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Posts Tagged ‘Schrödinger

“There is nothing more wonderful than a list, instrument of wondrous hypotyposis”*…

 

Da Vinci would carry around a notebook, where he would write and draw anything that moved him. “It is useful,” Leonardo once wrote, to “constantly observe, note, and consider.” Buried in one of these books, dating back to around the 1490s, is a to-do list. And what a to-do list…

Check it out (if not off) at “Leonardo Da Vinci’s To Do List (Circa 1490) Is Much Cooler Than Yours.”

* Umberto Eco, The Name of the Rose

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As we prioritize prioritization, we might spare a thought for Erwin Rudolf Josef Alexander Schrödinger; he died on this date in 1961.  A physicist best remembered in his field for his contributions to the development of quantum mechanics (e.g., the Schrödinger equation), and more generally for his “Schrödinger’s cat thought experiment– a critique of the Copenhagen interpretation of quantum mechanics– he also wrote on philosophy and theoretical biology.  Indeed, both James Watson, and independently, Francis Crick, co-discoverers of the structure of DNA, credited Schrödinger’s What is Life? (1944), with its theoretical description of how the storage of genetic information might work, as an inspiration.

It seems plain and self-evident, yet it needs to be said: the isolated knowledge obtained by a group of specialists in a narrow field has in itself no value whatsoever, but only in its synthesis with all the rest of knowledge and only inasmuch as it really contributes in this synthesis toward answering the demand, “Who are we?”

– from Science and Humanism, 1951

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Written by LW

January 4, 2017 at 1:01 am

“in this case there were three determinate states the cat could be in: these being Alive, Dead, and Bloody Furious”*…

 

Of all the bizarre facets of quantum theory, few seem stranger than those captured by Erwin Schrödinger’s famous fable about the cat that is neither alive nor dead. It describes a cat locked inside a windowless box, along with some radioactive material. If the radioactive material happens to decay, then a device releases a hammer, which smashes a vial of poison, which kills the cat. If no radioactivity is detected, the cat lives. Schrödinger dreamt up this gruesome scenario to mock what he considered a ludicrous feature of quantum theory. According to proponents of the theory, before anyone opened the box to check on the cat, the cat was neither alive nor dead; it existed in a strange, quintessentially quantum state of alive-and-dead.

Today, in our LOLcats-saturated world, Schrödinger’s strange little tale is often played for laughs, with a tone more zany than somber. It has also become the standard bearer for a host of quandaries in philosophy and physics. In Schrödinger’s own time, Niels Bohr and Werner Heisenberg proclaimed that hybrid states like the one the cat was supposed to be in were a fundamental feature of nature. Others, like Einstein, insisted that nature must choose: alive or dead, but not both.

Although Schrödinger’s cat flourishes as a meme to this day, discussions tend to overlook one key dimension of the fable: the environment in which Schrödinger conceived it in the first place. It’s no coincidence that, in the face of a looming World War, genocide, and the dismantling of German intellectual life, Schrödinger’s thoughts turned to poison, death, and destruction. Schrödinger’s cat, then, should remind us of more than the beguiling strangeness of quantum mechanics. It also reminds us that scientists are, like the rest of us, humans who feel—and fear…

More of this sad story at “How Einstein and Schrödinger Conspired to Kill a Cat.”

* Terry Patchett

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As we refrain from lifting the box’s lid, we might spare a thought for Charles Babbage; he died on this date in 1871.  A mathematician, philosopher, inventor and mechanical engineer, Babbage is best remembered for originating the concept of a programmable computer.  Anxious to eliminate inaccuracies in mathematical tables. By 1822, he built small calculating machine able to compute squares (1822).  He then produced prototypes of portions of a larger Difference Engine. (Georg and Edvard Schuetz later constructed the first working devices to the same design which were successful in limited applications.)  In 1833 he began his programmable Analytical Machine (AKA, the Analytical Engine), the forerunner of modern computers, with coding help from Ada Lovelace, who created an algorithm for the Analytical Machine to calculate a sequence of Bernoulli numbers— for which she is remembered as the first computer programmer.

Babbage’s other inventions include the cowcatcher, the dynamometer, the standard railroad gauge, uniform postal rates, occulting lights for lighthouses, Greenwich time signals, and the heliograph opthalmoscope.  He was also passionate about cyphers and lock-picking.

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Playing at life…

 

For years both scientists and science fiction writers have suggested that a sufficiently advanced civilisation could– and thus would– create a simulated universe.  And since simulations beget simulations (within simulations, within simulations, etc., etc.), there would ultimately be many more simulated universes than real ones…  meaning that it would be more likely than not that any one universe– say, ours– is artificial.

Silas Beane, working with a team at the University of Bonn says he have evidence this may be true.  The Physics arXiv Blog at Technology Review explains:

 

First, some background. The problem with all simulations is that the laws of physics, which appear continuous, have to be superimposed onto a discrete three dimensional lattice which advances in steps of time.

The question that Beane and co ask is whether the lattice spacing imposes any kind of limitation on the physical processes we see in the universe. They examine, in particular, high energy processes, which probe smaller regions of space as they get more energetic

What they find is interesting. They say that the lattice spacing imposes a fundamental limit on the energy that particles can have. That’s because nothing can exist that is smaller than the lattice itself.

So if our cosmos is merely a simulation, there ought to be a cut off in the spectrum of high energy particles.

It turns out there is exactly this kind of cut off in the energy of cosmic ray particles,  a limit known as the Greisen–Zatsepin–Kuzmin or GZK cut off.

This cut-off has been well studied and comes about because high energy particles interact with the cosmic microwave background and so lose energy as they travel  long distances.

But Beane and co calculate that the lattice spacing imposes some additional features on the spectrum. “The most striking feature…is that the angular distribution of the highest energy components would exhibit cubic symmetry in the rest frame of the lattice, deviating significantly from isotropy,” they say.

In other words, the cosmic rays would travel preferentially along the axes of the lattice, so we wouldn’t see them equally in all directions.

That’s a measurement we could do now with current technology. Finding the effect would be equivalent to being able to to ‘see’ the orientation of lattice on which our universe is simulated…

Read the whole mind-blowing story (including some comforting caveats) at “The Measurement That Would Reveal The Universe As A Computer Simulation” (and find Beane’s paper here).

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As we wonder if there’s a “reset” button, we might spare a thought for the extraordinary Erwin Rudolf Josef Alexander Schrödinger; he died on this date in 1961.  A physicist best remembered in his field for his contributions to the development of quantum mechanics (e.g., the Schrödinger equation), and more generally for his “Schrödinger’s cat thought experiment– a critique of the Copenhagen interpretation of quantum mechanics– he also wrote on philosophy and theoretical biology.  Indeed, both James Watson, and independently, Francis Crick, co-discoverers of the structure of DNA, credited Schrödinger’s What is Life? (1944), with its theoretical description of how the storage of genetic information might work, as an inspiration.

It seems plain and self-evident, yet it needs to be said: the isolated knowledge obtained by a group of specialists in a narrow field has in itself no value whatsoever, but only in its synthesis with all the rest of knowledge and only inasmuch as it really contributes in this synthesis toward answering the demand, “Who are we?”

– from Science and Humanism, 1951

 source

Written by LW

January 4, 2013 at 1:01 am

To See What Condition My Condition Was In…

Could Quantum Mechanics be wrong?

The philosophical status of the wavefunction — the entity that determines the probability of different outcomes of measurements on quantum-mechanical particles — would seem to be an unlikely subject for emotional debate. Yet online discussion of a paper claiming to show mathematically that the wavefunction is real has ranged from ardently star-struck to downright vitriolic since the article was first released as a preprint in November 2011.

The paper, thought by some to be one of the most important in quantum foundations in decades, was finally published last week in Nature Physics (M. F. Pusey, J. Barrett & T. Rudolph Nature Phys. http://dx.doi.org/10.1038/nphys2309; 2012), enabling the authors, who had been concerned about violating the journal’s embargo, to speak about it publicly for the first time. They say that the mathematics leaves no doubt that the wavefunction is not just a statistical tool, but rather, a real, objective state of a quantum system…

The authors have some heavyweights in their corner: their view was once shared by Austrian physicist and quantum-mechanics pioneer Erwin Schrödinger, who proposed in his famous thought experiment that a quantum-mechanical cat could be dead and alive at the same time. But other physicists have favoured an opposing view, one held by Albert Einstein: that the wavefunction reflects the partial knowledge an experimenter has about a system. In this interpretation, the cat is either dead or alive, but the experimenter does not know which. This ‘epistemic’ interpretation, many physicists and philosophers argue, better explains the phenomenon of wavefunction collapse, in which a quantum state is fundamentally changed by measuring it…

Read the full story in Nature.

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As we listen for the tell-tale purr, we might spare a thought for Gerbert d’Aurillac (who became Pope Sylvester II); he died on this date in 1003.  Gerbert/Sylvester was never canonized; indeed, in his day, he dogged with rumors that he was a sorcerer in league with the devil… which appear to have been the work of reactionary forces resisting both Sylvester’s attempts to rid the Church of corruption (especially simony, the sale of sacraments and indulgences) and his attempts to popularize mathematics, astronomy and mechanics for lay audiences.  Inspired by translations of Arabic texts, he built clocks, invented the hydraulic organ, crafted astronomical instruments, and renewed interest in the abacus for use in mathematical calculations (in the process of which, he seems to have introduced Arabic numerals [except zero]).  It’s not a stretch to suggest that Gerbert/Sylvester began Europe’s long march out of the Dark Ages.

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Adventures in Cosmology: Starting out Simply…

Why was entropy so low at the Big Bang? (source: Internet Encyclopedia of Philosophy)

Back in 2010, SUNY-Buffalo physics professor Dejan Stojkovic and colleagues made a simple– a radically simple– suggestion:  that the early universe — which exploded from a single point and was very, very small at first — was one-dimensional (like a straight line) before expanding to include two dimensions (like a plane) and then three (like the world in which we live today).

The core idea is that the dimensionality of space depends on the size of the space observed, with smaller spaces associated with fewer dimensions. That means that a fourth dimension will open up — if it hasn’t already — as the universe continues to expand.  (Interesting corollary: space has fewer dimensions at very high energies of the kind associated with the early, post-big bang universe.)

Stojkovic’s notion is challenging; but at the same time, it would help address a number of fundamental problems with the standard model of particle physics, from the incompatibility between quantum mechanics and general relativity to the mystery of the accelerating expansion of the universe.

But is it “true”?  There’s no way to know as yet.  But Stojkovic and his colleagues have devised a test using the Laser Interferometer Space Antenna (LISA), a planned international gravitational observatory, that could shed some definitive light on the question in just a few years.

Read the whole story in Science Daily, and read Stojkovic’s proposal for experimental proof in Physical Review Letters.

As we glance around for evidence of that fourth dimension, we might bid an indeterminate farewell to Ilya Prigogine, the Nobel Laureate whose work on dissipative structures, complex systems, and irreversibility led to the identification of self-organizing systems, and is seen by many as a bridge between the natural and social sciences.  He died at the Hospital Erasme in Brussels on this date in 2003.

Prigogine’s 1997 book, The End of Certainty, summarized his departure from the determinist thinking of Newton, Einstein, and Schrödinger in arguing for “the arrow of time”– and “complexity,” the ineluctable reality of irreversibility and instability.  “Unstable systems” like weather and biological life, he suggested, cannot be explained with standard deterministic models.  Rather, given their to sensitivity to initial conditions, unstable systems can only be explained statistically, probabilistically.

source: University of Texas

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