# Practical Influences ~ Leo

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 25, 2017

When the Moon enters a zodiac sign it adds instinctive reaction, unconscious predestination, sensiti

Readable.cc makes RSS feeds readable. Cost-free and ad-free.

Articles from en.wordpress.com Sign up to subscribe to RSS feeds for personalised reading.

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 25, 2017

When the Moon enters a zodiac sign it adds instinctive reaction, unconscious predestination, sensiti

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 25, 2017

An international team led by the University of Chicago’s Institute for Molecular Engineering has discovered how to manipulate a weird quantum interface between light and matter in silicon carbide along wavelengths used in telecommunications.

The work advances the possibility of applying quantum mechanical principles to existing optical fiber networks for secure communications and geographically distributed quantum computation. Prof. David Awschalom and his 13 co-authors announced their discovery in Physical Review X.

“Silicon carbide is currently used to build a wide variety of classical electronic devices today,” said Awschalom, the Liew Family Professor in Molecular Engineering at UChicago and a senior scientist at Argonne National Laboratory. “All of the processing protocols are in place to fabricate small quantum devices out of this material. These results offer a pathway for bringing quantum physics into the technological world.”

The findings are partly based on theoretical models of the materials performed by Awschalom’s co-authors at the Hungarian Academy of Sciences in Budapest. Another research group in Sweden’s Linköping University grew much of the silicon carbide material that Awschalom’s team tested in experiments at UChicago. And another team at the National Institutes for Quantum and Radiological Science and Technology in Japan helped the UChicago researchers make quantum defects in the materials by irradiating them with electron beams.

Quantum mechanics govern the behavior of matter at the atomic and subatomic levels in exotic and counterintuitive ways as compared to the everyday world of classical physics. The new discovery hinges on a quantum interface within atomic-scale defects in silicon carbide that generates the fragile property of entanglement, one of the strangest phenomena predicted by quantum mechanics.

Entanglement means that two particles can be so inextricably connected that the state of one particle can instantly influence the state of the other, no matter how far apart they are.

“This non-intuitive nature of quantum mechanics might be exploited to ensure that communications between two parties are not intercepted or altered,” Awschalom said.

The findings enhance the once-unexpected opportunity to create and control quantum states in materials that already have technological applications, Awschalom noted. Pursuing the scientific and technological potential of such advances will become the focus of the newly announced Chicago Quantum Exchange, which Awschalom will direct.

An especially intriguing aspect of the new paper was that silicon carbide semiconductor defects have a natural affinity for moving information between light and spin (a magnetic property of electrons). “A key unknown has always been whether we could find a way to convert their quantum states to light,” said David Christle, a postdoctoral scholar at the University of Chicago and lead author of the work. “We knew a light-matter interface should exist, but we might have been unlucky and found it to be intrinsically unsuitable for generating entanglement. We were very fortuitous in that the optical transitions and the process that converts the spin to light is of very high quality.”

The defect is a missing atom that causes nearby atoms in the material to rearrange their electrons. The missing atom, or the defect itself, creates an electronic state that researchers control with a tunable infrared laser.

“What quality basically means is: How many photons can you get before you’ve destroyed the quantum state of the spin?” said Abram Falk, a researcher at the IBM Thomas J. Watson Resarch Center in Yorktown Heights, N.Y., who is familiar with the work but not a co-author on the paper.

The UChicago researchers found that they could potentially generate up to 10,000 photons, or packets of light, before they destroyed the spin state. “That would be a world record in terms of what you could do with one of these types of defect states,” Falk added.

Awschalom’s team was able to turn the quantum state of information from single electron spins in commercial wafers of silicon carbide into light and read it out with an efficiency of approximately 95 percent.

The duration of the spin state–called coherence–that Awschalom’s team achieved was a millisecond. Not much by clock standards, but quite a lot in the realm of quantum states, in which multiple calculations can be carried out in a nanosecond, or a billionth of a second.

The feat opens up new possibilities in silicon carbide because its nanoscale defects are a leading platform for new technologies that seek to use quantum mechanical properties for quantum information processing, sensing magnetic and electric fields and temperature with nanoscale resolution, and secure communications using light.

“There’s about a billion-dollar industry of power electronics built on silicon carbide,” Falk said. “Following this work, there’s an opportunity to build a platform for quantum communication that leverages these very advanced classical devices in the semiconductor industry,” he said.

Most researchers studying defects for quantum applications have focused on an atomic defect in diamond, which has become a popular visible-light testbed for these technologies.

“Diamond has been this huge industry of quantum control work,” Falk noted. Dozens of research groups across the country have spent more than a decade perfecting the material to achieve standards that Awschalom’s group has mastered in silicon carbide after only a few years of investigation.

“There are many different forms of silicon carbide, and some of them are commonly used today in electronics and optoelectronics,” Awschalom said. “Quantum states are present in all forms of silicon carbide that we’ve explored. This bodes well for introducing quantum mechanical effects into both electronic and optical technologies.”

Researchers now are beginning to wonder if this type of physics also may work in other materials, Falk noted.

“Moreover, can we rationally design a defect that has the properties we want, not just stumble into one?” he asked.

Defects are the key.

“For decades the electronics industry has come up with a myriad of tricks to remove all the defects from their devices because defects often cause problems in conventional electronics,” Awschalom explained. “Ironically, we’re putting the defects back in for quantum systems.”

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 23, 2017

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 23, 2017

*Three*

Why do we want a quantum theory of gravity? *We just want it, okay?*

Hold on, this isn’t me. This was the American theoretical physicist John Preskill at a conference earlier this year [1]. And though, in almost all probability, he was trying to be funny, this does give an idea about how difficult (and often, frustrating) it is for theoretical physicists to answer *why-do-we-want-this* or *what-use-doing-that* questions. (By the way, apart from his seminal contributions to the fields of quantum information and quantum gravity, Preskill is also famous for winning a black hole bet against Stephen Hawking which Hawking conceded by offering him a baseball encyclopedia.)

But something about the notion of *universality* in random matrix theory before I go on to talk about the theory of quantum gravity, cosmological inflation, black holes, *wormholes* and *time travel*. (Okay, I was kidding about the last two – no wormholes and time travel here.)

Large matrices with random entries have some very intricate (and interesting) statistical properties. And the reason they come in so handy in our attempts to answer questions of different sorts is the applicability of the statistical laws of random matrix ensembles to all those systems which have the same symmetries as those of the ensemble.

Quite often, these statistical laws correspond to the *eigenvalues* of the matrices. Eigenvalues are certain quantities associated with matrices. In fact, all square matrices (arrays of numbers with the same number rows and columns) can be characterised by their eigenvalues. And in most cases, computing the eigenvalues is not a very difficult task.

For a set of random numbers, it is very natural and useful to talk about the probability distribution – how probable the occurrence of each of the numbers is. Now, if your matrices have random elements, its eigenvalues will be random as well, which makes it useful to talk about the eigenvalue distributions of the ensembles.

These distributions in random matrix theory are *universal* in the sense that they don’t depend on the underlying structures as long as they have a common overall symmetry. In the context of a physical system, these eigenvalues correspond to the energy levels of the system and, in essence, contain the information about its dynamical properties. Superficially, this is what a lot of random matrix analyses is about. The energy spectra of systems which are difficult to interpret otherwise find meaning in the language of random matrix ensembles.

But understanding the underlying dynamics of many systems is not easy. And as we have come to realise in the case of black holes – it is certainly not.

Black holes are *interesting*; though calling them interesting might be an understatement. They are formed in a number of different ways all over the universe. Within the framework of the theory of general relativity, one can, in quite a straightforward manner, show that a black hole has a gravitational pull so huge that nothing can escape it, not even light.

But everything is not that straightforward. Though general relativity explains the force of gravitation, we believe our universe to be inherently quantum mechanical, that is, we expect every object in the universe to follow the laws of quantum theory. And taking quantum mechanical laws into consideration, one can show (as Hawking did for the first time in the early 1970s) that black holes radiate stuff [2]. Now, this may seem puzzling; in fact, it *is* puzzling. But what this radiation also indicates is that black holes are *thermal* objects – they have thermodynamic properties (say, temperature, for example) in a manner *similar* to how your daily cup of coffee does.

It is evident that black holes demand a better understanding than the one at present. And this can possibly be achieved by constructing a unified framework incorporating both gravity and quantum mechanical principles. This is somewhere random matrix analysis turns out to be useful – understanding energy spectra of black holes.

Depending on the theoretical framework in which the calculations are being done, black holes can be studied using different models. In principle, the details of the energy spectra can be worked out for each of these models. But as it turns out, not all black hole models are soluble. The trick is to then use random matrix models which can possibly mimic the expected properties.

Black holes have posed some of the most interesting challenges to those working in physics for the last hundred years. They have also motivated a quest for quantum gravity. However, a theory of quantum gravity will possibly also explain many other mysteries. One of them is *cosmological inflation*. Based on a large amount of astronomical data, it has been conjectured that our universe underwent a phase of extremely rapid expansion for a small fraction of second just after the *big bang*. This conjecture also explains the origin of the large scale structures in the universe pretty well. However, what is missing is a concrete theoretical underpinning of inflation itself. Among various proposals to explain inflation, there are a few which employ random matrix techniques as well [3]. But again, a complete understanding of inflation, like that of black holes, still belongs to the large set of open problems waiting to be solved!

[1] John Preskill, *Quantum Information and Spacetime (I)*, https://youtu.be/td1fz5NLjQs, Tutorial at the 20th Annual Conference on Quantum Information Processing, 2017.

[2] Leonard Susskind, *Black Holes and the Information Paradox*, Scientific American, April 1997.

[3] M.C. David Marsh, Liam McAllister, Enrico Pajer and Timm Wrase, *Charting an Inflationary Landscape with Random Matrix Theory*, JCAP **11**, 2013, [arXiv:hep-th/1307.3559].

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 23, 2017

Now that I’ve finished a marathon session of report-writing I thought I’d take a few minutes out this Friday afternoon, have a cup of tea and pass on a rather silly thought I had the other day about the relationship between Quantum Mechanics (and specifically the behaviour of spin therein) and voting behaviour in elections and referendums.

Gratuitous picture of a Stern-Gerlach experiment

For a start here’s a brief summary of the usual quantum-mechanical context as it relates to, e.g., electrons (rather than elections). Being fermions, electrons possess half-integer spin. This attribute has the property that a measurement of its component in any direction has only two possible values, ±½ in units of Planck’s constant. In the Stern-Gerlach experiment illustrated above, which measures the spin in the vertical direction of silver atoms emerging from a source, the outcome is either “up” or “down”, not some spread of values in between. Silver has a single unpaired electron which is why its atoms behave in this respect in the same way as an individual electron.

The way this is often described in physics textbooks is to say that the operator corresponding to spin in the z-direction has only two eigenstates (call these ↑ and ↓) ; the act of measurement has to select one of them, not some intermediate state. If the source is thermal then the spins of individual atoms have no preferred direction so 50% turn out to be ↑ and 50% to be ↓ as shown in the cartoon.

Once such measurement has been made, a given particle remains in the same eigenstate, which means that if it is passed through another similar measuring device it will always turn out to have spin pointing in the same direction. If you like, the particle has been `prepared’ in a given state by the act of measurement.

This applies as long as no attempt is made to make a measurement of the spin in a different direction, which is when the fun starts. If we start with a particle in the ↑ state and then pass it through an experiment that measures spin (say) with respect to the x-axis instead of the z-axis then the two allowed eigenstates are then not ↑ and ↓ but ← and →. A particle that was definitely spin-up would then be forced to decide between spin-left and spin-right (each would have a 50% probability).

Suppose now we took our long-suffering particle that began with spin ↑ after a measurement in the z-direction, then turned out to be spin → when we measured it in the x-direction. What would happen if we repeated the z-measurement? The answer is that “preparing” the particle in the → state destroys the information about the fact that it was previously prepared in the ↑ state – the outcome of this second z-measurement is that the particle that was previously definitely ↑ now has a 50% chance of being either ↑ or ↓.

So what does all this have to do with voting? It is clear than an election (or a referendum) is very far from a simple act of measurement. During the campaign the various sides of the debate make attempts to prepare a given voter in a given state. In the case of last year’s EU referendum the choice of eigenstates was `Leave’ or `Remain’; no other possibilities were allowed. The referendum then `prepared’ each voter in one or other of these possibilities.

If voters behaved quantum mechanically each would stay in their chosen state until some other measurement were attempted. But that’s exactly what did happen. Earlier this month there was a General Election. More than two parties were represented, but let’s simplify and assume there were only two options, `Labour’ and `Conservative’.

Now it is true that the `Leave’ camp was dominated by the right wing of the Conservative party, and the majority of Labour voters voted `Remain’, but there were a significant number of Labour Leave voters and a significant number of Tories voted Remain. While these pairs of states are therefore not exactly orthogonal, they are clearly not measuring the same thing so the situation is somewhat analogous to the spin measurement problem.

So along came the General Election result which `prepared’ voters in a state of `Labour’ or `Conservative’, with a slight preference for the latter whereas the earlier referendum had prepared a them in a state of `Leave’ versus `Remain’ with a slight preference for the former. From a quantum mechanical perspective, however, you can further argue that the General Election prepared the voters in such a way that should have erased memories of their vote in the referendum so the previous BrExit vote is now invalid.

There’s only one way to test this quantum-mechanical interpretation of voting patterns, and that is by repeating the EU Referendum…

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 22, 2017

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 22, 2017

Source: GizaDeathStar.com

Dr. Joseph P. Farrell Ph.D.

June 22, 2017

Ms. K.M. sent this article this week, and I *have* to blog about it, for it seems that some physicists are making the claim – not yet totally sanctioned by other physicists – of being able to manipulate the vacuum, and hence the vacuum (or zero point), energy itself:

Physicists Say They’ve Manipulated ‘Pure Nothingness’ And Observed The Fallout

Before we get to why I had an “oh my!” moment when I read this, and to my high octane speculation of the day, consider the following paragraphs:

Then, in 2015, a team led by Alfred Leitenstorfer from the University of Konstanz in Germany claimed they’d directly detected these fluctuations, by observing their influence on a light wave. The results were published in

Science.To do this, they fired a super short laser pulse – lasting only a few femtoseconds, which is a millionth of a billionth of a second – into a vacuum, and were able to see subtle changes in the polarisation of the light. They said these changes were caused directly by the quantum fluctuations.

It’s a claim that’s still being debated, but the researchers have now taken their experiment to the next level by ‘squeezing’ the vacuum, and say they’ve been able to observe the strange changes in the quantum fluctuations as a result.

…

That sounds weird, but in a vacuum, space and time behave in the same way, so it’s possible to examine one to learn more about the other.

Doing this, the team saw that when they ‘squeezed’ the vacuum, it worked kind of like squeezing a balloon, and redistributed the strange quantum fluctuations within it.

Now, in case you missed it, let’s boil all this down to two basic ideas:

(1) there is an energy in absolute vacuum, which is known by a variety of names; zero point energy, quantum fluctuations, vacuum energy and so on;

(2) that energy can be observed, or accessed, when one *changes the pure “shape” or geometry* of the vacuum itself. Indeed, viewed a certain way, the particles of physics are “changes of geometry” in the vacuum that are stable for some period of time.

Let this all sink in for a moment: scientists have found a way to “change the shape’ of the vacuum itself, and hence, have observed and accessed the strange and hitherto inaccessible world of that “quantum vacuum fluctuation.”

There is, so to speak, a purely abstract – non-physical – *topology* to the way even the vacuum – pure nothingness – behaves, and this is *manipulable* via *shape*. So the claim – which, let us note for the record, is still being debated by the scientific community reacting to this experiment – is to have achieved the God-like power to shape nothingness itself. For most people, this will seem at once a contradiction of religion and the ultimate testament of the folly of man. In point of fact, for certain versions of religion, man is a “co-worker” with God, even in his own salvation, and there is no real limit placed on what that “co-working” entails, even, perhaps, to the cosmological scale. (For those interested in the details, it is part of the *communicatio* or *circumincessio idiomatorum*). While this experiment is only a first, small step, it is also a gigantic step in terms of the implications, for it is suggesting that the vacuum is directly engineerable – as some have been maintaining for decades – via its shape or geometry. Indeed, it recalls the pyramid research of Ukrainian physicist Volodimir Krasnoholovets, and his co-authored papers with topologist Michel Bounias.

It also recalls that disturbing statement in the Babylonian war epic, the *Enuma Elish* (and yes, I persist in my opinion that the epic is a *war* epic and not, pace academia, a *creation* epic), that after a colossal war and the destruction of the planet/god Tiamat, he “remeasured the *structure of the deep*“, of “the abyss”.

See you on the flip side…

Read More At: GizaDeathStar.com

________________________________________________

Joseph P. Farrell has a doctorate in patristics from the University of Oxford, and pursues research in physics, alternative history and science, and “strange stuff”. His book The Giza DeathStar, for which the Giza Community is named, was published in the spring of 2002, and was his first venture into “alternative history and science”.

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 22, 2017

A solution to the longstanding problem of ensuring fair gambling between two separated parties, without the assistance of a trusted third party, is reported in a paper published online this week in npj Quantum Information. The proof-of-principle integrates both quantum mechanics and game theory and could potentially find application in internet gambling and casinos.

Gambling or betting on an event with an uncertain outcome is a widely practiced activity. However, despite its widespread usage and applications, fair gambling between two spatially separated parties cannot be conducted without the assistance of a trusted third party.

Imagine a gambler, Bob, wants to gamble with a casino, Alice. How does Bob know that the gambling machine provided by Alice is fair, especially in the case of online gambling? The standard solution to this problem is to introduce a trusted third party to make sure the gambling is fair to both parties. However, in some cases, a trusted third party does not exist.

Here, Pei Zhang and colleagues experimentally demonstrate a novel gambling protocol that enables fair gambling between two distant parties, without the help of a third party. They incorporate the key concepts and methods of game theory into quantum information theory to create a protocol that will ensure the two parties move their strategies to a Nash-equilibrium point (at this point, no player has anything to gain by unilaterally changing his or her own strategy), guaranteeing fairness through the physical laws of quantum mechanics.

Furthermore, the protocol prevents both parties in the game from tampering with the results. Thus, there is no need for a trusted third party, as any tampering can be easily detected or lowers the tampering party’s chance to win. The authors then show that the protocol can be easily adapted to a biased version, which would possibly allow it to be used in lotteries or casinos.

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 21, 2017

Australian scientists have recreated a famous experiment and confirmed quantum physics’s bizar

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 21, 2017

When the Moon enters a zodiac sign it adds instinctive reaction, unconscious predestination, sensiti

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 21, 2017

In the first post we discussed the fact that classical first-order logic is distributive, that is, pizza and (lemonade or water) is the same as (pizza and lemonade) or (pizza and water); or symbolically,

.

This time the aim will be to come up with an example demonstrating that this very intuitive identity does not always hold in quantum mechanics. To do that, we will need the uncertainty principle discussed in the previous post.

**Quantum cyclist**

We are going to use the uncertainty principle for position and momentum to construct a system which does not obey the distributive law. To make the numbers a bit simpler, we take , so the uncertainty relation looks like:

.

Recall the example with a cyclist from the first post, we observed that the cyclist being in some interval and having some velocity is the same as the cyclist being in the first half of the interval with the same velocity or the cyclist being in the second half of the interval with the same velocity. Now consider a (tiny!) quantum cyclist; for concreteness, suppose the cyclist is in the interval and has the momentum in the interval . For simplicity, we take the uncertainty to be the length of the interval1, so we are saying that the cyclist is equally likely to be anywhere between and and is equally likely to have any momentum between and . Hence we have and . Now let , and be the following statements about our system (i.e. about the cyclist):

= ‘cyclist has the momentum in ‘

= ‘cyclist is in ‘

= ‘cyclist is in ‘.

The distributive law is:

.

Note that the left-hand side of this identity is precisely what we have described above; the cyclist is in with momentum in . We calculate , which satisfies the uncertainty condition, and so the system is physically possible. On the right-hand side, however, we have , that is, the cyclist is in with momentum in , giving both and as . But this violates the uncertainty bound, since , which is certainly smaller than ! Since gives the same uncertainties, we must conclude that both terms on the right-hand side are physically impossible, and thus false. This makes all of the right-hand side false; we must, therefore, conclude that this identity cannot hold in this case, as it equates a true statement about the physical system with a false one.

The example above raises many questions for classical logic. Must we conclude that its axioms and rules of inference don’t always hold? If yes, what would be the axioms, and how would they account for the fact that classical logic is distributive? If no, how do we account for the anomaly described above? It is not even clear if there should be one formal system of reasoning flawlessly applicable in all situations to all possible systems. No matter the answers to these questions, the example certainly opens up the space for development of a formal system correctly describing the logic of quantum mechanics.2

1This is actually not quite correct, e.g. should really be . We can, however, get the uncertainties we want by scaling the intervals accordingly, but this doesn’t really contribute to the understanding, and so we drop the scaling for clarity.

2For further reading, see https://plato.stanford.edu/entries/qt-quantlog/.

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 21, 2017

When the Moon enters a zodiac sign it adds instinctive reaction, unconscious predestination, sensiti

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 20, 2017

There are a lot of ways to define science. The broadest might characterize it as a systematic proces

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 20, 2017

Seven Brief Lessons on Physics by Carlo Rovelli

My rating: 4 of 5 stars

Now I am not going to go so far out of my depth—or so far off-brand—as to write at length about even a popular science book on theoretical physics, especially when this is the first such book I’ve read since I was puzzling over John Gribbin and Paul Davies in my teens. I took advanced physics in high school with the legendary David Spahr, who taught and graded like a college professor, yet in my day rarely had one word said against him, because we knew he was too good for us (I recall that he would recite passages from Milton or FitzGerald’s *Rubaiyat* to illustrate scientific points or, more remarkably, to use as the bases of word problems). I got terrible grades, of course. Even today, my own students will tell you they are always having to correct my grade breakdowns for my classes because I cannot add to a hundred! Pathologically innumerate, I was even worse in high school: my English and history teachers thought I was a savant, whereas my math and science teachers judged me an idiot. Nevertheless, the more philosophical aspects of physics always fascinated me even though my mathematical comprehension halts at (or long before) the frontier of calculus.

So I took up this brief, lyrical digest of modern physics by the Italian physicist Carlo Rovelli (translated by Simon Carnell and Erica Segre). Written simply enough that it would not make a bad gift even for a middle-schooler, it is also a good book for readers primarily interested in arts and humanities, since Rovelli’s disquisitions on physics are philosophically informed. His commentaries on the implications of relativity theory, quantum mechanics, and the long attempt to reconcile the two bear on far more than technical scientific debate.

To wit: for many us who were reared within the cultural matrix of print culture and its Enlightenment politics, the infinitude of subjective worlds erupting out of the Internet has been alarming. It is probably not wrong to be worried about some of the extremes of group-level relativism promoted by the identitarian politics of both left and right factions today. But what if group-level relativism is bad because it is not relative enough? What if the law of the universe is, paradoxically, more granularly anarchic than cultural relativism, because every interaction between *any* two forces is a variable singularity? “Reality,” Rovelli comments, “is only interaction.” He goes on:

A handful of types of elementary particles, which vibrate and fluctuate constantly between existence and nonexistence and swarm in space, even when it seems that there is nothing there, combine together to infinity like the letters of a cosmic alphabet to tell the immense history of galaxies…

Derogating “postmodernism” (I too dislike it, but for different reasons) and preaching a return to “objective reality,” some contemporary thinkers call for a return to Gradgrindian fact. These thinkers often seem to be biologists or similar, but I recall learning in school that in the order of knowledge biology depends on chemistry, and chemistry depends in its turn on physics. When castigating the heirs of Nietzsche, our neo-Enlighteners might spare some venom to spit at the heirs of Heisenberg. For the physicist Rovelli, postmodernism errs only in maintaining the Kantian distinction between subjectivity and the truth that is out there, whereas it is the truth perceptible to science that itself renders even the outside or objective world a radically unstable, changeable quantity, continuously altering in interaction with its observers. It is not only the self that is decentered and unstable, but the entire cosmos, which may not even be there if you are not looking at it. What, for instance, are we to make of time as conceptually revised by the theory of loop quantum gravity?

Just as the idea of a continuous space that contains things disappears, so the idea of an elementary and primal “time” flowing regardless of things also vanishes. The equations describing grains of space and matter no longer contain the variable “time.” This doesn’t mean that everything is stationary unchanging. On the contrary, it means that change is ubiquitous—but elementary particles cannot be ordered in a common succession of “instants.” At the minute scale of the grains of space, the dance of nature does not take place to the rhythm of the baton of a single orchestral conductor, at a single tempo: every process dances independently with its neighbors, to its own rhythm. The passage of time is internal to the world, is born in the world itself in the relationship between quantum events that comprise the world and are themselves the source of time.

“The passage of time is internal to the world”: as a literary person, I am happy to know that cutting-edge physics beyond my ken confirms a lesson I learned long ago from Virginia Woolf.

Rovelli concludes his book with philosophical reflections on the nature of humanity and the universe. Rejecting German idealism’s anthropocentrism and its influence (he criticizes Kant, Schelling, and Heidegger by name), he takes his stand with Lucretius and Spinoza: our consciousness and our freedom are identical with the lawful, probabilistic surges of the matter and energy of which we are made, and our ever-shifting and ever-reflexive knowledge may, if we strive for it, as our ancestors strove to track their invisible prey by its visible tracks (Rovelli’s metaphor), come ever nearer to the truth. The truth is that the universe is a rippling plane of variously interacting quantities, a wave of singular events. Left unexplained is the source of our drive to know; the analogy to paleolithic hunting is a weak reductionism. What does this universe need with our need to understand it, and why is Rovelli so certain that our need does not differentiate us from the placidity of the rocks and stones and trees? Here physics gives way to metaphysics.

In any case, Rovelli’s physics, if it cannot provide the final answer to the fundamental questions, is highly useful in reminding this C-student in physics that the universe is almost unspeakably strange, and that appeals to “reality” may be less reassuring, though more poetically exciting, than they seem.

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 20, 2017

Quantum entanglement may be the solution to private communication and digital privacy in general. Who knew such a thing existed?! Until China captured worldwide attention with their first QE communications satellite, chances are this phenomenon wasn’t on your radar.

If you’re already lost, no worries. I even hesitated to write about this topic based on its complexity, but how could I turn down the opportunity to learn about and share such a cool concept, or any concept for that matter? No way. Let’s take this step by step; just enough to understand the concept without getting too tangled. It’s spooky stuff as you’ll soon find out.

To begin, let’s break it all the way down and start with quantum mechanics in general. What is that? It’s the study of the very basic components of matter such as atoms and electrons, and then even smaller than that. At this level, the rules of interaction change* and the field of quantum mechanics is born. QM in general strives to mathematically describe the interaction, or the new rules of interaction, of these subatomic* particles.

As QM evolves and we develop our understanding of how these particles interact, a whole new era of quantum technology will become available. The best part, is that these quantum tools seem to defy the laws of physics. So what happens when the rules are broken? Is the quantum revolution the next to come after the industrial revolution? We are just scratching the surface of this field and it will change the way our world works. So far, an unhackable communications network and communicating instantaneously over vast distances on Earth and through space are on the near horizon. So *how* is this possible?

This is where we get into quantum entanglement (QE) and spooky action at a distance. Let’s start with QE first. It’s a tricky one because quite frankly, no one truly understands how this works, yet. I’m going to borrow this explanation from the next web as they describe QE in the context of communication:

“…instead of sending information, you’ll create pairs of photons that mirror one another. This is called quantum entanglement. You’ll keep one of the photons, send someone else the other entangled photon, and then anything you do to your photon instantly happens to the other person’s photon.”

Yes, it’s a tricky concept to grasp. Let’s use the example of China’s satellite to clarify. Simply put, there’s one photon on Earth, and one photon in the satellite, and these photons have a relationship where they *mirror *whatever manipulation is made to their twin photon. So, enter a secret message in photon number one on Earth, and its twin photon in the satellite will instantly mirror the message. The best part is that this little understood phenomena was named by Einstein as spooky action at a distance,* because it’s exactly that, weird stuff.

We don’t know why these photons behave in this way, but we do know what we can use this for. I’ve listed two uses so far. First, this method of communication is unhackable with current technology. Quantum entanglement allows for communication with no transfer of signal. With no signal to intercept, there’s no way to hack the data. Second, is instant communication. The way the twin photons mirror each other instantaneously solves the issue of radio waves traveling through space over time. So don’t stress! If your bestie moves to Mars you’ll still be able to have real time conversations.

If I could write about theories such as this each day, I’d really be living the dream. Theory that develops into usable science is very exciting stuff, but also very complex. I admire the level of genius required to understand all this, and want to share it. So, for all posts, and this one in particular, I welcome feedback. Help me get it right. Comments, questions, corrections- bring it on! It’s a collective effort to move forward.

- *Rules change: such as Einstein’s laws of relativity
- *Subatomic– smaller than an atom (simply put)
- *Action at a distance– In physics, action at a distance is the concept that an object can be moved, changed, or otherwise affected without being physically touched (as in mechanical contact) by another object.

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 20, 2017

A team of Chinese scientists has realized the satellite-based distribution of entangled photon pairs over 1200 km. The photon pairs were demonstrated to be still entangled after travelling long distances and Bell’s inequality was shown to be violated under strict Einstein locality conditions.

This experiment was made through two satellite-to-ground downlinks with a summed length varying from 1600-2400 km. The obtained link efficiency is orders of magnitude higher than that of the direct bidirectional transmission of two photons through telecommunication fibers.

Quantum communication scientists have a fundamental interest in distributing entangled particles over increasingly long distances and studying the behavior of entanglement under extreme conditions. So far, entanglement distribution has only been achieved at a distance up to ~100 km due to photon loss in optical fibers or terrestrial free space.

One way to improve distribution lies in the protocol of quantum repeaters, whose practical usefulness, however, is hindered by the challenges of simultaneously realizing and integrating all key capabilities.

Another approach makes use of satellite- and space-based technologies, as a satellite can conveniently cover two distant locations on Earth. The main advantage of this approach is that most of the photons’ transmission path is almost in vacuum, with almost zero absorption and de-coherence.

To prove the feasibility of satellite- and space-based distribution research, ground-based studies were done that demonstrated bidirectional distribution of entangled photon pairs through a two-link terrestrial free-space channel, over distances of 600 m, 13 km, and 102 km, with an ~80-dB effective channel loss. Quantum communications on moving platforms in a high-loss situation and under turbulent conditions were also tested.

After these feasibility studies, a quantum science experiment satellite – Micius – was developed and launched from Jiuquan, China on August 16, 2016 with a mission of entanglement distribution. Cooperating with Micius are three ground stations (Delingha in Qinghai; Nanshan in Urumqi, Xinjiang; and Gaomeigu Observatory in Lijiang, Yunnan). The distance between Delingha and Lijiang (Nanshan) is 1203 km. The distance between the orbiting satellite and these ground stations varies from 500-2000 km.

Due to the fact that the entangled photons cannot be amplified as classical signals, new methods must be developed to reduce link attenuation in satellite-to-ground entanglement distribution. To optimize link efficiency, the scientists combined narrow-beam divergence with a high-bandwidth and high-precision acquiring, pointing, and tracking (APT) technique. By developing an ultra-bright space-borne two-photon entanglement source and high-precision APT technology, the team established entanglement between two single photons separated by 1203 km, with an average two-photon count rate of 1.1 Hz and state fidelity of 0.869 ± 0.085. Using the distributed entangled photons, the scientists performed the Bell test at space-like separation and without locality and freedom-of-choice loopholes.

Compared with previous methods of entanglement distribution by direct transmission of the same two-photon source — using the best performance and most common commercial telecommunication fibers, respectively — the effective link efficiency of the satellite-based approach is 12 and 17 orders of magnitude higher, respectively.

Distributed entangled photons are readily useful for entanglement-based quantum key distribution, which, so far, is the only way to establish secure keys between two distant locations on Earth without relying on trustful relay. Another immediate application is to exploit distributed entanglement to perform a variant of quantum teleportation protocol for remote preparation and control of quantum states.

This satellite-based technology opens up bright prospects for both practical quantum communications and fundamental quantum optics experiments at distances previously inaccessible on the ground.

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 20, 2017

For extracts from last week’s sermon please Click here

An extract from the latest guest sermon held at the UNSCIENTIFIC CHURCH OF NONRELIGIOUS ENTITIES.

All materials are ©UCNE

*The lecturer in attendance is Prof. Leslie Longstocking and today’s topic revolves around the concept of shared matter in the physical plane relating to NESP particles. *

Hello valued Travellers.

Following on from last week’s lecture on the Uniformity of the Unity by Professor Lightbody, I felt it fitting to share with you the latest research from our facility in Tatnugan.

In many ways I was with you in my absence last week and will definitely be with you for the following weeks, despite my physical body being far removed.

We are all comprised at an atomic level of the same particles, in essence a carbon based life form with shared origins from across this and other galaxies.

It is the interconnectedness of these particles that I wish to discuss in more detail with you today. In particular, with reference to accessing the embeded memory strands we now know to be present in individual particles.

*(Speaker points to a member of the audience whose hand is raised)*

I will allow a brief period for questions at the end of the lecture Traveller.

We have identified a singularity that exists within nonentity specific particles or NESP’s as we prefer to call them. These are particles that are not of origin, or rather in layman’s terms, non unique to the entity. They exist in a state of flux within all of us.

The existence of NESP’s was theorised by the UCNE over a decade ago. It has taken technological advances made in the last twelve months by our research staff to finally isolate and identify the particles.

A single test entity screened positive for over twenty six million NESP’s in our first initial trials. Subsequent improvements and refinements to instruments now indicate NESP’s exist in numbers exceeding billions in each entity, a far higher number than previously imagined.

Dating of individual particles is currently based on the embedded memory strands which has proven too time consuming and we are hopeful that further advances will allow for alternate dating sequences to be developed.

Origination of NESP’s based on quantum cycling is in the advanced stages and we will be able to identify origin in a simple screening process to allow the host targeted memory retrieval.

NESP’s have a non linear cycle of dispersion and it is now an established fact that absorption of these particles is not predetermined or governed by any mechanism, but rather a random instance of chance.

*(Murmer runs through the audience)*

Yes, we were as amazed to discover this. No two entities screened with NESP’s identified from similar cycles exhibited similar memory patterns, indicating a stastical randomness that cannot be explained away.

Travellers are unique in singularity as origin entities and it now appears they are also unique in terms of NESP’s. The diversity this will allow us to build up through the accessed memory strands will change our perception of our current reality in fundemental ways.

I would like to move onto the practical techniques we are now able to share with you for entity based memory retrieval from NESP’s.

*Transcript ends*

For a full transcription of this lecture please visit our website at UCNE

Go forth to Unity in Truth. Please sign the guest register below and leave your comments.

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 20, 2017

Quantum entanglement may be the solution to private communication and digital privacy in general. Who knew such a thing existed?! Until China captured worldwide attention with their first QE communications satellite, chances are this phenomenon wasn’t on your radar.

If you’re already lost, no worries. I even hesitated to write about this topic based on its complexity, but how could I turn down the opportunity to learn about and share such a cool concept, or any concept for that matter? No way. Let’s take this step by step; just enough to understand the concept without getting too tangled. It’s spooky stuff as you’ll soon find out.

To begin, let’s break it all the way down and start with quantum mechanics in general. What is that? It’s the study of the very basic components of matter such as atoms and electrons, and then even smaller than that. At this level, the rules of interaction change* and the field of quantum mechanics is born. QM in general strives to mathematically describe the interaction, or the new rules of interaction, of these subatomic* particles.

As QM evolves and we develop our understanding of how these particles interact, a whole new era of quantum technology will become available. The best part, is that these quantum tools seem to defy the laws of physics. So what happens when the rules are broken? Is the quantum revolution the next to come after the industrial revolution? We are just scratching the surface of this field and it will change the way our world works. So far, an unhackable communications network and communicating instantaneously over vast distances on Earth and through space are on the near horizon. So *how* is this possible?

This is where we get into quantum entanglement (QE) and spooky action at a distance. Let’s start with QE first. It’s a tricky one because quite frankly, no one truly understands how this works, yet. I’m going to borrow this explanation from the next web as they describe QE in the context of communication:

“…instead of sending information, you’ll create pairs of photons that mirror one another. This is called quantum entanglement. You’ll keep one of the photons, send someone else the other entangled photon, and then anything you do to your photon instantly happens to the other person’s photon.”

Yes, it’s a tricky concept to grasp. Let’s use the example of China’s satellite to clarify. Simply put, there’s one photon on Earth, and one photon in the satellite, and these photons have a relationship where they *mirror *whatever manipulation is made to their twin photon. So, enter a secret message in photon number one on Earth, and its twin photon in the satellite will instantly mirror the message. The best part is that this little understood phenomena was named by Einstein as spooky action at a distance,* because it’s exactly that, weird stuff.

We don’t know why these photons behave in this way, but we do know what we can use this for. I’ve listed two uses so far. First, this method of communication is unhackable with current technology. Quantum entanglement allows for communication with no transfer of signal. With no signal to intercept, there’s no way to hack the data. Second, is instant communication. The way the twin photons mirror each other instantaneously solves the issue of radio waves traveling through space over time. So don’t stress! If your bestie moves to Mars you’ll still be able to have real time conversations.

If I could write about theories such as this each day, I’d really be living the dream. Theory that develops into usable science is very exciting stuff, but also very complex. I admire the level of genius required to understand all this, and want to share it. So, for all posts, and this one in particular, I welcome feedback. Help me get it right. Comments, questions, corrections- bring it on! It’s a collective effort to move forward.

- *Rules change: such as Einstein’s laws of relativity
- *Subatomic– smaller than an atom (simply put)
- *Action at a distance– In physics, action at a distance is the concept that an object can be moved, changed, or otherwise affected without being physically touched (as in mechanical contact) by another object.

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 19, 2017

Where the is proper time and is the beginning of the universe.

Estakhr’s decomposition is a mathematical technique to separate the average and fluctuating parts of Big Bang.

where the denotes the proper time average called steady component of big bang and is fluctuating part called Big Bang’s perturbations (Big Bang’s Turbulence).

Estakhr’s Proper-Time Averaged of Material-Geodesic Equations Using this mathematical technique, (applications: Big Bang Hydrodynamics, Supernova Hydrodynamics, etc…)

EAMG equations are proper time-averaged equations of relativistic motion for fluid flow and used to describe Relativistic Turbulent Flows (such as big bang eruption and/or supernova, etc …).

Estakhr’s Proper-Time Averaged of Material-Geodesic Equations is an umberella term equation for Relativistic Astrophysics, Relativistic Jets, Gamma-Ray Burst, Big Bang Hydrodynamics, Supernova Hydrodynamics, Galaxy Hydrodynamics, Black hole Jets…

Big Bang’s remnant is the fluid dynamical structure resulting from the Big Bang’s explosion and all galaxies in this unified structure are connected to form a continuum structure, So the mechanical behavior of Big Bang’s materials must be modeled as continuous mass rather than discrete galaxies. Continuum Astromechanics assumes that the substance of Big Bang’s materials completely fills the space it occupies.

Author: Mr. ESTAKHR, Ahmad reza

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 19, 2017

When the Moon enters a zodiac sign it adds instinctive reaction, unconscious predestination, sensiti

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 18, 2017

In this post I will introduce the basic concepts of quantum mechanics, which we will need later to show that the quantum systems don’t always work according to the classical logic. The amount of concepts introduced may be a bit overwhelming, so it’s in fact enough to concentrate on the significance of the uncertainty principle discussed at the end of the post.1

**Quantum states**

In quantum mechanics, a physical system (e.g. a particle) is represented by a state, which is usually denoted by or . The state contains all the physical information about the system; what this means is best understood by analogy. We can think of a state as being equivalent to specifying the location of a car for any given time; from that we can obtain all the other physical properties, like velocity, which we get by calculating the difference in location between two instants in time.

**Measurements and observables**

The only way we can get information about a state is to measure it, which should be a fairly uncontroversial statement. Mathematically this is captured by acting on the state we want to measure by an operator, which is perhaps less intuitive. Continuing with the analogy of measuring the velocity of a car, the “velocity operator” for our car would calculate the difference in position of the car in some small time interval and then divide that difference by the time interval, while the “position operator” would simply read off the location of the car. Hence, with each measurable property (called observables), like position, velocity, momentum2 etc. we associate an operator, which is denoted by a capital letter.

An important property of quantum mechanics is that a measurement alters the state. That is, if we start with a state , and first measure its position , we end up with the state . Suppose we now want to know the momentum of the state, measuring will give the momentum of rather than that of . This is very different from classical physics, where the order of measurements (ideally) doesn’t affect the measured values.

To make things even more complicated, the measurement is always of statistical nature. That is, doesn’t have a certain value which will be measured every time, instead, we can think that there is a whole range or a set of values associated with . The average of these values is called the expectation value of , it is the statistical average obtained by measuring many identical states and then averaging over the measured values.

**Uncertainty**

Because of the statistical nature of the measurements, there is a natural uncertainty associated with each observable, denoted by for an observable . The uncertainty tells us how the values of the observable are spread around the average; if is small, there is almost no variation in the value of $A$, and we are very likely to measure the average value of the observable; on the other hand, if is very large, the value of $A$ could be almost anything, which amounts to the system having no information about that observable, as we could equally guess the value instead of measuring it. It is important to note that the uncertainty arises from the fact that an observable has a range of possible values, and is thus an inherent property of the theory, and consequently an inherent property of nature, provided that quantum mechanics is an accurate description of reality3. The quantum mechanical uncertainty therefore has nothing to do with experimental uncertainty or precision of our measurement devices.

It is possible that the measurement of doesn’t affect the measurement of , in which case and are said to commute, and they behave more or less like in classical physics. However, if two observables do not commute, there will be an uncertainty relation between them limiting the precision with which the system can have the properties represented by these observables. It so happens that position and momentum do not commute, which gives rise to the most famous uncertainty relation4:

.

This is to be read: the uncertainty in position multiplied with the uncertainty in momentum is always larger than (or equal to) some constant; the actual value of the constant is more or less irrelevant, what is important that it is larger than zero. One way to understand what the uncertainty relation conveys is to consider the extreme cases; suppose the position of a particle is known with a great precision, this means becomes very small, but the product must be greater than a constant no matter what, the only way this can be true is the uncertainty of momentum becoming very large, that is, the system loses all information about its momentum. Similarly, if momentum is known with a very high precision, the system loses all information about the location of the particle. What this means realistically is that there will always be some uncertainty in both position and momentum, and if more information is obtained about one of them, some information must be lost about the other.5

As a conclusion, I recommend this highly entertaining yet informative animation illustrating what kind of weird consequences all of this has.

1Although I promised not to introduce all the technical details, I couldn’t resist adding the mathematical derivation of the uncertainty principle as a separate document for those interested, though it may require some mathematical background.

2momentum is defined as mass times velocity

3All the experiments to date agree with the quantum mechanical predictions, indicating that the theory captures at least some features of nature correctly.

4An elegant way to derive the uncertainty principle using Fourier transforms can be found here. For an elementary derivation see the extra document.

5This simple inequality has far reaching implication is physics, for further reading see e.g. http://galileo.phys.virginia.edu/classes/751.mf1i.fall02/UncertaintyPrinciple.htm.

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 18, 2017

Disclaimer: This post is based on stories and previous research carried by a group of people at the

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 17, 2017

When the Moon enters a zodiac sign it adds instinctive reaction, unconscious predestination, sensiti

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 17, 2017

I have been reading up on the trans-Planckian problem with the black hole evaporation process.

An observer far away from a black hole sees photons of normal infared or radio wave energies coming from a black hole (i.e. << 1eV). If one calculates the energies that these photons should have once they are in the vicinity of the black hole horizon, the energy is becomes high – higher than the Planck energy, exponentially so. Of course if we ride with the photon down to the horizon, the photon blue shifts like mad, going ‘trans-Planckian’ – i.e. having more energy than the Planck energy.

Looked at another way: if a photon starts out *at* the horizon, then we won’t ever see it as a distant observer. So it needs to start out just above the horizon where the distance from the horizon is given by the Heisenberg uncertainty principle, and propagate to us. The problem is that the energy of these evaporating photons must be enormous at this quantum distance from the horizon – not merely enormous, but exponentially enormous. A proper analysis actually starts the photon off in the formation of the black hole, but the physics is the same.

Adam Helfer puts it well in his paper. Great clear writing and thinking.

Helfer, A. D. (2000). Trans–Planckian modes, back–reaction, and the Hawking process. Retrieved from https://arxiv.org/pdf/gr-qc/0008016.pdf See also See Helfer, A. D. (2005). Quantum Character of Black Holes. Retrieved from https://arxiv.org/pdf/gr-qc/0503053.pdf

My take is simple. After reading Hefler’s paper plus others on the subject, I’m fairly convinced that black holes of astrophysical size (or even down to trillions of tons) do not evaporate.

Lets get things straight here: the math behind Hawking evaporation is good: Hawking’s math for black hole evaporation is not in question.

It should be emphasized that the problems uncovered here are entirely physical, not mathematical. While there are some technical mathematical concerns with details of Hawking’s computation, we do not anticipate any real difficulty in resolving these (cf. Fredenhagen and Haag 1990). The issues are whether the physical assumptions underlying the mathematics are correct, and whether the correct physical lessons are being drawn from the calculations.

Hawking’s prediction of black hole evaporation is one of the great predictions of late 20th century physics.

Whether black holes turn out to radiate or not, it would be hard to overstate the significance of these papers. Hawking had found one of those key physical systems which at once bring vexing foundational issues to a point, are accessible to analytic techniques, and suggest deep connections between disparate areas of physics. (Helfer, A. D. (2003). Do black holes radiate? Retrieved from https://arxiv.org/pdf/gr-qc/0304042.pdf)

So its an important concept. In fact it *so* important that much of not only black hole physics but quantum gravity and cosmology all use or even *depend* on black hole evaporation. Papers with titles like “Avoiding the Trans-Planckian Problem in Black Hole Physics” abound.

There are so many theories in physics today that rely on an unreasonable extrapolation of the efficacy of quantum mechanics at energies and scales that are not merely larger than experimental data, but exponentially larger than we have experimental evidence for. Its like that old joke about putting a dollar into a bank account and waiting a million years – even at a few per cent interest your money will be worth more than the planet. A straightforward look at history shows that currency and banks live for hundreds of years – not millions. The same thing happens in physics – you can’t connect two reasonable physical states through an unphysical one and expect it to work.

The trans-Planckian problem is replicated perfectly in inflationary big bang theory.

The trans-Planckian problem seems like a circle the wagons type of situation in physics. Black hole evaporation now has too many careers built on it to be easily torn down.

**Torn down:**

To emphasize the essential way these high–frequency modes enter, suppose we had initially imposed an ultraviolet cut–off Λ on the in–modes. Then we should have found no Hawking quanta at late times, for the out–modes’ maximum frequency would be ∼ v′(u)Λ, which goes to zero rapidly. (It is worth pointing out that this procedure is within what may be fairly described as text–book quantum field theory: start with a cut–off, do the calculation, and at the very end take the cut–off to infinity. That this results in no Hawking quanta emphasizes the delicacy of the issues. In this sense, the trans–Planckian problem may be thought of as a renormalization–ambiguity problem.)

Some may argue that other researchers have solved the trans-Planckian problem, but its just too simple a problem to get around.

One way around it – which I assume is what many researchers think – is that quantum mechanics is somehow different than every other physical theory ever found, in that it has no UV, IR, no limits at all. In my view that is extremely unlikely. Quantum mechanics has limits, like every other theory.

- Zero point: Perhaps there is a UV cut – ( Λ ) . The quantum vacuum cannot create particles of arbitrarily large energies.
- Instant collapse. While its an experimental fact that QM has non-local connections, the actual speed of these connections is only tested to a few times the speed of light.
- Quantum measurement – Schrödinger’s cat is as Schrödinger initially intended it to be seen – as an illustration of the absurdity of QM in macroscopic systems.

If there is a limit on quantum mechanics – that QM is like any other theory – a tool that works very well in some domain of physical problems, then many many pillars of theoretical physics will have to tumble, black hole evaporation being one of them.

By
**quantum-mechanics « WordPress.com Tag Feed**
on June 17, 2017

In my previous post, I presented a method of visualizing wavefunctions that are inherently complex-valued using a single plot that shows both the probability density and phase but frozen in time. Here, I complete this visualization by animating the plot.

The wavefunction shown above is that of a particle in a 1D box of length , which is in equal superposition of the ground and the first excited state , i.e. .

Two things to consider regarding this plotting method:

- The phase is plotted first using
`imshow`

. - The probability density is plotted next as a “white”
`fill_between`

between the probability density and the top of the plot. - When we animate the whole figure, we basically reiterate the two plotting steps above.

Animating `fill_between`

is tricky. Interestingly, the workaround is quite simple. Appending the pointer to the plot and animating it works like a charm.

Here’s the code:

import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as colors from numpy import pi as pi import matplotlib.animation as animation def psi(x,t): # define your wavefunction here w1 = 1 # eigenfrequency w2 = 2 # eigenfrequency psi = np.sin(1*pi*x)*np.exp(1j*w1*t) + np.sin(2*pi*x)*np.exp(1j*w2*t) # wavefunction return psi def plotComplexFunction1D(x,psi): psi = np.conj(psi*np.exp(1j*pi)) # rotate zero angle to x-axis psipsi = np.abs(psi)**2 # probability density y = np.linspace(psipsi.min(),psipsi.max(),100) # range of values for y h = np.angle(np.conj(psi)) # takes the argument of the complex number z = np.tile(h, (y.size, 1)) # creates 2D image with phase along x # create the background colormap for the phase xylims = [x.min(),x.max(),y.min(),y.max()] a=ax.get_ylim() imax=plt.imshow(z,cmap='hsv',extent=xylims,aspect='auto', animated=True) imax.set_clim(vmin=-pi, vmax=pi) # fill the region above the curve with white pfill = plt.fill_between(x, psipsi, y2=max(a), color='w', animated=True) # plots the probability densit return imax, pfill def animate(x,t): ims = [] for i in range(4*15): t += np.pi / 15. im, pfill = plotComplexFunction1D(x,psi(x,t)) ims.append([im, pfill]) ani = animation.ArtistAnimation(fig, ims, interval=50, blit=True, repeat_delay=0) return ani t = 0 x = np.linspace(0,1,100) fig, ax = plt.subplots() ax.set_ylim([0, 3.5]) plt.ylabel('$|\Psi(x)|^2$') plt.xlabel('x') ax.spines['top'].set_visible(False) ax.set_yticks([]) plt.xticks([0,0.5,1],[0,'L/2','L']) ani = animate(x,t) # save animation # Set up formatting for the movie files Writer = animation.writers['ffmpeg'] writer = Writer(fps=15, metadata=dict(artist='Me'), bitrate=1800) ani.save('im.mp4', writer=writer)

Note that this code saves the animation to an mp4 file. I converted the video to gif using ezgif.com.

Have fun!

[Featured image is an analog oscilloscope I used in one of my research visits to the US. This is one of the old instruments available in the lab. These oldies rock!]

You're missing out. Please sign in or create an account.

Are you sure you wish to clear this list?

You're at the last article.