Common Sense isn’t so Common…

I went to the D programming conference back in August this year, and I ran into several interesting people. One was a former researcher of supergravity; I told him “Honestly I think supergravity is bullshit” he smiled and said “Yes, it pretty much is…”. He had a fantastically dry sense of humor (e.g. when giving his presentation he said “When you are programming, you don’t want to write harmful code…” I thought, yeah something that would harm the hardware; the speaker continues “…Like launching missiles.”). Another was an interesting software programmer that recommended me to the site “Common Sense Science“. It’s basically a pseudoscience site.

I looked through the links and noted that a number of them are to Creationist websites, which immediately told me this was as pseudoscientific as Lubos Motl and the Easter Bunny combined.  Looking at, e.g., the “Contradictions” page here are some of the problems:

“It is only a mathematical model consisting of equations and does not usually specify physical structure for elementary particles.”

I don’t know how well hidden this is, but historically science has always been described by mathematical models!

It’s complaining about the language that the theory is formulated in. Well, there’s a problem with this argument that Wittgenstein points out long ago: what can be said in one language can be said in any language, or languages are isomorphic (for the mathematicians out there ;)).

Their criticism that quantum mechanics does not specify the structure of subatomic particles is somewhat justified…since quantum mechanics explicitly assumes that we are dealing with point particles! I myself have entertained the view personally that subatomic particles could possibly have an “atomic” structure to them. Maybe they do, maybe they don’t, maybe we’ll never know!

But quantum theory works despite this “catastrophic contradiction” and even makes some of the best damn predictions in Human History! The Dirac Equation, Quantum Electrodynamics, the Hydrogen atom…need I continue?

“It frequently contradicts itself.”

It contradicts itself…because it contradicts itself.

Ah, well, it’s hard to argue against a tautology but this is a meaningless proposition. Old Wittgenstein should be rolling in his grave at a frequency that could generate power for all of Western Europe from this argument alone.

“It provides no mechanism for such fundamental processes as the exchange of energy.”

Actually, this is an interesting argument because I’ve dealt with dialecticians…philosophers obsessed with pseudoscience, holism, and “change”.

A thermodynamic process specifies the initial conditions of the process, then the final conditions when the process ends. Quantum theory does the same thing. So therefore, logically, thermodynamics is wrong! Despite being the one of most important things coming from the 19th Century (the other being the Stanley Steamer ;)).

The mechanism for exchanging energy, etc. is actually done through photons (Feynman diagrams anyone?). There is a sound explanation of what’s going on…and it dates back to the hydrogen atom quantization. Apparently these people never learned quantum theory, so “common sense” dictates they criticize it.

“Assumed properties of elementary particles.”

This argument is based on the previous argument, which is a considerably weak argument.

As I mentioned earlier, these people have links to Creationist websites…it turns out these people are Creationist philistines. For example, explaining life can only be done in the Judeo-Christian blah blah blah. After reading “can only be done with…Judeo-Christian” I stopped reading.

I refuse to part one pretty penny to purchase (yes, purchase) their technical papers since they appear to be crackpots already. (Nothing personal, dear Common Sense pseudo-Scientists, but I actually first derived the Lorentz factor by hand, geometrically from the two principles of Galilean relativity and the constancy of the speed of light back in high school…you mean to tell me that this is wrong because “there are contradictions” doesn’t jive with me.)

General Covariance Generally Irrelevant In Quantum Gravity?

Just a few quotes from Misner, Thorne, and Wheeler’s Gravitation (I love that book…it’s my Bible):

“By ‘prior geometry’ one means any aspect of the geometry of spacetime that is fixed immutably, i.e., that cannot be changed by changing the distribution of gravitating sources.“

(Italics are Misner, Thorne, and Wheeler’s; bold is my emphasis; this is on page 429)

“In this theory [Nordstrom's], the physical metric g (governor of rods and clocks and of test-particle motion) has but one changeable degree of freedom — the freedom in . The rest of g is fixed by the flat spacetime metric (’prior geometry’) .“

(The underlining is my emphasis; this is on page 429)

“Mathematics was not sufficiently refined in 1917 to cleave apart the demands for ‘no prior geometry’ and for a ‘geometric, coordinate-independent formulation of physics.’ Einstein described both demands by a single phrase, ‘general covariance.’ The ‘no-prior-geometry’ demand actually fathered general relativity, but by doing so anonymously, disguised as ‘general covariance,’ it also fathered half a century of confusion.“

(emphasis is mine; this is on page 431 of Misner, Thorne, and Wheeler).

Hmm…how could an approach to quantum gravity ignore something so pivotal in classical general relativity?

For some strange reason, Misner et al. think that “the ‘no-prior-geometry’ demand actually fathered general relativity”; so that logically means that we ignore the demand when quantizing gravity.

What could possibly go wrong? (Famous last words.)

As “shocking” as it may sound, when you use the weak field approximation, you are using a prior geometry. Misner, et al., point out this is “acceptable” as an approximation if . (It’s even stated explicitly in equation (18.1) of their tome!)

Is it all right for calculations? Yeah, it’s a good approximation; would it be wise to use this for quantization? Not really, since “the ‘no-prior-geometry’ demand actually fathered general relativity” and the linear approximation uses a “prior geometry”.

It might be “acceptable” for the weak approximation, i.e. where . Would it be the “final version” of quantum gravity? No, it would be only an approximation to the “final theory” at certain, specific regions…even then, it may not necessarily look anything remotely like the final theory. It may very well only give the approximate answers in the “quantum weak field”.

Is there any reason as to expect the quantization of an approximation that ignores the cornerstone of classical general relativity to be the “final version” of quantum gravity?

“Well, all the other field theories were doing it…”

That excuse doesn’t work for drugs, and it won’t work for field theories.

If gravity worked like “any other field theory”, we wouldn’t be having this discussion, now would we? The plain fact of the matter is that gravity is different…and that’s a good thing!

“But Einstein used the linear approximations for finding the Newtonian potential, and he made the buses run on time with them. And he lived in rainbows with leprechauns and magic pixies.”

Yes, that’s great…the linear approximation is a good approximation at the right scale. It simplifies computations, but that does not make it equivalent to having the metric be fully dynamical.

It is great for classical computations where using the metric would be burdensome…it is rather terrible for the fine details. It is the fine details that we are interested in however.

No one said quantum gravity was easy, just glamorous.

“But you can bootstrap your way back up to the full dynamical metric tensor!”

Interesting point, but not always true…point-in-case: gravitons. They really aren’t exactly linearized gravity insomuch as they are a quantization of it. Logically, the classical limit should return the linearized gravity, which should return the full blown metric…but you have to first return to the classical limit if you want the full dynamical metric! So this doesn’t really tell us anything new if we quantize it…perhaps it makes the linear approximation more approximate, but it is still requiring a prior geometry at the quantum scale. That sort of defeats the whole purpose.

IF we had a final theory of quantum gravity, THEN we wouldn’t have this problem; we could easily see how to get from the quantization of the linear approximation to the final theory. However, since we don’t have the final theory, we can’t really get rid of the prior geometry from the graviton approach.

So, although this is certainly true in the classical case, for the quantization of the linear approximation it’s rather unclear. It still uses a background metric, which indicates the existence of the prior geometry. IF there were some way to get rid of the background metric, THEN I would have less of a problem; but you can’t, so I have more of a problem.

Giving hand wavy arguments that quantum gravity will look “nothing like” classical gravity is rather unsatisfactory too. This means the concept of a dynamical background goes completely out the window?! This seems unlikely, and to someone who learned general relativity before quantum theory, very unsatisfying.

Such is life I suppose.

Lubos Motl: What An Honor!

I know I said I’d take the day off because I have to write an essay, but there are times when I have the urge to write prolific amounts.

The cause of this post is that Lubos Motl, the prophet of Strings, has written a prolific post on his blog dealing with the fallacious premises that I apparently begin with…unfortunately, I don’t really begin with them. Luckily String theory has the answer to everything! Kind of…

After reading through his post entirely, he either: 1) has terrible reading comprehension, 2) didn’t bother to read the posts (possibly skimmed them due to his importance as a string theorist), or 3) pulling red herrings to try and “prove” he’s right. It’s probably a combination of all three. Nearly a third to a half of the “myths” this guy “points out” is pulled out of his rectum. Well, I’m not afraid to say the emperor has no clothing (nothing’s stopped me so far).

It’s actually surprising to see a Harvard grad student not be able to read properly. No, not “surprise”, what would be the phrase I am looking for? “Horribly depressing beyond belief” yes that will suffice.

“Myth: The right theory of quantum gravity may be completely non-local“

I don’t know where Motl got this idea, perhaps he should try reading things a little closer. I previously stated:

“Worse, all the variables of general relativity are nonlocal (which isn’t necessarily a bad thing! Nonlocality is like cholesterol: there is the bad kind and the good kind, this is the good kind). Quantum Field theory deals with local variables.”

Dr. Motl rambles on to state that the correct theory of quantum gravity will be local, explains that nonlocality means that things move faster than light, and so forth. I think he needs to take this class more badly than me. There is a difference between the type of nonlocality in quantum theory which involves the wave function collapse in an EPR-like paradox transmitting information faster than light, and the nonlocality in the measurement of the position of Mercury via measuring the time it takes for radiation to hit Mercury and return to the observer with a nuclear clock. There are examples of nonlocal diffeomorphic quantities, e.g.

Where is a Laplacian quantity.

Overall there “appears to be” (uhoh, here’s another “big myth”) an inconsistency between locality and general covariance…this is the “Hole argument” in one of its many disguises. We now know better, perhaps this was what Motl was getting at but who knows.

“Myth: Quantization of gravity makes no sense at all“

Here Motl does the straightforward thing and attack the notion that quantum gravity makes no sense, what a surprise. OK, and…? He seems to be pulling this myth from his rectum.

“Myth: Gravity may be classical“

Hmm…again our dear prophet has some difficulties with his reading comprehension. The big push with semiclassical gravity was to assume gravity is classical and matter is quantized, then to see what you get.

“But but but this is impossible!” Well, semiclassical gravity is wrong (read: has been falsified), yeah. But it’s not really “impossible” (clearly not as it obviously has been formulated). As for it being physically impossible, we really couldn’t know or not…see Wittgenstein’s Tractatus for the impossibility of speaking logically of an illogical world.

“Myth: Only expectation values of operators follow their equations

The angry physicist writes something like the expectation values of Einstein’s equations, claiming that maybe, no other laws can be valid.”

Well thank goodness that Motl didn’t waste his time reading what I wrote, and instead just went directly to attack me! What a relief!

He is referring to the semiclassical gravity post, more specifically this section:

“We went on to discuss semiclassical gravity, where General Relativity is left as classical but the matter and energy is treated as quantum. He gave us another citation for this section (Page and Geilker, Physics Review Letters 47 (1981) p. 979. This changes Einstein’s field equation to

For the Einstein curvature tensor of spacetime , and the energy-momentum operator . This does not make sense since we are equating a tensor to an operator (it’s like equating a matrix of numbers to a matrix of operators, doesn’t work!). So we could possible make it an Eigenvalue equation:

Another possibility is to have

which is the expectation value of the quantized stress-energy tensor is equal to the “expectation value” of the Einstein tensor. This approach is called semi-classical gravity and was seriously considered in the 1960s.”

Motl’s description of the passage seems to indicate he either didn’t read it well or he has poor reading comprehension. Thank goodness he attributed it to me rather than the authors who came up with the idea (they’re in the passage above too!). If you can’t find it or you’re Motl, it’s Page and Geilker, Physics Review Letters 47 (1981) p. 979.

“Myth: Gravity waves could have continuous energy“

Again, this myth is pulled from Motl’s rectum.

“Myth: Quantum stress-energy tensor isn’t conserved“

I don’t exactly know why but the angry physicist argues that the covariant divergence of “T_{mn}” is not zero in the quantum theory.”

Well, this actually was an interesting argument, since he’s arguing that semiclassical gravity (since Motl may be reading, perhaps I should explain what “semiclassical gravity” is: treat matter as quantized and spacetime as classical) apparently doesn’t have any real problem and that I made up this problem. Oh snap, I didn’t make it up: here’s a technical paper on the problem whose first section deals with what I covered. Could it be that Dr. Motl, prophet of String theory, mystic saint that instantly perceives the truth, is full of it? No, never!

“Myth: The only task is to add nice hats“

Yes, that is the only task, as I’ve stated repeatedly in every post. Drat, you found me out Motl! If only there were some way to have actually proposed this!

“Myth: In the context of singularities, the only goal of quantum gravity is to make things look finite“

There are other goals of quantum gravity with regards to singularities? What more could there be other than removing them?! Motl didn’t elaborate on the other goals of quantum gravity in the context of singularities, but he did maunder on about irrelevant topics.

“Myth: The Hilbert space of black hole microstates is universal“

I don’t think that I have even mentioned the Hilbert space of a black hole, much less its microstates. Motl appears to be unjustly attacking Dr. Carlip, but I just can’t let him going around attacking researchers who are doing actual work progressing quantum gravity (yeah, I’ve got Carlip’s back on this one, I owe it to the man for letting me be in his course).

Well, I “would” have Carlip’s back on this one if Carlip didn’t do such a crackerjack job in his technical papers! He wrote in a paper back in 2005: “The black holes we are interested in are not two dimensional, of course, and despite some interesting speculation [22], there is no proven higher-dimensional analog to the Cardy formula.” –emphasis added (The reference is to E. Verlinde, eprint hep-th/0008140) This seems pretty damning to Motl’s argument:

“This is really Steve Carlip’s myth but it naturally fits into this text. In string theory, one can calculate the entropy of huge classes of black holes and other black things with charges, angular momenta, and diverse topologies in various dimensions. The calculation typically reduces to the Cardy’s formula: the microscopic machine to get the right exponential degeneracy of states boils down to the same method of counting of states in a conformal field theory.”

Hmm…it appears that Steve Carlip has somehow magically foreseen this prophet’s criticism and added salt to injury by actually criticizing it quite well.

“Myth: The problem of time means that everyone must work with non-local observables all the time“

Yes, that’s what I scribbled down in my notes, and wrote in the blog. I actually am starting to worry about poor Motl, seeing that his reading comprehension is worse than my 10 year old sister’s.

“Myth: We don’t know how to renormalize wave functions, and thus cannot really know how to get probabilities

Probabilities are always obtained as squared absolute values of probability amplitudes and there is never a problem with the normalization of the thing that is properly called a wave function - the state vector. It can simply be defined to be normalized to one. What we call “wave function renormalization” in quantum field theory is actually a renormalization of the field operators, not the actual wave function. The word “wave function” is only used for these operators because they may be thought as arising from single-particle wave functions by the second quantization.”

Now this grabbed my attention! Largely because Motl appears to be ignoring the fact that traditionally time has played the important role of renormalizing the wave function. By making time a coordinate, you have a problem with the renormalization of the wave function, and then a problem with getting the probabilities.

“Myth: “We don’t know if quantum gravity is generally covariant” is a meaningful sentence“

This myth that Motl is criticizing is rather perplexing…well, Motl’s criticism is anyways.

Here he does away with the notion that a good theory incorporates the predictions of preceding theories, and it makes new definite predictions. Instead, a good theory of quantum gravity is dependent on preserving general covariance.

I happen to agree with him that general covariance is an important feature of quantum gravity, it may or may not look the same in the quantized theory as it does in the classical theory, but to say that all theories without general covariance are wrong is too hasty a move. Things may look phenomenally different at the quantum level than expected classically.

“Myth: The Hamiltonian is 0 in any Hamiltonian formulation of classical general relativity“

Here Motl is merely venting his rage against the ADM machine. Frankly it works, so there’s not much to contest about it; and as for the Hamiltonian being zero, that’s covered in Henneaux’s Quantization of Gauge Systems. Perhaps Motl will read it one of these days (is anyone else finding it depressing that a first year freshman has read it but a Harvard professor has seemingly forgotten all of it?).

“Myth: A major task for quantum gravity is to find a nice field redefinition“

Perhaps, perhaps not…it seems that a major task for quantum gravity is to quantize gravity, but I’m a “radical thinker” in this regard. This really isn’t a “major task” and it hasn’t been presented as such, I commented in the semiclassical gravity post:

“There are a variety of other complications, like field redefinitions. It’s ambiguous enough in quantum field theory, but now it’s extraordinarily ambiguous! This is not a “fatal” objection, but it introduces complications.”

But Dr. Motl can feel free to keep ignoring what I write for as long as he likes (and people wonder why I’m angry!).

“Myth: Ordering ambiguities are an independent problem of a local quantum theory“

I love this man, he is like a magician: pulling myths from his hat.

Myth: Perhaps we could abandon this notion of the graviton and *gasp* move forward?

The existence of gravitational waves has been proven by the pulsars so that even the Swedes are satisfied. And the existence of quanta of energy carried by these waves is essentially proven at the beginning of the text. When quantum gravity is defined at a technical level, the scattering matrix for gravitons is not only the most important set of observables we have but, in some sense, the only one.

Also, any simple attempt to show a contradiction about the existence of gravitons is a result of sloppy thinking. Gravitons neither violate laws of thermodynamics nor they create infinite recursion, and the first somewhat technical analysis one can make shows that they are philosophically analogous, with almost all details, to photons.”

Ah yes, proof of gravitational waves MUST ONLY logically have the conclusion that gravitons exist…because geons would be only too logical.

It’s rather comical actually that Motl rushes from the given proof of gravitational waves to the conclusion that there must be gravitons as if there were no other explanations out there.

“Myth: We should quantize the curvature instead“

Perhaps this isn’t a myth insomuch as it is an idea from a sleep deprived fellow trying to come up with something to quantize. This is new to Motl, but in science you can’t say “That’s bullocks!” and not offer a replacement. That’s the whole point of paradigm shifts! True, offering the curvature as something else to quantize wasn’t the best alternative, but that’s irrelevant to the fact that’s largely ignored: it is an alternative. Either I or - far more likely - someone else will offer something better…it’s something to research!

“Myth: Gravity must be treated as geometry, not a field“

I’m not saying that gravity “must” be treated as geometry. What I am saying is that given String theory’s failure as a theory, and the failure of quantization of gravity as a force, it now seems logical that we should take another different approach. But hey! Some guys like walking into a wall repeatedly.

Apparently this is a myth though, as our prophet has now declared it to be against the will of Nature.

“Myth: But a geometric approach is better, isn’t it?

In physics, the primary way of dividing theories is into correct theories and wrong theories. A general attempt to divide ideas and tools into geometric ones and non-geometric ones is typically ill-defined - it depends on the definition of “geometry” which is a matter of historical and social coincidences in mathematics rather than a matter of well-defined differences. Our understanding what geometry is has been evolving for centuries. More importantly, the approach that is labeled “more geometric”, whether or not the reasons behind this terminology are rational or not, doesn’t have to be “more correct”.”

Motl seems to have the bit between his teeth to “prove” that the geometric interpretation of general relativity is the wrong thing to quantize…apparently.

He gives no argument as to why other than “Well, you shouldn’t be picky over the mathematical formulation of a theory”…but it is formulated as a geometric theory! How can one be so blind or decoupled from reality to say “Well, yeah it’s formulated that way…but that doesn’t mean we have to quantize it that way!”?!

“Myth: Something’s wrong with the weak-field expansions because they’re against the philosophy of GR“

Oh how silly of me, the weak field approximation of General Relativity is obviously far superior to the full blown theory. That’s why the full blown theory works in the weak and strong fields whereas the weak field approximation works only in the weak field.

One serious problem that it neglects is the really important feature emphasized by Misner, Thorne, and Wheeler in chapter 17.6 of their infamous Gravitation phone book. The title of the section explains it all: “ ‘NO PRIOR GEOMETRY’: A Feature Distinguishing Einstein’s Theory from other theories of Gravity“! Perhaps our dear Motl forgets, but with the weak field condition, there is a background metric and a background (i.e. prior) geometry. Like it or not, that’s an important part of the theory of General Relativity…it has nothing to do with “philosophy” as Motl would lead one to believe.

Einstein himself relied on the weak-field expansions intensely. That’s how he derived the Newton’s potential - even though he may have been able to find the exact Schwarzschild solution, too. And Einstein has also derived the existence of gravitational waves from the weak-field expansions, even though he used to love Mach’s principle that disagreed with the existence of gravity waves.

Perturbative expansions are among the paramount tools of physics and, indeed, all of science. Whoever denies their critical importance shows that he’s not really interested in the true answers to well-posed physical questions. Don’t get me wrong: I think that the full non-linear equations of general relativity are prettier if printed on a T-shirt than some particular calculation in the weakly curved regime. Well, it’s because detailed calculations are almost always uglier than the fundamental laws. But the real importance of Einstein’s equations as well as other fundamental laws is to allow us to make calculations in concrete situations - and the weak-field situations dominate.

The fact that a weak-field calculation looks less elegant than the equations you started with doesn’t allow you to say that there’s something wrong with this calculation. Only simpletons could say that something is wrong - or not even wrong - because of these irrational reasons. And they, in fact, do. As Einstein has said, only two things are infinite - human stupidity and the Universe - and we’re not sure about the latter.

No one is denying that they are great tools for calculational purposes. What is being denied is that they are equivalent to the full theory; they are approximations that work at a certain scale and in a certain region in the gravitational field.

Quantizing an approximation to a theory isn’t really satisfying…why not quantize Newtonian gravity and say “Well, it’s really the same thing as General Relativity at the right velocities and distances”?

Is it just me or is Motl being hypocritical by appealing to Einstein here but criticizing me for appealing to Einstein’s “philosophy of General Relativity”?

Would quantizing the full blown Einstein field equations be harder than the perturbative method? Yes, significantly harder, but what did you expect from quantum gravity? A deus ex machina that magically falls out of the sky into your lap that gives you everything?

Further, perhaps more important, it shows a complete neglect for the importance of the full blown field equations, and the lack of a prior geometry. Perhaps our dear Motl should read up on his General Relativity before criticizing others on it.

“Myth: All the components should be first quantized in isolation

This is what not only the angry physicist but whole communities of people think.”

Hey look at me mom! I’ve one-upped Monsieur Molliere’s bourgeois gentilhomme: I’ve been quantizing components first in isolation all my life without knowing it!

I assume he’s apparently criticizing the use of the time components of four-vectors and tensors are constraints (I can only assume because he’s being as ambiguous as possible)…or else the canonical decomposition of spacetime into space and time. Both are more or less equivalent with regard to gravity, and yeah it doesn’t really bother me.

However, Motl’s seemingly Hegelian appeal for the “interconnectedness” of space and time (in other words his appeal to the philosophy of General relativity…where have we heard of this before?) seems misplaced. It’s not as though time is surgically removed, it’s given a new role; perhaps one could suggest the obvious that time is a man made abstraction (put that in your Hegelian pipe and have some sort of unity of opposites involving smoking it and not smoking it too).

Since the use of time components as Lagrange Multipliers “works”, it seems that Motl’s entire point is purely philosophical. Ironic he appeals to the philosophy of general relativity after criticizing those that appeal to it! Such is life.

Graviton: The Particle that Never Was

I have started a little discussion on my about page and figured it be best to address the points made in a post dedicated to the heart of the matter: gravitons.

They are hypothetical massless particles that are the mediating boson of gravity…just like how photons are the mediating boson for electromagnetism. Intuitively, gravitons must be massless…otherwise they would generate graviton, since gravity is generated by mass (well, energy).

But, photons have energy (recall from special relativity: E=pc for a photon). Logically, gravitons would have energy. There is an infinite recursion here: energy creates gravitons, gravitons have energy, go back to step 1. This violates the first law of thermodynamics (energy conservation).

Perhaps we could abandon this notion of the graviton and *gasp* move forward? Although this is a string rant, it applies equally to loop quantum gravity due to its “graviton propagator” calculation by Rovelli a while back.

Perhaps one is approaching this the wrong way. Look at spacetime like a manifold. Each point (or rather quantized region) of spacetime has a certain curvature , why not quantize this? There are quantized curvatures, and so forth. This, in retrospect, is too semi-classical for my tastes, but there are a number of other ways to approach quantum gravity (personally, I think a more quantum geometric approach would be better - there should be some way to have some sort of quantized manifold, perhaps have a pseudo sum-over-histories quantization involving discretizing the manifold then “mashing” all the configurations for a given partition together?).

But, to sum up this rant, the notion of the graviton is an antiquity of the current paradigm of quantum field theory and either we need to apply this paradigm to geometry (instead of treating gravity as a field, go back to it being geometry) or we need a new paradigm. The latter seems preferable since the current paradigm has its problems (e.g. the renormalization problems - ignoring infinities is like ignoring depression, it’s not good for you!). The graviton it seems has problems with the conservation of energy, in addition to the problem that it has never been empirically observed.

Random Incoherent Thoughts From a Sleep Deprived Physics-Major

First off, I suppose I should give a little note on why I’m writing about Carlip’s class. If you go to my about, you’ll find that I studied at the CalTech library independently with a retired rocket scientist (I never enrolled at CalTech, I only read the books they have on physics and math!). I’ve stayed in touch with him and, due to the time constraints of college life, figured that this we could be a way to keep in touch with him while at the same time retaining the notes on the web…and yes, the about me page is correct, I really am an undergraduate at UC Davis (first year freshman if you really want to be precise).

I was thinking about an alternative to String theory, since in science you can’t say “You’re full of it!” then give no replacement for the theory…as tempting as it may be. Some have asked if I am a fan of loop quantum gravity, twistors, or what have you, and honestly I am impressed with some of these approaches. However, I do not really subscribe to any of these schools of thought (in the words of Goethe, I’m a self-made imbecile).

I seem to recall Einstein explaining to a group of reporters General Relativity as something along the lines of “I don’t know if you understand this or not, but most people think that if you remove all the matter and energy from the universe what you have left is space and time. What General Relativity says is that what you have, after removing all the matter and energy from the universe, is nothing.” Taking this view of gravity “generating” spacetime as opposed to it “deforming” some pre-existing spacetime, perhaps we could then make some “creator” and “annihilator” for discretized regions of space. The problem with this approach that I have is that it is the canonical decomposition of spacetime into space and time, which seems to be counterproductive philosophically.

Admittedly I just made this idea up in the last five minutes after a caffeine induced marathon of calculations, but hey! It does have some appeal! The only problem would be how to start (perhaps represent the universe, that is discrete regions of space, as an matrix and have a “creator matrix” and “annihilator matrix” such that and - coincidentally if you define the Hamiltonian as being proportional to the determinant of the annihilator and creator matrices, you should get but there is still the problem of picking canonical variables and that all this is just mathematical coincidence). A consequence is that quantum field theory could possibly be revised to use a finite dimensional Hilbert Space (the number of dimensions would be equal to the number of discrete regions in space - but even this isn’t guaranteed to be finite, it could also be countably infinite). Perhaps one ought to quantize curvature and try to see where curvature “creator” and “annihilator” operators leads to? I don’t know, these are random thoughts that seem like a good idea at the time. But now I have stopped thinking, and so I shall go back to doing my homework.