[A,BC] = [A,B]C + B[A,C]
This commutator product rule works just like the differentiation product rule:
assume that A is independent of C, you get the first term;
assume that A is independent of B, you get the second term.
— Me@2012-03-27 7:24:30 PM
2012.03.31 Saturday (c) All rights reserved by ACHK
A hologram can be cut in half, and each part still carries the whole picture. That’s because a hologram is the record of a light wave, and the information in a wave is spread over all of the space it occupies.
— arcnets
— physics forums
When a photograph is cut in half, each piece shows half of the scene. When a hologram is cut in half, the whole scene can still be seen in each piece. This is because, whereas each point in a photograph only represents light scattered from a single point in the scene, each point on a holographic recording includes information about light scattered from every point in the scene. Think of viewing a street outside your house through a 4 ft x 4 ft window, and then through a 2 ft x 2 ft window. You can see all of the same things through the smaller window (by moving your head to change your viewing angle), but you can see more at once through the 4 ft window.
— Wikipedia on Holography
2012.03.30 Friday ACHK
Lessons from the Light, 3
My yesterday self has already “dead”.
He has already “become” the universe.
That’s why he can feel the effects of whatever he has done.
— Me@2012.03.28
2012.03.29 Thursday (c) All rights reserved by ACHK
Single-world interpretation, 6.6
Since information cannot be lost, we, as software, cannot disappear, even if through dying.
— Me@2011.11.01
2012.03.28 Wednesday (c) All rights reserved by ACHK
… the universe is the sum total of all that is in existence. Physically, a (physical) observer outside of the universe would require the breaking of gauge invariance, and a concomitant alteration in the mathematical structure of the theory. Similarly, RQM conceptually forbids the possibility of an external observer. Since the assignment of a quantum state requires at least two “objects” (system and observer), which must both be physical systems, there is no meaning in speaking of the “state” of the entire universe.
This is because this state would have to be ascribed to a correlation between the universe and some other physical observer, but this observer in turn would have to form part of the universe, and as was discussed above, it is impossible for an object to give a complete specification of itself. Following the idea of relational networks above, an RQM-oriented cosmology would have to account for the universe as a set of partial systems providing descriptions of one another. The exact nature of such a construction remains an open question.
— Wikipedia on Relational quantum mechanics
2012.03.27 Tuesday ACHK
人生的時間長度固然重要；
但是，人生的時間闊度和時間深度，同樣重要。
— Me@2011.11.02
2012.03.26 Monday (c) All rights reserved by ACHK
Quantum logic can be formulated either as a modified version of propositional logic or as a noncommutative and non-associative many-valued (MV) logic.
— Wikipedia on Quantum logic
2012.03.25 Sunday ACHK
Single-world interpretation, 3.3
This world is a superposition of all possible worlds, subject to weightings.
— Me@2011.11.20
That’s what Feynman’s “summing over histories” means.
— Me@2011.11.02
2012.03.24 Saturday (c) All rights reserved by ACHK
From this principle, Einstein deduced that free-fall is actually inertial motion. Objects in free-fall really do not accelerate, but rather the closer they get to an object such as the Earth, the more the time scale becomes stretched due to spacetime distortion around the planetary object (this is gravity). An object in free-fall is in actuality inertial, but as it approaches the planetary object the time scale stretches at an accelerated rate, giving the appearance that it is accelerating towards the planetary object when, in fact, the falling body really isn’t accelerating at all. This is why an accelerometer in free-fall doesn’t register any acceleration; there isn’t any. By contrast, in Newtonian mechanics, gravity is assumed to be a force.
— Wikipedia on Equivalence principle
2012.03.23 Friday ACHK
Probability is one as many.
Probability is an one body statistics.
For example, expected value (in probability) is an one sample version of weighted average (in statistics).
— Me@2011.11.02
2012.03.22 Thursday (c) All rights reserved by ACHK
Like Clojure, Datomic incorporates an explicit model of time. All data is associated with a time and new data does not replace old data, but is added to it. Returning to our previous example, if John later changes his address, a new datom would be added to the database, e.g.
John, :street, “17 Maple St.”, T43
This mirrors the real world where the fact that John has moved does not erase the fact that John once lived on Swift St. This has multiple benefits: the ability to view the database at a point in time other than the present; no data is lost; the immutability of each datom allows for easy and pervasive caching.
— rjn945 15 days ago
— Hacker News
2012.03.21 Wednesday ACHK
Space is geometric relationships. It is not made of anything.
… the focus is on how nature responds to measurement, not on what space is “made of”. You take a finite set of geometric information and describe how it evolves.
You can say it is discretized because the area and volume operators are quantum operators with discrete spectrum —- but probabilities can mix the outcomes so that they can vary continuously.
… Maybe the main lesson is don’t take it too literally when popular writers say “discrete”. There may not be anything material there to be discrete or continuous. Geometry might be about information, or making measurements.
— How could spacetime become discretised at the Planck scale?
— marcus
2012.03.19 Monday ACHK
Physicists including your humble correspondent always preferred to keep the normal logic. I really don’t understand how one could work with von Neumann’s strange rules. The consistent histories, the most complete framework to interpret quantum mechanics today, imply that exactly those quantum histories (sequences of projection operators at different times) for which the classical rules of logic work – the consistent histories themselves – are allowed.
— John von Neumann: 104th birthday
— Lubos Motl
2012.03.18 Sunday ACHK
I decided that a reason contributing to the people’s misunderstanding of the meaning and validity of quantum mechanics is the prevailing focus on Schrodinger’s equation as the basic dynamical law.
Heisenberg’s equations for the operator are more direct a quantum counterpart of Newton’s equations of motion. In this picture, the only novelty are the nonzero commutators between the observables – the Heisenberg uncertainty principle etc.
— Density matrix and its classical counterpart
— Lubos Motl
2012.03.15 Thursday ACHK
這段改編自 2010 年 3 月 20 日的對話。
很大程度上，所謂「明白」，就是「找到一個適合自己的比喻」。所以，很大程度上，所謂「教學」，就是「利用比喻」，把新知識，轉化成聽眾的舊知識。如果你有才能，把天馬行空、無法感受到的事物，表達成直接具體、切身感受到的東西的話，你就為之有教學的天份。
空間比喻：
事實：原子核的半徑，只有整個原子的十萬分之一。原子核的體積，只有整個原子的 10^15 分之一。
教學：如果一個原子核的大小等於一粒塵埃，一個原子的大小就等於一間房子。
時間比喻：
事實：地球的年齡，是四十六億。
教學：有文字記載的歷史，大概由六千年前開始。先把這個數字，乘以一千。然後，把你得到的數字，再乘以一千。那就相當於地球的年齡。
— Me@2012.03.15
2012.03.15 Thursday (c) All rights reserved by ACHK
It seems that category theory is the new hype — almost nobody actually understands what it is about, or, more importantly, what it is for. Let me tell you what it is for — it’s an important technical tool in mathematical research, which gives you new, coherent language, sometimes provides you with an additional insight in the structure of the stuff you are researching and makes it easier to notice and classify similarities between different kind of structures. Unfortunately, it is almost completely useless and uninteresting by itself — because, well, what’s interesting in objects and arrows anyway?
What make category theory interesting are its connections with various field[s] and [in] math and computer science. That’s why introducing “category theory for dummies” makes completely no sense — it’s like following Erlangen program to teach kids about points, lines and circles on a plane. The need and the significance of Erlangen program arise when you learn about many different geometries, notice what they have in common and what they do not, and try to find out what the geometry is all about. Without it, the Erlangen program is all about abstract bullshit, and the situation is completely the same with category theory. But nobody writes or posts Erlangen program for dummies on HN. Why? “General theory of everything” hype, that’s why. Erlangen program is “general theory of geometry”, but geometry seems a bit pale when compared to everything.
If you really want to understand the significance of category theory, then learn set theory, then algebra, then topology, then algebraic topology and algebraic geometry, or take abstract programming languages theory path. If you don’t care about all this stuff, because you’re hyped on the category theory, then you’re missing the point — it’s like you wanted to learn about algebraic topology, but did not care about algebra or topology.
Also anything that has “for dummies” in title should invariably remind you of Norvig’s essay (google Peter Norvig 21 days).
— xyzzyz 171 days ago
— Hacker News
2012.03.14 Wednesday ACHK
One of the many articles on the Tricki that was planned but has never been written was about making it easier to solve a problem by generalizing it (which initially seems paradoxical because if you generalize something then you are trying to prove a stronger statement). I know that I’ve run into this phenomenon many times, and sometimes it has been extremely striking just how much simpler the generalized problem is.
edited Sep 26 2010 at 8:34
gowers
Great question. Maybe the phenomenon is less surprising if one thinks that there are ∞ ways to generalize a question, but just a few of them make some progress possible. I think it is reasonable to say that successful generalizations must embed, consciously or not, a very deep understanding of the problem at hand. They operate through the same mechanism at work in good abstraction, by helping you forget insignificant details and focus on the heart of the matter.
answered Sep 26 2010 at 10:27
Piero D’Ancona
— Generalizing a problem to make it easier
— MathOverflow
A general case has less information (details) than a special case.
— Me@2012.03.10
2012.03.13 Tuesday (c) All rights reserved by ACHK
During this period, Tom Banks, Willy Fischler, Stephen Shenker and Leonard Susskind formulated matrix theory, a full holographic description of M-theory using IIA D0 branes. This was the first definition of string theory that was fully non-perturbative and a concrete mathematical realization of the holographic principle. It is an example of a gauge-gravity duality and is now understood to be a special case of the AdS/CFT correspondence.
— Wikipedia on String theory
2012.03.12 Monday ACHK
Well, in some sense, the Wheeler-DeWitt equation is nothing else than Einstein’s equations that you encountered elsewhere – potentially simplified and reduced in a minisuperspace formulation.
But if something like the Wheeler-DeWitt equation is the only equation that defines what can happen in a quantum gravity system, your task actually becomes harder, not easier. You must artificially reparameterize your physical states according to a new observable (e.g. the total volume of the Universe at some “moment”) that will play the role of your time (recall that there’s no preferred choice of coordinates in general relativity) – and with this new “gauge-fixed” choice of your time, you will find out that the Wheeler-DeWitt “H=0” equation becomes non-trivial.
— Why and how energy is not conserved in cosmology
— Lubos Motl
Bryce DeWitt first published this equation in 1967 under the name “Einstein–Schrodinger equation”; it was later renamed the “Wheeler–DeWitt equation”.
…
Solutions to the Wheeler-DeWitt equation have therefore been interpreted as the Universal wave function.
This property is known as timelessness [disambiguation needed]. The reemergence of time requires the tools of decoherence and clock operators.
— Wikipedia on Wheeler–DeWitt equation
Timelessness is a property of the Wheeler-deWitt equation in canonical quantum gravity.
— Wikipedia on Timeless
2012.03.08 Thursday ACHK
Block time, 3
There are logically flawed conclusions in the show made out of various careless arguments, too. For example, it’s being said that one must adopt “eternalism” – all of the spacetime, whether it is in the past or in the future – is equally real. But such a conclusion is once again sloppy. Nothing like that follows from relativity. And in fact, relativity combined with quantum mechanics implies things like the “free will theorem” which pretty much refutes eternalism.
— The Fabric of the Cosmos II
— Lubos Motl
If we consider the universal wave function, there is no collapse, then the block time is allowed.
— Me@2011.11.19
2012.03.04 Sunday (c) All rights reserved by ACHK
Physics Town 
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