The Astrology Podcast • Dec 23, 2022 Our annual year ahead astrology forecast for 2023, with astrologers Chris Brennan, Austin Coppock, Leisa Schaim, and Diana Rose Harper. At the beginning of the episode we give a big picture view of some of the major transits happening next year, such as Mars finishing its retrograde in Gemini, Saturn moving into Pisces, Pluto moving into Aquarius, a Venus retrograde in Leo, and eclipses moving from the Taurus-Scorpio axis to the Aries-Libra axis. Some of the themes we talked about were the emergence of AI (artificial intelligence) with Saturn finishing its transit through Aquarius and Pluto getting ready to start a 20 year transit through that sign, as well as the escape to the imaginal realm with Saturn entering Pisces and beginning a long sign-based conjunction with Neptune. In the second half of the show we go through a quarter by quarter and month by month breakdown of 2023, discussing in more detail some of the quicker astrological transits next year, such as the fact that the three main Mercury retrograde periods will all occur in earth signs. There are timestamps below for when we talk about different alignments and parts of the year.

New Thinking Allo • Dec 23, 2022 This video is a special release from the original Thinking Allowed series that ran on public television from 1986 until 2002. It was recorded in about 1989.  Conscious living and conscious dying require that we bring our pain into our hearts, rather than wall ourselves off from it. In this moving and personal program, The late Stephen Levine illustrates this point by referring to several cases of dying individuals with whom he has worked. He also discusses the use of imagery in healing, maintaining that each individual should choose imagery consistent with their own sensibility. Poet and meditation teacher, Stephen Levine was author of Healing into Life and Death, Who Dies?, Meetings on the Edge, A Gradual Awakening and Grist for the Mill (co-authored with Ram Dass). Now you can watch all of the programs from the original Thinking Allowed Video Collection, hosted by Jeffrey Mishlove. Subscribe to the new Streaming Channel (https://thinkingallowed.vhx.tv/) and watch more than 350 programs now, with more, previously unreleased titles added weekly. New!! Free month of the classic Thinking Allowed streaming channel for New Thinking Allowed subscribers only. Use code THINKFREELY.

What is a gas lighting narcissist?

Narcissistic gaslighting is a form of emotional abuse that involves intentionally manipulating or distorting the truth to instill self-doubt in someone. ^1,2,3. Gaslighting is a form of narcissistic abuse that involves tactics that cause a person to question their sanity and doubt their perception of reality.Mar 8, 2022

Narcissist Gaslighting: What It Is, Signs, & How Cope

Is it common for narcissists to gaslight?

You might be a victim of narcissist gaslighting. This is a type of manipulation that is often used by people with Narcissistic Personality Disorder (NPD). It can make you feel like you’re going crazy and leave you feeling isolated and alone.Jul 26, 2022

Narcissist Gaslighting: What It Is, How To Recognize It & What …

(Inspired by Steve Hines)

God: An Anatomy

by Francesca Stavrakopoulou

An astonishing and revelatory history that re-presents God as he was originally envisioned by ancient worshippers–with a distinctly male body, and with superhuman powers, earthly passions, and a penchant for the fantastic and monstrous.

[A] rollicking journey through every aspect of Yahweh’s body, from top to bottom (yes, that too) and from inside out … Ms. Stavrakopoulou has almost too much fun.”–The Economist

The scholarship of theology and religion teaches us that the God of the Bible was without a body, only revealing himself in the Old Testament in words mysteriously uttered through his prophets, and in the New Testament in the body of Christ. The portrayal of God as corporeal and masculine is seen as merely metaphorical, figurative, or poetic. But, in this revelatory study, Francesca Stavrakopoulou presents a vividly corporeal image of God: a human-shaped deity who walks and talks and weeps and laughs, who eats, sleeps, feels, and breathes, and who is undeniably male.

Here is a portrait–arrived at through the author’s close examination of and research into the Bible–of a god in ancient myths and rituals who was a product of a particular society, at a particular time, made in the image of the people who lived then, shaped by their own circumstances and experience of the world. From head to toe–and every part of the body in between–this is a god of stunning surprise and complexity, one we have never encountered before. 

(Goodreads.com)

Genius Turner

Nov 12, 2022 (medium.com)

“These conflicts [between religion and science] have all sprung from fatal errors” — Einstein

I. Walk in the Footsteps of Genius

A year or so ago, New York City endured a brutal snowstorm. Unfortunately for me, I had to jog that Sunday night.

In case you’re wondering why I “had” to jog, ahem, just know I take Aristotle’s insight to heart: “We are what we repeatedly do. Excellence, then, is not an act — but a habit.”

(*Note: Aristotle’s maxim forms the core of Covey’s classic The 7 Habits of Highly Effective People.)

For the above reason, scrawled across the front of my favorite workout T-shirt reads the message:

Winning is a habit. Unfortunately, so is losing.

In short, armed with “success is the only option” as a mindset, my mind was set on jogging three miles, the blizzard notwithstanding.

About 15–20 minutes into the jog, I knew my character was on the verge of being tested.

“Success is the only option,” I mumbled to myself. But unfortunately, slogging thru the snow left me feeling like B-Rabbit in Eminem’s song — “His palms are sweaty, knees weak, arms are heavy.”

Like an exhausted boxer in the final round, the jabs of wind and flurries of snow battered my face. Blurred my vision. I could see my foot but couldn’t see beyond a foot.

In short, upon making my return slog back home, I simply let reason be my guide:

Step after step, I put my feet in the footprints left for me in the snow.

Sure, those footprints were my own, yet so far as it concerned the present moment — the trail belonged to the past.

The more I followed the path, which had been carved out for me, the more I came to appreciate why Socrates advised this:

“Use your time in improving yourself by other men’s writings, so that you shall gain easily what others have labored hard for.”

At once it dawned on me I’d uncovered a beautiful metaphor hidden in a snowstorm!

“No wonder I love reading Einstein so much,” I mumbled to myself. After all, common sense, which takes us further than any other trait, suggests reading arguably the smartest person in history is a good idea.

In short, just as when lost in a blizzard I wisely follow in the footprints left for me, when lost in ideas — I wisely follow in the footsteps of genius personified — Albert Einstein.

II. How Einstein Paved the Way for my ‘Religious-Science’

One morning while at his Berlin home, Einstein received an urgent telegram. It was from Rabbi Herbert S. Goldstein.

“Do you believe in God?” Rabbi Goldstein wrote. Apparently he expressed concern that Einstein — history’s most famous scientist — had been somewhat undermining religion.

Ahem, though Rabbi Goldstein expected an answer long and sour, Einstein kept it short and sweet:

“I believe in Spinoza’s God . . .” Einstein wired back.

For those initiated into the mysteries, “Spinoza’s God” is merely a code-word. For what? For mathematical theology. You see, such views derive from the ancient Greeks. Pythagoras and Plato in particular.

And my, oh, my did Albert love those philosophers of ancient Greeks! Heck, he read them every night before bed after all.

It’s not by accident the first philosopher was also the first mathematician (Pythagoras). Perhaps Lord Kelvin best summed up Einstein’s insight when he called “mathematics the only true metaphysics.”

(*Note: quick rule of thumb — anytime you see the word “logical,” you’re also seeing the word mathematical.)

From archeological to zoological, each instance of logic is inherently mathematics. This explains why today — logic is treated as a subfield of mathematics/philosophy.

The above insight reveals the core of Einstein’s grand insight: if science deals with the cosmological and religion the theological, well, could it be:

“Conflicts between science and religion have all sprung from fatal errors[?]” — Einstein

Bingo!

In Einstein’s eyes, without religious legs — science forever remains Stephen Hawking. As for religion, without scientific eyes — religion forever remains Ray Charles…

III. The Socratic Method → the Scientific Method

“The beginning of wisdom is a definition of words”

— Socrates

Armed with the Socratic method, Einstein revealed the true nature of the scientific method.

“Logic will get you from A to B,” he noted, “[but] imagination will take you everywhere.” What Einstein figured out about his beloved was this: science never extends beyond accounting for how related facts condition each other.

Notice what’s being suggested here…

…Those quantum leaps of imagination, which propelled Einstein to almost superhuman levels, he attributed to a mysterious “cosmic religious feeling.”

Because the scientific method is inherently logic, G.K. Chesterton famously pointed out why “you can only find truth with logic if you have already found truth without it.”

When viewed in a true light, science can be likened to a GPS device: though the system can navigate its user to a given destination, it can’t input itself with a destination.

Bingo!

Einstein rebuked his own profession, going so far as to confess “it is equally clear that knowledge of what is does not open the door directly to what should be.”

Science, then, when left to its own devices proves “lame” indeed.

In Einstein’s view, religion/spirituality alone can tell science where to go, not how to get there per se. And vice versa. Notice how the “Master of Those Who Really Know” draws a sharp line in the epistemological division of labor.

In short, Einstein’s following classic passage sheds light on one of history’s greatest insights:

Mere thinking cannot give us a sense of the ultimate and fundamental ends. To make clear these fundamental ends and valuations, and to set them fast in the emotional life of the individual, seems to me precisely the most important function which religion has to perform in the social life of man.

IV. The Allegory of the Siamese Twins

“You don’t see something until you have the right metaphor to let you perceive it”

— James Gleick

Of each person’s 60,000 daily thoughts, researchers estimate roughly 80 percent occur in pictures.

“See what I mean?” goes the saying.

Excellent!

For this reason, Aristotle concluded mastery of metaphors is a sure sign of genius. After all, a metaphor reaches for the heavens . . . strips a metaphysical idea of its “meta” . . . and then brings it back down to the physical.

In short, let’s try a hand at playing the part of Prometheus. Of course, we’re venturing not to defy the gods by stealing their fire, but instead — we long for a firey metaphysical truth. And then once snatched from the heavens, let’s then bring it back down to Earth…

…Abracadabra!

Once upon a time there lived Siamese twins conjoined at the heart.

Due to the condition, Dr. Necessity split them apart! So each brother had to go thru life with only half a heart.

The surgery left one twin with the Herculean half of the heart; the other inherited the half with exceptional vision. Each asset, however, came with a liability.

Attached to the gift of vision was paralysis. Stamped on the gift of strength was blindness.

The brothers hated each other due to this unfair trade-off.

Everyone around town knew them by their nicknames “Rel” and “Sci.”

Both had reputations that stretched far and wide:

Rel’s fame grew due to having the greatest vision and Sci’s popularity soared due to having the greatest strength.

And so, quite naturally — each brother strove to compensate for his birth defect. How? By maximizing the natural advantage.

Sci adopted a “scientific method” to bodybuilding. “What better way to elevate myself above my paralyzed twin,” he reasoned, “than to become the most powerful body [of knowledge] the world has ever known?”

Rel, on the other hand, religiously sharpened his vision to a god-like point. “What better way to elevate myself over my blind brother,” he envisioned, “than to become the greatest visionary the world has ever known?”

Clearly, such a split by the twin brothers — who were first split at birth — only served to heighten the animosity.

One morning a fire alarm woke up the twins.

Sci caught whiff of the smoke…

Rel caught glimpse of the fire…

Unfortunately by the time each recognized the smoke and fire, the entire home had been filled with flames.

As fate would have it, though, the only place without fire was the room shared by the twins since birth. But clearly this posed a major problem.

Unlike prior cases in which each twin’s strength compensated for his weakness, not this time around.

Sure, the visionary Rel could clearly see the approaching fire — and thereby gauge its distance. Ahh, but unfortunately Rel’s wheelchair had been burnt to ashes. Rel was stuck!

As for Sci, though he was more than capable of escaping by foot, his blindness meant he could no more see the exit than could Rel run to it.

This left the twins with only one possible solution.

Fortunately the invisible hand of necessity nudged Sci to sprint in the direction of his brother’s cry for help.

Upon arrival, Sci lifted Rel onto his massive shoulders. Aww, finally Rel could fulfill his dream of imitating Newton by sitting on a giant’s shoulders.

“Run here, brother!” Rel cried out. “Turn there, dear brother!”

With Rel in the driver’s seat and Sci serving as the vehicle, together they climbed out of the window.

Lo and behold:

The answer to the riddle lay hidden in a partnership.

As the smoke cleared, Rel and Sci finally embraced.

Both cried tears of joy.

“I guess, one hand ‘watches’ the other,” Rel joked.

Sci smiled. “And one hand ‘lifts’ the other.”

With the heart separated at birth restored to its original oneness, Rel’s vision combined with Sci’s strength amounted to a match made in Heaven. And on Earth too.

The twins lived happily ever after…

Here lies the Allegory of the Siamese Twins!

The End.

V. The Takeaway

According to legend, Jesus of Nazareth is said to have been a Pisces…

Perhaps this explains why a fish symbolizes Christianity, why Jesus fed the masses with “two fish” and why his disciples were called “fishers of men.”

Armed with the above insight, perhaps Einstein (born on Pi Day) and Genius Turner (born on Leap Day) have far more in common than merely being born under the sign affectionately known as the “genius/weirdo.”

Perhaps…

As part of the initiation into the mysteries, the wise men of old used to teach the true geniuses of the world carry on silent conversations between the ears and pages alike.

Logan Smith went so far as to say what he prizes most “in a good author is not what he says but what he whispers.” Hence it’s long been said two people can’t possibly read the same book.

As Emerson once put it:

We are always reasoning from the seen to the unseen. Hence the perfect intelligence that exists between wise men of remote ages. A man cannot bury his meanings so deep in his book but time and like-minded men will find them.

Plato had a secret doctrine, had he? What secret can he conceal from the eyes of Bacon? of Montaigne? of Kant? Therefore Aristotle said of his works, “They are published and not published.”

In short, Einstein had a secret doctrine, had he?

What secret can one fish conceal from the eyes of another?

On many a night, I’ve wondered how Einstein — a century ago — foresaw the coming of Religious-Science.

And sure enough from the grave, dear Einstein whispered in my third ear: “Religious geniuses of all ages have been distinguished by this kind of religious feeling.”

Perhaps the key to unlocking this cosmic religious feeling, to which Einstein alluded, calls for mastering the following technique:

individuals intrinsically inclined to instinctively inspect inwardly inborn, invisible instruction indispensable to innately inspire indescribable insights informally indicative of ingeniously intellectual interpretations of information!

Armed with the above superpower of genius, Einstein made the following prediction: “Science not only purifies the religious impulse of the dross of its anthropomorphism, but also [will] contribute to a religious spiritualization of our understanding.”

Initially a lowly patent clerk, Einstein dared to be great. He contested the immortal Sir Isaac Newton. Scathing criticism ensued.

Of course, Einstein countered by arguing how could critics “punish me for my contempt for authority [when] fate made me an authority myself”?

And it is in such a spirit of truth that I, the lowly student, dare contest the master. After all, millions daily quote Einstein’s famed maxim that “science without religion is lame; religion without science is blind.”

Ahem, perhaps Einstein had it backwards…

…It’s religion who, without scientific legs, is Stephen Hawking. And science — without religious vision — is Ray Charles. The cosmic religious feeling can best foresee the goal of life, but science alone has the power to realize it.

Bingo!

Genius Turner’s painted word-portrait The Heaven on Earth Code merely reflects my humble attempt to finish what “the Master of Those Who Know” started.

Today’s genius is tomorrow’s common sense. Perhaps future generations will look back at today’s folly — regarding our attempts to split these Siamese twins — as do we now frown upon yesterday’s attempt to place Earth at the center of our solar system.

(*Wink, wink to the fellow Pisces, Copernicus.)

Future generations will embrace a scientific religion or Religious-Science.

In short, “The Master of Those Who Really Know” put it best:

“The religion of the future will be a cosmic religion. It should transcend a personal God and avoid dogmas and theology. Covering both the natural and the spiritual, it should be based on a religious sense arising from the experience of all things, natural and spiritual, as a meaningful unity”

— Albert Einstein

Translation is a 5-step process of “straight thinking in the abstract.” The first step is an ontological statement of being beginning with the syllogism: “Truth is that which is so. That which is not truth is not so. Therefore Truth is all there is.” The second step is the sense testimony (what the senses tell us about anything). The third step is the argument between the absolute abstract nature of truth from the first step and the relative specific truth of experience from the second step. The fourth step is filtering out the conclusions you have arrived at in the third step. The fifth step is your overall conclusion.

The Ukraine Emergency Translation Group meets every Friday at 11 a.m. Pacific time via Zoom. We call it the Ukraine Emergency Translation Group but we welcome Translations about anything. Here are sense testimonies (2nd steps) we translated and their corresponding conclusions: (5th steps) this week.

2) Illness can control person’s life. 
5) All there is is Truth. 

2) Sometimes those who care for others, whether parents or physicians, care more about authority over others than care for others.
5) Truth’s love for Itself oozes out from every pore of Its existence.

All Translators are welcome to join us on Fridays at 11 a.m. Pacific time. The link is: https://us06web.zoom.us/j/83608167293?pwd=cFRsckVibXMwTGJ0KzhaV0R2cWJtdz09

For information about Translation or other Prosperos classes go to: https://www.theprosperos.org/teaching

Some comments from group members about this group:

“I like the group interaction and different perspectives. Also, at least for me, it gives me a sense of accountability and keeps the practice fresh in my mind. ” –Sarah Flynn

“This group has freed me up to have more fun with my Translations.”
–Mike Zonta

Winter Solstice Peace Gathering daily thru December 25 at 1:30 PM Pacific time 

Link: https://empathymatters.org/now/events-list/

(Courtesy of Larry Lawhorn)

The Hierophant

The Hierophant (or Pope, High Priest) is numbered five and is concerned with matters of faith, religion, belief and morality. This is the wise teacher, full of esoteric and occult knowledge. He can help us to understand the mysteries around and within us.

The Hierophant is a holy man, but is in essence both male and female. He has a healthy connection with life and living – someone who has experienced life in full and now has the experience and wisdom needed in order to teach others.

He is usually seen holding his index and middle finger extended, as though pointing at something. This symbolism is important, because the human Will is considered to be directed by these two fingers. The Hierophant is an archetype which represents the culmination of human development.

His abilities reside like seeds within every one of us. We all have the ability to travel where he has already explored. He holds the keys to transformation.

(via angelaths.com and Alan Blackman)

Capricorn New Moon

The Capricorn New Moon tunes us into the most practical and authoritative sides of ourselves and helps us tackle projects that need a cool head and strategic action. We may be up against certain time limits or dealing with people and situations that need “reining in.” This is somewhat underlined by the New Moon’s wide, degree-based square to Neptune in Pisces, where a matter may feel all at sea without a strong vision steering us forward.

This New Moon makes a much tighter square aspect to Jupiter in Aries, emphasizing the tension between cardinal signs. Here we have a combination of the long term vision and the short-term goal. The Saturn-ruled goat is typically painstaking and known for its stamina and longevity. The Mars-ruled ram is usually impatient and heads forward with less care and preparation — not unlike the Knight of Wands in the tarot. Results are achieved, either through following rules or via a more immediate, reckless approach. Whilst both may have their virtues, impacts could differ. And, of course, how that affects us depends on whose viewpoint from which we see the situation.

Anyone with a strong need to carefully tiptoe forward is likely to feel uneasy from the impatient, bucking qualities of the Aries ram approach! On the contrary, for one who puts results first, and tidiness and conventions second, the Capricorn goat’s insistence on following set procedures could prove frustrating. Yet, with a square, we nearly always need to be prepared to give and take to avoid negative results. Some tolerance is needed to navigate the course ahead.

The Moon is disposited by Saturn, which is often famous for managing a more Spartan regime for a time. Particularly, as Saturn is in Aquarius, the pressure to do right by others and navigate a path of rules or procedures seems strong. Saturn, still in a separating square to Uranus, once again emphasizes the idea of something a little out of the blue. Yet, even if we couldn’t have anticipated every event coming our way and find ourselves in a temporary phase of difficulty or discomfort, we could, perhaps, console ourselves with the universal knowledge that “this too shall pass.”

Saturn and Uranus are also, respectively, semi-sextile and trine Venus and Mercury in Capricorn, suggesting that our careful steps forward — effectively remove our cap to those people or situations that demand respect and adherence to protocols — will, in one way or another, stand important relationships and crucial conditions in good stead. We may also experience enhanced communication at this time, if even briefly. The best advice sometimes arrives in a few useful lines or phrases — and occasionally, just simply “yes” or “no”!

This article is from the Mountain Astrologer by Diana McMahon Collis

SCIENCE

DEC 18, 2022 8:00 AM (Wired.com)

The past and future are tightly linked in conventional quantum mechanics. A tweak could let quantum possibilities increase as space expands.

The expansion of space spells trouble for quantum mechanics, by presenting particles with a growing smorgasbord of options for where to be.VIDEO: DVDP/QUANTA MAGAZINE

A JARRING DIVIDE cleaves modern physics. On one side lies quantum theory, which portrays subatomic particles as probabilistic waves. On the other lies general relativity, Einstein’s theory that space and time can bend, causing gravity. For 90 years, physicists have sought a reconciliation, a more fundamental description of reality that encompasses both quantum mechanics and gravity. But the quest has run up against thorny paradoxes.

Hints are mounting that at least part of the problem lies with a principle at the center of quantum mechanics, an assumption about how the world works that seems so obvious it’s barely worth stating, much less questioning.

Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research develop­ments and trends in mathe­matics and the physical and life sciences.

Unitarity, as the principle is called, says that something always happens. When particles interact, the probability of all possible outcomes must sum to 100 percent. Unitarity severely limits how atoms and subatomic particles might evolve from moment to moment. It also ensures that change is a two-way street: Any imaginable event at the quantum scale can be undone, at least on paper. These requirements have long guided physicists as they derive valid quantum formulas. “It’s a very restrictive condition, even though it might seem a little bit trivial at first glance,” said Yonatan Kahn, an assistant professor at the University of Illinois.

But what once seemed an essential scaffold may have become a stifling straitjacket preventing physicists from reconciling quantum mechanics and gravity. “Unitarity in quantum gravity is a very open question,” said Bianca Dittrich, a theorist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada.

The main problem is that the universe is expanding. This expansion is well described by general relativity. But it means that the future of the cosmos looks totally different from its past, while unitarity demands a tidy symmetry between past and future on the quantum level. “There is a tension there, and it’s something quite puzzling if you think about it,” said Steve Giddings, a quantum gravity theorist at the University of California, Santa Barbara.

Concern over this conflict has been in the air for years. But recently, two quantum gravity theorists may have found a way to loosen unitarity’s buckles to better fit our growing cosmos. Andrew Strominger and Jordan Cotler of Harvard University argue that a more relaxed principle called isometry can accommodate an expanding universe while still satisfying the stringent requirements that first made unitary a guiding light.

“You don’t need unitarity,” said Strominger. “Unitarity is too strong of a condition.”

While many physicists are receptive to the isometry proposal—some have even come to similar conclusions independently—opinions vary as to whether the update is too radical or not radical enough.

A Fixed Sum

In everyday life, events can’t help but play out in a unitary way. A coin toss, for instance, has a 100 percent chance of coming up heads or tails.

But a century ago, the pioneers of quantum mechanics made a surprising discovery—one that elevated unitarity from common sense to a hallowed principle. The surprise was that, mathematically, the quantum world operates not by probabilities but by more complicated numbers known as amplitudes. An amplitude is essentially the degree to which a particle is in a certain state; it can be a positive, negative or imaginary number. To calculate the probability of actually observing a particle in a certain state, physicists square the amplitude (or, if the amplitude is an imaginary number, they square its absolute value), which gets rid of the imaginary and negative bits and produces a positive probability. Unitarity says the sum of these probabilities (really, the squares of all the amplitudes) must equal 1.

It’s this twist—the squaring of hidden amplitudes to calculate the outcomes we actually see—that gives unitarity teeth. As a particle’s state changes (as it flies through a magnetic field, say, or collides with another particle), its amplitudes change too. In working out how a particle is allowed to evolve or interact, physicists use the fact that amplitudes never change in a way that disrupts the fixed sum of their squares. In the 1920s, for instance, this unitarity requirement guided the British physicist Paul Dirac to discover an equation that implied the existence of antimatter. “I was not interested in considering any theory which would not fit in with my darling,” Dirac wrote, referring to unitarity.

Physicists keep probabilities and amplitudes in line by tracking how the quantum state of a particle moves around in Hilbert space—an abstract space representing all possible states available to the particle. The particle’s amplitudes correspond to its coordinates in Hilbert space, and physicists capture changes to the particle with mathematical objects called matrices, which transform its coordinates. Unitarity dictates that a physically allowed change must correspond to a special “unitary” matrix that rotates the particle’s state in Hilbert space without changing that the sum of the squares of its coordinates equals 1.

It’s a mathematical fact with philosophical consequences: If you know the specific unitary matrix corresponding to some change over time, any quantum state can be swiveled into the future or unswiveled into the past. It will always land on another viable state in the Hilbert space, which never grows or shrinks. “The past completely determines the future, and the future completely determines the past,” said Cotler. “It’s related to the statement that information is neither created nor destroyed.”

And yet, this bedrock assumption seems to conflict with the universe that surrounds us.

A Cosmic Clash

Galaxies are flying ever farther apart. While our expanding universe is a perfectly valid solution to the equations of general relativity, physicists have increasingly realized that its growth spells trouble for quantum mechanics, by presenting particles with an expanding smorgasbord of options for where to be and how to behave. As space grows, how can the Hilbert space of possibilities not grow with it? “It’s definitely true that there are more degrees of freedom in the universe now than in the early universe,” said Nima Arkani-Hamed, a theoretical physicist at the Institute for Advanced Study in Princeton, New Jersey.

“I’ve felt for many years [that] it was the elephant in the room,” said Strominger.

Giddings sharpens the issue with a paradoxical thought experiment set in a universe that’s both unitary and expanding. Imagine taking the current state of the universe, said Giddings, and adding “one innocuous photon”—perhaps lodged in newly created space halfway between here and the Andromeda galaxy. Unitarity insists that we must be able to calculate what this universe looked like in the past, unswiveling its quantum state as much as we wish.

But rewinding the state of the universe plus an extra photon creates a glitch. Going into the past, the universe gets smaller, and the wavelength of photons will shrink too. In our real universe, this isn’t a problem: A photon shrinks only until the moment of its creation through some subatomic process; the reversal of that process will make it disappear. But the extra photon wasn’t created by that special process, so instead of disappearing when you turn back time, its wavelength will eventually get impossibly small, concentrating its energy so greatly that the photon collapses into a black hole. This creates a paradox, absurdly implying that—in this fictional, expanding universe—microscopic black holes convert into photons. The thought experiment suggests that a naïve mashup of unitarity and cosmic expansion doesn’t work.

Dittrich thinks unitarity smells fishy on more general grounds. Quantum mechanics treats time as absolute, but general relativity messes with the ticking of clocks, complicating the notion of change from one moment to the next. “I personally never relied so much on unitarity,” she said.

The question is: What sort of alternative framework could accommodate both cosmic expansion and the rigid mathematics of quantum theory?

Unitarity 2.0

Last year, Strominger struck up a collaboration with Cotler, who splits his time between quantum gravity research and quantum information theory—the study of information stored in quantum states. The duo realized that there is a well-studied scheme in quantum information theory that resembles the expanding universe: quantum error correction, a scheme where a small message made from quantum states is redundantly encoded inside a bigger system. Perhaps, they thought, the contents of the young universe are similarly stitched into the modern cosmos’s swollen form.

“In hindsight, the obvious answer is this is exactly what people doing quantum encoding have been doing,” Strominger said.

In a paper earlier this year, the two homed in on a class of transformations that quantum error-correcting codes belong to, known as isometries. An isometric change resembles a unitary one with added flexibility.

Think of an electron that can occupy two possible locations. Its Hilbert space consists of all possible combinations of amplitudes in the two locations. These possibilities can be imagined as the points on a circle—every point has some value in both the horizontal and vertical directions. Unitary changes rotate states around the circle but do not expand or shrink the set of possibilities.

To visualize an isometric change, though, let the universe of this electron swell just enough to allow a third position. The electron’s Hilbert space grows, but in a special way: It gains another dimension. The circle becomes a sphere, on which the particle’s quantum state can swivel around to accommodate mixtures of all three locations. The distance between any two states on the circle holds steady under the change—another requirement of unitarity. In short, the options increase, but without unphysical consequences.

“Working with isometries is sort of a generalization” of unitarity, said Giddings. “It keeps some of the essence.”

Our universe would have a Hilbert space with a huge number of dimensions that proliferate continuously as real space expands. As a simpler proof of concept, Strominger and Cotler studied the expansion of a toy universe consisting of a line ending in a receding mirror. They calculated the probability that the universe would grow from one length to another.

For such calculations, quantum practitioners often use the Schrödinger equation, which predicts how a quantum system evolves in time. But changes dictated by the Schrödinger equation are perfectly reversible; its “literal purpose in life is to enforce unitarity,” Arkani-Hamed said. So instead, Strominger and Cotler used an alternative version of quantum mechanics dreamed up by Richard Feynman, called the path integral. This method, which involves tallying up all the paths a quantum system can take from some starting point to an endpoint, has no trouble accommodating the creation of new states (which appear as branching paths leading to multiple endpoints). In the end, Strominger and Cotler’s path integral spit out a matrix encapsulating the growth of the toy cosmos, and it was indeed an isometric matrix rather than a unitary one.

“If you want to describe an expanding universe, the Schrödinger equation as it stands just won’t work,” Cotler said. “But in the Feynman formulation, it keeps on working on its own volition.” Cotler concludes that this alternative way of doing quantum mechanics based on isometry “will be more useful to us in understanding an expanding universe.”

A Mirage of Possibilities

Relaxing unitarity could resolve the glitches in the thought experiment that has troubled Giddings and others. It would do so through a conceptual change to how we think about the relationship between the past and the future, and which states of the universe are really possible.

To see why isometry solves the problem, Cotler describes a toy universe, one born in one of two possible initial states, 0 or 1 (a two-dimensional Hilbert space). He makes up an isometric rule to govern this universe’s expansion: At every successive moment, each 0 becomes 01, and each 1 becomes 10. If the universe starts at 0, its first three moments will see it grow as follows: 0 → 01 → 0110 → 01101001 (an 8D Hilbert space). If it starts at 1, it will become 10010110. The string captures everything about this universe—all its particles’ positions, for instance. A considerably longer string made from superpositions of 0s and 1s presumably describes the real universe.

At any given time, the toy universe has two possible states: one arising from 0 and another arising from 1. The initial one-digit configuration has been “encoded” in a larger, eight-digit state. That evolution resembles a unitary one, in that there are two possibilities at the beginning and two at the end. But the isometric evolution provides a more capable framework for describing the expanding universe. Crucially, it does so without creating the freedom to add, say, an extra photon between here and Andromeda, which would spell trouble when you turn back the clock. Imagine, for instance, that the universe is in the 01101001 state. Flip the first 0 to a 1—representing a minor, local tweak, such as the extra photon—and you’ll get a state that looks fine on paper (11101001), with a seemingly valid set of coordinates in the larger Hilbert space. But knowing the specific isometric rule, you can see that such a state has no parent state. This imaginary universe could never have arisen.

“There are some configurations of the future that don’t correspond to anything in the past,” Cotler said. “There’s nothing in the past that would evolve into them.”

Giddings has proposed a similar principle for ruling out paradoxical states he encountered while studying black holes last year. He calls it “history matters,” and it holds that a given state of the universe is only physically possible if it can evolve backward without generating contradictions. “This has been kind of a lingering puzzle,” he said. Strominger and Cotler “are taking that puzzle and using it to try to motivate possibly a new way of thinking about things.”

Giddings thinks the approach deserves further development. So does Dittrich, who came to similar realizations about isometry a decade ago while attempting to formulate a toy quantum theory of space-time with her collaborator Philipp Höhn. One hope is that such work could eventually lead to the specific isometric rule that might govern our universe—a rather more complicated prescription than “0 goes to 01.” A true cosmological isometry, Cotler speculates, could be verified by calculating which specific patterns in the distribution of the matter in the sky are possible and which aren’t, and then testing those predictions against observational data. “If you look closer at it, you’ll find this but not this,” he said. “That could be really useful.”

To Isometry and Beyond

While such experimental evidence could accrue in the future, in the near term, evidence for isometry is more likely to come from theoretical studies and thought experiments showing that it helps combine the malleability of space-time with the amplitudes of quantum theory.

One thought experiment where unitarity looks creaky involves black holes, intense concentrations of matter that warp space-time into a dead end. Stephen Hawking calculated in 1974 that black holes evaporate over time, erasing the quantum state of anything that fell in—a seemingly blatant unitarity violation known as the black hole information paradox. If black holes have Hilbert spaces that mature isometrically, as Cotler and Strominger hypothesize, physicists may face a somewhat different puzzle than they thought. “I don’t think there can be a solution that doesn’t take this into account,” Strominger said.

Another prize would be a detailed quantum theory that described not just how the cosmos grows, but where everything came from in the first place. “We have no universe, and all of a sudden we have a universe,” Arkani-Hamed said. “What the hell kind of unitary evolution is that?”

For his part, however, Arkani-Hamed doubts that swapping in isometry for unitarity goes far enough. He is one of the leaders of a research program that is trying to break free of many fundamental assumptions in quantum theory and general relativity, not just unitarity.

Whatever theory comes next, he suspects, will take a completely novel form, just as quantum mechanics was a clean break from Isaac Newton’s laws of motion. As an illustrative example of what a new form might look like, he points to a research program stemming from a 2014 discovery he made together with Jaroslav Trnka, his student at the time. They showed that when certain particles collide, the amplitude of each possible outcome equals the volume of a geometric object, dubbed the amplituhedron. Calculating the object’s volume is much easier than using standard methods for computing the amplitudes, which laboriously reconstruct all the ways a particle collision might play out, moment by moment.

Intriguingly, while the amplituhedron gives answers that obey unitarity, the principle isn’t used to construct the shape itself. Neither are any assumptions about how particles move in space and time. The success of this purely geometric formulation of particle physics raises the possibility of a fresh perspective on reality, one free from the cherished principles that currently conflict. Researchers have gradually been generalizing the approach to explore related geometric shapes pertaining to different particles and quantum theories.

“[It] may be a different way to organize unitarity,” Cotler said, “and perhaps it has the seeds to transcend it.”

Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.