Friday, July 29, 2011

Will Ireland Rescue Us All ?

Forget the eye candy, the prose is what is important.

But srsly, Ireland has a Ladies' Rugby Team? Who knew? (I actually got that pic by Google imaging "Irish Landscape" (I SO love the country), and look what popped up!)

Originally posted November 2010.


People who know me best know I'm all about the promotion of GOOD Science and Mathematics, especially among the young, therefore I consider this page from IrishTimes.com to be particularly important in the sense of getting the word out.

I feel this way for no moralistic or altruistic reasons. I have completely selfish reasons, those being I want my children to grow up in a world that is as good and well-informed as it could possibly be, and thus save our species from eventually: extinction. Yes, Science will find the way, but it won't unless it's promoted. If we place our future in the hands of the politicians and the tradesmen who tell them how to vote, as certainly seems to be the current state of affairs, then we're doomed. I think we're currently 50/50 regarding our survival.

WHY should the next Gauss enter Mathematics or the next Einstein enter Physics, when Wall Street promises so much more? A shame really, but the future is as always a big question mark. As long as the Internet exists, then the potential to change opinions exists as well. Let's promote Sci and Math as much as possible. I have a Marketing degree (MBA) on top of my Bachelor's in Mechanical Engineering, so feel free to pick my brains.

In the meantime, props to Ireland:

Brainteaser posters aim to get people thinking about physics


DICK AHLSTROM, Science Editor (IrishTimes.com)


PHYSICISTS HAVE found a novel way to get people to engage with their subject during Science Week. The Institute of Physics has plastered buses and trains across the island with posters asking important questions.
One for example asks: “Two filled cola cans, one frozen, one liquid, roll down a short smooth slope – which one gets to the bottom first?”
Another asks: “What happens if you try to light a candle inside an orbiting space station?”
The poster campaign, Transport Yourself with Physics, was all about getting the public to engage with the subject, said Alison Hackett, policy officer with the institute.
The institute, with the support of the Government’s Discover Science and Engineering programme, organised the campaign, which was launched to coincide with Science Week Ireland.
The posters are now visible on buses and trains in Galway, Cork, Limerick and Waterford. In Dublin they are installed along Dart and Arrow train services and on Dublin Bus. About 200 buses in Northern Ireland have posters in place, Ms Hackett said.
There is also a degree of instant gratification for those looking for answers to these burning questions. You can text your multiple-choice answer to a specified number at standard text rates, and get an instant response congratulating you or giving you the correct answer.
“Physics is all about asking questions and being curious about the world around us,” Ms Hackett said. “The posters grab people’s attention before challenging their idea of physics.”
The questions are engaging but you have to think before answering. “Most of the questions do surprise,” she said, for example: “A clock on the equator runs slower, faster or identical to one on the North Pole?”
The numbers to text multiple-choice answers to are 087-9382257 in the Republic and 028-71042040 in the North.
Find more questions at iopireland.org/questioncards.
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Wednesday, July 27, 2011

21 Interpretations of Mach's Principle !?

"Many Physicists do not agree that Einstein’s theory of relativity really solved/implemented Mach’s Principle (completely or at a degree)."

... Astrophysicist Christine Cordula Dantas.

Dr. Dantas


It's nice to see Professor Dantas return to blogging at her new weblog "Toy Universes". Initially she wrote a nice exposition of "Mach's Principle", and how even to this day "interpretations" are controversial, indeed there are 21 different ones!

After giving a short series of weblog posts about Tensors, she has recently returned to Mach's, here, an important subject since it laid one of the two cornerstones (the other being the constancy of the speed of light) that a 16-yr-old born in Ulm, Germany would ponder for ten years, eventually leading to his Special Theory of Relativity being published while a Swiss Patent Clerk in 1905.
In theoretical physics, particularly in discussions of gravitation theories, Mach's principle (or Mach's conjecture[1]) is the name given by Einstein to an imprecise hypothesis often credited to the physicist andphilosopher Ernst Mach.
The idea is that the local motion of a rotating reference frame is determined by the large scale distribution of matter, as exemplified by this anecdote:
You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don't move?
Mach's principle says that this is not a coincidence—that there is a physical law that relates the motion of the distant stars to the local inertial frame. If you see all the stars were whirling around you, Mach suggests that there is some physical law which would make it so you would feel a centrifugal force. There are a number of rival formulations of the principle. It is often stated in vague ways, like "mass out there influences inertia here". A very general statement of Mach's principle is "Local physical laws are determined by the large-scale structure of the universe."[2]
This concept was a guiding factor in Einstein's development of the general theory of relativity. Einstein realized that the overall distribution of matter would determine the metric tensor, which tells you which frame is rotationally stationary. Frame dragging and conservation of gravitational angular momentum makes this into a true statement in the general theory in certain solutions. But because the principle is so vague, many distinct statements can be (and have been) made which would qualify as a Mach principle, and some of these are false. The Gödel rotating universe is a solution of the field equations which is designed to disobey Mach's principle in the worst possible way. In this example, the distant stars seem to be rotating faster and faster as one moves further away. This example doesn't completely settle the question, because it hasclosed timelike curves.

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History

The basic idea also appears before Mach's time, in the writings of George Berkeley.[3] The book Absolute or Relative Motion? (1896) by Benedict Friedländer and his brother Immanuel contained ideas similar to Mach's principle.


Einstein's use of the principle

There is a fundamental issue in Relativity theory. If all motion is relative, how can we measure the inertia of a body? We must measure the inertia with respect to something else. But what if we imagine a particle completely on its own in the universe? We might hope to still have some notion of its state of rotation. Mach's principle is sometimes interpreted as the statement that such a particle's state of motion has no meaning in that case.
In Mach's words, the principle is embodied as follows:
[The] investigator must feel the need of... knowledge of the immediate connections, say, of the masses of the universe. There will hover before him as an ideal insight into the principles of the whole matter, from which accelerated and inertial motions will result in the same way.[4]
Albert Einstein seemed to view Mach's principle as something along the lines of:
...inertia originates in a kind of interaction between bodies...[5]
In this sense, at least some of Mach principles are related to philosophical holism. Mach's suggestion can be taken as the injunction that gravitation theories should be relational theories. Einstein brought the principle into mainstream physics while working on general relativity. Indeed it was Einstein who first coined the phrase Mach's principle. There is much debate as to whether Mach really intended to suggest a new physical law since he never states it explicitly.
The writing in which Einstein found inspiration from Mach was "The Science of Mechanics", where the philosopher criticized Newton's idea of absolute space, in particular the argument that Newton gave sustaining the existence of an advantaged reference system: what is commonly called "Newton's bucket argument".
In his Philosophiae Naturalis Principia Mathematica, Newton tried to demonstrate that one can always decide if one is rotating with respect to the absolute space, measuring the apparent forces that arise only when an absolute rotation is performed. If a bucket is filled with water, and made to rotate, initially the water remains still, but then, gradually, the walls of the vessel communicate their motion to the water, making it curve and climb up the borders of the bucket, because of the centrifugal forces produced by the rotation. Newton says that this thought experiment demonstrates that the centrifugal forces arise only when the water is in rotation with respect to the absolute space (represented here by the reference frame solidal with the earth, or better, the distant stars); instead, when the bucket was rotating with respect to the water no centrifugal forces were produced, this indicating that the latter was still with respect to the absolute space.
Mach, in his book, says that the bucket experiment only demonstrates that when the water is in rotation with respect to the bucket no centrifugal forces are produced, and that we cannot know how the water would behave if in the experiment the bucket's walls were increased in depth and width until they became leagues big. In Mach's idea this concept of absolute motion should be substituted with a total relativism in which every motion, uniform or accelerated, has sense only in reference to other bodies (i.e., one cannot simply say that the water is rotating, but must specify if it's rotating with respect to the vessel or to the earth). In this view, the apparent forces that seem to permit discrimination between relative and "absolute" motions should only be considered as an effect of the particular asymmetry that there is in our reference system between the bodies which we consider in motion, that are small (like buckets), and the bodies that we believe are still (the earth and distant stars), that are overwhelmingly bigger and heavier than the former. This same thought had been expressed by the philosopher George Berkeley in his De Motu. It is then not clear, in the passages from Mach just mentioned, if the philosopher intended to formulate a new kind of physical action between heavy bodies. This physical mechanism should determine the inertia of bodies, in a way that the heavy and distant bodies of our universe should contribute the most to the inertial forces. More likely, Mach only suggested a mere "redescription of motion in space as experiences that do not invoke the term space".[6] What is certain is that Einstein interpreted Mach's passage in the former way, originating a long-lasting debate.
Most physicists believe Mach's principle was never developed into a quantitative physical theory that would explain a mechanism by which the stars can have such an effect. Although Einstein was intrigued and inspired by Mach's principle, Einstein's formulation of the principle is not a fundamental assumption of general relativity. There have been attempts to formulate a theory which is more fully Machian, such as Brans–Dicke theory, but most physicists argue that none have been fully successful.


Mach's principle in modern General Relativity

Einstein—before completing his development of the general theory of relativity—found an effect which he interpreted as being evidence of Mach's principle. We assume a fixed background for conceptual simplicity, construct a large spherical shell of mass, and set it spinning in that background. The reference frame in the interior of this shell will precess with respect to the fixed background. This effect is known as the Lense–Thirring effect. Einstein was so satisfied with this manifestation of Mach's principle that he wrote a letter to Mach expressing this:
it... turns out that inertia originates in a kind of interaction between bodies, quite in the sense of your considerations on Newton's pail experiment... If one rotates [a heavy shell of matter] relative to the fixed stars about an axis going through its center, a Coriolis force arises in the interior of the shell; that is, the plane of a Foucault pendulum is dragged around (with a practically unmeasurably small angular velocity).[5]
The Lense–Thirring effect certainly satisfies the very basic and broad notion that "matter there influences inertia here"[7] The plane of the pendulum would not be dragged around if the shell of matter were not present, or if it were not spinning. As for the statement that "inertia originates in a kind of interaction between bodies", this too could be interpreted as true in the context of the effect.
More fundamental to the problem, however, is the very existence of a fixed background, which Einstein describes as "the fixed stars." Modern relativists see the imprints of Mach's principle in the Initial-Value Problem. Essentially, we humans seem to wish to separate spacetime into slices of constant time. When we do this, Einstein's equations can be decomposed into one set of equations, which must be satisfied on each slice, and another set, which describe how to move between slices. The equations for an individual slice are elliptic partial differential equations. In general, this means that only part of the geometry of the slice can be given by the scientist, while the geometry everywhere else will then be dictated by Einstein's equations on the slice.
In the context of an asymptotically flat spacetime, the boundary conditions are given at infinity. Heuristically, the boundary conditions for an asymptotically flat universe define a frame with respect to which inertia has meaning. By performing a Lorentz transformation on the distant universe, of course, this inertia can also be transformed.


See also


References

  1. ^ Hans Christian Von Bayer, The Fermi Solution: Essays on Science, Courier Dover Publications (2001),ISBN 0486417077, page 79
  2. ^ Stephen W. Hawking & George Francis Rayner Ellis (1973). The Large Scale Structure of Space–Time. Cambridge University Press. p. 1. ISBN 0521099064.
  3. ^ G. Berkeley (1726). The Principles of Human Knowledge. See paragraphs 111–117, 1710.
  4. ^ Mach, Ernst (1960). The Science of Mechanics; a Critical and Historical Account of its Development. LaSalle, IL: Open Court Pub. Co.. LCCN 60010179. This is a reprint of the English translation by Thomas H. MCormack (first published in 1906) with a new introduction by Karl Menger
  5. ^ a b A. Einstein, letter to Ernst Mach, Zurich, 25 June 1923, in Misner, Charles; Thorne, Kip S.; and Wheeler, John Archibald (1973). Gravitation. San Francisco: W. H. Freeman. ISBN 0-7167-0344-0.
  6. ^ Barbour, Julian; and Pfister, Herbert (eds.) (1995). Mach's principle: from Newton's bucket to quantum gravity. Boston: Birkhauser. ISBN 3-7643-3823-7. (Einstein studies, vol. 6)
  7. ^ Bondi, Hermann; and Samuel, Joseph (July 4, 1996). "The Lense–Thirring Effect and Mach's Principle".arXiv:gr-qc/9607009 [gr-qc]. doi:10.1016/S0375-9601(97)00117-5. A useful review explaining the multiplicity of "Mach principles" which have been invoked in the research literature (and elsewhere).


Further reading

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Monday, July 25, 2011

Quantum Information and Technology



Quantum technology is a new field of physics and engineering, which transitions some of the stranger features of quantum mechanics, especially quantum entanglement, into practical applications such asquantum computing, quantum cryptography, quantum simulation, quantum metrology, quantum sensing, and quantum imaging.
The field of quantum technology was first outlined in a 1997 book by Gerard J. Milburn,[1] which was then followed by a 2003 article by Jonathan P. Dowling and Gerard J. Milburn,[2][3] as well as a 2003 article byDavid Deutsch.[4] The field of quantum technology has benefited immensely from the influx of new ideas from the field of quantum information processing, particularly quantum computing. Disparate areas of quantum physics, such as quantum optics, atom optics, quantum electronics, and quantum nanomechanical devices, have been unified under the search for a quantum computer and given a common language, that ofquantum information theory.


References

  1. ^ Schrödinger's Machines, G.J.Milburn, W H Freeman & Co. (1997)
  2. ^ "Quantum Technology: The Second Quantum Revolution,"J.P.Dowling and G.J.Milburn, Phil. Trans. R. Soc. A 361, 3655 (2003)
  3. ^ "Quantum Technology: The Second Quantum Revolution," J.P.Dowling and G.J.Milburn, arXiv:quant-ph/0206091v1
  4. ^ "Physics, Philosophy, and Quantum Technology," D.Deutsch in the Proceedings of the Sixth International Conference on Quantum Communication, Measurement and Computing, Shapiro, J.H. and Hirota, O., Eds. (Rinton Press, Princeton, NJ. 2003)


External links


In quantum mechanics, quantum information is physical information that is held in the "state" of a quantum system. The most popular unit of quantum information is the qubit, a two-level quantum system. However, unlike classical digital states (which are discrete), a two-state quantum system can actually be in a superposition of the two states at any given time.
Quantum information differs from classical information in several respects, among which we note the following:
  • It cannot be read without the state becoming the measured value,
  • An arbitrary state cannot be cloned,
  • The state may be in a superposition of basis values.
However, despite this, the amount of information that can be retrieved in a single qubit is equal to one bit. It is in the processing of information (quantum computation) that the differentiation occurs.
The ability to manipulate quantum information enables us to perform tasks that would be unachievable in a classical context, such as unconditionally secure transmission of information. Quantum information processing is the most general field that is concerned with quantum information. There are certain tasks which classical computers cannot perform "efficiently" (that is, in polynomial time) according to any known algorithm. However, a quantum computer can compute the answer to some of these problems in polynomial time; one well-known example of this is Shor's factoring algorithm. Other algorithms can speed up a task less dramatically - for example, Grover's search algorithm which gives a quadratic speed-up over the best possible classical algorithm.
Quantum information, and changes in quantum information, can be quantitatively measured by using an analogue of Shannon entropy, called the von Neumann entropy. Given a statistical ensemble of quantum mechanical systems with the density matrix ρ, it is given by
S(\rho) = -\operatorname{Tr}(\rho \ln \rho). \,
Many of the same entropy measures in classical information theory can also be generalized to the quantum case, such as Holevo entropy and the conditional quantum entropy.

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Quantum information theory

The theory of quantum information is a result of the effort to generalise classical information theory to the quantum world. Quantum information theory aims to answer the following question:
What happens if information is stored in a state of a quantum system?
One of the strengths of classical information theory is that physical representation of information can be disregarded: There is no need for an 'ink-on-paper' information theory or a 'DVD information' theory. This is because it is always possible to efficiently transform information from one representation to another. However, this is not the case for quantum information: it is not possible, for example, to write down on paper the previously unknown information contained in the polarisation of a photon.
In general, quantum mechanics does not allow us to read out the state of a quantum system with arbitrary precision. The existence of Bell correlations between quantum systems cannot be converted into classical information. It is only possible to transform quantum information between quantum systems of sufficient information capacity. The information content of a message \mathcal{M} can, for this reason, be measured in terms of the minimum number n of two-level systems which are needed to store the message: \mathcal{M} consists of n qubits. In its original theoretical sense, the term qubit is thus a measure for the amount of information. A two-level quantum system can carry at most one qubit, in the same sense a classical binary digit can carry at most one classical bit.
As a consequence of the noisy-channel coding theorem, noise limits the information content of an analog information carrier to be finite. It is very difficult to protect the remaining finite information content of analog information carriers against noise. The example of classical analog information shows that quantum information processing schemes must necessarily be tolerant against noise, otherwise there would not be a chance for them to be useful. It was a big breakthrough for the theory of quantum information, when quantum error correction codes and fault-tolerant quantum computation schemes were discovered.


See also


Journals

Among the journals in this field are


External links and references

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