Science without Determinism

[Actaeon]

Perhaps I'm simply close minded, but the more science moves toward chaos theory and the like, the more I appreciate Einstein's unyielding determinism. From my perspective, there is something inherently incongruous about disproving determinism scientifically, since science is based on experimentation, which in turn relies on the presumption that the same conditions will produce the same result. You're an intelligent bunch. What am I missing here?

[Student of Trinity]

Nothing is moving towards chaos theory. People have been studying more about the complicated properties of nonlinear equations, but nobody has introduced any new fundamental equations into physics. Any chaos in physics is chaos that has been there since Newton's day. We're just looking at it more closely now.

 

Chaos is deterministic. It's just that it's very sensitive to initial conditions, so you need to know the present REALLY precisely to predict the future very far. But with enough computer power we can still predict fairly far ahead based on available data even for some technically chaotic systems.

 

So in fact there's no big change involved in chaos.

 

What Einstein famously objected to was the non-determinism of quantum measurement. However one feels about this, though, it has proven perfectly compatible with experimental method. You just have to broaden your definition of 'same result'. In quantum experiments, the same conditions reliably produce the same probability distribution of results. And since electrons and such are really cheap and plentiful, you can easily run quantum experiments very many times under the same conditions — in particular, very many more times than the number of distinct observed outcomes — and confirm that the results are random but governed by the same probability distribution whenever the conditions are the same.

 

That might not have made Einstein happy, but it has proven quite compatible with scientific progress.

[Slawbug]

Scientific Progress Goes 'Bok'

[Upon Mars.]

That's the whole point weather it is determined or not.

It's going to be hard to prove one or the other.

 

But i'd rather read Sophocles and say much like Oedipus that i am in control of my destiny; contrary to belief Oedipus rex isn't really a tragedy... he chose many things.

So here's an exemple that science is not the only thing turning away from determinism.

Even religion is far from it, when it suit's it's case.

[Alorael at Large]

What Einstein objected to was randomness, as SoT says. It may not seem elegant, but it definitely seems true. It's true at such small levels, though, that calling it non-deterministic is like calling rolling a die billions of times non-deterministic. This is conceivably true, but in practice it's irrelevant.

 

—Alorael, who also doesn't think science relies on input A producing output B. If this does not happen, you have learned something about the connection between A and B. This is, in fact, important to quantum mechanics. It's only an issue if either A can produce anything or B can appear sometimes no matter what the input is.

[Upon Mars.]

Thanks for the information;

So basically we were using quantum mechanics before we discovered gravity?

I mean by that that we had the answer just under our nozes right?

[Alorael at Large]

I can't tell if you're serious or not, but the answer is no. Quantum mechanics really don't affect anything observable without a fair amount of modern equipment. Not being able to accurately predict things just made previous models wrong.

 

—Alorael, who supposes the answer was also immediately available. The lack of infinitely powerful ultraviolet was a dead giveaway. The fact that nobody jumped directly from there to quantization just proves everyone used to be dumb.

[Student of Trinity]

Actually Max Planck was a highly competent theoretical physicist, as well as a genius who earned his PhD at 21 and was a full Professor by 31, ten years before he discovered the quantization of energy. Without benefit of hindsight, it was not at all clear that the ultraviolet catastrophe in black-body radiation demanded a radical solution, because it was not clear that the equipartition theorem really applied to short wavelength light.

 

The obvious boring but messy solution to the catastrophe was just that short wavelengths of light somehow fail to come into the ideal form of thermal equilibrium with the walls of a hot container. Exactly how light can get emitted and absorbed by matter was not understood then, so there must have seemed to be plenty of wiggle room in this direction. Planck spent a lot of time trying to understand the interaction of light and matter, however, and got far enough to see that there was actually much less wiggle room than it appeared.

[Alorael at Large]

Joking!

 

And Max Planck was clearly a genius. He solved the ultraviolet catastrophe without actually caring much about ultraviolet catastrophe.

 

—Alorael, who can take potshots at Nobel Laureates when he has more Nobel Prizes to his name.

[Student of Trinity]

Yeah, I realized it was a joke, but this has sort of been a pet peeve of mine for a long time, because now even when we do understand quantum mechanics, we still don't understand equipartition or equilibration very well. And taking them for granted in explaining the origin of quantum mechanics, which is what all the textbooks I know do, has the effect of making people take them for granted even more.

[Slawbug]

Originally Posted By: upon mars

But i'd rather read Sophocles and say much like Oedipus that i am in control of my destiny; contrary to belief Oedipus rex isn't really a tragedy... he chose many things.

Isn't the whole point of Oedipus Rex -- or at least the moral it hits you over the head with -- that Oedipus makes choices in an attempt to control his destiny and escape the fate that has been decreed for him, but he is unable to do so?

[Ephesos]

Pretty sure that was the point. Hubris and all that jazz.

[Kelandon]

Originally Posted By: Inestimable Sirs

He solved the ultraviolet catastrophe without actually caring much about ultraviolet catastrophe.

This made me crazy when I found this out in my history of physics class. Apparently the ultraviolet catastrophe was not a big deal on anyone's mind back in the day. It was based on such obviously faulty assumptions anyway that, while it was mildly troubling that if failed so badly, it wasn't all that big a deal that it failed. There were other things that people did care about that were failing badly at the time that Plank set out to figure out, but not that one.

SoT has pointed out before that everything in quantum mechanics except measurement itself is deterministic. The wave function evolves deterministically over time, etc. This has led to a lot of hand-wringing about "measurement" — what the heck is it, exactly, and why is it so darn special?

There's some idea that physics is full of math, and some people even want to say that if you get the math right, then that's the important thing, and everything else is secondary. (People used to tease Heisenberg that he was that way, whereas Niels Bohr was very much the opposite.) But I think the history of quantum mechanics illustrates that physics needs to be able to be expressed in words, too, and if we can't decide what the words should be — if we can't get the words right — then that's almost as bad as getting the math wrong. People argued for decades (and to some extent still do) about the right words to use in expressing quantum mechanics — and they kept arguing because it's important!

[Student of Trinity]

It is important, but not for knowing what measurements to make or what devices we can build. 'Shut up and calculate' works fine for those purposes.

 

Where the words may come to matter more practically is in trying to apply quantum mechanics, or conceivably change it, in circumstances where its application is not so unambiguous. Namely, the so-called 'mesoscopic' regime, where dozens to thousands of degrees of freedom are all interacting non-trivially, but on length and time scales small enough that classical mechanics does not yet apply.

 

According to quantum mechanics, there is nothing terribly special about this regime; it's just more complicated. But quantum mechanics has never actually been tested in this regime, until around now. Now we're getting into it. So pretty soon now we'll be able to summon the shades of Schroedinger and Boltzmann together to a seance, and compel them to talk to one another. We'll see what they have to say.

[Celtic Minstrel]

Chaos theory is a bit of a misnomer. As SoT said, it doesn't actually involve any randomness at all, and it's completely deterministic.

 

As for getting the right words, perhaps that's also important for really understanding QM?

[Randomizer]

Words have power. Getting the words right helps cut down on confusion so everyone has the same idea of what's being described. Some subfields have different meanings ascribed to the same words.

 

Try reading Gravitation by Misner, Thorne, and Wheeler where three different mathematical notations are used in the equations for general relativity. The joke was that the book was written by three authors that never met. So you have the same topics written in each notation.

[Student of Trinity]

MTW, also known affectionately as 'the phone book' because it's a three inch thick paperback, has never been considered a fantastically good GR text. It's just that in a sense it's the only GR text, because it's the only one that makes a serious effort at covering all the basic topics in a pedagogical way.

 

I had the good fortune to learn basic GR instead from a dedicated dyed-in-the-wool general relativist who was pedantic as all true relativists are, but charismatic as only some are. He looked a lot like a Guardian from a Green Lantern comic, and learning GR from him was kind of like learning physics from God: gentle but uncompromising, lucid but thorough.

 

(GR = 'General Relativity'. In 1905 Albert Einstein updated Galileo's 1632 theory of relativity to make it consistent with Clerk Maxwell's 1865 theory of electromagnetism. In the 1905 theory only non-accelerating reference frames were considered; because of the restriction to this special case, the theory is called the 'special theory of relativity', or 'special relativity'. In 1916 (after a preliminary version in 1915), Einstein extended his theory to include all possible spacetime co-ordinate systems; this is 'general relativity'. The big surprise — and the thing that lifts Einstein head and shoulders above everyone else — is that general relativity is also a theory of gravity. In fact, it's the modern theory of gravity; Newtonian 'universal gravitation' is now considered only an approximation to Einstein's more exact theory.)

 

(It's downright silly, really, how huge an achievement this was by Einstein. We can put it this way. If Einstein had only done special relativity, he would have entirely deserved his public reputation, which is based just on it — the general public knows nothing of GR. If someone else had then come along and created General Relativity, extending Einstein's special relativity and incorporating gravity at the same time, then this person would unquestionably rank higher in physics than Einstein would have if he had not done GR. But the same darn guy did both!)

 

(In fact he also quantized light, predicted Bose-Einstein condensation, discovered quantum non-locality, and invented fluctuation-dissipation relations. By modern standards he should have been entitled, by my count, to no less than six Nobel prizes. He only actually got one; no-one else has ever won or deserved more than two. But I guess we could say it doesn't matter. He had the Einstein prize: he was Einstein.)

 

 

[Alorael at Large]

He got more fame than Feynman. I think he'd be content. And at some point awards become a nice but unhelpful recognition of accomplishment. Einstein didn't quite single-handedly revolutionize all of physics, but he certainly got his hands in enough of the field to be unavoidable. And he had the hair.

 

—Alorael, who would like to learn something from God someday. He just hopes it's not the Old Testament God. That could get awkward very quickly.

[Swimmin' Salmon]

I really like watching Feynman teach. He was pretty clever.

[Celtic Minstrel]

Originally Posted By: Student of Trinity

(In fact he also quantized light, predicted Bose-Einstein condensation, discovered quantum non-locality, and invented fluctuation-dissipation relations. By modern standards he should have been entitled, by my count, to no less than six Nobel prizes. He only actually got one; no-one else has ever won or deserved more than two. But I guess we could say it doesn't matter. He had the Einstein prize: he was Einstein.)

And the Nobel prize he won wasn't even for his most ground-breaking work, right?

[Niemand]

It was for the photo-electric effect, which from a vantage point 90 years later seems interesting but nowhere near as spectacular as much of his other work.

[Randomizer]

Einstein got his Nobel prize for his least controversial work at the time. Discovering an effect is a sure way to get a Nobel prize considering the number that have been awarded.

[Student of Trinity]

It was less spectacular in the sense that it was less thorough. Relativity was, both times, kind of a slam dunk: Einstein worked it all out, and about all that's been done since is work out consequences and particular solutions for the equations he posulated. For his theory of the photoelectric effect, Einstein invented the photon. He quantized light. This was definitely as profound in its way as relativity, but it took forty more years before a coherent full theory of quantum electrodynamics was hammered out, and Einstein didn't really contribute to that big project.

 

Anyway the Nobel committee managed not to completely ignore relativity. Einstein's citation was "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect".

[cfgauss]

Originally Posted By: Student of Trinity

Exactly how light can get emitted and absorbed by matter was not understood then, so there must have seemed to be plenty of wiggle room in this direction.

I was under the impression that most of these arguments could be (and had been) ruled out on fairly general grounds, at least qualitatively?

I'm also confused as to why you say "we don't understand equipartition or equilibrium very well." We understand them very well. (Unless you mean the way scientists unfortunately tend to use the word understand as in "we understand it very very well but not completely.") I mean, they certainly are not usually well explained, but that's a whole other story .

Originally Posted By: Student of Trinity

MTW, also known affectionately as 'the phone book' because it's a three inch thick paperback, has never been considered a fantastically good GR text. It's just that in a sense it's the only GR text, because it's the only one that makes a serious effort at covering all the basic topics in a pedagogical way.

I never thought it was too bad. It's only problems are that it's very wordy, and overly qualitative compared to what people want to do with calculations, but in this case that's good, since in order to not go totally nuts and try to invent Lorentz invariance violating gravity, you really need to carefully understand things.

People also tend to talk about Einstein not doing much with regards to field theory, or really much else after GR and the foundations of QM, but if you look at the stuff he was publishing about in, say, the '50s, it was stuff like Kaluza-Klein theories. So, basically, he was working on pre-string theory .

edit:
Oh, also, to clarify on what was said earlier about chaos. Chaos is only deterministic when you have either no measurement errors or small enough scales which are suppressed somehow. Although the latter is technically more "morally" true than literally true. In fact, you can find chaotic maps that will, e.g., map any arbitrarily small neighborhood of the plane to the entire plane. (Although I do not believe any physical system is likely to do this!)

[Kelandon]

It was hard to award him a Nobel Prize for GR when GR had so few tested predictions. I mean, the Eddington thing was a big deal a few years after Einstein published, but it wasn't until the 1960's or so that people could do precise enough measurements in the right conditions to test a lot of the other predictions.

 

That's one of the tricky parts of working on fundamental physics, really.

[cfgauss]

Originally Posted By: Kelandon

It was hard to award him a Nobel Prize for GR when GR had so few tested predictions. I mean, the Eddington thing was a big deal a few years after Einstein published, but it wasn't until the 1960's or so that people could do precise enough measurements in the right conditions to test a lot of the other predictions.

That's one of the tricky parts of working on fundamental physics, really.

Technically, that's true, but GR is actually exactly the same as SR in some sense. Fairly generally, GR is the simplest extension of SR to local reference frames. Mathematically speaking, GR follows from SR just like x=2 follows from x^2=4. But a bit more complicated .

Indeed, in that GR bible that was mentioned earlier, it's mentioned that one never actually has to know about GR to do GR. If you really wanted to, you could *always* do SR and get the same answers if you were careful not to mix distant reference frames! (You can only mix frames close together.) So GR and local SR are really exactly the same theory (and you only really test local SR) so every test of SR automatically tests GR!
[Edit: this is true in the same sense that Newton's "infinitesimal" calculus ("SR") is the same as modern limit calculus ("GR"), their structure seems very different, but if you're careful all the answers you get are identical, even though infinitesimals can be a huge pain sometimes.]

The surprising thing is that local SR came from E&M, and gives you gravity! It's almost like there's a bigger picture here, huh?

This, by the way, is part of the reason theorists found it so disturbing that quantum mechanics works fantastically well with SR, but fails with GR. (Although the failing is not as bad as is often reported!) Now-a-days (that is, from the ~'80s on) it's been fairly well understood what's going on.

[Student of Trinity]

The electron had only been discovered in 1897, nothing of atomic structure was known, and the specific heat of solids was a standing puzzle. So the interaction of light and matter was a pretty murky area in 1900. The obvious thing to try would have been to model the unknown atomic structures that emit and absorb light with collections of charged harmonic oscillators. That was what Planck did, as theoretical background to his empirical proposal.

 

Equipartition is understood today in the sense that we can assume various nice statistical ensembles and work out their consequences. But our grounds for invoking ensembles are hand-wavy at best.

 

Einstein's Kaluza-Klein theories were classical; he made no contributions to quantum field theory. Extra dimensions are a detail in string theory, not the main idea.

 

Simply applying Lorentz invariance locally would mean constructing a generally co-ordinate independent formalism in flat spacetime. But the main point of GR is that spacetime can be curved, and its curvature has a specific relation to the energy, momentum, and pressure of that matter that occupies it. SR says nothing about curvature.

 

Any curved space is still locally flat. This is a subtle point, but here's how I explain it. I once found a snippet from a Flat Earther publication that proudly claimed a negative empirical test of earth's curvature. After hearing one too many times about how ships disappearing over the horizon were passing over the curvature of the earth, a couple of these fanatics had sailed out a few miles themselves, and found that the sea was still just as flat out there as ever. And they thought that this observation disproved the curvature of the earth. Now, it might be very hard to explain to these guys just what they were missing, but I think most people can see where they went wrong. And the crucial thing that those brave Flat Earther sailors failed to understand is exactly what is meant by the statement that any curved space is locally flat.

 

Anyway, the analogy is that SR is the part of spacetime geometry that those Flat Earther sailors might have been able to understand. GR is the part they definitely wouldn't. This is a big distinction, so it's really not true that GR is just localized SR.

[Celtic Minstrel]

Originally Posted By: cfgauss

Oh, also, to clarify on what was said earlier about chaos. Chaos is only deterministic when you have either no measurement errors or small enough scales which are suppressed somehow. Although the latter is technically more "morally" true than literally true.

Chaos is deterministic because if you put a specific specific set of numbers in, you'll always get the same result. It's chaotic because if you round one of those numbers to one less decimal place, you'll get a different result.

Originally Posted By: cfgauss

In fact, you can find chaotic maps that will, e.g., map any arbitrarily small neighborhood of the plane to the entire plane. (Although I do not believe any physical system is likely to do this!)

Well, the cardinality of any section of the plane is the same as the cardinality of the whole plane, so yes you can find bijections between them. But what has that to do with chaos?

[Student of Trinity]

I believe that he means an area-preserving map, plus all numbers of iterations of it. It's easy to define infinitely stretching maps that spread a small region into the whole plane in one shot, but the idea is that any single iteration of this map preserves area.

 

Iterated area-preserving maps are often used as toy models for Hamiltonian chaos. Since Hamiltonian time evolution preserves phase space area, taking an equally spaced sequence of snapshots of Hamiltonian evolution does represent an iterated area-preserving map.

[Celtic Minstrel]

...I have no idea what you just said.

[cfgauss]

Originally Posted By: Celtic Minstrel

Chaos is deterministic because if you put a specific specific set of numbers in, you'll always get the same result.

Yes, but chaos without perfect measurements is nondetermanistic. If you make a measurement, you are inherently talking about a probability distribution that, under your chaotic system, evolves in time into some crazy looking distribution that may even in principle do something as perverse as allow every possible value with equal probability for late-time measurements. You can loosely think of this by thinking about what happens to the 1-sigma neighborhood around the point under the map.

Non-chaotic maps (essentially by definition) map that one sigma neighborhood to "reasonable neighborhoods" which typically preserve a sensible notion of evolution of error bounds.

You can also think of chaos as having something to do with entropy by thinking along these lines, but that's more of a technical discussion than I feel like going into!

Originally Posted By: Student of Trinity

Einstein's Kaluza-Klein theories were classical; he made no contributions to quantum field theory. Extra dimensions are a detail in string theory, not the main idea.

Well, so's E&M, and exactly the idea of KK theories was to combine the classical versions of all of the gauge theories known at the time. Once you have that, it is, in principle, an easy matter to quantize them by imposing commutation relations.

And in fact, the excitement behind KK theories was partly due to the extra unexpected fields they created that could be identified with particles. The hope was the force-carrying fields would all be from the geometry, and matter fields would be in the spew of moduli fields that came out.

Einstein and the other people working on them were certainly aware of field theory's development at the time, and were incredibly clever to see that you could actually get almost the same thing with KK theories. Their only mistake was hoping that the cannonical commutation relations could also come out of geometry, which is a bit too simple to hope for (but by no means unreasonable to guess is true).

And that's why (aside from anomaly cancellation, etc) that extra dimensions are very much the main idea in string theory! Them, and their structure is what makes it possible for the theory to have any hope of reproducing a sensible particle spectrum at all! (You can try to have 4d strings, but as we learned in the 60s and 70s those fail hilariously to reproduce anything that looks realistic.)

Quote:

Any curved space is still locally flat. This is a subtle point, but here's how I explain it. I once found a snippet from a Flat Earther publication that proudly claimed a negative empirical test of earth's curvature.

Yeah... but... they were doing it wrong... that's not really an argument for anything at all .

Quote:

This is a big distinction, so it's really not true that GR is just localized SR.

It is in fact not only true, it is exactly true! It is a simple (and fun!) exercise to prove that, writing the SR action, and making lorentz transforms local instantly gives you GR. That is, local lorentz transforms are diffeomorphisms. A more fun, but less simple, exercise to do is to carefully work out all the differential geometry details as you do this and watch where all the exciting stuff appears out of nowhere! (AFAIK no text does this carefully, it's something you've got to do yourself.)

Now, to be sure, it would be a huge pain to analyze any extreme case of GR in only SR correctly, but you definitely could do it. The same algebra magic you do in the action to write the covarinat derivatives to turn SR into GR is how you'd compare SR frames in the right GR way. But you would just look at it as a local "linearization" from an SR point of view. This is actually exactly why you can trivially do uniform acceleration in SR even though you "shouldn't" be able to do it. Everything about curvature, or other GR ideas are hidden inside this apparent "linearization," but it's still there, just as how uniform acceleration in SR works even though that should need curvature to do properly.

A problem for the industrious reader: how is the covariant derivative above related to the ones in qfts and gauge theories? (Harder, but more exciting, problem: write every gauge theory (including GR) so they all look identical!)

[Sporefrog]

This thread is amazingly incomprehensible. I love it, keep it up

[cfgauss]

Originally Posted By: Sporefrog

This thread is amazingly incomprehensible. I love it, keep it up

I didn't study string theory so everyone could understand me . But if you want clarification on anything I'll be happy to try to explain, if it's possible to do without several weeks' worth of lectures.

[Hypnotic]

I have given up on this thread. All I see are terribly long posts that do not make any sense. Still its good to learn things even if you forget them straight after you learnt them.

[A less presumptuous name.]

Originally Posted By: Celtic Minstrel

...I have no idea what you just said.

This

[Sudanna]

Yes, because they actually understand this particular bit of reality, unlike we laymorons.

[Celtic Minstrel]

Originally Posted By: cfgauss

Yes, but chaos without perfect measurements is nondetermanistic.

That's not what nondeterminism means. Chaos is deterministic because, with perfect measurements, you can predict the outcome exactly.

[cfgauss]

Originally Posted By: Celtic Minstrel

Originally Posted By: cfgauss

Yes, but chaos without perfect measurements is nondetermanistic.

That's not what nondeterminism means. Chaos is deterministic because, with perfect measurements, you can predict the outcome exactly.

It's exactly what nondeterminism means. It means you can't determine exactly what happens. It doesn't really have an exact formal definition, and I think that's part of the confusion. But the idea is that distributions assigned to measurements are always delta functions in a limiting sense. But this doesn't happen for the example I gave.

Specifically, you have a function f:R^2->R^2 such that
f(a) = p is well-defined for all a and p in R^2,
but,
if I = D_r(a) a disc centered at a with radius r,
f(I) = R^2
for ALL r>0 in R.

Then, if you have non-exact measurements you can simplistically characterize your measurements as being some distribution on D_r(a). That is, I measure something like "distance = |a| +/- r".

If f represents a physical system, say, the x-y coordinates of a chaotic pendulum at time t0 as a function of initial x-y positions. Then what does this mean?

I measure at time 0 the coordinates a=(x0, y0), with an uncertainty r, so I'm certain to whatever confidence interval I like the actual value lies inside of D_r(a).

I take f(a) to find my most likely value for the pendulum later. Now, I'd like to calculate the probability distribution associated with it to find out how likely the value is f(a) given my initial accuracy.

So I find f(D_r(a)). But that's all of R^2! Since my distribution must be normalized to 1, that tells me the probability that at time t0 my coordinates are f(a) is zero! [Edit: it's 0 because you've smeared the finite area disc to the whole of R^2]

In other words, this system is so chaotic, that any measurement you make at time 0 is completely uncorrelated to any other measurement you make at any other time!

Surely the most extreme example of nondeterministic that you can get!

Of course, real systems aren't quite as bad, but they can be nearly as bad. Often, the best you can hope for is some kind of exponential suppression in your correlation between initial and "late time" states.

This is something that's possible to investigate numerically with, e.g., a pendulum on a spring and a computer, to see exactly how bad this effect is in realistic cases. Though you have to be careful the chaos doesn't ruin your numerics of course!

And again, this has something to do with entropy. If you ever take a grad-level stat mech class (or a good undergrad one, but I don't know that such a thing exists; in fact I have doubts that good grad ones exist too ) you'll show how entropy comes about classically by arguments like I have, but in phase space instead of configuration space (ie, entirely classically!).

So in an idealized case, this example is deterministic. But if you know less than everything about the system, it's completely nondeterministic!

Contrast this all with a simple mechanical system (eg, a point moving in a potential) where you can just easily plug an analytical solution into the error propagation formula to calculate not only finite but sensible probabilities. In that case, by making your errors arbitrarily small, you can make your late-time measurements as accurate as you like---the definition of deterministic!

[Swimmin' Salmon]

The intellectual elites have won. No drinks thread, just one for strings.

[Celtic Minstrel]

Originally Posted By: cfgauss

So in an idealized case, this example is deterministic. But if you know less than everything about the system, it's completely nondeterministic!

But the whole point of determinism is the idea that if you know the initial state exactly, you can uniquely predict the outcome. Which makes your example deterministic, not nondeterministic.

[Student of Trinity]

What is "the SR action"? There are Lorentz invariant actions for various fields other than gravity, but the metric itself has no action of its own in SR. Insofar as mere terminology matters, the normal definition is that SR means flat spacetime. What's more than just terminology, though, is the fact that to get GR you need to do more than just relax the assumption that the metric is flat. You also need to add the Einstein-Hilbert action, which isn't there at all in SR.

 

Classical Kaluza-Klein simply is not quantum field theory by any stretch. You can get mass quantization by compactifying the fifth dimension, but this does nothing to make the gauge fields into operators. Quantizing Kaluza-Klein has all the same trouble as quantizing GR: no-one knows how to fix the gauge without reference to some background metric, and if you try to proceed by perturbing around some given metric, the theory is manifestly non-renormalizable.

 

GR can be considered a gauge theory, but it is not like other gauge theories because the gauge field for Lorentz transformations is the Christoffel symbol, but in GR it's important that this is derived from a metric, for which no analog exists in other theories. This brings us back to the Einstein-Hilbert action: it's an action that can't be generalized to other gauge theories, because it needs the metric. It's not the only possible or even the only reasonable action, for a Lorentz group gauge theory (the Kretschmann scalar would be fine, for instance). it's just the one that correctly describes gravity.

[Dantius]

I'm sorry. I really am. Your discussion of arcane physics, relativity, advanced scientific knowledge, and other things laymen were not wont to know, has brought the only possible punishment upon yourself. This must be done. It is divine retribution.

 

TIMECUBE!!!!!

 

 

I am wiser than any god or scientist, for I have squared the circle and cubed Earth's sphere, thus I have created 4 simultaneous separate 24 hour days within a 4-corner (as in a 4-corner classroom) rotation of Earth.

*******************************************************************************

When the Sun shines upon Earth, 2 - major Time points are created on opposite sides of Earth - known as Midday and Midnight. Where the 2 major Time forces join, synergy creates 2 new minor Time points we recognize as Sunup and Sundown.

The 4-equidistant Time points can be considered as Time Square imprinted upon the circle of Earth. In a single rotation of the Earth sphere, each Time corner point rotates through the other 3-corner Time points, thus creating 16 corners, 96 hours and 4-simultaneous 24 hour Days within a single rotation of Earth - equated to a Higher Order of Life Time Cube.

+++++++++++++++++++++++++++++++++++++++++++++++++++++

-1 x -1= +1 is WRONG, it is academic stupidity and is evil. The educated stupid should acknowledge the natural antipodes of +1 x +1 = +1 and -1 x -1 = -1 exist as plus and minus values of opposite creation - depicted by opposite sexes and opposite hemispheres.

[The Mystic]

Dantius - Could you please try not to hurt my eyes with posts like that? Thank you.

[Dantius]

That's the whole point- if there was a prize for least-aesthetically designed webpage ever, Timecube wins hands down. It would also win the "incomprehensible", "insane", and "unintentionally hilarious" awards, too.

[The Mystic]

No, just "painful to people whose eyes are slightly more sensitive than normal." I'd like to keep my retinas intact, thank you very much; I'm probably on the path to eventual blindness as it is, and don't want to rush.

[Callie]

Why is it such a big deal that people are discussing subjects you can't comprehend? There was absolutely no need to interrupt the thread in such an abrupt manner.

[Ephesos]

*cough*... you know, a link to the site would've been just fine. No need to go wrecking up the place.

 

Also, I wouldn't really even call it a site. More like a drunken rant rendered in long-winded HTML. Anyone who clicks the link should be warned, it's very odd.

[Dantius]

I didn't link because of a few racist and anti-semetic comments. I just excerpted the crazier parts. What is it about the Internet that makes any crank who can get a website believe that they have uncovered the grand unified theory of everything EVER that will win the the Nobel Prize and accolades of the masses? I could never figure this out.

[Alorael at Large]

Huh. I didn't know that Time Cube was anything but harmless quackery. The dabbling in reactionary politics makes me a bit disappointed in what I thought was incomprehensible but inoffensive New Age hilarity.

 

—Alorael, who apologizes for further derailing the detangling of the mysteries of relativity. You may carry on.

[Swimmin' Salmon]

I prefer my root beer to have been made with real cane sugar.