thoughts on gymnastics and Hinduism

[spoonless]

Gymnastics has started up again, I am super excited about that. They got rid of Saturdays for the summer, and I'd been waiting all summer for the fall to come so I could start going again. Went the first time on Saturday, and... oh so good. It's funny, I've been thinking a lot lately about what I want out of life, and have been realizing how totally lost I am. But when I sit down and try to figure it out, I always come back to the only thing that I know for absolute sure I want... which is to be able to do gymnastics every day of the week. I can't accomplish that in the town I'm living in--the YMCA is so sick of me bugging them about it, they no longer even return my phone-calls. And the other gymnastics programs in town are similarly kids only. I don't mind driving up to Chicago once per week for the time being, but I will eventually need more than once a week. I'm ok with waiting though. But as a long term goal, I do hope to move toward that within the next 10 years.

I spent 10 hours on Sunday reading Wikipedia articles on Hinduism. I've had this happen to me before, reading too much Wikipedia in one day--I've noticed it's one of the few things lately that I'm somewhat dangerously addicted to. I broke for 30 minutes to eat lunch, although for some of that half hour I just brought my food over to the computer to read while I was eating! Literally, when I get interested in a topic on Wikipedia, I find it's almost impossible to pull myself away from the computer, I just keep saying "1 more click, I have to read this link and then I'll go do something else!" Fortunately, as opposed to most weekends where I've got lots of stuff I wanted to get done, I really did have enough time to relax that weekend, and reading Wikipedia is one of the most relaxing things for me. Normally, 10 hours of Wikipedia reading I would consider "way too much" but it was only slightly too much this time because I got a lot out of it and enjoyed it.

The more I read about Hinduism, the more I realized how much more complex it is than any other religion I've encountered. Just trying to find all of the names of the various sacred texts involved took me through at least 10 pages alone, and I'm not quite sure I've found them all (and certainly don't remember them all). The main ones that stick out in my mind though are the 4 Vedas, the Upanishads (there's about 200 of them!), the Brahma Sutras, and the Puranas. This only scratches the surface though, and as I say, I don't even remember most of the names of the texts that I read about, and I didn't even read any of them directly (although I did briefly open up one of the Upanishads to see what it looked like). I also don't think I even scratched the surface on getting a handle on all the different variants of Hinduism. Unlike much simpler more narrow coherent religions like Christianity, there is so much more variation within it. For example, there are monotheistic sects of Hinduism, there are polytheistic sects, and there are atheist and/or pantheist sects. There are dualist versions of Hinduism, and also non-dualist versions.

So far, the one that stands out as the most resonant with me and interesting to me, is Advaita Vedanta. (Although that's not to say there isn't some other version that would be better that I haven't found yet.) This interpretation actually makes so many of my confusing thoughts about how to view deities make more sense. In Advaita Vedanta, Brahman is absolute, ultimate reality... the continuous whole that has no attributes, boundaries, form or shape of its own. In physics, you'd call this the "unified field theory" or the "theory of everything". Pantheists would call this "God" but not regular monotheists since it is not a someone but a something. The problem is, Brahman is an abstraction that stands for everything but as such has no properties or attributes to distinguish it from anything else... since there *is* nothing else. So how can you possibly comprehend it? There's not really any way to actively meditate on it or to worship it. The solution, according to Advaita Vedanta, is for humans to personify Brahman by projecting animate qualities onto it, which then becomes an omnipotent being called Ishvara (essentially, the same as God or Allah from monotheistic religions). But this still leaves Ishvara mostly formless and personalityless. So you have to project more qualities onto Ishvara, which then splits Him into the holy trinity (or as Hindus call it, the Trimurti)... Brahma, Vishnu, and Shiva (creator, maintainer, and destroyer... in physics, these are called "creation operator", "propagator", and "annihilation operator"). These three deities then each have 11 eminations, 11 different even more concrete ways in which they can appear to humans on earth. (On a side note, it's a somewhat interesting numerological coincidence that string theory (well, really M-Theory) requires 11 dimensions of spacetime, and the Qabalastic tree of life involves 11 Sephirot; I'm not sure if anyone has tried to line either of these up with the 11 forms of each Hindu god though). Similarly, there are 3 goddesses, the Tridevi: Lakshmi, Parvati, and Saraswati. The female counterparts of the holy trinity. They also each have 11 eminations. This leads to a total of 33 gods and 33 godesses, although it's interesting that this interpretation sort of combines atheism, pantheism, theism, and polytheism all into one unified theory. It makes a lot of sense to me posed in that way. The abstract formless attributeless Brahman is more true but less useful than if you split it into more concrete manifestations and worship those individually. (Note: some of the specifics on how the gods and goddesses divide up I may be confusing with other versions of Hinduism, but putting together lots of different stuff I've read, some a while back, this is the most coherent picture I can come up with.)

Another thing I really like about Advaita Vedanta is that it's explicitly non-dualist. There are other versions of Hinduism (for instance, Dvaita Vedanta) where they succumb to dualism, and believe--as Descartes mistakenly did--that there is both a spirit world and a material world, or at least both of those different kinds of substances in the world. This is something I think modern science has pretty thoroughly refuted. I knew that Buddhism for the most part was non-dualist, but it's encouraging to see there are threads of Hinduism that are as well. Unfortunately I get the sense that most people who believe in Advaita Vedanta are more like idealists than materialists, but in some ways that seems like a minor difference compared to the difference between dualism and monism. (After all, in some ways you could just view it as different take on what the best word is to call the single substance that makes up everything... and admittedly there are good reasons why really neither of the two standard choices offered are quite right. I just happen to think that materialism is the clear cut answer if you had to choose one or the other).

Also, I really like the phrase "Ayamātmā brahmā", something from the Mandukya Upanishad. It means "This Atman is Brahman". Atman is the soul of an individual, and Brahman is the whole universe (or God, in the pantheistic sense). It identifies part with whole in a very holographic way. I haven't had this thought about any phrase since I got my first tattoo, but suddenly I had the thought that this would make a really awesome tattoo! Not that I would get it without doing more research into what it really means and how it connects to other things. But it's a neat idea, and very parallel to similar thoughts I've had over the past few years. Strange that all of this was just sitting here all of the time, and I never read it until now... putting these different pieces together.

Comments

[nasu-dengaku.livejournal.com]

Hinduism is a giant and very old open-source project. It's been forked numerous times, and the various forks are sometimes completely different from one another.

[spoonless.livejournal.com]

Yeah, that was the main thing I got from my readings. But letting something be a body of work that evolves with the times and is open to new ideas seems so much more healthy than the way most religions work (closed and fixed for the most part, until there's a violent revolution of some kind and a sect splits off and declares the rest enemies).

[easwaran.livejournal.com]

Except that if you think that there's a fact of the matter about things, then when it forks you have to think that at least one of them is getting things wrong. Of course, most religions seem to deal with the problem of "the other guys are wrong" with a level of violence that is clearly uncalled-for. But I don't really understand the notion of religious tolerance - if you believe in one of these things, then you think that everyone else is totally wrong about the most important thing in the world!

[spoonless.livejournal.com]

This was well put, and I completely agree. (Although I'd also emphasize that there is a middle ground between having to accept all branches as true and having to reject all branches but one... keep the most fruitful branches that seem the most promising, and let older branches that didn't work out wither).

My main point is that a body of knowledge that has never had any forking because it includes in it the axiom that anything put in there from the start is unquestionably true has no chance of being right. It will never even get off the ground. Whereas a body of knowledge that has at least explored different possibilities and grown in response to them stands at least a chance that one or more of the branches is onto something. Granted, it may take a while to sift through the branches, but I'd suspect that the ones that were far off the mark in obvious ways have withered over time anyway.

It seems sort of like the difference between trying to design an AI from scratch versus letting one evolve in response to its environment. Also, I should mention that one of the first things I noticed about your profile was that you tried a lot of different political viewpoints on at various points. I view that as an indicator that you may have some knowledge of politics, compared to someone who has remained a lifelong X all their life, and insists that they knew all along from birth that there was only one correct political party. This is the difference I'm noticing between Hinduism and most religions I'm familiar with.

[easwaran.livejournal.com]

I always wondered what my name meant! (The "s" is really halfway between an "s" and an "sh" in English - Sanskrit and most other Indian languages have three sounds where we have two, and this one is supposed to be the one in the middle. Similarly, the "w" is really halfway between a "w" and a "v" - most Indian languages have only one sound where we have two. The initial vowel can be spelled as "I" or "E" or "Ea" or "Ee". And I think there are many words where the "a" or "an" ending are just alternates in different dialects.)

Also, with these "parallels" between Hinduism and quantum physics, are you just joking? These seem to be parallels on the level that people might use in books like "The Tao of Physics" and so on, but it doesn't seem to me that it captures at all the relevant interest of the physical concepts.

Also, I find it interesting that in all these interpretations it always seems like Brahma or Brahman is the most important deity, and yet in practice the biggest cults in India seem to be the cult of Shiva and the cult of Vishnu.

[spoonless.livejournal.com]

Neat--it didn't even occur to me that ishvara and easwaran were the same word.

I think you're making a mistake though in identifying Brahma and Brahman. From my readings, I got that they refer to very different concepts. Nevertheless, I am not sure of that and it does make me wonder why the words are so close... also, the phrase "Ayamātmā brahmā" I mentioned supposedly translates to "this Atman is Brahman" which would seem to indicate they are the same. But I don't think they are--will have to read more on that to figure it out.

I also wondered why Vishnu and Shiva have their own branches of Hinduism (Vaishnavism and Shaivism, which overlap other divisions of Hinduism) and are so widely worshipped, whereas Brahma does not have his own branch... although there are versions of Hinduism that view them all on the same footing.

[easwaran.livejournal.com]

I think some of the confusion is that there are many different case endings on Sanskrit words, and the same word will sometimes end with a vowel and sometimes with a nasal or something else. "Brahma" and "Brahman" may differ in other ways as well.

[spoonless.livejournal.com]

Regarding the parallels to physics, joking seems like the wrong word. Although in the case of the "11" coincidence it is purely for entertainment... it seems "neat" to me that they happen to be the same, but rationally I cannot think of any reason why this could have been a case of anticipation.

The other stuff is more serious. In particular, I really do think there is a sense where Brahman is being used to mean the same thing that's meant by TOE or unified field. Nevertheless, as I said I think the main difference is that Brahman has a more idealist connotation while TOE has a more materialist connotation. I think I have lots more thinking on that to do, though, as sometimes I'm not quite sure how to phrase what the distinction between these two is.

I have to admit, that while I've always assumed that the people who write those quantum - Eastern metaphysics books (like Kapra) were full of crap, after finding out this stuff about Advaita Vedanta, I'm struck by the parallels enough to actually kind of want to go read one of those books to see what they say.

[easwaran.livejournal.com]

Is the sense in which Brahman is the same thing as a unified field just the sense that it is a single thing that is identical to the world as a whole? Basically like Spinoza's idea of God? (Which was considered heretical by most European theologians.) It seems to me that there is some similarity between that and a unified field (and in fact, I know some philosophers that are currently arguing on the basis of quantum field theory that the universe is really one indivisible whole and that all objects we're familiar with are dependent on it, rather than the whole being dependent on the parts), but I don't see the connection to a theory of everything. In particular, I don't see how it gives rise to a theory.

[spoonless.livejournal.com]

By the way, just found an interesting blog, on the so-called "Mathematics of Spirituality". It's all about Advaita Vedanta, and how supposedly it can be made mathematically rigorous:

http://www.mathematicsofspirituality.com/

also, cross-linked with it is the "Advaita Math blog":

http://advaitamath.blogspot.com/

Unfortunately, the actual papers they link to look kind of like BS to me. But it's still interesting that someone would even try to do this. Well, I suppose Frank Tipler did publish a book called the "Physics of Christianity" but I feel like that was nonsense on a much more ridiculous scale. This seems at least half serious, if crackpot.

[easwaran.livejournal.com]

There is a large genre of this stuff, claiming that the Vedas already contain all of relativity and/or quantum mechanics. I believe that a lot of it is also connected to the revisionist history that claims that Indo-Aryan languages are indigenous to the sub-continent and were spoken in Harappa and Mohenjo-Daro rather than coming with Indo-Iranian invaders, and this is all connected to right-wing Hindu nationalist politics. Not in all cases of course, but it seems to get pushed by those politicians, because of its nationalist appeal.

At least Frank Tipler does really know the physics...

[spoonless.livejournal.com]

Interesting, thanks for the warning. The name "John Hagelin" comes to mind here, a while back I ran across some stuff by him that looked a bit similar, although I'm not sure if it was a part of this movement you're talking about. I know he was a follower of that big transcendental meditation guru, and published some work on grand unified theories that was supposedly based on something from the Vedas... and then ran for President several times as the Natural Law candidate. He also published a paper (in some kind of fake journal I think, possibly run by Maharishi University or something) called "is consciousness the unified field?

Are these language debates at all related to the Nazi theories that nordic people were the original Aryans and brought the original language down into India through invasion? (Actually, it sounds like maybe the Nazis exaggerated in one direction, and these Hindu nationalists are exaggerating in the other direction?)

[easwaran.livejournal.com]

I don't know how much the Maharishi stuff and Natural Law Party stuff relates to this - they might be into some Hindu nationalist pride too. But the big thing is with the Bharatiya Janata Party in India, which I believe considers only certain versions of Hinduism appropriate, and thinks that Hindu-ness is a fundamental part of being India. (Officially, the country is founded as a secular country, even though Pakistan is officially Muslim.)

I think the BJP and the Nazis both have some related ideas about Aryan purity and racial essences. Here's an interesting discussion of the political uses of the various Aryan origin stories, from someone who clearly seems to have political affiliation for the theory that Aryans are the people of Mohenjo-Daro and Harappa.

It seems to me that the evidence is pretty incontrovertible that the Indo-Aryan languages (along with the rest of the Indo-European language family) have an origin somewhere in either the central Asian steppes or the Caucasus or the Black Sea region, at most a thousand years before the Indus valley civilization was established. The question is just whether the modern speakers of the languages are descendants of some sort of invasion, or whether they are descendants of the indigenous people, who just adopted a foreign language for some reason. (There are similar issues in the Afroasiatic language family - it's clear that the Hausa language of Nigeria, the languages of Ethiopia, Ancient Egyptian, Hebrew, and Arabic, are all languages descended from a single origin. But it's not clear whether any or all of these people are descended from the speakers of that original language - and given the apparent racial differences between Nigerians, Ethiopians, and Arabs, it seems likely that at least one of these cases involved some group of people changing languages. And it doesn't help us know whether the Ancient Egyptians were "black" or "white".)

[spoonless.livejournal.com]

Is the sense in which Brahman is the same thing as a unified field just the sense that it is a single thing that is identical to the world as a whole? Basically like Spinoza's idea of God?

I haven't read Spinoza firsthand, but for some reason the descriptions of Spinoza's idea of God never made me think of physics, whereas reading the descriptions of Brahman make me go "yup, that's exactly it". I'm not sure how to say what the difference is though, but yes... they are supposed to be pretty similar.

I know some philosophers that are currently arguing on the basis of quantum field theory that the universe is really one indivisible whole and that all objects we're familiar with are dependent on it, rather than the whole being dependent on the parts), but I don't see the connection to a theory of everything. In particular, I don't see how it gives rise to a theory.

In physics, the terms "unified field theory" and "theory of everything" are usually treated as synonyms.

Although I suppose when I try to consider what the words mean logically, I could imagine that the words "theory of everything" is a bit more general. In principle, I suppose it could refer to any theory that accurately describes the world, but usually the emphasis is on the idea of unification, that all of the two main field theories used to described the world--the classical field theory called general relativity, and the quantum field theory called the Standard Model--are somehow both contained in a larger, single field theory. This is either referred to as the "unified field theory" or the "theory of everything", where those are usually just two ways of referring to the same thing.

[easwaran.livejournal.com]

The distinction I'm after here is between the field, and the theory of that field. I would have thought (from the very quick description here) that one might compare Brahman to a field, but not to a theory of the field (perhaps Hinduism, or a particular branch of it, might play the role of the theory).

And of course, you could theoretically have a "theory of everything" that didn't have a unified field (there might just be two irreducibly distinct fields that do different things) and you could have a theory of a unified field that wasn't a theory of everything (just because a field unites gravity and electroweak doesn't automatically guarantee that it includes everything). Though that's not the worry I was on about.

[spoonless.livejournal.com]

The distinction I'm after here is between the field, and the theory of that field.

I see. I think maybe why the two don't seem that different to me while they seem more different to you is that physicists (especially those working on quantum field theory or string theory) often use the word "theory" to refer to a particular mathematical structure rather than to a hypothesized description of reality.

Often a physicist can prove that a particular theory (meaning--a mathematical structure that has some desired property) exists, but the details of that theory will be incalculable. (Actually, that's true of the theory I did my dissertation on, the Pentagon Model--except that we couldn't *quite* prove that it exists, only that it might.) And by exists I mean in the Platonic sense, rather than "is a true description of the world".

Another thing that happens is that physicists will study a theory that is dubbed a "toy model" where it's known not to correspond to the real world, but will be a useful testing ground for other hypotheses that could not be tested on one that is closer to reality. Then you have to make an argument that whatever properties you're interested in should be similar between the two which of course gets into a lot of hand waving. Nevertheless, this type of thing happens fairly often in the literature. I'm sure mathematicians would look at it and cringe, since it's based on appeals to intuition and guesswork rather than proof.

[easwaran.livejournal.com]

Hmmm... it still seems to me that you might have different theories of (say) the electromagnetic wavefunction. These are different mathematical structures that you hypothesize it might have. The theory claims that the physical object is in some important sense isomorphic to the mathematical object, and thus you call the mathematical object the theory. But the theory is still distinct from the wave itself, at least as I see it.

This does get close to some important questions about the way mathematical modeling works though.

[spoonless.livejournal.com]

The theory claims that the physical object is in some important sense isomorphic to the mathematical object, and thus you call the mathematical object the theory. But the theory is still distinct from the wave itself, at least as I see it.

I think how you view this depends heavily on your views in philosophy of science and metaphysics. It depends both on how realist a view you take about mathematical structures, and on how realist a view you take towards physical "reality".

A Copenhagenist, representing the extreme antirealist position, might say that there is nothing the mathematical theory is isomorphic to, the mathematical structures are creations of the human mind intended for the purpose of predicting events/experiences. Not as a model of some transcendant "Reality". Perhaps I'm exaggerating that viewpoint a little bit, but I think that's pretty close to how a lot of people in physics view it.

At the other extreme, you have people like Max Tegmark who have proposed that there is no difference whatsoever between mathematical structures and reality. All mathematical structures exist, and we happen to find ourselves in one particularly complex one that supports life. Calling this one "physical" and the other mathematical is just an illusion. This is closer to my point of view, although I've begun to doubt whether this can really be satisfactory.

A third view might be that the only difference between a mathematical model and physical reality is some kind of substance, like Brahman, that instantiates the model.

I guess I should also point out that the reason these issues come up with a TOE but not with normal theories, is that any other theory is intended as an approximation to reality, while a TOE is intended to exactly represent (or perhaps be) reality, with no approximations used.

[easwaran.livejournal.com]

I was just talking with Matt several times in the last few weeks about the Schrödinger equation - I had never calculated solutions for it before, and he didn't know what it meant that the set of possible wave functions was an infinite-dimensional vector space.

Anyway, I thought it was interesting that even for the toy models (the completely free particle, the particle in a box, the particle in a finite potential well), calculating the solutions requires some awful hand-waving. At least, in the discussions in wikipedia, they claimed that there are sinusoidal solutions to the equation for the completely free particle, even though the sinusoids are just as non-normalized as the exponentials. And for the other two, we have to assume that the space of possible wave-functions includes ones that have discontinuities in certain derivatives at certain points, in a way that intuitively makes sense, but I saw no mathematical justification for.

[spoonless.livejournal.com]

Yes, it's ironic that for the two most commonly used operators used in quantum mechanics--the position operator and the momentum operator--neither of them has eigenstates (for the free-particle case) that are actually in the Hilbert space. The momentum eigenstates are sinusoids, and as you say, non-normalizable (and therefore not physically allowed). While the position eigenstates are Dirac delta distributions, which are not even functions! (They're just the limit of a series of functions.) So neither of them are actually in the space you're supposedly working in. And neither of them ever happen in the real world.

There's a fairly intuitive way to understand why they never happen in the real world though. You can't localize a particle to be at an exact location, because then the uncertainty in the position would be zero, which would yield an infinite uncertainty in momentum. Conversely, you can't have a perfect sinusoid that stretches out all the way to the boundary of spacetime (infinite uncertainty in position) which is what would be required in order to perfectly measure the position of something.

The moral of the story is just that you can never precisely measure position or momentum, you always have to measure some combination. The position and momentum operators are mathematical idealizations of real measurements that you can do which consist of combinations of them.

[easwaran.livejournal.com]

Why can't you have a perfect sinusoid that stretches out across all of spacetime? (Note - if we're treating spacetime as R^n then it has no boundary, so it's not stretching out "all the way to the boundary of spacetime".) It seems like your intuitive way of understanding this presupposes some sort of uncertainty principle, but I thought this was supposed to be proving the uncertainty principle rather than presupposing it.

Also, I guess I hadn't realized that this was supposed to have some connection with measurement - I thought the Schrödinger equation was just some equation that the wavefunction should always satisfy (though it's unclear to me why there should be some constant that we can call the "energy" for which the wavefunction is an eigenvector).

[spoonless.livejournal.com]

Why can't you have a perfect sinusoid that stretches out across all of spacetime? (Note - if we're treating spacetime as R^n then it has no boundary, so it's not stretching out "all the way to the boundary of spacetime".)

An actual wavefunction "in the real world" is supposed to be an indicator of the probability of finding the particle at each location if you were to measure its position. So physical wavefunctions have to be normalized to 1, otherwise the whole interpretation in terms of probability would fall apart. This means that if you're working in a space like R^n it has to fall off to zero as you approach infinity. You might be able to find a mathematical function that obeys the Schrodinger equation, but if so it cannot correspond to an actual state the particle could be in. It's sometimes called a "non-physical" wavefunction because it fails to satisfy one or more requirements that real wavefunctions satisfy (like being normalized to 1).

Incidentally, I think if you are working in a space that has a finite volume then this is not an issue. By "boundary" I just meant "out to infinity"--I see why this is a very confusing word to use here and I should have avoided it. I think the reason why I (and others) are used to using "boundary of spacetime" to mean infinity is that often the only way to formulate things in QFT is to work in a finite box and then take the limit as the size goes to infinity... although you still make sure the values of all fields (and their wavefunctions) go to zero at the boundary, otherwise you'd end up with a big problem when you tried to make the size infinite. Only if you were working in such a box (or some kind of compact space) and not intending to take any limits would you be allowed to have a non-zero wavefunction at the boundary. Of course, this *could* be the situation in real life, so if that's the case then pure sinusoidal functions could be perfectly physical--however, in practice you still wouldn't really expect to ever find one that stretches all the way across the universe. Particles travel in wavepackets, they are typically localized to pretty small regions.

[easwaran.livejournal.com]

Particles travel in wavepackets, they are typically localized to pretty small regions.

This doesn't make sense to me - I didn't think anything other than a perfect sinusoid or exponential was a solution to the equation, so I don't understand how these wavepackets work. Is it only because actual particles are always in the presence of a potential field of some sort?

[spoonless.livejournal.com]

See my other comment regarding energy eigenstates (stationary states). Most physical states are superpositions of stationary states, not stationary states themselves.

I suspect the version of the Schrodinger Equation you're talking about is the time-independent Schrodinger equation. All wavefunctions obey the time-dependent Schrodinger equation, but only stationary states obey the time-independent. The time independent Schrodinger equation is really just a convenient way to find the stationary states of a system. Stationary states have trivial time-dependence (all that happens is their phase rotates in time, while their magnitude remains constant). These are then used to build up the rest of the states of the system, most of which have non-trivial time dependence. A typical state in the real world would be a wavepacket, where the size of the packet spreads over time as it travels along.

[spoonless.livejournal.com]

Also, I guess I hadn't realized that this was supposed to have some connection with measurement - I thought the Schrödinger equation was just some equation that the wavefunction should always satisfy (though it's unclear to me why there should be some constant that we can call the "energy" for which the wavefunction is an eigenvector).

It's tough to find anything in quantum mechanics that isn't related to measurement somehow =) You don't have to think about measurement here, I guess, if you don't want to. It's just that the reason position and momentum are usually chosen as nice bases to work in, because they correspond *roughly* (but not exactly) to common types of measurements that are done. The Schrodinger equation in its abstract form is an operator equation, but the more commonly used "wave equation" that is also sometimes referred to as the Schrodinger equation (and was what Schrodinger was initially working with) is "the Schrodinger equation in the position basis". You can write it down in any basis, or you can just write it as an operator equation that is basis-independent. Each basis has a different set of eigenstates associated with it, that usually correspond to physical observables.

Regarding energy, in one sense it's no different from any other physical observable. The only thing that makes it special is that it is the conserved quantity associated with time-translation. Any system which has laws of physics that have no explicit reference to a specific time (like say, the big bang) must conserve energy, because of this relationship. This is true both in classical mechanics and in quantum mechanics, but one implication that has in quantum mechanics is that eigenstates of the energy operator (Hamiltonian) are time-independent. That's why energy eigenstates are special, they are sometimes referred to as "stationary" states since they do not change over time like most states do (actually, their phase can change, just not the magnitude which determines the underlying probability distribution).

Incidentally, when you say "for which the wavefunction is an eigenvector", that's not true of most wavefunctions. Most wavefunctions are not an eigenstate of energy... only stationary states are. However, stationary states are usually the first thing you want to find when you're studying a new quantum system, since it's very easy to build any more complicated time-dependent state out of a superposition of the simpler stationary states.

[easwaran.livejournal.com]

I'm skeptical about the amount that measurement ought to be central to the theory - scientists seem to be attracted to this view for bad metaphysical reasons. But I don't really know.

Most wavefunctions are not an eigenstate of energy... only stationary states are. However, stationary states are usually the first thing you want to find when you're studying a new quantum system, since it's very easy to build any more complicated time-dependent state out of a superposition of the simpler stationary states.

Ah, that's useful to know. So there are in fact plenty of states that don't have a well-defined energy in this sense (where the energy is the eigenvalue). That's useful to know! This didn't seem to be mentioned in the wikipedia article about the Schrodinger equation.

[spoonless.livejournal.com]

Anyway, regarding the position and momentum eigenstates, this is a typical pattern that happens... you pick some case where the math is easy to work out, even if it's a huge approximation and not realistic. Then use that as a conceptual tool to understand more complicated cases.

In this case, I'm not sure I would even call it handwaving, because it has been worked out pretty rigorously... it's just that the details of it are never taught to undergrads, or even grad students usually.

[easwaran.livejournal.com]

But I guess it trains physicists to accept handwaving in the mathematics.

[spoonless.livejournal.com]

I think this is true--it gets students used to the fact that physics is complicated enough that you will never be able to understand it if you try to derive every detail in a step by step proof. You have to learn to skip steps sometimes and reason by analogy, and trust that the work others have done in working out the details is sound. One of the hardest parts of physics is trying to know when you should be suspicious that some step was done in too cavalier a way, and when you should not bother verifying every step. You just have to develop a knack for spotting which kinds of handwaving holds up and which kind falls apart under scrutiny.

[spoonless.livejournal.com]

In particular, I don't see how it gives rise to a theory.

Perhaps I didn't actually address this directly. You're right, nothing in Vedanta as far as I know gives rise to an actual TOE, it just claims that one exists.

In some ways, you might think the idea that there exists a "Theory of Everything" is trivially true. Although in other ways, it's a specific hypothesis, a claim about the nature of reality. I guess it just depends on how narrowly you define the phrase. Usually it's used in a more narrow sense than just "some theory that describes the world". I think there is in particular a sense that there are no individual objects that interact with each other (aside from the approximate concepts our minds construct), and no precise way to separate any part from the whole.

[ankh-f-n-khonsu.livejournal.com]

The Upanishads are well-worth reading, IMO.