Category Archives: physics

Mute Hole

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I saw a nice example in a fountain in Vienna once. Water flows smoothly down a channel, faster and faster, until it pours off the edge in a small waterfall. If you tap the water’s smooth surface with your finger, a wave goes out. In the region where the water flows more slowly than the speed of this wave, it goes out in all directions — but faster downstream than upstream. In the region where the water flows faster than the speed of this wave, the whole wave is carried downstream: no information propagates upstream. Between these regions there is a boundary: an ‘event horizon’. No information from water waves can get out of this event horizon. (Well, at least that’s true for waves of small amplitude and certain frequencies.) So it acts a bit like a black hole.

And the really interesting thing is that if you quantize this problem, you’ll get Hawking radiation! Roughly speaking, wave-antiwave pairs will form right near the event horizon, thanks to quantum fluctuations, and some of the waves will escape upstream!

People sometimes call the sound analogue of a black hole a dumb hole, not because the analogy is stupid, but because ‘dumb’ also means ‘unable to speak’. (I guess ‘mute hole’ would be a politically correct substitute.)

— Liquid Light

— John Baez

2011.12.25 Sunday ACHK

Grassmann numbers

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And because they are intrinsically mathematical in character, their relevance for physics is actually enough to show that the world cannot be classical.

— Lubos Motl

2011.12.22 Thursday ACHK

研究經費

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Being a child/student = being a scientist without the need of worrying about the research funding

兒童本來都是科學家，每天也在研究新天新地新事物。

兒童和科學家的唯一主要分別是，兒童毋須終日煩惱研究經費。

— Me@2011.12.16

2011.12.19 Monday (c) All rights reserved by ACHK

Quantum probability and Classical probability, 5

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Probability theory 1.3

Quantum probability is almost the same as classical probability.

The only difference is that while classical probability is due to ignorance, quantum probability is due to superposition of eigenstates of the universal wave function and the ignorance of its details. We ignore the microstate details of the measuring-device/observer.

If we know all the details of the universal wave function, we will be able to predict what the final wave function will be. The final wave function will still be a superposition of a lot of different eigenstates. There is no real wave function collapse.

— Me@2011.11.20

2011.12.13 Tuesday (c) All rights reserved by ACHK

Quantum probability and Classical probability, 2

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… the telltale difference between the quantum and the classical notions of probability is that the former is subject to interference and the latter is not.

— The Fabric of the Cosmos

— by Brian Greene

Classical probability does not allow more than one eigenstates co-exist at the same time. (superposition)

— Me@2011.12.02

2011.12.11 Sunday (c) All rights reserved by ACHK

Universal wave function, 4

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Single-world interpretation, 4

That is, components of the wavefunction are decoupled from a coherent system, and acquiring phases from their immediate surroundings. A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level), but its ultimate fate remains an interpretational issue.

— Wikipedia on Quantum decoherence

The universal wave function is deterministic?

— Me@2011.11.20

2011.12.07 Wednesday ACHK

Wave–particle duality, 4

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It has been argued that there are never exact particles or waves, but only some compromise or intermediate between them. One consideration is that zero dimensional mathematical points cannot be observed. Another is that the formal representation of such points, the Kronecker delta function is unphysical, because it cannot be renormalized. Parallel arguments apply to pure wave states.

    “Such positions states are idealised wavefunctions [..] Whereas the momentum states are infinitely spread out, the position states are infinitely concentrated. Neither is normaliseable[..]”

— R Penrose, Road to Reality p.521 s21.11
   
— Wikipedia on Wave–particle duality

Particle is a single pulse. Wave is a train of infinite pulses. Both are physically impossible.

— Me@2011.11.29

2011.11.30 Wednesday (c) All rights reserved by ACHK

Hidden variable

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Universal wave function, 2

Assuming Bell’s theorem is correct, any hidden variable theory must be non-local.

Here is my guess:

The hidden variable is the wave function of the measuring device, aka the environment, which involves the rest of the universe.

In short, the hidden variable is the wave function of the whole universe.

— Me@2011.11.28

2011.11.28 Monday (c) All rights reserved by ACHK

Quantum decoherence 5.4

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Wave function collapse is a process of losing the superposition information to the environment.

The remaining problem is that we still cannot predict which part of the information will be lost.

— Me@2011.11.20

In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior.

Decoherence can be viewed as the loss of information from a system into the environment (often modeled as a heat bath), since every system is loosely coupled with the energetic state of its surroundings.

That is, components of the wavefunction are decoupled from a coherent system, and acquiring phases from their immediate surroundings.

— Wikipedia on Quantum decoherence

2011.11.23 Wednesday (c) All rights reserved by ACHK

Frequency probability and Bayesian probability, 2

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Bayesian probability interprets the concept of probability as “a measure of a state of knowledge”, …

— Wikipedia on Bayesian probability

Frequency probability interprets the concept of probability as a frequency or a physical property of a system.

— based on Wikipedia on Bayesian probability

— Me@2011.11.22

The conflict is due the false assumption that we can separate the observed and the observer.

If we abandon that assumption and form a system containing both the observed and the observer, “a measure of a state of knowledge” is one of the physical properties of the system. Frequency probability and Bayesian probability have the same meaning.

— Me@2011.11.22

2011.11.22 Tuesday (c) All rights reserved by ACHK

Wheeler’s delayed choice experiment

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Quantum decoherence 5.3
 
 
In the delayed choice experiment, the wave function of the system (the photons and the environment) is also in a superposition of eigenstates, not just the wave functions of the individual photons are.

All the past is there, but our present measurement “chooses” which part to see. 

— Me@2011.10.21
 
 
The chosen part must be a consistent story, according the quantum mechanics.

The chosen part is what we called “an observer”.

— Me@2018-01-22 09:35:02 PM
 
 
 
2011.11.20 Sunday (c) All rights reserved by ACHK

Delayed choice quantum eraser

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Quantum decoherence 5.2 | Event Realism 5 | 事件實在論 5

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For a delayed choice quantum eraser, both interference patterns are there.

But since they overlap each other, you cannot see them individually.

— Me@2011.10.21

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One of the easiest ways of “making sense” of the delayed-choice paradox is to examine it using Bohmian mechanics. The surprising implications of the original delayed-choice experiment led Wheeler to the conclusion that “no phenomenon is a phenomenon until it is an observed phenomenon”, which is a very radical position. Wheeler famously said that the “past has no existence except as recorded in the present“, and that the Universe does not “exist, out there independent of all acts of observation”.

— Wikipedia on Wheeler’s delayed choice experiment

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What we do in the present does not change the past, but change we can see/say about the past.

— Wheeler on Delayed choice quantum eraser

— paraphrased

— Me@2018-02-04 03:40:27 PM

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2011.11.19 Saturday (c) All rights reserved by ACHK