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Cryptoverse: Ether snaps at bitcoin’s heels in race for crypto crown – Reuters

Souvenir tokens representing cryptocurrency Bitcoin and the Ethereum network, with its native token ether, plunge into water in this illustration taken May 17, 2022. REUTERS/Dado Ruvic/Illustration

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Sept 13 (Reuters) - For years, ether could barely dream of challenging its big brother bitcoin. Now, its ambitions may be becoming more realistic.

The second-biggest cryptocurrency is taking market share from bitcoin ahead of an all-important "Merge" software upgrade that could sharply reduce the energy usage of its Ethereum blockchain, should the developers pull it off in coming days.

Bitcoin's dominance, or its share of the crypto market's market value, has slipped to 39.1% from this year's peak of 47.5% in mid-June, according to data platform CoinMarketCap. Ether, on the other hand, has climbed to 20.5% from 16%.

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The upstart is still a long way from overtaking bitcoin as the No.1 cryptocurrency, a reversal known to aficionados as "the flippening". It's made up ground, though; in January 2021, bitcoin reigned supreme at 72%, while ether occupied a slender 10%.

As for price, one ether is now worth 0.082 bitcoin , near December 2021 highs and sharply above the 2022 low of 0.049 in June.

"People are now viewing Ethereum as essentially a safe asset because they've seen the success of the network, they think it's not going anywhere," said Joseph Edwards, head of financial strategy at fund management firm Solrise Finance.

"There's a permanency to how Ethereum is perceived in the crypto ecosystem."

The Merge, expected to take place on Thursday after several delays, could lead to wider use of the blockchain, potentially boosting ether's price - although nothing is certain in a capricious crypto market. read more

Ethereum forms the backbone of much of the "Web3" vision of an internet where crypto takes centre stage, powering applications involving crypto offshoots such as decentralised finance and non-fungible tokens - although this much-hyped dream is still unrealised.

Bitcoin and ether have both nearly halved this year on concerns about supersized interest rate hikes from central banks. Nonetheless, investors seem to like the look of the Merge, with ether up over 65% since the end of June. Bitcoin has barely budged in the same period.

"We're going to see (ether's) attractiveness to some investors who are concerned about energy consumption," said Doug Schwenk, CEO of Digital Asset Research, although he cautioned that ether was still a long way behind bitcoin.

The diminishing bitcoin dominance in crypto's current bear market is a departure from previous market cycles when investors sold lesser tokens - "altcoins" - in favor of the more liquid and reliable bitcoin.

Dethroning the king is no easy feat, though.

Bitcoin is still by far the most well-known cryptocurrency. Mainstream investors who have dipped their toes in the crypto market since 2020 have tended to turn first to bitcoin, as the most liquid and widely-traded token.

Its market cap of $427 billion is still more than double Ether's $210 billion, and market participants firmly believe the original digital coin remains the gold standard in crypto due to its limited supply.

Some market players say bitcoin's grip on the crypto crown is still strong, even if it has to accept other contenders. For example, Hugo Xavier, CEO of K2 Trading Partners, said its dominance could improve to 50%-60% range if the crypto market turns bullish but it is unlikely to touch 70% again.

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Reporting by Medha Singh and Lisa Pauline Mattackal in Bengaluru; Editing by Tom Wilson and Pravin Char

Our Standards: The Thomson Reuters Trust Principles.

Opinions expressed are those of the author. They do not reflect the views of Reuters News, which, under the Trust Principles, is committed to integrity, independence, and freedom from bias.

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Top Crypto Analyst Issues Bitcoin and Ethereum Alert, Predicts Pullback for BTC and ETH As Merge Draws Near – The Daily Hodl

A popular crypto analyst who is building a following with timely Bitcoin calls is warning traders that both BTC and Ethereum (ETH) could be setting up for a leg down.

Pseudonymous crypto strategist Credible tells his 338,100 Twitter followers that while Bitcoin managed to put together a decent bounce from around $18,500 on September 7th, he believes that BTCs short-term upside is limited and that the king crypto could be looking at a trip back down to $20,000.

Looking solid. A wave one close tomorrow above $20,700 should confirm the reclaim. May retest the $20,700 on the lower timeframe but a solid close tomorrow and we will look good to continue to $23,000. After, expecting a rejection and a revisit to range lows/$20,000 for a higher low before continuation UP.

Looking at Credibles chart, he predicts an immediate bounce for BTC after his expected corrective move to $20,000. At time of writing, BTC is changing hands for $21,913.

As for Ethereum, Credible says that ETH also has some room to rally in the near term, but he predicts a steep correction after the king altcoin hits his target.

ETH up some 20% from the bounce zone and now almost at my upside target. Again, looking for continuation up to $1,800-$,1900 expecting a rejection there and likely new local lows after. Most dont want to hear this but it is what it is.

Looking at Credibles chart, he predicts a pullback down to the $1,200 level for Ethereum, which is a 36% devaluation should ETH hit his target of $1,900.

At time of writing, ETH is trading for $1,752, flat on the day.

Featured Image: Shutterstock/Art Furnace/Natalia Siiatovskaia

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Top Crypto Analyst Issues Bitcoin and Ethereum Alert, Predicts Pullback for BTC and ETH As Merge Draws Near - The Daily Hodl

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Former Goldman Sachs Executive Says Bitcoin and Crypto Bottom Already In, Predicts Big Shift in Macro Backdrop – The Daily Hodl

Former Goldman Sachs executive Raoul Pal thinks the bottom is in for Bitcoin (BTC), Ethereum (ETH) and the overall crypto markets.

The Real Vision chief executive says in a new YouTube video that traders and investors should look 12 to 18 months ahead as asset markets tend to price the future.

Right now, we can hear people all on Twitter say, Were going into a recession. Its clear theres going to be another leg down in equities because they need to price in the recession. Thats assuming that everything operates in real-time. But it doesnt.

So when I look at the year-on-year rates of change of lets say the NASDAQ and compare it to the ISM Index, which is my guide to the business cycle It suggests that the NASDAQ is pricing in ISM at around 40. ISM at 40 is in a relatively deep recession. ISM at 47 is usually a recession level. And 40 is something to the order of magnitude of negative 2% GDP growth. So its already priced in.

The ISM Manufacturing Index is viewed as an indicator of the health of the US economy. It currently sits at 52.8 as of September 1st, according to Investing.com.

Pal also thinks its likely that inflation goes negative within the next 18 months, which he says is good news for risk assets like crypto.

If we look out 12 months, the recession is behind us, rates are lower and inflation is low. So that is a very good outcome for risk assets and crypto. Crypto bottomed in June. We had the retest. Bitcoin had a retest only two days ago, and I think it was the retest.

My DeMark indicators, which I use mainly for my technical analysis gave me that signal. ETH had a much stronger signal in June.

Im thinking the markets are forward-looking. I think the sentiment is extremely bearish, and were going into a potential change in the macro.

Traders use the DeMark indicator to spot possible reversals in trends.

Bitcoin is trading at $22,191 at time of writing. Ethereum is trading at $1,692.

I

Featured Image: Shutterstock/Panuwatccn/Vandathai

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Former Goldman Sachs Executive Says Bitcoin and Crypto Bottom Already In, Predicts Big Shift in Macro Backdrop - The Daily Hodl

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The Greatest Trick Ever Played, And How Bitcoin Shatters The Illusion – Bitcoin Magazine

This is an opinion editorial by Andrew Axelrod, a Bitcoin educator and writerwhose LinkedIn posts have orange pilled thousands.

"The devil's finest trick is to persuade you that he does not exist." Charles Baudelaire

The second greatest trick was convincing the world he is good. Ken Ammi

Throughout history, people have always been blinded by the cathedral of their times. Ideas of chivalry, caste systems and royal bloodlines were all incredibly powerful constructs that towered above any possible scrutiny, let alone rebuke.

Today is no different.

Just as fish cannot perceive the water they swim in, it is also difficult for people to recognize the cathedrals for what they truly are. Grandiose narratives, fanciful myths, and seductive lies make for invisible chains.

They are the walls of Platos Cave. They are the scrolling green code of the Matrix.

And no prisoner can break free from shackles that remain hidden.

Such illusions are shattered by bitcoin like waves breaking against solid rock. This is because bitcoin unveils the three most powerful and enduring illusions of our time those of the competent central planner, the common good, and fiat money.

Let us now step through the looking glass and dissect these magic tricks one by one, starting with the competence of central planners.

Ah yes, central planners. They aspire to positions of power in the guise of charismatic figureheads, lofty intellectuals, the spiritually enlightened or impressive polymaths whos vast knowledge spans the fields of economics, finance, healthcare, engineering, infrastructure, energy policy and oooohhhh so many more.

Even better, they are packaged and sold as benevolent leaders that strive for a better tomorrow, acting only out of altruism and for love of the common good. Truth and justice are their names.

Intellect, wisdom and hearts of gold? Sign me up!

Of the three, this is perhaps the easiest illusion to dispel.

At its best, politics is often described as the act of jumping in front of a moving parade while claiming credit. And at its worst, central planners get drunk on the myth of their own competence which inevitably turns the parade into a chain gang shuffle.

This is because central planning at its heart must rely on coercion. Voluntary actions occur organically, bottom up, and on the individual level. By definition, they do not need to be centrally orchestrated.

Next, putting aside the laughable notion that an individual mortal could possess any meaningful level of mastery across so many complex domaines and ignoring the fact that these are flesh and blood humans, naturally prone to self-interest and subject to all the usual dark appetites, it is equally insane to think that an abstraction such as the common good could ever be agreed on let alone achieved.

But that, of course, is the entire point.

The common good has always been in the eye of the beholder and is therefore highly susceptible to every possible perversion. It is ideally malleable custom tailored camouflage for the central planner.

In the name of the common good, central planners then take upon themselves the right to decide on the conflicts of nations, on conscription in war, on the hollowing out of industry, on the allocation of rations, on the burden of tax (either directly at gunpoint or discretely through inflation) and, most importantly, on who gets to be first in line at the money printers trough.

Bitcoin of course flips this on its head. More on that later.

But how does such a ludicrous belief in central planning perpetuate itself the deranged idea that a miniscule group of people, or oftentimes even a sole individual, should with the flick of a pen decide the wellbeing and economic fate of millions?

It all comes back to the delusion of the common good.

It is precisely this belief in the common good taken to its extreme, a belief in paradise on earth, that justifies the greatest abuses.

This is the corrosive narrative which central planners always draw on for legitimacy and which they use to feed their lust for control. Because ideas of eutopia justify any means to accomplish their end, central planners can use them to maximum effect. Not only do they make dubious claims of a eutopia, but also insist on possessing knowledge of the righteous path that leads to it.

Why go through the trouble of building such a cathedral?

Contrary to the common cynics belief, the vast majority of people want to be perceived as doing good and arent prone to extremism a benefit of normal distributions.

Therefore, evil has to cloak itself in the mantle of virtue or else be rejected.

After all, the road to perdition is famously paved with good intentions.

And what could be more well intentioned than the pursuit of heaven on earth.

This is what lifted the Communists into power, perhaps the most outspoken central planners of them all. It is also what gives the jihadis credibility in the eyes of the faithful and what fueled the rise of Nazi Germany.

The common good is the perfect narrative for central planners to seize the reins of power and gives their followers the iron conviction to follow through on even the most heinous of acts.

And who would dare speak out against them? Who would be so cruel as to deny paradise.

Because when it comes to bringing about heaven on earth no price is too steep, no sacrifice sufficient and no body count too high.

What do another million dead matter if paradise awaits just around the corner. It is never enough, the bloodlust cannot be slaked.

The nameless mass graves of 80 million killed at the hands of Mao, the 40 million under Stalin, the 20 million under Hitler, the 3.5 million under the Kims and the 3 million under Pol Pot they all attest to this slaughtered in the name of this most depraved of fantasies.

The sad irony is that although paradise is an illusion, hell on earth is very real.

One need look no further than North Korea, where people are publicly executed for the crime of making unauthorized phone calls.

In fact, eutopia and dystopia aren't opposites they're synonyms.

And the surest way to arrive at this terrible destination is to concentrate ultimate power in the hands of a few, in the hands of central planners.

The carrot of eutopia combined with the stick of an emergency whether it be a classless and plentiful society threatened by the greedy bourgeoisie, or the promise of a thousand year Aryan rule to crush the corrupting globalists or the establishment of a glorious caliphate as a stronghold against the aggressing infidels these narratives are all designed to rally a core group of true believers and convince the wider public to enshrine in central planners extraordinary powers.

But how then do the actual mechanics of coercion work at scale and how is the average person ensnared beyond just turning a blind eye?

How does the narrative actually transmit into reality?

Through fiat money.

In the words of Henry Kissinger: Who controls money, controls the world.

This is the greatest trick ever played.

If the competent central planner and the common good can be called illusions, fiat money makes these look like cheap parlor tricks by comparison.

Most civilized societies have concluded that central planning of the economy is generally a bad idea. A committee of central planners overriding the free market by setting the prices of commodities, goods and services has always lead to great misery and starvation.

But when it comes to money, suddenly the rules seem to magically change.

At the center of every modern economy sits a central bank whos explicit mandate is to control the supply of money through its balance sheet and set its price through interest rate fixing.

How can this contradiction be rationalized?

Jordan Peterson famously remarked that only half the lesson of World War II had been learnt.

By this he meant that wed grappled with the snakepit of national socialism but not the communist den of vipers a tragic consequence of the Allies expedient alignment with the Soviets against the Third Reich.

One key consequence of this was that central planners were allowed to nest in the corridors of power and permitted to desecrate once hallowed institutions.

For example, it is now perfectly acceptable for academics to self-identify as Marxists, which nearly 20% of professors in the social sciences do.

But even still, the notion that at least half the lesson was learnt is hopelessly optimistic.

The lessons of the past have been reduced to a wild goose chase for the modern day equivalent of an angry-sounding German man in leather boots and a silly-looking mustache. Its a stultifying distraction from the underlying culprit of fiat money which allowed such madmen to rule in the first place. While society is preoccupied with a frenzied scavenger hunt for goose-stepping fascists, literal central banks have been put in charge of the money. As we will see, this is a clear pattern.

The money printer allows central planners to override free market choices.

What instrument of control could possibly be more perfect.

Endless wars can now be financed with just the push of a button, destructive policies can be pursued no matter the cost and when challenged, central planners can bribe their opposition into compliance with promises of a universal basic income, of free education and health care, and of subsidized housing for the needy.

And all of this they can deliver, if only given the power of the printer.

Fiat money lets central planners hide the true cost of their destructive decisions by papering over them. And when society inevitably collides with the walls of reality, this provides central planners with the perfect emergency to centralize even more.

In their greatest time of need, people blinded by panic will turn to the arsonists and beg them to extinguish the fire.

As the black hole of money printing distorts price signals, misallocates assets, and debases societys savings, people will actually blame late stage capitalism for the deterioration.

Not recognizing the caustic effects of fiat money and centralized power, people will instead cry out for more of the same poison that ails them. When decades of loose monetary policy and insatiable money printing drove America into the Great Depression of the 1930s, the remedy was more centralization.

What followed was the outlawing of gold with Executive Order 6102, the last bulwark against fiat, and thereafter an unprecedented nationalization of private industry that fed the war machine.

In fact, FDR was able to centralize so much power that he became de facto president for life and died while serving his fourth term in office the only president to ever do so. After his death, a 22nd amendment was hastily added to the constitution, setting a two-term limit on the presidency.

The massive military industrial complex that was erected during this time and has since grown by orders of magnitude, gorging itself on money printing, is something Americans are still contending with unable to extricate themselves from multiplying conflicts.

When Weimar Germany collapsed under the hyperinflationary fires of the papiermark, the answer was again to centralize. Only this time, the Fhrer used fiat to turn Germany into a giant weapons manufacturer and burnt Europe to the ground.

And when Lenins Soviet Union was ravaged by three successive hyperinflations due to Communist profligacy, Stalin seized the mantle of power, then turned around and brutally butchered the Russian people. In fact, Soviet Russia burnt through a total of seven versions of the fiat ruble and endured seven painful resets.

The central planners fiat trick became so routine that Soviet workers would famously joke: We pretend to work and they pretend to pay. But of course, every fiat money must find a point of exhaustion, when the money printers ink runs dry. It is for this reason, that the seemingly opposite Eastern communist and Western capitalist systems were at least similar in this way:

Both ultimately believed in top-down control through fiat money.

Only the communists, spurred on by a more rabid fanaticism, made the fatal mistake of centralizing every nut and bolt of their economy, involving the government in decisions ranging from the harvesting of crops to the manufacturing of shoes and the production of cars. This ended in incomprehensible human suffering.

Central planners in the West took a more tactful approach by first allowing their economies to self organize and fatten up before milking them dry via centralized money.

And so, fiat is the greatest trick ever played. It is also the ultimate heist, allowing central planners to siphon off a populations entire productivity and exhaust its every resource through the counterfeiting of money. Fiat money is watermelon socialism capitalist green on the outside and communist red at its core.

As justification, central planners must contort themselves into impressive mental pretzels and invert the truth. Some of these brazen lies famously include:

Thats right.

War is peace. Slavery is freedom. Ignorance is strength.

But what if money could not be printed at will? If money bore an actual cost, then central planners maleficence would become almost instantly and laughably obvious. The peoples pocket could no longer be picked with inflation and the central planners incompetence would incur an immediate and tangible cost. Want to wage wars? Youll need to pay for them. Want to fund wasteful government programs? Youll need to justify them. Want to bankrupt your citizens and leave them destitute? Youll need to face them.

Central planners could no longer destroy the world on credit and would be required to close out their tab. The cost of unproductive and wrongheaded action would come to bear immediately and allow society to course correct. This is what bitcoin does by separating money and state. It takes the central planners favorite tool of coercion and snaps it in half like a brittle twig. Once money can no longer be printed, what good are moral posturing and illusions of grandeur.

Bitcoin strips the lie of the common good down to the hollow and empty shell that it really is and exposes any shred of unearned competence the central planners have left.

Their trick revealed, central planners will finally be forced to take a bow they just shouldnt expect any applause.

This is a guest post by Andrew Axelrod. Opinions expressed are entirely their own and do not necessarily reflect those of BTC Inc or Bitcoin Magazine.

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Mooners and Shakers: Ravencoin soars and Bitcoin pumps, but Ethereum flattens out ahead of Merge – Stockhead

Okay, Ravencoin. Whats this one all about then? Its pumping, so lets peck into it. Meanwhile Bitcoins been on a bit of a surge, too, while Ethereum is currently lazing on a deck chair hoping for a decent Merge tan.

Deep into that crypto winter darkness peering, long I stood there, wondering, fearing, doubting, dreaming dreams no shadowy super coder ever dared to dream before. Quoth the Ravencoin, Nevermore.

Edgar Allen Poe didnt quite write that.

That said we can 99.93% say for sure that the legendary 19th century American fountain pen and opioid user wouldve been a crypto fan. Probably. Apparently, he had a keen interest in cryptography and, in fact, had something of an influence on the modern science.

Would love to get into that a bit morebut weve got magic internet money to natter about.

Now, what the squawk is Ravencoin (RVN) then and why is it flapping and ca-cawwing its way up the daily cryptocurrency top 100 chart? Would it surprise you to learn that, in a roundabout sort of way, its Merge related? Nope? Didnt think so.

Ravencoin is not, however, a Proof-of-Stake coin, and its not new. Launched in 2018, the protocol is an Ethereum mining alternative that uses a Proof-of-Work consensus algorithm blockchain that mimics Bitcoins 21 million-coin supply.Its got its own, sophisticated tokenised ecosystem that uses RVN for various DeFi and NFT applications.

According to CoinGecko data, Ravencoin has surged about 30% over the past day and more than 95% over the week.

Why? Well, all things Ethereum (well, aside from ETH itself today) seem to be taking turns at grabbing the spotlight in the lead up to the leading smart contract blockchains Merge to Proof-of-Stake.

Despite the ESG, carbon-reducing positivity that the Merge move is partly building its momentum on, there are still a fair amount of mining, PoW fans out there, making their case and seeking mining alternatives as the main Ethereum chain swaps lanes. Thats partly it, but perhaps the main reason is this

The RVN pump in price has basically coincided with the news major global crypto exchange FTX announced the listing of Ravencoin perpetual futures on September 12.

Onto other crypto-related pumpery and dumpery

With the overall crypto market cap at US$1.1 trillion and down about 0.3% since yesterday, heres the current state of play among top 10 tokens according to CoinGecko.

As youd expect, the chart tells the story here. Basically Bitcoin, Ethereum rival Solana and XRP are the only things in the green over the past 24 hours.

Lets check in on Solana (SOL) for a sec It seems determined to dodge the Merge shadow. Is there a reason for the exuberance? Other than some ongoing positivity based around the Helium projects potential migration, nothing major that were seeing

Although theres this, too Solana is Ethereums greatest rival for NFT-based activity and that appears to be spiking on Solana market place Magic Eden again, according to crypto-data gurus Nansen

As for Bitcoin, its kicked with some confidence into what most think is going to be a vortex of volatility this week. BTC is now trading back above US$22k at the time of writing, after closing its latest weekly candle at US$21,800. Thats the OG cryptos highest weekly close for about a month.

In the very short term, the US dollar tapering off and seemingly hitting some chart-based resistance seems to be helping Bitcoin, other cryptos and stonks so far this week.

Dont forget, though (well, you can if you want), that the fresh US Consumer Price Index inflation-related data for the month of August is set to be released. And, for those who are a tad over-exposed to risk assets, lately these figures have been a recipe for nervy toilet sessions and/or Hey EVERYONE, this rounds on me!

Sweeping a market-cap range of about US$8.4 billion to about US$446 million in the rest of the top 100, lets find some of the biggest 24-hour gainers and losers at press time. (Stats accurate at time of publishing, based on CoinGecko.com data.)

DAILY PUMPERS

Ravencoin (RVN), (market cap: US$783 million) +32%

Hedera (HBAR), (mc: US$1.6 billion) +10%

The Graph (GRT), (mc: US$932 million) +9%

Helium (HNT), (mc: US$682 million) +6%

NEAR Protocol (NEAR), (mc: US$3.9 billion) +5%

DAILY SLUMPERS

Terra(LUNA), (market cap: US$661 million) -28%

Terra Luna Classic (LUNC), (mc: US$2.13 billion) -21%

Celsius Network (CEL), (mc: US$608 million) -9%

Rocket Pool (RPL), (mc: US$588 million) -7%

Amp (AMP), (mc: US$472 million) -6%

Well, probably shoulda known this would happen. As soon as we open our traps about a Terra LUNA revival, its coins go and dump harder than that Brent Naden spear tackle a couple of months back. If you follow such things, that is.

This, however, doesnt change the fact that both LUNA (or LUNA2 as its also now known) and LUNC have made stupendous gains just recently.

That said, as per yesterdays column, weve been very much cautioning with buyer beware when it comes to CeFi tokens struggling for revival, especially considering Terra LUNAs catastrophic and crypto-contagion-inducing collapse in May.

Touch them with an extendable barge pole? Not financially advising on that, or anything for that matter, as theres, unsurprisingly, no qualification for that hanging in my pool room.

A selection of randomness and pertinence that stuck with us on our morning moves through the Crypto Twitterverse

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Mathematical formulation of quantum mechanics – Wikipedia

Mathematical structures that allow quantum mechanics to be explained

The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces (L2 space mainly), and operators on these spaces. In brief, values of physical observables such as energy and momentum were no longer considered as values of functions on phase space, but as eigenvalues; more precisely as spectral values of linear operators in Hilbert space.[1]

These formulations of quantum mechanics continue to be used today. At the heart of the description are ideas of quantum state and quantum observables, which are radically different from those used in previous models of physical reality. While the mathematics permits calculation of many quantities that can be measured experimentally, there is a definite theoretical limit to values that can be simultaneously measured. This limitation was first elucidated by Heisenberg through a thought experiment, and is represented mathematically in the new formalism by the non-commutativity of operators representing quantum observables.

Prior to the development of quantum mechanics as a separate theory, the mathematics used in physics consisted mainly of formal mathematical analysis, beginning with calculus, and increasing in complexity up to differential geometry and partial differential equations. Probability theory was used in statistical mechanics. Geometric intuition played a strong role in the first two and, accordingly, theories of relativity were formulated entirely in terms of differential geometric concepts. The phenomenology of quantum physics arose roughly between 1895 and 1915, and for the 10 to 15 years before the development of quantum mechanics (around 1925) physicists continued to think of quantum theory within the confines of what is now called classical physics, and in particular within the same mathematical structures. The most sophisticated example of this is the SommerfeldWilsonIshiwara quantization rule, which was formulated entirely on the classical phase space.

In the 1890s, Planck was able to derive the blackbody spectrum, which was later used to avoid the classical ultraviolet catastrophe by making the unorthodox assumption that, in the interaction of electromagnetic radiation with matter, energy could only be exchanged in discrete units which he called quanta. Planck postulated a direct proportionality between the frequency of radiation and the quantum of energy at that frequency. The proportionality constant, h, is now called Planck's constant in his honor.

In 1905, Einstein explained certain features of the photoelectric effect by assuming that Planck's energy quanta were actual particles, which were later dubbed photons.

All of these developments were phenomenological and challenged the theoretical physics of the time. Bohr and Sommerfeld went on to modify classical mechanics in an attempt to deduce the Bohr model from first principles. They proposed that, of all closed classical orbits traced by a mechanical system in its phase space, only the ones that enclosed an area which was a multiple of Planck's constant were actually allowed. The most sophisticated version of this formalism was the so-called SommerfeldWilsonIshiwara quantization. Although the Bohr model of the hydrogen atom could be explained in this way, the spectrum of the helium atom (classically an unsolvable 3-body problem) could not be predicted. The mathematical status of quantum theory remained uncertain for some time.

In 1923, de Broglie proposed that waveparticle duality applied not only to photons but to electrons and every other physical system.

The situation changed rapidly in the years 19251930, when working mathematical foundations were found through the groundbreaking work of Erwin Schrdinger, Werner Heisenberg, Max Born, Pascual Jordan, and the foundational work of John von Neumann, Hermann Weyl and Paul Dirac, and it became possible to unify several different approaches in terms of a fresh set of ideas. The physical interpretation of the theory was also clarified in these years after Werner Heisenberg discovered the uncertainty relations and Niels Bohr introduced the idea of complementarity.

Werner Heisenberg's matrix mechanics was the first successful attempt at replicating the observed quantization of atomic spectra. Later in the same year, Schrdinger created his wave mechanics. Schrdinger's formalism was considered easier to understand, visualize and calculate as it led to differential equations, which physicists were already familiar with solving. Within a year, it was shown that the two theories were equivalent.

Schrdinger himself initially did not understand the fundamental probabilistic nature of quantum mechanics, as he thought that the absolute square of the wave function of an electron should be interpreted as the charge density of an object smeared out over an extended, possibly infinite, volume of space. It was Max Born who introduced the interpretation of the absolute square of the wave function as the probability distribution of the position of a pointlike object. Born's idea was soon taken over by Niels Bohr in Copenhagen who then became the "father" of the Copenhagen interpretation of quantum mechanics. Schrdinger's wave function can be seen to be closely related to the classical HamiltonJacobi equation. The correspondence to classical mechanics was even more explicit, although somewhat more formal, in Heisenberg's matrix mechanics. In his PhD thesis project, Paul Dirac[2] discovered that the equation for the operators in the Heisenberg representation, as it is now called, closely translates to classical equations for the dynamics of certain quantities in the Hamiltonian formalism of classical mechanics, when one expresses them through Poisson brackets, a procedure now known as canonical quantization.

To be more precise, already before Schrdinger, the young postdoctoral fellow Werner Heisenberg invented his matrix mechanics, which was the first correct quantum mechanics the essential breakthrough. Heisenberg's matrix mechanics formulation was based on algebras of infinite matrices, a very radical formulation in light of the mathematics of classical physics, although he started from the index-terminology of the experimentalists of that time, not even aware that his "index-schemes" were matrices, as Born soon pointed out to him. In fact, in these early years, linear algebra was not generally popular with physicists in its present form.

Although Schrdinger himself after a year proved the equivalence of his wave-mechanics and Heisenberg's matrix mechanics, the reconciliation of the two approaches and their modern abstraction as motions in Hilbert space is generally attributed to Paul Dirac, who wrote a lucid account in his 1930 classic The Principles of Quantum Mechanics. He is the third, and possibly most important, pillar of that field (he soon was the only one to have discovered a relativistic generalization of the theory). In his above-mentioned account, he introduced the braket notation, together with an abstract formulation in terms of the Hilbert space used in functional analysis; he showed that Schrdinger's and Heisenberg's approaches were two different representations of the same theory, and found a third, most general one, which represented the dynamics of the system. His work was particularly fruitful in many types of generalizations of the field.

The first complete mathematical formulation of this approach, known as the Diracvon Neumann axioms, is generally credited to John von Neumann's 1932 book Mathematical Foundations of Quantum Mechanics, although Hermann Weyl had already referred to Hilbert spaces (which he called unitary spaces) in his 1927 classic paper and book. It was developed in parallel with a new approach to the mathematical spectral theory based on linear operators rather than the quadratic forms that were David Hilbert's approach a generation earlier. Though theories of quantum mechanics continue to evolve to this day, there is a basic framework for the mathematical formulation of quantum mechanics which underlies most approaches and can be traced back to the mathematical work of John von Neumann. In other words, discussions about interpretation of the theory, and extensions to it, are now mostly conducted on the basis of shared assumptions about the mathematical foundations.

The application of the new quantum theory to electromagnetism resulted in quantum field theory, which was developed starting around 1930. Quantum field theory has driven the development of more sophisticated formulations of quantum mechanics, of which the ones presented here are simple special cases.

A related topic is the relationship to classical mechanics. Any new physical theory is supposed to reduce to successful old theories in some approximation. For quantum mechanics, this translates into the need to study the so-called classical limit of quantum mechanics. Also, as Bohr emphasized, human cognitive abilities and language are inextricably linked to the classical realm, and so classical descriptions are intuitively more accessible than quantum ones. In particular, quantization, namely the construction of a quantum theory whose classical limit is a given and known classical theory, becomes an important area of quantum physics in itself.

Finally, some of the originators of quantum theory (notably Einstein and Schrdinger) were unhappy with what they thought were the philosophical implications of quantum mechanics. In particular, Einstein took the position that quantum mechanics must be incomplete, which motivated research into so-called hidden-variable theories. The issue of hidden variables has become in part an experimental issue with the help of quantum optics.

A physical system is generally described by three basic ingredients: states; observables; and dynamics (or law of time evolution) or, more generally, a group of physical symmetries. A classical description can be given in a fairly direct way by a phase space model of mechanics: states are points in a symplectic phase space, observables are real-valued functions on it, time evolution is given by a one-parameter group of symplectic transformations of the phase space, and physical symmetries are realized by symplectic transformations. A quantum description normally consists of a Hilbert space of states, observables are self-adjoint operators on the space of states, time evolution is given by a one-parameter group of unitary transformations on the Hilbert space of states, and physical symmetries are realized by unitary transformations. (It is possible, to map this Hilbert-space picture to a phase space formulation, invertibly. See below.)

The following summary of the mathematical framework of quantum mechanics can be partly traced back to the Diracvon Neumann axioms.[3]

Each isolated physical system is associated with a (topologically) separable complex Hilbert space H with inner product |. Rays (that is, subspaces of complex dimension 1) in H are associated with quantum states of the system.

In other words, quantum states can be identified with equivalence classes of vectors of length 1 in H, where two vectors represent the same state if they differ only by a phase factor. Separability is a mathematically convenient hypothesis, with the physical interpretation that countably many observations are enough to uniquely determine the state. "A quantum mechanical state is a ray in projective Hilbert space, not a vector. Many textbooks fail to make this distinction, which could be partly a result of the fact that the Schrdinger equation itself involves Hilbert-space "vectors", with the result that the imprecise use of "state vector" rather than ray is very difficult to avoid."[4]

Accompanying Postulate I is the composite system postulate:[5]

Composite system postulate

The Hilbert space of a composite system is the Hilbert space tensor product of the state spaces associated with the component systems. For a non-relativistic system consisting of a finite number of distinguishable particles, the component systems are the individual particles.

In the presence of quantum entanglement, the quantum state of the composite system cannot be factored as a tensor product of states of its local constituents; Instead, it is expressed as a sum, or superposition, of tensor products of states of component subsystems. A subsystem in an entangled composite system generally can't be described by a state vector (or a ray), but instead is described by a density operator; Such quantum state is known as a mixed state. The density operator of a mixed state is a trace class, nonnegative (positive semi-definite) self-adjoint operator normalized to be of trace 1. In turn, any density operator of a mixed state can be represented as a subsystem of a larger composite system in a pure state (see purification theorem).

In the absence of quantum entanglement, the quantum state of the composite system is called a separable state. The density matrix of a bipartite system in a separable state can be expressed as = k p k 1 k 2 k {displaystyle rho =sum _{k}p_{k}rho _{1}^{k}otimes rho _{2}^{k}} , where k p k = 1 {displaystyle ;sum _{k}p_{k}=1} . If there is only a single non-zero p k {displaystyle p_{k}} , then the state can be expressed just as = 1 2 , {textstyle rho =rho _{1}otimes rho _{2},} and is called simply separable or product state.

Physical observables are represented by Hermitian matrices on H. Since these operators are Hermitian, their eigenvalues are always real, and represent the possible outcomes/results from measuring the corresponding observable. If the spectrum of the observable is discrete, then the possible results are quantized.

By spectral theory, we can associate a probability measure to the values of A in any state . We can also show that the possible values of the observable A in any state must belong to the spectrum of A. The expectation value (in the sense of probability theory) of the observable A for the system in state represented by the unit vector H is | A | {displaystyle langle psi |A|psi rangle } . If we represent the state in the basis formed by the eigenvectors of A, then the square of the modulus of the component attached to a given eigenvector is the probability of observing its corresponding eigenvalue.

For a mixed state , the expected value of A in the state is tr ( A ) {displaystyle operatorname {tr} (Arho )} , and the probability of obtaining an eigenvalue a n {displaystyle a_{n}} in a discrete, nondegenerate spectrum of the corresponding observable A {displaystyle A} is given by P ( a n ) = tr ( | a n a n | ) = a n | | a n {displaystyle mathbb {P} (a_{n})=operatorname {tr} (|a_{n}rangle langle a_{n}|rho )=langle a_{n}|rho |a_{n}rangle } .

If the eigenvalue a n {displaystyle a_{n}} has degenerate, orthonormal eigenvectors { | a n 1 , | a n 2 , , | a n m } {displaystyle {|a_{n1}rangle ,|a_{n2}rangle ,dots ,|a_{nm}rangle }} , then the projection operator onto the eigensubspace can be defined as the identity operator in the eigensubspace:

Postulates II.a and II.b are collectively known as the Born rule of quantum mechanics.

When a measurement is performed, only one result is obtained (according to some interpretations of quantum mechanics). This is modeled mathematically as the processing of additional information from the measurement, confining the probabilities of an immediate second measurement of the same observable. In the case of a discrete, non-degenerate spectrum, two sequential measurements of the same observable will always give the same value assuming the second immediately follows the first. Therefore the state vector must change as a result of measurement, and collapse onto the eigensubspace associated with the eigenvalue measured.

For a mixed state , after obtaining an eigenvalue a n {displaystyle a_{n}} in a discrete, nondegenerate spectrum of the corresponding observable A {displaystyle A} , the updated state is given by = P n P n tr ( P n P n ) {textstyle rho '={frac {P_{n}rho P_{n}^{dagger }}{operatorname {tr} (P_{n}rho P_{n}^{dagger })}}} . If the eigenvalue a n {displaystyle a_{n}} has degenerate, orthonormal eigenvectors { | a n 1 , | a n 2 , , | a n m } {displaystyle {|a_{n1}rangle ,|a_{n2}rangle ,dots ,|a_{nm}rangle }} , then the projection operator onto the eigensubspace is P n = | a n 1 a n 1 | + | a n 2 a n 2 | + + | a n m a n m | {displaystyle P_{n}=|a_{n1}rangle langle a_{n1}|+|a_{n2}rangle langle a_{n2}|+dots +|a_{nm}rangle langle a_{nm}|} .

Postulates II.c is sometimes called the "state update rule" or "collapse rule"; Together with the Born rule (Postulates II.a and II.b), they form a complete representation of measurements, and are sometimes collectively called the measurement postulate(s).

Note that the projection-valued measures (PVM) described in the measurement postulate(s) can be generalized to positive operator-valued measures (POVM), which is the most general kind of measurement in quantum mechanics. A POVM can be understood as the effect on a component subsystem when a PVM is performed on a larger, composite system (see Naimark's dilation theorem).

Though it is possible to derive the Schrdinger equation, which describes how a state vector evolves in time, most texts assert the equation as a postulate. Common derivations include using the DeBroglie hypothesis or path integrals.

Postulate III

The time evolution of the state vector | ( t ) {displaystyle |psi (t)rangle } is governed by the Schrdinger equation, where H ( t ) {displaystyle H(t)} is the observable associated with the total energy of the system (called the Hamiltonian)

i d d t | ( t ) = H ( t ) | ( t ) {displaystyle ihbar {frac {d}{dt}}|psi (t)rangle =H(t)|psi (t)rangle }

Equivalently, the time evolution postulate can be stated as:

Postulate III

The time evolution of a closed system is described by a unitary transformation on the initial state.

| ( t ) = U ( t ; t 0 ) | ( t 0 ) {displaystyle |psi (t)rangle =U(t;t_{0})|psi (t_{0})rangle }

For a closed system in a mixed state , the time evolution is ( t ) = U ( t ; t 0 ) ( t 0 ) U ( t ; t 0 ) {displaystyle rho (t)=U(t;t_{0})rho (t_{0})U^{dagger }(t;t_{0})} .

The evolution of an open quantum system can be described by quantum operations (in an operator sum formalism) and quantum instruments, and generally does not have to be unitary.

Furthermore, to the postulates of quantum mechanics one should also add basic statements on the properties of spin and Pauli's exclusion principle, see below.

In addition to their other properties, all particles possess a quantity called spin, an intrinsic angular momentum. Despite the name, particles do not literally spin around an axis, and quantum mechanical spin has no correspondence in classical physics. In the position representation, a spinless wavefunction has position r and time t as continuous variables, = (r, t). For spin wavefunctions the spin is an additional discrete variable: = (r, t, ), where takes the values;

That is, the state of a single particle with spin S is represented by a (2S + 1)-component spinor of complex-valued wave functions.

Two classes of particles with very different behaviour are bosons which have integer spin (S = 0, 1, 2, ...), and fermions possessing half-integer spin (S = 12, 32, 52, ...).

The property of spin relates to another basic property concerning systems of N identical particles: Pauli's exclusion principle, which is a consequence of the following permutation behaviour of an N-particle wave function; again in the position representation one must postulate that for the transposition of any two of the N particles one always should have

( , r i , i , , r j , j , ) = ( 1 ) 2 S ( , r j , j , , r i , i , ) {displaystyle psi (dots ,,mathbf {r} _{i},sigma _{i},,dots ,,mathbf {r} _{j},sigma _{j},,dots )=(-1)^{2S}cdot psi (dots ,,mathbf {r} _{j},sigma _{j},,dots ,mathbf {r} _{i},sigma _{i},,dots )}

i.e., on transposition of the arguments of any two particles the wavefunction should reproduce, apart from a prefactor (1)2S which is +1 for bosons, but (1) for fermions.Electrons are fermions with S = 1/2; quanta of light are bosons with S = 1. In nonrelativistic quantum mechanics all particles are either bosons or fermions; in relativistic quantum theories also "supersymmetric" theories exist, where a particle is a linear combination of a bosonic and a fermionic part. Only in dimension d = 2 can one construct entities where (1)2S is replaced by an arbitrary complex number with magnitude 1, called anyons.

Although spin and the Pauli principle can only be derived from relativistic generalizations of quantum mechanics, the properties mentioned in the last two paragraphs belong to the basic postulates already in the non-relativistic limit. Especially, many important properties in natural science, e.g. the periodic system of chemistry, are consequences of the two properties.

The time evolution of the state is given by a differentiable function from the real numbers R, representing instants of time, to the Hilbert space of system states. This map is characterized by a differential equation as follows:If |(t) denotes the state of the system at any one time t, the following Schrdinger equation holds:

i d d t | ( t ) = H | ( t ) {displaystyle ihbar {frac {d}{dt}}left|psi (t)rightrangle =Hleft|psi (t)rightrangle }

where H is a densely defined self-adjoint operator, called the system Hamiltonian, i is the imaginary unit and is the reduced Planck constant. As an observable, H corresponds to the total energy of the system.

Alternatively, by Stone's theorem one can state that there is a strongly continuous one-parameter unitary map U(t): H H such that

(This symbol permutes a product of noncommuting operators of the form

d d t A ( t ) = i [ H , A ( t ) ] + A ( t ) t , {displaystyle {frac {d}{dt}}A(t)={frac {i}{hbar }}[H,A(t)]+{frac {partial A(t)}{partial t}},}

i d d t | ( t ) = H i n t ( t ) | ( t ) {displaystyle ihbar {frac {d}{dt}}left|psi (t)rightrangle ={H}_{rm {int}}(t)left|psi (t)rightrangle }

i d d t A ( t ) = [ A ( t ) , H 0 ] . {displaystyle ihbar {frac {d}{dt}}A(t)=[A(t),H_{0}].}

The interaction picture does not always exist, though. In interacting quantum field theories, Haag's theorem states that the interaction picture does not exist. This is because the Hamiltonian cannot be split into a free and an interacting part within a superselection sector. Moreover, even if in the Schrdinger picture the Hamiltonian does not depend on time, e.g. H = H0 + V, in the interaction picture it does, at least, if V does not commute with H0, since

So the above-mentioned Dyson-series has to be used anyhow.

The Heisenberg picture is the closest to classical Hamiltonian mechanics (for example, the commutators appearing in the above equations directly translate into the classical Poisson brackets); but this is already rather "high-browed", and the Schrdinger picture is considered easiest to visualize and understand by most people, to judge from pedagogical accounts of quantum mechanics. The Dirac picture is the one used in perturbation theory, and is specially associated to quantum field theory and many-body physics.

Summary:

The original form of the Schrdinger equation depends on choosing a particular representation of Heisenberg's canonical commutation relations. The Stonevon Neumann theorem dictates that all irreducible representations of the finite-dimensional Heisenberg commutation relations are unitarily equivalent. A systematic understanding of its consequences has led to the phase space formulation of quantum mechanics, which works in full phase space instead of Hilbert space, so then with a more intuitive link to the classical limit thereof. This picture also simplifies considerationsof quantization, the deformation extension from classical to quantum mechanics.

The quantum harmonic oscillator is an exactly solvable system where the different representations are easily compared. There, apart from the Heisenberg, or Schrdinger (position or momentum), or phase-space representations, one also encounters the Fock (number) representation and the SegalBargmann (Fock-space or coherent state) representation (named after Irving Segal and Valentine Bargmann). All four are unitarily equivalent.

The framework presented so far singles out time as the parameter that everything depends on. It is possible to formulate mechanics in such a way that time becomes itself an observable associated with a self-adjoint operator. At the classical level, it is possible to arbitrarily parameterize the trajectories of particles in terms of an unphysical parameter s, and in that case the time t becomes an additional generalized coordinate of the physical system. At the quantum level, translations in s would be generated by a "Hamiltonian" H E, where E is the energy operator and H is the "ordinary" Hamiltonian. However, since s is an unphysical parameter, physical states must be left invariant by "s-evolution", and so the physical state space is the kernel of H E (this requires the use of a rigged Hilbert space and a renormalization of the norm).

This is related to the quantization of constrained systems and quantization of gauge theories. Itis also possible to formulate a quantum theory of "events" where time becomes an observable (see D. Edwards).

The picture given in the preceding paragraphs is sufficient for description of a completely isolated system. However, it fails to account for one of the main differences between quantum mechanics and classical mechanics, that is, the effects of measurement.[6] The von Neumann description of quantum measurement of an observable A, when the system is prepared in a pure state is the following (note, however, that von Neumann's description dates back to the 1930s and is based on experiments as performed during that time more specifically the ComptonSimon experiment; it is not applicable to most present-day measurements within the quantum domain):

For example, suppose the state space is the n-dimensional complex Hilbert space Cn and A is a Hermitian matrix with eigenvalues i, with corresponding eigenvectors i. The projection-valued measure associated with A, EA, is then

where B is a Borel set containing only the single eigenvalue i. If the system is prepared in state

Then the probability of a measurement returning the value i can be calculated by integrating the spectral measure

over Bi. This gives trivially

The characteristic property of the von Neumann measurement scheme is that repeating the same measurement will give the same results. This is also called the projection postulate.

A more general formulation replaces the projection-valued measure with a positive-operator valued measure (POVM). To illustrate, take again the finite-dimensional case. Here we would replace the rank-1 projections

Since the Fi Fi* operators need not be mutually orthogonal projections, the projection postulate of von Neumann no longer holds.

The same formulation applies to general mixed states.

In von Neumann's approach, the state transformation due to measurement is distinct from that due to time evolution in several ways. For example, time evolution is deterministic and unitary whereas measurement is non-deterministic and non-unitary. However, since both types of state transformation take one quantum state to another, this difference was viewed by many as unsatisfactory. The POVM formalism views measurement as one among many other quantum operations, which are described by completely positive maps which do not increase the trace.

In any case it seems that the above-mentioned problems can only be resolved if the time evolution included not only the quantum system, but also, and essentially, the classical measurement apparatus (see above).

An alternative interpretation of measurement is Everett's relative state interpretation, which was later dubbed the "many-worlds interpretation" of quantum physics.

Part of the folklore of the subject concerns the mathematical physics textbook Methods of Mathematical Physics put together by Richard Courant from David Hilbert's Gttingen University courses. The story is told (by mathematicians) that physicists had dismissed the material as not interesting in the current research areas, until the advent of Schrdinger's equation. At that point it was realised that the mathematics of the new quantum mechanics was already laid out in it. It is also said that Heisenberg had consulted Hilbert about his matrix mechanics, and Hilbert observed that his own experience with infinite-dimensional matrices had derived from differential equations, advice which Heisenberg ignored, missing the opportunity to unify the theory as Weyl and Dirac did a few years later. Whatever the basis of the anecdotes, the mathematics of the theory was conventional at the time, whereas the physics was radically new.

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How the Universe really makes something from nothing – Big Think

Whoever said, you cant get something from nothing must never have learned quantum physics. As long as you have empty space the ultimate in physical nothingness simply manipulating it in the right way will inevitably cause something to emerge. Collide two particles in the abyss of empty space, and sometimes additional particle-antiparticle pairs emerge. Take a meson and try to rip the quark away from the antiquark, and a new set of particle-antiparticle pairs will get pulled out of the empty space between them. And in theory, a strong enough electromagnetic field can rip particles and antiparticles out of the vacuum itself, even without any initial particles or antiparticles at all.

Previously, it was thought that the highest particle energies of all would be needed to produce these effects: the kind only obtainable at high-energy particle physics experiments or in extreme astrophysical environments. But in early 2022, strong enough electric fields were created in a simple laboratory setup leveraging the unique properties of graphene, enabling the spontaneous creation of particle-antiparticle pairs from nothing at all. The prediction that this should be possible is 70 year old: dating back to one of the founders of quantum field theory: Julian Schwinger. The Schwinger effect is now verified, and teaches us how the Universe truly makes something from nothing.

This chart of the particles and interactions details how the particles of the Standard Model interact according to the three fundamental forces that Quantum Field Theory describes. When gravity is added into the mix, we obtain the observable Universe that we see, with the laws, parameters, and constants that we know of governing it. Mysteries, such as dark matter and dark energy, still remain.

In the Universe we inhabit, its truly impossible to create nothing in any sort of satisfactory way. Everything that exists, down at a fundamental level, can be decomposed into individual entities quanta that cannot be broken down further. These elementary particles include quarks, electrons, the electrons heavier cousins (muons and taus), neutrinos, as well as all of their antimatter counterparts, plus photons, gluons, and the heavy bosons: the W+, W-, Z0, and the Higgs. If you take all of them away, however, the empty space that remains isnt quite empty in many physical senses.

For one, even in the absence of particles, quantum fields remain. Just as we cannot take the laws of physics away from the Universe, we cannot take the quantum fields that permeate the Universe away from it.

For another, no matter how far away we move any sources of matter, there are two long-range forces whose effects will still remain: electromagnetism and gravitation. While we can make clever setups that ensure that the electromagnetic field strength in a region is zero, we cannot do that for gravitation; space cannot be entirely emptied in any real sense in this regard.

Instead of an empty, blank, three-dimensional grid, putting a mass down causes what would have been straight lines to instead become curved by a specific amount. No matter how far away you get from a point mass, the curvature of space never reaches zero, but always remains, even at infinite range.

But even for the electromagnetic force even if you completely zero out the electric and magnetic fields within a region of space theres an experiment you can perform to demonstrate that empty space isnt truly empty. Even if you create a perfect vacuum, devoid of all particles and antiparticles of all types, where the electric and magnetic fields are zero, theres clearly something thats present in this region of what a physicist might call, from a physical perspective, maximum nothingness.

Travel the Universe with astrophysicist Ethan Siegel. Subscribers will get the newsletter every Saturday. All aboard!

All you need to do is place a set of parallel conducting plates in this region of space. Whereas you might expect that the only force theyd experience between them would be gravity, set by their mutual gravitational attraction, what actually winds up happening is that the plates attract by a much greater amount than gravity predicts.

This physical phenomenon is known as the Casimir effect, and was demonstrated to be true by Steve Lamoreaux in 1996: 48 years after it was calculated and proposed by Hendrik Casimir.

The Casimir effect, illustrated here for two parallel conducting plates, excludes certain electromagnetic modes from the interior of the conducting plates while permitting them outside of the plates. As a result, the plates attract, as predicted by Casimir in the 1940s and verified experimentally by Lamoreaux in the 1990s.

Similarly, in 1951, Julian Schwinger, already a co-founder of the quantum field theory that describes electrons and the electromagnetic force, gave a complete theoretical description of how matter could be created from nothing: simply by applying a strong electric field. Although others had proposed the idea back in the 1930s, including Fritz Sauter, Werner Heisenberg, and Hans Euler, Schwinger himself did the heavy lifting to quantify precisely under what conditions this effect should emerge, and henceforth its been primarily known as the Schwinger effect.

Normally, we expect there to be quantum fluctuations in empty space: excitations of any and all quantum fields that may be present. The Heisenberg uncertainty principle dictates that certain quantities cannot be known in tandem to arbitrary precision, and that includes things like:

While we normally express the uncertainty principle in terms of the first two entities, alone, the other applications can have consequences that are equally profound.

This diagram illustrates the inherent uncertainty relation between position and momentum. When one is known more accurately, the other is inherently less able to be known accurately. Every time you accurately measure one, you ensure a greater uncertainty in the corresponding complementary quantity.

Recall that, for any force that exists, we can describe that force in terms of a field: where the force experienced by a particle is its charge multiplied by some property of the field. If a particle passes through a region of space where the field is non-zero, it can experience a force, depending on its charge and (sometimes) its motion. The stronger the field, the greater the force, and the stronger the field, the greater the amount of field energy exists in that particular region of space.

Even in purely empty space, and even in the absence of external fields, there will still be some non-zero amount of field energy that exists in any such region of space. If there are quantum fields everywhere, then simply by Heisenbergs uncertainty principle, for any duration of time that we choose to measure this region over, there will be an inherently uncertain amount of energy present within that region during that time period.

The shorter the time period were looking at, the greater the uncertainty in the amount of energy in that region. Applying this to all allowable quantum states, we can begin to visualize the fluctuating fields, as well as fluctuating particle-antiparticle pairs, that pop in-and-out of existence due to all of the Universes quantum forces.

Even in the vacuum of empty space, devoid of masses, charges, curved space, and any external fields, the laws of nature and the quantum fields underlying them still exist. If you calculate the lowest-energy state, you may find that it is not exactly zero; the zero-point (or vacuum) energy of the Universe appears to be positive and finite, although small.

Now, lets imagine turning up the electric field. Turn it up, higher and higher, and what will happen?

Lets take an easier case first, and imagine theres a specific type of particle already present: a meson. A meson is made of one quark and one antiquark, connected to one another through the strong force and the exchange of gluons. Quarks come in six different flavors: up, down, strange, charm, bottom, and top, while the anti-quarks are simply anti-versions of each of them, with opposite electric charges.

The quark-antiquark pairs within a meson sometimes have opposite charges to one another: either + and - (for up, charm, and top) or + and - (for down, strange, and bottom). If you apply an electric field to such a meson, the positively charged end and the negatively charged end will be pulled in opposite directions. If the field strength is great enough, its possible to pull the quark and antiquark away from one another sufficiently so that new particle-antiparticle pairs are ripped out of the empty space between them. When this occurs, we wind up with two mesons instead of one, with the energy required to create the extra mass (via E = mc) coming from the electric field energy that ripped the meson apart in the first place.

When a meson, such as a charm-anticharm particle shown here, has its two constituent particles pulled apart by too great an amount, it becomes energetically favorable to rip a new (light) quark/antiquark pair out of the vacuum and create two mesons where there was one before. A strong enough electric field, for long-enough lived mesons, can cause this to occur, with the needed energy for creating more massive particles coming from the underlying electric field.

Now, with all of that as background in our minds, lets imagine weve got a very, very strong electric field: stronger than anything we could ever hope to make on Earth. Something so strong that it would be like taking a full Coulomb of charge around ~1019 electrons and protons and condensing each of them into a tiny ball, one purely of positive charge and one purely of negative charge, and separating them by only a meter. The quantum vacuum, in this region of space, is going to be extremely strongly polarized.

Strong polarization means a strong separation between positive and negative charges. If your electric field in a region of space is strong enough, then when you create a virtual particle-antiparticle pair of the lightest charged particle of all (electrons and positrons), you have a finite probability of those pairs being separated by large enough amounts due to the force from the field that they can no longer reannihilate one another. Instead, they become real particles, stealing energy from the underlying electric field in order to keep energy conserved.

As a result, new particle-antiparticle pairs come to exist, and the energy required to make them, from E = mc, reduces the exterior electric field strength by the appropriate amount.

As illustrated here, particle-antiparticle pairs normally pop out of the quantum vacuum as a consequences of Heisenberg uncertainty. In the presence of a strong enough electric field, however, these pairs can be ripped apart in opposite directions, causing them to be unable to reannihilate and forcing them to become real: at the expense of energy from the underlying electric field.

Thats what the Schwinger effect is, and unsurprisingly, its never been observed in a laboratory setting. In fact, the only places where it was theorized to occur was in the highest-energy astrophysical regions to exist in the Universe: in the environments surrounding (or even interior to) black holes and neutron stars. But at the great cosmic distances separating us from even the nearest black holes and neutron stars, even this remains conjecture. The strongest electric fields weve created on Earth are at laser facilities, and even with the strongest, most intense lasers at the shortest pulse times, we still arent even close.

Normally, whenever you have a conducting material, its only the valence electrons that are free to move, contributing to conduction. If you could achieve large enough electric fields, however, you could get all of the electrons to join the flow. In January of 2022, researchers at the University of Manchester were able to leverage an intricate and clever setup involving graphene an incredibly strong material that consists of carbon atoms bound together in geometrically optimal states to achieve this property with relatively small, experimentally accessible magnetic field. In doing so, they also witnesses the Schwinger effect in action: producing the analogue of electron-positron pairs in this quantum system.

Graphene has many fascinating properties, but one of them is a unique electronic band structure. There are conduction bands and valence bands, and they can overlap with zero band gap, enabling both holes and electrons to emerge and flow.

Graphene is an odd material in a lot of ways, and one of those ways is that sheets of it behave effectively as a two-dimensional structure. By reducing the number of (effective) dimensions, many degrees of freedom present in three-dimensional materials are taken away, leaving far fewer options for the quantum particles inside, as well as reducing the set of quantum states available for them to occupy.

Leveraging a graphene-based structure known as a superlattice where multiple layers of materials create periodic structures the authors of this study applied an electric field and induced the very behavior described above: where electrons from not just the highest partially-occupied energy state flow as part of the materials conduction, but where electrons from lower, completely filled bands join the flow as well.

Once this occurs, a lot of exotic behaviors arose in this material, but one was seen for the first time ever: the Schwinger effect. Instead of producing electrons and positrons, it produced electrons and the condensed-matter analogue of positrons: holes, where a missing electron in a lattice flows in the opposite directions to the electron flow. The only way to explain the observed currents were with this additional process of spontaneous production of electrons and holes, and the details of the process agreed with Schwingers predictions from all the way back in 1951.

Atomic and molecular configurations come in a near-infinite number of possible combinations, but the specific combinations found in any material determine its properties. Graphene, which is an individual, single-atom sheet of the material shown here, is the hardest material known to humanity, and in pairs-of-sheets it can create a type of material known as a superlattice, with many intricate and counterintuitive properties.

There are many ways of studying the Universe, and quantum analogue systems where the same mathematics that describes an otherwise inaccessible physical regime applies to a system that can be created and studied in a laboratory are some of the most powerful probes we have of exotic physics. Its very difficult to foresee how the Schwinger effect could be tested in its pure form, but thanks to the extreme properties of graphene, including its ability to withstand spectacularly large electric fields and currents, it arose for the very first time in any form: in this particular quantum system. As coauthor Dr. Roshan Krishna Kumar put it:

When we first saw the spectacular characteristics of our superlattice devices, we thought wow it could be some sort of new superconductivity. Although the response closely resembles those routinely observed in superconductors, we soon found that the puzzling behavior was not superconductivity but rather something in the domain of astrophysics and particle physics. It is curious to see such parallels between distant disciplines.

With electrons and positrons (or holes) being created out of literally nothing, just ripped out of the quantum vacuum by electric fields themselves, its yet another way that the Universe demonstrates the seemingly impossible: we really can make something from absolutely nothing!

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Ireland is gearing up for the next generation of quantum technologies – SiliconRepublic.com

UCDs Dr Steve Campbell reflects on the past, present and future of Irelands role in the advancement of quantum technologies.

Many fundamental theories of physics have resulted in important technological revolutions, such as engines and refrigerators from thermodynamics, or modern electronics from electromagnetism.

Recent decades have seen great strides taken in our ability to prepare and manipulate systems such as individual atoms, electrons, or photons which are so small and isolated that they can only be accurately described using quantum mechanics.

Now, the seemingly exotic rules of the quantum world are providing remarkable new opportunities for technological breakthroughs.

In this endeavour, Ireland has a remarkably intimate and grand history. The Irish physicist John Bell provided the fundamental breakthrough to test the veracity of arguably the most counterintuitive aspect of quantum mechanics its inherent non-local character which now lies at the heart of this technological revolution.

Nonlocality refers to the curious fact that, for quantum systems comprised of two or more constituents that have interacted (imagine, for example, two electrons that collided at some point), the act of measuring one of these electrons affects the state of the other, even if they are separated by vast distances.

Bells nonlocality arises from a very fundamental aspect of quantum mechanics concerning how strong correlations can be. Think of a light switch and the bulb it is connected to. In so-called classical physics the world of Newton and Einstein the switch can only be on or off, never anything in between, and the state of the bulb is correlated with the state of the switch.

Quantum mechanics tells us that before we look at the switch, it can exist in a combination (or superposition, in the quantum lingo) of the possibilities. Essentially, it can simultaneously be both on and off. The resulting correlation with the bulb due to this superposition is what we call entanglement.

Once thought to be a fundamental flaw in quantum theory, quantum superposition and entanglement are now established physical phenomena and are ushering in a new wave of devices which utilise these distinctly quantum mechanical effects as resources. These quantum technologies include the most accurate sensors allowed by the laws of physics, unbreakable communication channels and, most excitingly, entirely new paradigms for computation and information processing.

While there has been steady activity in the area of quantum information in Ireland for more than 25 years, recently there has been a significant surge. Driven largely by grassroots activity, supported through national and European funding, virtually every Irish higher education institution is host to an internationally recognised group at the forefront of quantum science and technology.

This has precipitated several major initiatives, such as the establishment of research centres at University College Dublin (UCD) and Tyndall National Institute at University College Cork, and the recently launched MSc in quantum science and technology at Trinity College Dublin, which saw its first cohort of graduates this summer.

These activities feed into the overarching goal to train the next generation of quantum scientists and engineers and to facilitate key knowledge exchange between major industry players with a presence in Ireland, such as IBM, Microsoft, Dell, Google, Intel, homegrown quantum computing enterprise Equal1, and our universities.

The symbiotic relationships being created across these sectors are allowing our researchers to attack a range of exciting challenges from simulating complex molecular dynamics to developing ultraprecise sensors and beyond.

The Irish quantum community is coming together to meet the grand challenge of developing quantum devices. The Irish Research Council, in conjunction with the Shared Island initiative from the Department of An Taoiseach, recently funded EQUITY: ire Strategy for Quantum Information and Technology.

The first activity under this scheme brought together most of Irelands leading scientists in the field, together with major industry representatives, for a two-day workshop to discuss where Ireland stands currently and where we are poised to make an impact.

Several directions are now driving forward including major projects on quantum computing architectures, quantum sensing, and developing a secure quantum communications network. In an age where the protection of our personal data is more important than ever, this last point is highly relevant beyond the ivory tower of academia.

Most of all, EQUITY placed high importance on ensuring that the impact of quantum technologies reached as broad an audience as possible. One step in achieving this goal is with the upcoming Quantum Festival at UCD, where quantum researchers across the whole Island of Ireland will come together to showcase their work.

This event also includes a public lecture by leading quantum securities expert Dr Eleni Diamanti, CNRS research director at the LIP6 Laboratory of Sorbonne University in Paris. In her lecture, Secure communication in a quantum world, Diamanti will explain how the way in which we transmit information is changing thanks to quantum mechanics, what that means for security, and how quantum technologies are poised to impact so many aspects of our lives.

By Dr Steve Campbell

Dr Steve Campbell is a theoretical physicist at the UCD School of Physics and a member of the UCD Centre for Quantum Engineering, Science, and Technology (C-QuEST).

Dr Eleni Diamanti will speak at the UCD Quantum Festival on 29 September. Register for free here.

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Honoring a UC San Diego Landmark and Its Lasting Impact on Physics – University of California San Diego

Mayer Hall recognized as the birthplace of density functional theory

(L-R): Dean Boggs, Professor Schuller, Professor Emeritus Sham and Executive Vice Chancellor Simmons hold the plaque commemorating Mayer Hall as a historic landmark. Photos by: Daniel Orren / UC San Diego Health.

Is there magic in the walls of Mayer Hall? This is the question Oleg Shpyrko, chair of the Department of Physics at the University of California San Diego, asked the audience gathered in the auditorium for a daylong series of events to celebrate the buildings designation as a historical site by the American Physical Society (APS).

Mayer Hall, after all, was named after famed theoretical physicist Maria Goeppert Mayerthe second woman ever to win the Nobel Prize in physics. It was also the birthplace of metamaterials which, among other things, have been used to create Harry Potter-like invisibility cloaks. In the labs of Mayer Hall, many novel high-temperature superconductors and quantum materials were developed. It was also in Mayer Hall where Walter Kohn and Lu Jeu Sham created the Kohn-Sham equation as part of their work in establishing density functional theory, or DFT.

Shpyrko concluded that, no, there wasnt magic inside the walls of Mayer Hall, but there was magic in the people who worked there.

And there was magic in the pivotal Kohn-Sham equation. Its subsequent impact on everything from new materials design to drug discovery led APS to designate Mayer Hall a historical site, stating that DFT is the most used technique for calculating the properties of nuclei, molecules, polymers, macromolecules, surfaces and bulk materials in the chemical, biological and physical sciences.

In the early part of the 20th century, the development of quantum mechanics allowed physicists to learn about the properties and behavior of atoms. Traditionally, the Schrdinger equation was used to determine the probabilistic location and behavior of a particle, including the complexity associated with quantum superposition, which is the basis of the famous Schrdingers cat paradox.

As a result, this equation requires a significant amount of computational effort for each individual electron as well as interactions with every other electron and nuclei. Even a single water molecule contains 10 electrons. Thus, determining the electron behavior of larger molecules quickly becomes prohibitive, akin to controlling the behavior of hundreds of quantum-mechanical Schrdingers kittens who are actively interacting with each other while occupying many locations at once.

From 1964-1966, Kohn and Sham laid the foundation of a computation method based on a single-particle approach, which became known as the Kohn-Sham equation and formed the basis of density functional theory.

DFT simplified the previous process by using the density of all the electrons in the system to determine electron behavior. Researchers no longer needed to focus on each individual electron, but used their collective density as the single variable to solve for, transforming the way quantum mechanics research was performed.

DFT is known as an ab initio, or first principle method, because it can predict material properties for unknown systems without any experimental input. So while it does not precisely solve the Schrdinger equation, it does offer a close approximation at a fraction of the computational effort.

Understanding the electronic properties of complex systems is essential to the design and engineering of new materials and drugs. DFT has been used to study and develop the properties of important materials such as novel semiconductors, new catalysts, neuromorphic materials and complex molecules.

For instance, drug discovery uses DFT as a fast and efficient method to limit the number of drugs that must be experimentally tested for their efficacy in the treatment of many diseases. Thanks to DFT, the time and cost of drug development have been considerably reduced.

The UC San Diego School of Physical Sciences and the physics department worked together to create an engaging, informative day of events to celebrate Mayer Halls designation. Although APS officially named Mayer Hall a historic site in 2021, the celebration was postponed until now due to the pandemic.

Distinguished Professor of Physics Ivan Schuller and Shpyrko welcomed attendees before opening the day with a series of lectures on the impacts of DFT. Researchers and experts from around the world provided insight into the ways DFT continues to shape science, engineering and medicine. The talks touched on everything from materials physics and molecular dynamics to drug discovery and supercomputing.

Dean Boggs spoke about the spirit of discovery that exists in the School of Physical Sciences.

We were thrilled to welcome everyone in-person for this event, stated Dean of the School of Physical Sciences Steven E. Boggs. More than just background on DFT itself, these talks highlighted the spirit of discovery that is still present on our campus. The School of Physical Sciences has lived at the heart of that spirit since the universitys founding.

After the lectures and a panel discussion, the university held a dedication ceremony and plaque unveiling. From APS, President Jon Bagger and former President Jim Gates commented on how meaningful the designation was and the continuing importance of DFT.

UC San Diegos Executive Vice Chancellor Elizabeth H. Simmons noted that the groundbreaking work of Kohn, Sham and colleague Pierre Hohenberg was only one example of the extraordinary talent found in the School of Physical Sciences.

The efforts of faculty like Kohn, Sham, Mayer, Roger Tsien, Sally Ride, Harold Urey and others are testament to our universitys remarkable history as a community of visionaries who push boundaries and break barriers to change the world, she said. Their transformative impacts across academic disciplines and in the lives of student and faculty colleagues will continue to reverberate into the future.

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What is the standard model? – Space.com

The Standard Model of physics is the theory of particles, fields and the fundamental forces that govern them.

It tells us about how families of elementary particles group together to form larger composite particles, and how one particle can interact with another, and how particles respond to the fundamental forces of nature. It has made successful predictions such as the existence of the Higgs boson, and acts as the cornerstone for theoretical physics.

One way to think about the Standard Model is as a family tree for particles. For example, the Standard Model tells us how the atoms that make up our bodies are made of protons and neutrons, which in turn are made of elementary particles called quarks.

Related: What are bosons?

Keith Cooper is a freelance science journalist and editor in the United Kingdom, and has a degree in physics and astrophysics from the University of Manchester. He's the author of "The Contact Paradox: Challenging Our Assumptions in the Search for Extraterrestrial Intelligence" (Bloomsbury Sigma, 2020) and has written articles on astronomy, space, physics and astrobiology for a multitude of magazines and websites.

The Standard Model is considered by physicists, such as Glenn Starkman at Case Western Reserve University, as one of the most successful scientific theories (opens in new tab) of all time, but on the flip-side, scientists have also recognized that it is incomplete, in the same way that Isaac Newton's theory of universal gravitation derived from his laws of motion, while remarkably successful, was not the whole picture and required Albert Einstein's General Theory of Relativity to fill in the missing gaps.

The Standard Model was drawn together in the 1960s and early 1970s from the work of a cadre of pioneering scientists, but in truth its origins extend back almost 100 years earlier. By the 1880s, it was becoming apparent that there were positively and negatively charged particles produced when gasses are ionized, and that these particles must be smaller than atoms, which were the smallest known structures at the time. The first subatomic particle to be identified, in cathode rays (opens in new tab), was the negative electron in 1897 by the British physicist and subsequent Nobel Prize winner, J. J. Thomson (opens in new tab).

Then, in 1911, Hans Geiger and Ernest Madsen, under the supervision of the Nobel Laureate Ernest Rutherford (opens in new tab) at the University of Manchester, performed their famous 'gold foil' experiment, in which alpha particles (helium nuclei) were fired at a thin gold foil. Some of the alpha particles passed right through the atoms in the foil, while others were scattered left and right and a small fraction bounced right back.

Rutherford interpreted this as meaning that atoms contained a lot of empty space that the alpha particles were passing through, but that their positive charge was concentrated in a nucleus at their center, and on the occasions an alpha particle hit this nucleus dead on, it was scattered. Further experimentation by Rutherford in 191920 found that an alpha particle fired into air could knock a positively charged particle out of a nitrogen atom in the air, turning it into carbon in the process. That particle was the proton (opens in new tab), which gives the atomic nucleus its positive charge. The proton's neutrally charged partner, the neutron, was identified in 1932 by James Chadwick (opens in new tab) at Cambridge, who also won the Nobel Prize.

So, the picture of particle physics in the early 1930s seemed relatively straightforward atoms were made of two kinds of 'nucleons', in the guise of protons and neutrons, and electrons orbited them.

But things were already quickly starting to become more complicated. The existence of the photon was already known, so technically that was a fourth particle. In 1932 the American physicist Carl Anderson discovered the positron (opens in new tab), which is the antimatter equivalent of an electron. The muon was identified in 1936 by Anderson and Seth Neddermeyer (opens in new tab), and then the pion was discovered in 1947 (opens in new tab) by Cecil Powell. By the 1960s, with the advent of fledgling particle accelerators, hundreds of particles were being discovered, and the scientific picture was becoming very complicated indeed. Scientists needed a way of organizing and streamlining it all, and their answer to this was to create the Standard Model, which is the crowning glory of the cumulative work of the physics community of that era.

According to the Standard Model, there are three families of elementary particles. When we say 'elementary', scientists mean particles that cannot be broken down into even smaller particles. These are the smallest particles that together make up every other particle.

The three families are leptons, quarks and bosons. Leptons and quarks are known as Fermions because they have a half-integer spin. Bosons, on the other hand, have a whole-integer spin. What does this mean?

Spin, in the context of quantum physics, refers to spin angular momentum. This is different to orbital angular momentum, which describes Earth's spin around the sun, Earth's spin around its rotational axis, and even the spin of a spinning top. On the other hand, spin angular momentum is a quantum property intrinsic to each particle, even if that particle is stationary. Half-integer spin particles have spin values that are half-integers, so 1/2, 3/2, etc. The bosons have whole integer spin values, eg 1, 2, 3 etc.

Leptons include electrons, muons, tau particles and their associated neutrinos. Quarks are tiny particles that, when joined together, form composite particles such as protons and neutrons. Particles that are made of quarks are called hadrons (hence the Large Hadron Collider), with composite particles formed of odd numbers of quarks, usually three, being called baryons, and those made of two quarks called mesons. Bosons are force carriers they transfer the electromagnetic force (photons), the weak force (Z and W bosons), the strong nuclear force (gluons), and the Higgs force (Higgs boson).

Each 'family' consists of six known particles (except the bosons, which we'll explain later) that come in pairs called 'generations.' The most stable and least massive particles of the family form the first generation. Because of their stability, meaning that they don't decay quickly, all stable matter in the universe is made from first generation elementary particles. For example, protons are formed of two 'up' quarks and one 'down' quark, which are the two most stable quarks.

There are 17 known elementary particles 6 leptons, 6 quarks, but only 5 bosons. There's one force carrier missing the graviton. The Standard Model predicts that gravity should have a force-carrying boson, in the guise of the graviton. Gravitational waves are, in theory, formed from gravitons. However, detecting the graviton will be no mean feat. Gravity is the weakest of the four fundamental forces. You might not think so, after all it keeps your feet on the ground, but when you consider that it takes the entire mass of the planet to generate enough gravity to keep your feet on the ground, you might get a sense that gravity isn't as strong as, say, magnetism can be, which can pick up a paperclip against the gravitational pull of Earth. Consequently, individual gravitons do not interact with matter that easily they are said to have a low cross section of interaction (opens in new tab). Gravitons may have to remain hypothetical for the time being.

As wonderful as the Standard Model is, it describes only a small fraction of the universe. The European Space Agency's Planck spacecraft (opens in new tab) has confirmed that everything that we can see in the cosmos planets, stars and galaxies accounts for just 4.9% of all the mass and energy in the universe (opens in new tab). The rest is dark matter (26.8%) and dark energy (68.3%), the nature of which are completely unknown and which are definitely not predicted by the Standard Model.

That's not all that's unknown. One big question in physics is whether the elementary particles really are elementary, or whether there is hidden physics underlying them. For example, String Theory posits that elementary particles are made from tiny vibrating strings. Then there's the question of antimatter equal amounts of matter and antimatter (opens in new tab) should have been created in the Big Bang, but this would mean we should not be here at all, because all the matter and antimatter should have annihilated each other. Today we see that the universe contains mostly matter, with very little antimatter. Why is there this asymmetry?

Then there's the question of why particles have the masses that they do, and why the forces have the strengths that they have, and why particles are broken down into the three families of leptons, quarks and bosons. That they just are isn't a good enough answer for physicists they want to understand why, and the Standard Model does not tell them.

In an effort to bring the Standard Model up to speed to face these challenges, scientists have introduced the idea of supersymmetry. If true, then supersymmetry would mean that every particle in the Standard Model has a supersymmetric partner with a much greater mass, and a spin that is different by one-half to their Standard Model partners. This would unify fermions with bosons, since the integer-spin fermions would have half-integer-spin super-partners, and the half-integer-spin bosons would have integer-spin super-partners. The least massive and most stable supersymmetry particles would also have no electric charge and interact only very weakly with normal matter, which sounds very much like the properties of dark matter.

Meanwhile, at the very highest energies analogous to those that existed in the first moment after the Big Bang, supersymmetry predicts that the weak force, the strong force and the electromagnetic force would all have the same strength, and essentially be the same force. Scientists call such a concept a 'Grand Unified Theory'.

According to the CERN website, supersymmetry could also help explain the surprisingly small mass of the Higgs boson (opens in new tab), which is 125 GeV (125 billion electronvolts). While this is relatively high, it is not as high as expected. The existence of extremely massive supersymmetric partners would balance things out. And they must be extremely massive, because the Large Hadron Collider (LHC), nor any other particle accelerator before it, has found any evidence for the existence of supersymmetric partners so far, leading some scientists to doubt that supersymmetry is real. If supersymmetric particles exist, then they must be more massive than the LHC can detect; for example, the mass of the gluino (opens in new tab), which is the supersymmetric partner of the gluon that mediates the strong force binding quarks together inside protons and neutrons, has been ruled out up to 2 trillion eV.

So supersymmetry is in danger and physicists are now scrambling to find a replacement theory that can advance upon the Standard Model and explain the Higgs boson's mass, as well as dark matter, Grand Unified Theories and everything else. There are no strong candidates to replace supersymmetry yet, and supersymmetry may still win out, but for now physicists will have to make do with the imperfect world of the Standard Model.

CERN's website (opens in new tab) features more information about the Standard Model.

The U.S. Department of Energy explains the Standard Model (opens in new tab) on their own site.

The Institute of Physics also describes the Standard Model (opens in new tab) on their website.

Follow Keith Cooper on Twitter @21stCenturySETI (opens in new tab). Follow us on Twitter @Spacedotcom (opens in new tab) and on Facebook (opens in new tab).

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