Category Archives: physics

Anthropic principle, 2.3

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In fact, lots of astrophysicists think the anthropic issue, rather than signaling a problem with modern science, points toward a deeper understanding of the universe. Rees likes to use our solar system as an analogy. Says Rees: “If Earth were the only planet in the universe, you’d be astonished that we just happened to be exactly the right distance from the sun to be habitable.” That would be absurdly improbable, but it becomes much less so when you realize that the Milky Way almost certainly has millions of planets. With so many possibilities, it’s not surprising that at least one planet is friendly to life.

And so, he contends, it might be with the cosmos. What we think of as the “universe,” argues Rees, could well be just one of trillions of universes on an indescribably vaster stage called the multiverse. Each of those universes would have different laws and characteristics. Most of them are totally unlivable; like Earth, ours just happens to be one of the lucky ones.

— Cosmic Conundrum

— By Michael D. Lemonick; J. Madeleine Nash

— Time (magazine)

The correct version of anthropic principle should be called the anti-anthropic principle.

— Me@2011.11.10

2012.03.02 Friday ACHK

Anthropic principle, 2.2

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You may say – and some people actually say – that the anthropic reasoning is not similar to religion, but instead, it is analogous to Darwin’s theory because the Universe “compete” much like the animals, and there is no explicit God there. Well, it is as analogous as much as the evolutionary theory itself is analogous to creationism, but not more. Darwin’s theory has pretty well-defined rules and mechanisms. The animals are doing all these familiar things and they live together – and compete – according to some schemes that are deeply rooted in biology, chemistry, and physics – and that we can predict.

On the other hand, the arena of very many Universes that “compete” has no testable rules like that, and therefore it mimicks religion. (Of course, if someone could derive really exact rules that govern the Universes in the multiverse, the situation would change.)

— The anthropic lack of principles

— Lubos Motl

2012.03.02 Friday ACHK

Anthropic principle, 2.1

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The vacuum structure of the theory, called the string theory landscape (or the anthropic portion of string theory vacua), is not well understood. String theory contains an infinite number of distinct meta-stable vacua, and perhaps 10^520 of these or more correspond to a universe roughly similar to ours — with four dimensions, a high planck scale, gauge groups, and chiral fermions. Each of these corresponds to a different possible universe, with a different collection of particles and forces.

Some physicists believe this is a good thing, because it may allow a natural anthropic explanation of the observed values of physical constants, in particular the small value of the cosmological constant. The argument is that most universes contain values for physical constants that do not lead to habitable universes (at least for humans), and so we happen to live in the most “friendly” universe. This principle is already employed to explain the existence of life on earth as the result of a life-friendly orbit around the medium-sized sun among an infinite number of possible orbits (as well as a relatively stable location in the galaxy).

— Wikipedia on String theory

The correct version of anthropic principle should be called anti-anthropic principle.

— Me@2011.11.10

2012.03.01 Thursday ACHK

Logical arrow of time, 2

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However, the right definition of the past and the future is independent of these sign conventions for spacetime coordinates. The right definition says that

    The future is evolving from the past (and the present).

Correspondingly, the calculations that are designed to theoretically mimic this evolution have the same arrow:

    The future is calculated from the past (and the present) as long as we use the usual calculations that resemble the evolution.

It’s important that you can’t exchange the words “future” and “past” in the sentence above.

That doesn’t mean that science can never say anything about the past, by manipulating with the present data or the data from a closer past. But this type of calculation is different from predictions of the future. It follows different formulae, too. They’re the formulae of logical inference, e.g. Bayesian inference.

And as we have explained many times, the results of this inference – the retrodictions – always depend on our priors. So the knowledge of the present is enough to calculate the future (classically) or to predict the unique probabilities of various states in the future (quantum mechanically). But it is simply never enough to calculate the unique state or unique probabilities of various states in the past.

— Logical arrow of time and terminology

— Lubos Motl

2012.02.28 Tuesday ACHK

Definite

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Universal wave function, 14

Quantum decoherence makes the macroscopic world appear definite.

In fact, Nature is fundamentally a superposition of definite states.

So the world, either microscopic or macroscopic, is definite in a sense that the universal wave function is evolving deterministically; and

is indefinite in a sense that it is not in a particular eigenstate.

— Me@2011.11.19

2012.02.27 Monday (c) All rights reserved by ACHK

Everett’s relative-state formulation

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Universal wave function, 13

Everett noticed that the unitary, deterministic dynamics alone decreed that after an observation is made each element of the quantum superposition of the combined subject-object wavefunction contains two “relative states”: a “collapsed” object state and an associated observer who has observed the same collapsed outcome; what the observer sees and the state of the object have become correlated by the act of measurement or observation. The subsequent evolution of each pair of relative subject-object states proceeds with complete indifference as to the presence or absence of the other elements, as if wavefunction collapse has occurred, which has the consequence that later observations are always consistent with the earlier observations. Thus the appearance of the object’s wavefunction’s collapse has emerged from the unitary, deterministic theory itself. (This answered Einstein’s early criticism of quantum theory, that the theory should define what is observed, not for the observables to define the theory). Since the wavefunction appears to have collapsed then, Everett reasoned, there was no need to actually assume that it had collapsed. And so, invoking Occam’s razor, he removed the postulate of wavefunction collapse from the theory.

— Wikipedia on Everett’s relative-state formulation

2012.02.26 Sunday ACHK

Single-world interpretation, 6.5

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If this is the case, then wave function is deterministic. There is no free will. The free will is due to the ongoing superposition of eigenstates. Locally, we see superposition of “a and b” collapse to (such as) a. Globally, we also see b “goes to” the environment. Nothing is lost in a sense that no information is lost.

Then what happens when you make a choice by collapsing a wave function?

Free will, like wave function collapse, is a local illusion.

Since information cannot be lost, we always exist.

— Me@2011.11.20

2012.02.25 Saturday (c) All rights reserved by ACHK

Single-world interpretation, 6.2

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In the Many-worlds interpretation (MWI), when we say that “a + b” collapses to “a”, there is a shift of definition of “you”.

MWI is in one sense correct: choice b version of you still exists. But the trick is that he is not in another universe. He is in the environment of this universe.

And perhaps in reverse, you are also part of the environment of him.

— Me@2011.11.20

2012.02.22 Wednesday (c) All rights reserved by ACHK

Double slit experiment

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Feynman has said that all the surprising wisdom of quantum mechanics is hiding in the double slit experiment. If you think about it carefully enough, you will ultimately figure out all the important and amazing new features of the world that quantum mechanics uncovers.

— Lubos Motl

2012.02.14 Tuesday ACHK

Quantum discord

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In quantum information theory, quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. It includes correlations that are due to quantum physical effects but do not necessarily involve quantum entanglement.

… quantum correlations can be present in certain mixed separable states; In other words, separability alone does not imply the absence of quantum effects. The notion of quantum discord thus goes beyond the distinction which had been made earlier between entangled versus separable (non-entangled) quantum states.

Nonzero quantum discord indicates the presence of correlations that are due to noncommutativity of quantum operators. For pure states, the quantum discord becomes a measure of quantum entanglement, more specifically, in that case it equals the entropy of entanglement.

Evidence has been provided for poignant differences between the properties of quantum entanglement and quantum discord. It has been shown that quantum discord is more resilient to dissipative environments than is quantum entanglement.

… surprisingly, the classical correlation actually decreases as the quantum discord increases.

— Wikipedia on Quantum discord

[Quantum discord is] the amount of entanglement needed in the task of state-merging.

— Jun 10 ’11 at 13:32

— Frederic Grosshans

2012.02.10 Friday ACHK

Mirror symmetry, 2

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In physics and mathematics, mirror symmetry is a relation that can exist between two Calabi-Yau manifolds. It happens, usually for two such six-dimensional manifolds, that the shapes may look very different geometrically, but nevertheless they are equivalent if they are employed as hidden dimensions of string theory. The classical formulation of mirror symmetry relates two Calabi-Yau threefolds M and W whose Hodge numbers h1,1 and h1,2 are swapped; string theory compactified on these two manifolds lead to identical effective field theories.

… Andrew Strominger, Shing-Tung Yau, and Eric Zaslow have showed that mirror symmetry is a special example of T-duality: the Calabi-Yau manifold may be written as a fiber bundle whose fiber is a three-dimensional torus. The simultaneous action of T-duality on all three dimensions of this torus is equivalent to mirror symmetry.

— Wikipedia on Mirror symmetry (string theory)

2012.02.10 Friday ACHK

Layer, 2

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Everyone is not a part of the universe, but the whole of the universe.

Everyone is a layer of the universe.

— Me@2012-02-06 11:31:17 PM

2012.02.09 Thursday (c) All rights reserved by ACHK

Reductionism 2

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Holism

Holism is the idea that natural systems (physical, biological, chemical, social, economic, mental, linguistic, etc.) and their properties, should be viewed as wholes, not as collections of parts. This often includes the view that systems somehow function as wholes and that their functioning cannot be fully understood solely in terms of their component parts.

Reductionism is sometimes seen as the opposite of holism. Reductionism in science says that a complex system can be explained by reduction to its fundamental parts. For example, the processes of biology are reducible to chemistry and the laws of chemistry are explained by physics.

— Wikipedia on Holism

2012.02.06 Monday ACHK

Index notation

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Symmetries are the result of a redundant, but useful, description of a theory.

In fact, one of the main uses of index notation is just to manifest the symmetry.

— Fields

— Warren Siegel

Siegel authored an extensive (885pg) textbook called Fields, now in its 3rd edition. It is notable in that it follows a very modern approach and incorporates many topics (including string theory) not found in other field theory textbooks. He advocates a “symmetry-based” approach and uses this in his Quantum Field Theory I&II classes. The textbook is also notable in that it is completely an “electronic book” and can be downloaded for free from Siegel’s website.

— Wikipedia on Warren Siegel

2012.02.05 Sunday ACHK