Wednesday, March 30, 2022

Does Quantum Mechanics Really Need Complex Numbers? Yes!

We know that observable quantities - like a sunspot's magnetic field intensity -  are all, by necessity, real numbers—but the underlying wavefunctions and quantum states usually involve the unphysical number i,  or Ö -1.  Also, the presence of  i   in QM is not just ancillary or peripheral to the phenomenon, such as the intensity distribution associated with an ideal diffraction grating, e.g.

A exp(i q) =  [ 1 + e id   +  e i2d   +  e i3d  +.......     exp(i(N-1) d)

 It is rather central and intrinsic to the wave function  y (r,t)   peculiar to both the Schrodinger and Heisenberg formulations.  But one is led to ask: Are imaginary numbers a necessary feature of the theory, or are they just an artifact of its formulation, so that an all-real formulation could be found that works just as well?  This topic came up in a recent issue of Physics Today, in the article by Johanna L. Miller,  who writes:

"That’s a subtle question. One can always represent the space of complex numbers as a two-dimensional space of real numbers, with one dimension representing a complex number’s real part and the other the imaginary part."

See, for example, my previous post on the topic:


But as Miller notes, "quantum states themselves are represented mathematically as multidimensional spaces—and as it turns out, the combination of dimensions upon dimensions significantly complicates the mathematics of how quantum systems interact."

The fastest, most expeditious way to grasp this is to compute the probability density for the quantum wave function.  In general,  one is interested in where a single particle (say hydrogen electron) is located in a given volume so that we can write:

y (r,t) y *(r,t) dV

For the probability the particle lies somewhere in an element of volume dV.  More specifically and after applying the normalization condition, to locate the particle between a* and a:

aa’  =     ò aa   y dx  =   1

We note that for the electron in the 1s state we have:  P = ½y (1s) y (1s) *½

Yielding the graphic result:

This is the giveaway for all subatomic behavior showing that the particle - in this case electron - cannot be localized to a position, say like a planet in celestial mechanics.  We can only obtain a probability value for where it might be, not an exact, pinpointed location.  This informs us that the QM wave function or state function is not the same as say the wave function for electromagnetic (EM) waves. For example, in the latter case, radio astronomers can precisely locate the position of an object emanating EM radio waves by tracing back the source position from its radio flux e.g.

FLUX/  F v  =    ò I v   (q,  fcos  q dw

But no similar analogy applies for locating a particle using the wave function of QM.  In their new work, as  noted in the PT article,  Miguel Navascués of the Austrian Academy of Sciences in Vienna and colleagues refine the question: Is it possible to formulate a version of quantum theory that retains some of the key mathematical properties of standard quantum theory—in particular, that the composition of two systems is represented by their tensor product—but that uses only real numbers? They found that the answer is no.

Navascués and colleagues devised an experiment for which any such real-valued theory predicts different results than standard quantum theory. The experiment is only a little more involved than the one used to test Bell’s inequality, e.g.

The basic set up of the Navascués  et al experiment is shown in the diagram below:

 Adapted from M.-O. Renou et al., Nature 600, 625 (2021)

 Of two pairs of entangled particles, 'Bob' receives one of each, and the other two go to 'Alice' and 'Charlie'. Bob makes a joint measurement on his particles, and Alice and Charlie each choose from a few different measurements to make on theirs. As with Bell’s inequality, theories can be distinguished by the predictions they make about the correlations among the measurement outcomes.

Unlike with Bell’s inequality, however, calculating the expected correlations is extremely difficult. To find an upper bound for real-valued theories, Navascués and colleagues embarked on a computation so involved that they ran out of computer memory. They had to make do with a looser bound than they were hoping for. What they found was a computed value of  6Ö2  = 8.489  for standard quantum theory. However, the uppermost bound was 7.66, i.e. for a real-valued formulation.

There followed an experiment (by Jian -Wei Pan and colleagues at the University of Science and Technology of China) carried out using superconducting qubits, for which a value of 8.09 was observed.  This comfortably put the result of the experiment in the realm of complex quantum theory. There followed yet another experiment (using photons) by a Chinese group based at Southern University of Science and Technology at Shenzhen which also vindicated complex QM.

Basically, from last January, two groups carried out the experiment—and both found results in favor of standard complex-valued quantum theory.  But hold strain. According to the author of the PT piece (Johanna Miller) neither Chinese group "has closed the loopholes in their respective experiments."  That means the jury is still out on whether real or complex numbers afford the better description of the quantum world. Never fear, however, I am confident those loopholes will soon be closed and complex -valued numbers will prevail. Call it a gut feeling.   

Not yet mentioned, but pointed out by physicist David Bohm (Wholeness and the Implicate Order, pp. 237-38) , is the core role of complex numbers in the algebras that underpin quantum theory, i.e.

"It is significant that by mathematizing the general language in terms of an initially undefined and unspecified algebra, we arrive naturally at the sort of algebras used in current quantum theory for ‘particles with spin’, i.e. products of matrices and  quaternions. These algebras have in addition, however, a significance going beyond that of technical calculations carried out in the quantum theory. For example, the quaternions imply invariance under a group of transformations similar to rotations in three-dimensional space."

Related to this are the Pauli spin matrices, i.e.

Which occur in the Pauli equation  taking into account the interaction between the  of a particle  spin  and the external EM field.  This and the fact that the pure states of a quantum mechanical system are represented by unit vectors  in a complex separable Hilbert space, known as the state space, are convincing enough for me.  That is, that the edifice of quantum mechanics is fundamentally based on complex -imaginary numbers.

Future students of quantum mechanics, it seems, will have no choice but to grapple with the mathematics of imaginary numbers. (M.-O. Renou et al., Nature 600, 625, 2021.) Which is not a bad thing given they already appear in so much of physics, i.e. the portrayal of the complex amplitudes associated with an ideal diffraction grating.  Not to mention one particular form for unstable (electrostatic) plasma waves, e.g.

ikE = 4p e (ien o kE) [1/ m i    -   1/ m(w  - k vo )

Thus, the widespread use of complex numbers in physics, and their special meaning in QM prefigures their acceptance as the dominant formalism. Nonetheless the ongoing entanglement experiments -- apart from giving quantum physicists something to do - should point the way toward dealing with those onerous loopholes. (In whatever form they take)

See Also:


Wholeness and the Implicate Order

Tuesday, March 29, 2022

Telling It Like It Is: Negative Polling 'Muricans- on Ukraine & Inflation - Really Don't Deserve Biden


         "Uh, lemme see. Ukraine bad. Inflation bad.. Biden in office. It gotta be his fault!

"Why do voters seem determined to believe things that aren’t true? One can attribute some dissatisfaction to the relentless “sky is falling” media coverage. But let’s face it: Voters are grumpy, frustrated and tired after covid and annoyed about gas prices. They might know Biden spent months trying to pass his agenda but didn’t get what he wanted. And so confirmation bias is likely setting in for a lot of Americans, telling them everything must be bad... 

But if they don’t know jobs have been created, how can Democrats expect them to know that Republicans voted against covid funding, food assistance, and funding for states and cities to keep cops on the beat (all in the American Rescue Plan)? Or that most Republicans voted against infrastructure spending?" - Jennifer Rubin, Washington Post, 'What's A White House To Do About Clueless Voters?'

It isn't possible to say it any other way: Most of the poll respondents giving Biden low polling 'marks' - specifically in a just released NBC/WSJ poll (71% express "little confidence" and 55% "disapproval" of his handling of war in Ukraine) are miserable brats, FOX addicts and nincompoops.  For sure they don't deserve Joe Biden as president.  The results issued last night on NBC News infuriated us, but showed the deplorable level to which reason, sound mental judgment and yes- political intelligence - have evaporated.  As I predicted would happen (following the Afghan withdrawal) if too many continued to go to FOX News for answers.

What exactly is it these negative polling losers want from Biden, say that would change perceptions?  The answer is likely nothing would satisfy these imps, wallowing in their still pandemic-incited adversity and blaming Biden for it.  Take these Ukraine invasion polls, showing this 71 percent expressing little confidence. WHY?

What do these delirious twits want? What? The actions of this president are circumscribed.  You can't just dispatch troops,  MIG -29 fighter jets (from Poland) or an aircraft carrier laden with cruise missiles to the Black Sea.  Nor can you try to establish 'No fly' zones over Ukraine which would entail invading the same airspace,  close contact with Russian fighter jets, potential misfires ....and tactical nukes exchanged.  Followed by all -out nuclear war.  

Do these ignorant  cretins even know or recall that the Russians  reserve the right to employ tactical nuclear weapons if at anytime they feel overwhelmed by conventional armed forces?   

See, for example, the WSJ piece from yesterday: Putin’s Warnings Amplify Nuclear Fears  noting:

When Russia unveiled previously secret details of its nuclear- weapons doctrine for the first time in 2020, it confirmed something U.S. war planners had long suspected: Moscow would be willing to use atomic arms to keep from losing a conventional war.

Don't think Biden - U.S. is doing enough for Ukraine? Then read this from the WaPO;

Russia warns U.S. to stop arming Ukraine

Three weeks ago The Hill tried to shed more light on the disconnect of brain and poll response, pontificating:


  "Americans normally rally around the president when there is a foreign policy crisis, but a combination of Biden’s fumbling of the Afghanistan withdrawal and a complete inability to restrain Putin seems to have left the public with little confidence. Biden has been viewed as a weak leader — and weak relative to Trump — in polling that goes back to 2020. Putin’s dismissive attitude toward Biden hardly improved that perception. Any American admiration for strong leadership is accruing to Ukraine President Volodymyr Zelensky, not Biden."

 As for the claim of "Biden's fumbling of the Afghanistan withdrawal",  I already skewered that B.S. back in August, e.g.

  • Don't Blame Biden For Taliban Takeover In Afghanistan

    • As for claim of  "the total inability to restrain Putin" - what do these asswits expect Biden to do?  Smuggle a Navy SEAL team in to kidnap or kill him?  Dispatch a CIA K-group to poison his borscht with potassium cyanide? 

      And look, anyone who would weight or poll Trump  as "stronger" over Biden now doesn't even have the IQ of an ape.  In truth, if Trump had been at the helm we'd all have been blown up 3 times over in a nuclear holocaust. Biden has orchestrated a unified front of  27 NATO countries to punish Russia with severe economic sanctions. And these are causing a world of hurt, even inciting Putin's oligarchs to abandon him.  Biden has also delivered over $1 trillion worth of Stinger anti-aircraft missiles, Switch-blade drones and Javelin anti-tank weapons to the Ukrainians.  In addition to other weapons and munitions, they have used this arsenal to hold ground and even beat back Russian advances, i.e. in a suburb of Kyiv.  Indeed, the Ukrainians have the Russkies on the ropes in an asymmetric war, e.g. the WSJ piece yesterday, p. A13:

      Ukraine’s Asymmetric War

      Noting the advantages being gained, i.e. to mount attacks on Russian supply lines, disrupt planned air sorties, wreak general havoc. All accomplished with limited supplies and manpower, but with those resources applied much more tactically, skillfully.

      MSNBC's falling ratings in tandem with FOX's climb shows better than any other indicator how American brains have been gutted and left for Right wing fodder.  Mainly because these defunct brains aren't processing what's happening. Which is what is reflected in the polls that keep dinging Biden. As our Dutch friends Franz and Jane recently told us: "We thought Americans had more sense than to give such stupid poll responses!"  

      To which Janice replied: "Then you don't know these Americans who get most of their news off social media, FOX News and dumb friends."

      The lame responses to do with Biden's handling of the Ukraine war are matched only by the disdain for Biden on the economy, and especially inflation. This despite the fact - as I have noted - the inflation is directly related to the pandemic's impact on supply chains, followed by renewed demand for goods by too many.  But rather than appreciating Biden for putting more money into their hands - via the American Rescue Plan and other assistance-  they want to blame him for inflation!

      Such as one enclave of swing voters in Phoenix highlighted in an WSJ piece last Friday.  They, like the morons dinging him on Ukraine, really don't deserve him as president. I guess they'd rather have "macho" man and orange traitor Trump whom they actually believe would be better for the economy. (A slim 34% of Americans think Biden is doing a good job handling the economy) One wonders what they're drinking or smoking.

      One of the dolts in Phoenix when asked to expand on her negative polling actually emitted this brainless nonsense: "Well, it has to be on Biden! I don't recall anything like this in the last administration!"  

      Can we please help this forlorn woman's brain by amplifying some  neurons in her temporal lobes?  The Covid pandemic did not strike until the last year of Trump's term (2020).  Then, the assface made a mess of things by refusing to address supply problems even then (e.g. in terms of masks, respirators etc.) and let many other basic support systems falter.  The true fact?  (Associated press article in Denver Post Sunday p. 1A): 

      "Biden inherited from the Trump administration a budget deficit that was equal in size to 14.9 % of the entire U.S. economy.  Thanks to Biden's policy plans and programs - including the American Rescue Plan - the upcoming budget year will be BELOW 5% of the total U.S. economy -putting the country finally on a sustainable path."

        How many Americans - many of whom are now glued to FOX just for spurious infotainment- even know this?  I warrant not one in 50. How many know - or can process (from basic economics) - that these lower deficit totals will be easier to manage even if interest rates are high? 

      How did such lower deficit totals manifest?  Did FOX News tell them that they reflect the solid recovery in hiring that occurred - in large part - because of Biden's $1.9 trillion coronavirus relief package?  That the added jobs translated into additional tax revenue, even with higher inflation?   Thus, the government collected nearly $300 billion in higher revenues compared to 2020?  Did FOX tell them that?  Of course not!  All you got from FOX was "Biden is stoking inflation with reckless spending"- from the likes of Maria Bartiromo, e.g.

                                           "B-Biden Bad!  B-Biden Bad! Right, Tucker?"

                               "Right, Maria! Now repeat it again for our dumb viewers..."

      Do the obsessive FOX viewers even know that the print side of NewsCorp (The WSJ) also has echoed the positives?  I.e. in yesterday's piece   (p. A2, Economy Gets Tech-Spending Boost) by David Harrison who writes:

      American businesses are ramping up technology investment and other capital spending as they emerge from the pandemic. If sustained, that investment boom could boost productivity and living standards and counteract inflation pressure. Private nonresidential business investment grew 7.4% in 2021 from the previous year after adjusting for inflation, the fastest pace since 2012 and a strong bounceback from the 5.3% decline in 2020.

      In a way it's sad, it's pathetic, but also understandable. Too many Americans are at loose ends and feeling a total loss of control over their lives.  We get it.  Perhaps again,  the best theory is from author William Davies ( 'Nervous States: Democracy And The Decline Of Reason') who notes the peculiar effects of over -stimulation (say by doom watching or scrolling- especially on social media) resulting in terrible decisions owing to neurochemical misfires.  He specifically cites cases where the "desperation for control" leads to self-sabotage, and even deliberately seeking to sabotage one's own prosperity.  (This is even apart from forgetting the roiling upheaval that marked every hour of every day of Trump's reign.)

      This seems to be the case now with these negative polling (on Biden) Americans. Like deranged lemmings ready to hurtle over a cliff they are so beset by a feeling of impotence they'd ditch Biden (and the Dems) if they could and go back to the Reeps and Trump.  They actually desire a change, any change- no matter it leads them and the nation to utter desolation and destruction.  This is a deadly syndrome which I already wrote about as it pertains to what happened to the Germans of the Weimar Republic, e.g.'  

      We have to hope these peevish, unsettled, distracted Americans - this deranged and misled majority - snap out of their stupor before it's too late.  That is, before the midterms! As Eugene Robinson reminds us in his WaPo column  

      That’s no party. That’s the Republican Hot Mess.:  

      "Yes, this is an election year, and the Hot Mess (GOP)  could take control of one or even both houses of Congress. At a time of overlapping crises at home and abroad, that is a gamble the nation should not take — and an outcome Democrats and independents must do everything in their power to prevent."

      See Also:

      by Robert Becker | April 4, 2022 - 5:37am | permalink


      Here are four self-evident truths, notable because the party allegedly in power remains oblivious to them – indeed, to the less conscious engines of human behavior:

      1) Mandated choices, especially by media-plied (and lied to) voters, are driven more by emotions than reason, logic or facts (even to verify minimal job competence, let alone simple truths);

      2) Today’s slick 24/7 media profits by maximizing irrational, often negative responses, for the right – fear, outrage, and anxiety; Obama managed to induce positive feelings of hope and optimism;

      3) Electoral “campaigns” no longer have beginnings or ends, thus “elections” don’t legitimate winners, just provide rather old-fashioned hurdles for non-stop politicking to leap or knock over. When losers don’t concede, and certified results are defied, even slandered, the paramount distinction between order and anything goes disorder vanishes.

      4) Sustainable leadership means running campaigns that leverage unconscious or gut instincts (likability, TV appeal, drama and entertainment, passion for novelty (new horses) along with rejection of baggage-laden old-timers.

      Biden Democrats are in epic denial on these matters, refusing to shift political operations despite what barbaric Trump, Trumpism and FOX TV make uncomfortably clear: irrationality, grievance, and divisive cheap shots capture more coverage than reason, evidence, and reality. Can a party favoring reason out-slug a party aiming low and addicted to lying, law-breaking, slander, and misdirection? Can Dems not learn to appeal equally to reason and emotion?


      by Robert Becker | March 14, 2022 - 6:06am | permalink


      The puzzler I raise today: what does Biden’s curious 25% popularity falloff say about him, those polled, the presidency, and the world? Something lurched with surprising suddenness, but not the ever-predictable, right-leaning centrist: he governs as he campaigned, cautiously as the iconic, modest moderate. He remains loyal to getting things done (however compromised), talking up bipartisanship (a pipe dream), climate change as challenge (but not looming catastrophe, say, like Ukraine), even that negotiation, reality and reason still matter (increasingly in doubt).

      Disturbingly more than ever, politics comes down to performance and misdirection, even magic thinking, thanks to dirty money, incessant media propaganda, and entombed electorates


      by Michael T. Klare | April 5, 2022 - 5:22am | permalink

      Monday, March 28, 2022

      Most Chaotic Oscars Ever? Maybe - But Academy Blows It Again By Not Giving 'Best Picture' Award To 'DUNE'


                        Will Smith loses it, and whacks Chris Rock last night for a joke

      It was a freaking, jarring sight, but showed how unchecked emotions can  cloud judgment and get the better of brains.  In this case a brief 'GI Jane' riff by Chris Rock about Jada Pinkett Smith,  triggering the lizard brain of 'Best Actor' winner Will Smith.  Though he initially smiled at the joke he could see wife Jada was not smiling, so he launched onto the stage and slapped Rock - then unleashing an F-bomb:  

      "Keep your fucking mouth offa my wife!"   

      All at once the Academy Awards briefly came to a stunning halt last night as the earlier light -hearted mood at the Dolby Theater changed.  My psychology post doc niece, Shayl, has the most logical explanation for Smith's wild act: displaced rage.  He was actually enraged at himself for initially laughing at the joke - then realized wife Jada was not amused. Instantly, he flew into a rage - at himself- but displaced the target by swatting Chris Rock.  Sounds to me like a plausible hypothesis.

      Smith, in his own Oscar spiel in the next hour, showed clearly how the film ('King Richard') had gotten inside his head and emotions.  Smith cried throughout his speech, in which he apologized to the Academy of Motion Picture Arts and Sciences and his fellow nominees for the disruption,  but never apologized to Rock.  (For his part, Rock joked backstage after the ceremony: "I just got punched in the face by Muhammad Ali and didn’t get a scratch.”)

      As for Smith, after being handed his Oscar he then went on to babble:

      “I look like the crazy father, just like they said about Richard Williams,” 

      Smith said, possibly trying to lighten the mood of the still shocked audience. “But love will make you do crazy things.”  

      Actually, the lizard brain will make you do more crazy things.  Just ask all those tens of millions of Reepo Goobers who have sucked up the Big Lie bunkum, and the 58 percent of citizens who really believe Biden is doing a "terrible" job. (More on this in another post).

       The Academy took pains to point out that the moment was not planned, said a person close to the Oscars production who spoke on the condition of anonymity because they weren’t authorized to comment publicly. Smith, who played Richard Williams (the father of tennis prodigies Venus and Serena) in the biopic “King Richard,” appeared onstage about 40 minutes later to accept his prize for best actor.

      All week long a series of articles, mainly in the LA Times, had noted how ABC - which televises the awards -  had not been happy about the low ratings last year (only 10.4 m viewers) and wanted greater emphasis on more popular films.  This as opposed to the more obscure, 'indie' type niche films that virtually no one  - in the general public at least - sees, or is even aware of.   The Academy had the chance to set that aright last night but blew it, awarding the "Best Picture" Oscar to a film 'CODA' about deaf people, that virtually no one in our circle (and I am sure others) ever heard of.

      While a "heartwarming" film, as the LA Times described it, this movie did not merit the 'Best Picture'.  Anymore than 'Hurt Locker' merited the award over 'Avatar' some 12 years earlier, e.g.'

      For perspective, by the time the final award was announced, 'DUNE' had already grabbed six Oscars, including:  Sound, Cinematography, Visual Effects, Original Music Score, Film Editing and Production Design.  And I had already written a post last year how it had been the first film to actually entice us to go back to the movies- in an actual theater, e.g.  

      In addition, DUNE grossed the most ($400m) of any of the nominees, and ranked 11th overall in Box office pull from all the past year's films. In other words, it was clearly a film of quality that was also highly popular. It was the perfect candidate to set the Oscars back on the track to higher ratings, as opposed to a quirky indie tilt- even more pronounced this year because CODA was a streamed entity (from Apple) and not a major studio effort. 

       The Academy, in its rarefied, isolated perch may realize that it has blown it again and paved the way for even worse ratings next year.

      Though, true, the Will Smith running off the rails incident  this Oscars may well lure eyeballs of the morbidly curious next time around - making viewers wonder which star will pop off next!

      See Also:

      The slap heard around the world: Will Smith really did hit Chris Rock at the Oscars


      Yes, that was the most chaotic Oscars in history

      Sunday, March 27, 2022

      Spectacular Planetary Event Visible Early Monday Morning - Next One Will Be 22 Years From Now


      It isn't often that a planetary event occurs that won't happen again for decades- in this case until 2040.  But such will be the case early Monday morning - roughly 45 minutes before sunrise,  when Venus, Mars and Saturn appear very close together near the horizon. The top graphic shows the view from my planetarium program (Cybersky) registering at 5:30 a.m. local time. Venus is at the top, followed by Saturn then Mars - slightly off to one side - and the crescent Moon.  A more observer -oriented (horizon- based) perspective is shown below with the relative positions the same:

      Physically, of course, the 4 objects aren’t really close together at all.  It is merely how they appear in terms of the angular distances in the sky.  See e.g.

      Revisiting Simple Angular Measurements....

      Venus will be actually be some 69 million miles distant from earth while Mars will be 169 million miles away. Saturn will be 978 million miles away.

      But from the perspective of earth, their positions as they orbit around the Sun will make them appear so close together that they will be visible within the same binocular field.  For readers interested in seeing this sight all 3 objects ought to be easy to pick out.  Venus is always the brightest (which is why it's so often mistaken for a "UFO") while Saturn is between Venus and the Moon and slightly brighter than Mars. Mars is reddish in color, hence the nickname, "Red planet". 

       This alignment is well worth it to get up early and check out, as we plan to do, with our trusty 7 x 50 mm binoculars.  But you don't really need any optical instrument to see the splendid sight, just your two eyes. And if you miss it, it won't appear again until September 6, 2040.