "symmetry" means that you can measure something in an experiment, change your experiment in a specific way, and your measurement does not change. For instance, most experiments have "translational symmetry." If I measure the boiling point of water at my house, I'll get something near 100°C. If I pack up my apparatus and bring it your house (the "transformation"), I'll get the same result. In the case of special relativity, the experiment is "measure the speed of light in a vacuum" and the transformation is "move at a constant velocity." In order for this to come out for all observers, your measurements of lengths and distances have be different in experiments that are moving relative to you than they are in experiments that are stationary relative to you. The transformation between space and time was first worked out by Lorentz, so it gets his name, and theories where special relativity works are called "Lorentz invariant."

There are some other useful symmetries in physics. In the physical descriptions of small systems, like two colliding baseballs, the dynamics are the same whether you run time forwards or backwards. We say those systems are "invariant under time reversal," or "T-invariant." If you've studied electricity and magnetism, you remember that the choice for which sort of charge is positive and which negative is arbitrary — some people call it "wrong," since in ordinary electric circuits the negatively charged electrons go against the direction of the current. Electrodynamics is "unchanged if you conjugate the charges," or "C-invariant." And you might remember in electrodynamics struggling with the "right-hand rule," which is how you determine the direction of magnetic fields and magnetic forces. If you accidentally use your left hand you'll get the wrong direction for the magnetic field. But if you consistently use your left hand you'll get the correct directions for the forces, which is what you can measure in any experiment. So electricity and magnetism are unchanged if you switch your right hand and your left hand. This transformation is called "parity" or P, and is what a mirror does.

Since all three of these transformations (C switching charges, P switching right and left, T switching past and future) are symmetries of electrodynamics, people thought for a long time that they must also be symmetries inside atoms and nuclei. But in the 1950s it became clear that the "weak nuclear interaction," which can change a proton into a neutron, is not invariant under P. The initial indications are a little subtle, but the discovery experiment was very geometrical: a team made a sample of radioactive atoms all spin the same way, and found that the decay products went more towards the atoms' "north poles" than their "south poles." If you have a spinning atom you have to use the right-hand rule to define which end of the axis is north, so this experiment showed that weak interactions distinguish right from left.

You can also transform more than one of C, P, T at once. It turns out that the transformation from matter to antimatter is to flip the charge and to flip any spins. So a "CP" transformation turns particles into antiparticles, and a "CP-invariant" theory is one where particles and antiparticles are the same. Like parity, CP is a symmetry of most systems. But at some point in the history of the universe there was a big difference between particles and antiparticles, which led to our world not having very much antimatter. There is CP violation in particles with strange quarks and particles with bottom quarks, but it is not big enough to explain our matter-dominated universe. Testing CP violation by making particles and antiparticles and seeing whether they are the same is a big industry in physics right now. That's what's happening at the "B factory" accelerators, which make bottom quarks. It's the motivation for CERN's program to combine antiprotons and antielectrons into antihydrogen: is an antihydrogen atom really have, for instance, the same energy levels as a hydrogen?

But there are only so many ways to make antimatter. Another track to measure CP violation is to construct at geometrical observable. For instance, most fundamental particles have a magnetic dipole moment, but no one has ever observed a fundamental particle with an electric dipole moment. That's because the electric and magnetic fields are different under CP: both change sign under C, but you need a right-hand rule only for the magnetic moment. There's kind of a race right now to find an electric dipole: people are looking at muons, electrons, neutrons, and various heavy nuclei. Finding an electric dipole moment would tell you how much a CP-violating interaction has to contribute to the workings of a stable system. Go back to the water-boiling thought experiment. If I bring my boiling-point temperature measurement kit to your house, I'll still measure 100°C — unless you live at high altitude, in which case I'll get a somewhat lower temperature if I measure carefully enough. The fact that my water-boiling experiment depends on my altitude reveals that there's an interaction I didn't think of initially. In this case the interaction is between the vapor pressure of water and the ambient pressure of the atmosphere, and I can test that by doing the experiment again in a pressure-controlled chamber (at anyone's house).

What does all this have to do with Lorentz symmetry? Well it turns out that if you make a theory invariant under Lorentz transformations, it's also invariant under the combined transformation CPT. (This is why people say that "antimatter is the same as ordinary matter traveling backwards in time": the CP gives you antimatter, and after T any relativistic theory has to give you all the same predictions again.) Apparently Hořava's model isn't invariant under parity transformations. At some level maybe that's okay: the universe isn't invariant under parity transformations, either. But turning that statement into an observable to measure is a tricky thing. And even if you can find an observable to measure there is the question of the size of the effect. Parity violation in weak interactions went unnoticed for a long time because the weak interactions are … weak. It's quite plausible that Lorentz violation in quantum gravity would only show up near black holes, and that any related effect in Earth's gravity would be smaller than other noise.
posted by fantabulous timewaster at 11:46 PM on June 27, 2009 [26 favorites]

*kisses Metafilter* I love you so much.
posted by snwod at 12:08 AM on June 28, 2009

Ack! I have to go get flea medicine, please no more incredibly informative, compelling, funny comments til I get back.
posted by Mister_A at 5:43 AM on June 28, 2009

You should usually post the links when posting these stories, only people whose universities subscribe can download the articles linked from arstechnica.
posted by jeffburdges at 5:47 AM on June 28, 2009

nat and fantabulous timewaster are right-on. I'll just add one more comment about Lorentz invariance.

It isn't directly about gravity, it's something that arises from special relativity, and therefore must be accounted for in modern theories of gravity and quantum mechanics. Basically, most people have the idea that no matter how fast they're going, their clocks will tick at the same rate as anyone else, and any distances they measure (say, the length of a moving train) will be in agreement with everyone else. You can think of this as being a sort of "Newtonian invariance" (warning, made up terminology), no matter who's looking, they agree.

Special relativity says that this invariance is wrong: different observers will have their clocks ticking at different rates, they will disagree on measured distances. But the disagreements can be calculated in advance, and critically, there are some quantities that people will agree upon. For instance, if two observers (far from strong gravitational fields) see two events in space time, then they will agree upon the quantity:
distance between events^2 - c^2 * time between events^2
(where c^2 is the speed of light squared).

This is the origin of the phrase "Lorentz invariance". Now, there are other implications, but basically, if someone says a theory is Lorentz-invariant, it means that it's consistent with special relativity. This is critical, because we have a TON of observations validating special relativity. This new theory is NOT Lorentz invariant. Now, in principle it could still be okay, but it would have to be very nearly Lorentz invariant as long as space-time curvature was low.
posted by Humanzee at 6:23 AM on June 28, 2009 [2 favorites]

I can't wait till someone FPPs the New Scientist explanation of this and we can all bitch about it being too dumbed down.
posted by Artw at 7:53 AM on June 28, 2009 [1 favorite]

"And you might remember . . . struggling with the "right-hand rule," . . . If you accidentally use your left hand you'll get the wrong direction for the magnetic field. But if you consistently use your left hand you'll get the correct directions for the forces . . ." -Fantabulous Timewaster

Being a southpaw, I did this in a Physics 103 quiz many many years ago. Thanks for the memories.
posted by whuppy at 7:51 AM on June 29, 2009 [1 favorite]

fantabulous timewaster:

That was awesome. We need more people like you who can produce layman's explanations of advanced physics. (I know a lot more math and physics than the average joe, but not enough to follow quantum mechanics or the real math involved in relativity, let alone trying to reconcile the two theories.)
posted by spitefulcrow at 1:11 PM on June 29, 2009 [1 favorite]

A few recently published papers indicate that the long-running attempt to unite quantum mechanics and relativity might be finally seeing some compelling progress.

Quantum field theory successfully combines QM and special relativity. It's including general relativity that causes the headaches and employment of high energy theoretical physicists.
posted by Premeditated Symmetry Breaking at 1:59 PM on June 29, 2009

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