Category Archives: physics

Portal

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時空幻境 3

Portal is a 2007 single-player first-person puzzle-platform video game developed by Valve Corporation.

The game primarily comprises a series of puzzles that must be solved by teleporting the player’s character and simple objects using “the handheld portal device”, a device that can create inter-spatial portals between two flat planes.

By Kaini [CC-BY-SA-3.0], from Wikimedia Commons

The game’s unique physics allows momentum to be retained through portals, requiring creative use of portals to maneuver through the test chambers.

— Wikipedia on Portal (video game)

2012.04.21 Saturday ACHK

Weak isospin

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Weak isospin is to the weak interaction what electric charge is to the electromagnetism, and what color charge is to strong interaction.

— Wikipedia on Weak interaction

2012.04.20 Friday ACHK

De Broglie–Bohm theory, 3.2

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Universal wave function, 17.2

Relativity

Pilot wave theory is explicitly nonlocal. As a consequence, most relativistic variants of pilot wave theory need a foliation of space-time. While this is in conflict with the standard interpretation of relativity, the preferred foliation, if unobservable, does not lead to any empirical conflicts with relativity.

The relation between nonlocality and preferred foliation can be better understood as follows. In de Broglie–Bohm theory, nonlocality manifests as the fact that the velocity and acceleration of one particle depends on the instantaneous positions of all other particles. On the other hand, in the theory of relativity the concept of instantaneousness does not have an invariant meaning. Thus, to define particle trajectories, one needs an additional rule that defines which space-time points should be considered instantaneous. The simplest way to achieve this is to introduce a preferred foliation of space-time by hand, such that each hypersurface of the foliation defines a hypersurface of equal time.

However, this way (which explicitly breaks the relativistic covariance) is not the only way. It is also possible that a rule which defines instantaneousness is contingent, by emerging dynamically from relativistic covariant laws combined with particular initial conditions. In this way, the need for a preferred foliation can be avoided and relativistic covariance can be saved.

…

There has been work in developing relativistic versions of de Broglie–Bohm theory.

— Wikipedia on De Broglie–Bohm theory

2012.04.18 Wednesday ACHK

De Broglie–Bohm theory, 3.1

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Universal wave function, 17.1

The non-local hidden variables predict a genuine violation of the Lorentz symmetry. I think that all these theories predict such a brutal violation of the Lorentz symmetry that they are safely ruled out, too.

— Lubos Motl

The de Broglie–Bohm theory is explicitly non-local: The velocity of any one particle depends on the value of the wavefunction, which depends on the whole configuration of the universe. Because the known laws of physics are all local, and because non-local interactions combined with relativity lead to causal paradoxes, many physicists find this unacceptable.

This theory is deterministic. Most (but not all) variants of this theory that support special relativity require a preferred frame. 

— Wikipedia on De Broglie–Bohm theory

2012.04.16 Monday ACHK

Consistent histories, 2

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Single-world interpretation, 8

The interpretation based on consistent histories is used in combination with the insights about quantum decoherence. Quantum decoherence implies that irreversible macroscopic phenomena (hence, all classical measurements) render histories automatically consistent, which allows one to recover classical reasoning and “common sense” when applied to the outcomes of these measurements.

— Wikipedia on Consistent histories

2012.04.14 Saturday ACHK

Causality

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To define causality, we need the concept of “before”.

So we need the concept of “simultaneity”.

In relativity, “simultaneity” is defined by the speed of light.

Therefore, “causality” is based on “the speed of light”.

— Me@2012-04-10 12:07:36 PM

2012.04.13 Friday (c) All rights reserved by ACHK

Block spacetime, 5

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This position has lead him to face the following problem: if time is not part of the fundamental theory of the world, then how does time emerge? In 1993, in collaboration with Alain Connes, Rovelli has proposed a solution to this problem called the thermal time hypothesis. According to this hypothesis, time emerges only in a thermodynamic or statistical context. If this is correct, the flow of time is an illusion, one deriving from the incompleteness of knowledge.

— Wikipedia on Carlo Rovelli

2012.04.12 Thursday ACHK

Englert–Greenberger duality relation

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The Englert–Greenberger duality relation relates the visibility, V, of interference fringes with the definiteness, or distinguishability, D, of the photons’ paths in quantum optics. As an inequality:

    D^2 + V^2 <= 1 

The relationship was first experimentally shown by Greenberger and Yassin in 1988. It was later theoretically derived by Jaeger, Shimony, and Vaidman in 1995, and over a year later it was also mentioned by Englert, in 1996.

— Wikipedia on Englert–Greenberger duality relation

2012.04.11 Wednesday ACHK

Single-world interpretation, 7

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One consequence is that every observation can be thought of as causing the combined observer-object’s wavefunction to change into a quantum superposition of two or more non-interacting branches, or split into many “worlds”.

— Wikipedia on Many-worlds interpretation

That is incorrect.

Let’s consider the double-slit experiment. For simplicity, we regard the event “a person reads the device reading” as a classical event.

Before installing the measuring device, we do not know which slit a photon goes through. The photon state is in a superposition of eigenstates: 

| photon > = a | left > + b | right >

(According to the meaning of probability, |a|^2 + |b|^2 = 1.) In other words, if we send enough such kind of photons through the double-slit apparatus, we get the interference pattern. 

After installing the measuring device, we know which slit a photon goes through. According to the Copenhagen interpretation, when the photon passes through the double-slit apparatus, the photon-state “collapses” to one of the two eigenstates, such as | left >. However, a more accurate point of view is that, according to the quantum decoherence interpretation, the photon-and-device state becomes a superposition of a lot of eigenstates. Most of such eigenstates are corresponding to the macrostate of passing-through-the-left-slit, |left>_macro_state. 

The above many-worlds-interpretation statement assumes that there is a |right>_macro_state.

It is true in a sense that, since the photon-and-device involves a lot of particles, there are so many eigen-microstates. Some are certainly corresponding to the |right>_macro_state.

It is false in a sense that the weighting of the |right>_macro_state is so small that such macrostate is not meaningful in a macroscopic context, for example:

| photon-and-device > = 10^23 |left>_macro_state + 0.001 |right>_macro_state + other possible macrostates

— Me@2012-04-07 11:03:12 AM

2012.04.09 Monday (c) All rights reserved by ACHK

EPR paradox, 3

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It turns out that the usual rules for combining quantum mechanical and classical descriptions violate the principle of locality without violating causality.

Causality is preserved because there is no way for Alice to transmit messages (i.e. information) to Bob by manipulating her measurement axis. Whichever axis she uses, she has a 50% probability of obtaining “+” and 50% probability of obtaining “-“, completely at random; according to quantum mechanics, it is fundamentally impossible for her to influence what result she gets.

Furthermore, Bob is only able to perform his measurement once: there is a fundamental property of quantum mechanics, known as the “no cloning theorem”, which makes it impossible for him to make a million copies of the electron he receives, perform a spin measurement on each, and look at the statistical distribution of the results. Therefore, in the one measurement he is allowed to make, there is a 50% probability of getting “+” and 50% of getting “-“, regardless of whether or not his axis is aligned with Alice’s.

— Wikipedia on EPR paradox

In fact, a theorem proved by Phillippe Eberhard shows that if the accepted equations of relativistic quantum field theory are correct, it should never be possible to experimentally violate causality using quantum effects (see reference [6] for a treatment emphasizing the role of conditional probabilities).

— Wikipedia on Delayed choice quantum eraser

2012.04.08 Sunday ACHK

Bell’s theorem, 3

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EPR paradox, 2

Two assumptions drove the desire to find a local realist theory:

1. Objects have a definite state that determines the values of all other measurable properties, such as position and momentum.

2. Effects of local actions, such as measurements, cannot travel faster than the speed of light (in consequence of special relativity). Thus if observers are sufficiently far apart, a measurement made by one can have no effect on a measurement made by the other.
   
— Wikipedia on Bell’s theorem

It is no longer possible to adhere to both the principle of locality (that distant objects cannot affect local objects), and counterfactual definiteness, a form of ontological realism implicit in classical physics. Some interpretations of quantum mechanics hold that a system lacks an actualized property until it is measured, which implies that quantum systems exhibit a non-local behaviour. Bell’s theorem proved that every quantum theory must either violate local realism or counterfactual definiteness.

— Wikipedia on Naive realism

1. The principle of locality:

There are two possible meanings of “locality” here.

1.1 The principle is correct in a sense that no causal influence can be faster than light.

1.2 The principle is incorrect in a sense that distant particles can be entangled. Correlation without causation can be instantaneous.

Assume that a pair of particles are entangled. Measuring one particle will collapse the wave function, which governs both particles, instantaneously.

2. Counterfactual definiteness:

2.1 It is correct in a sense that an object has a definite quantum state.

2.2 It is incorrect in a sense that, most often than not, the definite quantum state is not corresponding to a definite classical state (aka eigenstate). Instead, that quantum state is a superposition of different eigenstates. 

— Me@2012-04-07 11:36:01 AM

2012.04.07 Saturday (c) All rights reserved by ACHK

Digital physics, 4

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Moreover, there is this statement that “distances smaller than Planck length don’t exist” that confuses many people. They heard it and misunderstood it, thinking it applies to coordinate differences. It can only apply to Lorentz-invariant “proper” distances, otherwise relativity is broken.

– Lubos Motl Jan 23 ’11 at 8:19

2012.04.06 Friday ACHK

Godel 1.1

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A major early proponent of formalism was David Hilbert, whose program was intended to be a complete and consistent axiomatization of all of mathematics. Hilbert aimed to show the consistency of mathematical systems from the assumption that the “finitary arithmetic” (a subsystem of the usual arithmetic of the positive integers, chosen to be philosophically uncontroversial) was consistent (i.e. no contradictions can be derived from the system).

Godel’s conclusion in his incompleteness theorems was that you cannot prove consistency within any axiomatic system rich enough to include classical arithmetic.

— Wikipedia on Formalism (mathematics)

2012.04.05 Thursday ACHK

No-cloning theorem

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The no-cloning theorem is a result of quantum mechanics that forbids the creation of identical copies of an arbitrary unknown quantum state.

The state of one system can be entangled with the state of another system. For instance, one can use the Controlled NOT gate and the Walsh-Hadamard gate to entangle two qubits. This is not cloning. No well-defined state can be attributed to a subsystem of an entangled state. Cloning is a process whose end result is a separable state with identical factors.

Consequences

    The no-cloning theorem prevents us from using classical error correction techniques on quantum states. For example, we cannot create backup copies of a state in the middle of a quantum computation, and use them to correct subsequent errors. Error correction is vital for practical quantum computing, and for some time this was thought to be a fatal limitation. In 1995, Shor and Steane revived the prospects of quantum computing by independently devising the first quantum error correcting codes, which circumvent the no-cloning theorem.

    The no cloning theorem prevents us from viewing the holographic principle for black holes as meaning we have two copies of information lying at the event horizon and the black hole interior simultaneously. This leads us to more radical interpretations like black hole complementarity.

— Wikipedia on No-cloning theorem

2012.04.01 Sunday ACHK