5 thoughts on “Theoretical physics: The origins of space and time

  1. shinichi Post author

    Theoretical physics: The origins of space and time

    Many researchers believe that physics will not be complete until it can explain not just the behaviour of space and time, but where these entities come from.

    Zeeya Merali, Nature, 28 August 2013

    “Imagine waking up one day and realizing that you actually live inside a computer game,” says Mark Van Raamsdonk, describing what sounds like a pitch for a science-fiction film. But for Van Raamsdonk, a physicist at the University of British Columbia in Vancouver, Canada, this scenario is a way to think about reality. If it is true, he says, “everything around us — the whole three-dimensional physical world — is an illusion born from information encoded elsewhere, on a two-dimensional chip”. That would make our Universe, with its three spatial dimensions, a kind of hologram, projected from a substrate that exists only in lower dimensions.

    This ‘holographic principle’ is strange even by the usual standards of theoretical physics. But Van Raamsdonk is one of a small band of researchers who think that the usual ideas are not yet strange enough. If nothing else, they say, neither of the two great pillars of modern physics — general relativity, which describes gravity as a curvature of space and time, and quantum mechanics, which governs the atomic realm — gives any account for the existence of space and time. Neither does string theory, which describes elementary threads of energy.

    Van Raamsdonk and his colleagues are convinced that physics will not be complete until it can explain how space and time emerge from something more fundamental — a project that will require concepts at least as audacious as holography. They argue that such a radical reconceptualization of reality is the only way to explain what happens when the infinitely dense ‘singularity’ at the core of a black hole distorts the fabric of space-time beyond all recognition, or how researchers can unify atomic-level quantum theory and planet-level general relativity — a project that has resisted theorists’ efforts for generations.

    “All our experiences tell us we shouldn’t have two dramatically different conceptions of reality — there must be one huge overarching theory,” says Abhay Ashtekar, a physicist at Pennsylvania State University in University Park.

    Finding that one huge theory is a daunting challenge. Here, Nature explores some promising lines of attack — as well as some of the emerging ideas about how to test these concepts.

    NIK SPENCER/NATURE; Panel 4 adapted from Budd, T. & Loll, R. Phys. Rev. D 88, 024015 (2013)

    One of the most obvious questions to ask is whether this endeavour is a fool’s errand. Where is the evidence that there actually is anything more fundamental than space and time?

    A provocative hint comes from a series of startling discoveries made in the early 1970s, when it became clear that quantum mechanics and gravity were intimately intertwined with thermodynamics, the science of heat.

    In 1974, most famously, Stephen Hawking of the University of Cambridge, UK, showed that quantum effects in the space around a black hole will cause it to spew out radiation as if it was hot. Other physicists quickly determined that this phenomenon was quite general. Even in completely empty space, they found, an astronaut undergoing acceleration would perceive that he or she was surrounded by a heat bath. The effect would be too small to be perceptible for any acceleration achievable by rockets, but it seemed to be fundamental. If quantum theory and general relativity are correct — and both have been abundantly corroborated by experiment — then the existence of Hawking radiation seemed inescapable.

    A second key discovery was closely related. In standard thermodynamics, an object can radiate heat only by decreasing its entropy, a measure of the number of quantum states inside it. And so it is with black holes: even before Hawking’s 1974 paper, Jacob Bekenstein, now at the Hebrew University of Jerusalem, had shown that black holes possess entropy.

    But there was a difference. In most objects, the entropy is proportional to the number of atoms the object contains, and thus to its volume. But a black hole’s entropy turned out to be proportional to the surface area of its event horizon — the boundary out of which not even light can escape. It was as if that surface somehow encoded information about what was inside, just as a two-dimensional hologram encodes a three-dimensional image.

    In 1995, Ted Jacobson, a physicist at the University of Maryland in College Park, combined these two findings, and postulated that every point in space lies on a tiny ‘black-hole horizon’ that also obeys the entropy–area relationship. From that, he found, the mathematics yielded Einstein’s equations of general relativity — but using only thermodynamic concepts, not the idea of bending space-time1.

    “This seemed to say something deep about the origins of gravity,” says Jacobson. In particular, the laws of thermodynamics are statistical in nature — a macroscopic average over the motions of myriad atoms and molecules — so his result suggested that gravity is also statistical, a macroscopic approximation to the unseen constituents of space and time.

    In 2010, this idea was taken a step further by Erik Verlinde, a string theorist at the University of Amsterdam, who showed2 that the statistical thermodynamics of the space-time constituents — whatever they turned out to be — could automatically generate Newton’s law of gravitational attraction.

    And in separate work, Thanu Padmanabhan, a cosmologist at the Inter-University Centre for Astronomy and Astrophysics in Pune, India, showed3 that Einstein’s equations can be rewritten in a form that makes them identical to the laws of thermodynamics — as can many alternative theories of gravity. Padmanabhan is currently extending the thermodynamic approach in an effort to explain the origin and magnitude of dark energy: a mysterious cosmic force that is accelerating the Universe’s expansion.

    Testing such ideas empirically will be extremely difficult. In the same way that water looks perfectly smooth and fluid until it is observed on the scale of its molecules — a fraction of a nanometre — estimates suggest that space-time will look continuous all the way down to the Planck scale: roughly 10−35 metres, or some 20 orders of magnitude smaller than a proton.

    But it may not be impossible. One often-mentioned way to test whether space-time is made of discrete constituents is to look for delays as high-energy photons travel to Earth from distant cosmic events such as supernovae and γ-ray bursts. In effect, the shortest-wavelength photons would sense the discreteness as a subtle bumpiness in the road they had to travel, which would slow them down ever so slightly.

    Giovanni Amelino-Camelia, a quantum-gravity researcher at the University of Rome, and his colleagues have found4 hints of just such delays in the photons from a γ-ray burst recorded in April. The results are not definitive, says Amelino-Camelia, but the group plans to expand its search to look at the travel times of high-energy neutrinos produced by cosmic events. He says that if theories cannot be tested, “then to me, they are not science. They are just religious beliefs, and they hold no interest for me.”

    Other physicists are looking at laboratory tests. In 2012, for example, researchers from the University of Vienna and Imperial College London proposed5 a tabletop experiment in which a microscopic mirror would be moved around with lasers. They argued that Planck-scale granularities in space-time would produce detectable changes in the light reflected from the mirror (see Naturehttp://doi.org/njf; 2012).

    Loop quantum gravity

    Even if it is correct, the thermodynamic approach says nothing about what the fundamental constituents of space and time might be. If space-time is a fabric, so to speak, then what are its threads?

    One possible answer is quite literal. The theory of loop quantum gravity, which has been under development since the mid-1980s by Ashtekar and others, describes the fabric of space-time as an evolving spider’s web of strands that carry information about the quantized areas and volumes of the regions they pass through6. The individual strands of the web must eventually join their ends to form loops — hence the theory’s name — but have nothing to do with the much better-known strings of string theory. The latter move around in space-time, whereas strands actually are space-time: the information they carry defines the shape of the space-time fabric in their vicinity.

    Because the loops are quantum objects, however, they also define a minimum unit of area in much the same way that ordinary quantum mechanics defines a minimum ground-state energy for an electron in a hydrogen atom. This quantum of area is a patch roughly one Planck scale on a side. Try to insert an extra strand that carries less area, and it will simply disconnect from the rest of the web. It will not be able to link to anything else, and will effectively drop out of space-time.

    Loop quantum gravity

    This simulation shows how space evolves in loop quantum gravity. The colours of the faces of the tetrahedra indicate how much area exists at that given point, at a particular moment of time.

    One welcome consequence of a minimum area is that loop quantum gravity cannot squeeze an infinite amount of curvature onto an infinitesimal point. This means that it cannot produce the kind of singularities that cause Einstein’s equations of general relativity to break down at the instant of the Big Bang and at the centres of black holes.

    In 2006, Ashtekar and his colleagues reported7 a series of simulations that took advantage of that fact, using the loop quantum gravity version of Einstein’s equations to run the clock backwards and visualize what happened before the Big Bang. The reversed cosmos contracted towards the Big Bang, as expected. But as it approached the fundamental size limit dictated by loop quantum gravity, a repulsive force kicked in and kept the singularity open, turning it into a tunnel to a cosmos that preceded our own.

    This year, physicists Rodolfo Gambini at the Uruguayan University of the Republic in Montevideo and Jorge Pullin at Louisiana State University in Baton Rouge reported8 a similar simulation for a black hole. They found that an observer travelling deep into the heart of a black hole would encounter not a singularity, but a thin space-time tunnel leading to another part of space. “Getting rid of the singularity problem is a significant achievement,” says Ashtekar, who is working with other researchers to identify signatures that would have been left by a bounce, rather than a bang, on the cosmic microwave background — the radiation left over from the Universe’s massive expansion in its infant moments.

    Loop quantum gravity is not a complete unified theory, because it does not include any other forces. Furthermore, physicists have yet to show how ordinary space-time would emerge from such a web of information. But Daniele Oriti, a physicist at the Max Planck Institute for Gravitational Physics in Golm, Germany, is hoping to find inspiration in the work of condensed-matter physicists, who have produced exotic phases of matter that undergo transitions described by quantum field theory. Oriti and his colleagues are searching for formulae to describe how the Universe might similarly change phase, transitioning from a set of discrete loops to a smooth and continuous space-time. “It is early days and our job is hard because we are fishes swimming in the fluid at the same time as trying to understand it,” says Oriti.

    Causal sets

    Such frustrations have led some investigators to pursue a minimalist programme known as causal set theory. Pioneered by Rafael Sorkin, a physicist at the Perimeter Institute in Waterloo, Canada, the theory postulates that the building blocks of space-time are simple mathematical points that are connected by links, with each link pointing from past to future. Such a link is a bare-bones representation of causality, meaning that an earlier point can affect a later one, but not vice versa. The resulting network is like a growing tree that gradually builds up into space-time. “You can think of space emerging from points in a similar way to temperature emerging from atoms,” says Sorkin. “It doesn’t make sense to ask, ‘What’s the temperature of a single atom?’ You need a collection for the concept to have meaning.”

    In the late 1980s, Sorkin used this framework to estimate9 the number of points that the observable Universe should contain, and reasoned that they should give rise to a small intrinsic energy that causes the Universe to accelerate its expansion. A few years later, the discovery of dark energy confirmed his guess. “People often think that quantum gravity cannot make testable predictions, but here’s a case where it did,” says Joe Henson, a quantum-gravity researcher at Imperial College London. “If the value of dark energy had been larger, or zero, causal set theory would have been ruled out.”

    Causal dynamical triangulations

    That hardly constituted proof, however, and causal set theory has offered few other predictions that could be tested. Some physicists have found it much more fruitful to use computer simulations. The idea, which dates back to the early 1990s, is to approximate the unknown fundamental constituents with tiny chunks of ordinary space-time caught up in a roiling sea of quantum fluctuations, and to follow how these chunks spontaneously glue themselves together into larger structures.

    The earliest efforts were disappointing, says Renate Loll, a physicist now at Radboud University in Nijmegen, the Netherlands. The space-time building blocks were simple hyper-pyramids — four-dimensional counterparts to three-dimensional tetrahedrons — and the simulation’s gluing rules allowed them to combine freely. The result was a series of bizarre ‘universes’ that had far too many dimensions (or too few), and that folded back on themselves or broke into pieces. “It was a free-for-all that gave back nothing that resembles what we see around us,” says Loll.

    Causal dynamical triangulation

    This simplified version of causal dynamical triangulation uses just two dimensions: one of space and one of time. The video shows two-dimensional universes generated by pieces of space assembling themselves according to quantum rules. Each colour represent a slice through the universe at particular time after the Big Bang, which is depicted as a tiny black ball.

    But, like Sorkin, Loll and her colleagues found that adding causality changed everything. After all, says Loll, the dimension of time is not quite like the three dimensions of space. “We cannot travel back and forth in time,” she says. So the team changed its simulations to ensure that effects could not come before their cause — and found that the space-time chunks started consistently assembling themselves into smooth four-dimensional universes with properties similar to our own10.

    Intriguingly, the simulations also hint that soon after the Big Bang, the Universe went through an infant phase with only two dimensions — one of space and one of time. This prediction has also been made independently by others attempting to derive equations of quantum gravity, and even some who suggest that the appearance of dark energy is a sign that our Universe is now growing a fourth spatial dimension. Others have shown that a two-dimensional phase in the early Universe would create patterns similar to those already seen in the cosmic microwave background.


    Meanwhile, Van Raamsdonk has proposed a very different idea about the emergence of space-time, based on the holographic principle. Inspired by the hologram-like way that black holes store all their entropy at the surface, this principle was first given an explicit mathematical form by Juan Maldacena, a string theorist at the Institute of Advanced Study in Princeton, New Jersey, who published11 his influential model of a holographic universe in 1998. In that model, the three-dimensional interior of the universe contains strings and black holes governed only by gravity, whereas its two-dimensional boundary contains elementary particles and fields that obey ordinary quantum laws without gravity.

    Hypothetical residents of the three-dimensional space would never see this boundary, because it would be infinitely far away. But that does not affect the mathematics: anything happening in the three-dimensional universe can be described equally well by equations in the two-dimensional boundary, and vice versa.

    In 2010, Van Raamsdonk studied what that means when quantum particles on the boundary are ‘entangled’ — meaning that measurements made on one inevitably affect the other12. He discovered that if every particle entanglement between two separate regions of the boundary is steadily reduced to zero, so that the quantum links between the two disappear, the three-dimensional space responds by gradually dividing itself like a splitting cell, until the last, thin connection between the two halves snaps. Repeating that process will subdivide the three-dimensional space again and again, while the two-dimensional boundary stays connected. So, in effect, Van Raamsdonk concluded, the three-dimensional universe is being held together by quantum entanglement on the boundary — which means that in some sense, quantum entanglement and space-time are the same thing.

    Or, as Maldacena puts it: “This suggests that quantum is the most fundamental, and space-time emerges from it.”

    Nature 500,516–519 (29 August 2013) doi:10.1038/500516a



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  2. shinichi Post author



    ブリティッシュ・コロンビア大学(カナダ・バンクーバー)の物理学者Mark Van Raamsdonkは、「ある朝目覚めて、自分がコンピューターゲームの中で生きていたことを悟ったと想像してみてください」と話し始めた。そしてSF映画のような状況を説明していったが、彼にとって、現実について考える方法論の1つが、このようなシナリオなのだ。もしそれが正しいとしたら、「私たちの周りにある全てのもの、すなわち、三次元の物理的世界の全体が、どこか別の場所にある二次元のチップ上に符号化された情報から生じた幻影であることになります」と彼は言う。それはまさにホログラムのようなもので、二次元平面に記録された情報から、3つの空間次元を持つ私たちの宇宙を完全に再現しているわけだ。

    理論物理学の仮説には奇妙なものが多いが、中でもこの「ホログラフィック原理」の奇抜さは飛び抜けている。普通の仮説ではまだ奇抜さが足りないと考える研究者が少数派ながら存在し、Van Raamsdonkもその1人なのだ。現代物理学を支える2本の巨大な柱は、重力を時空の曲がりとして記述する一般相対性理論と、原子の領域を支配する量子力学である。しかし少数派は、いずれも時間と空間が存在することについて何の説明もしていない、と不満をもらす。エネルギーの基本単位となるひもについて記述するひも理論に対しても同様だ。

    Van Raamsdonkと彼の同僚たちは、「空間と時間がより基本的な存在から生じてくる仕組みを説明できないかぎり、物理学は完全なものとはいえない」と信じている。そのためには、少なくともホログラフィーと同じくらい大胆な概念が必要になる。そして現実という概念を根源から再構築することによってのみ、未解決の問題が解決できると主張する。例えば、ブラックホールの中心にある無限に高密度の「特異点」では、時空の構造が大きく歪んで全てが認識不可能になるが、では、こうした特異点で何が起こるのだろうか? また、理論家たちの数十年にわたる努力にもかかわらず、原子レベルの量子論と惑星レベルの一般相対性理論との統一は成し遂げられていないが、どうすれば両者を統一できるのだろうか?

    「現実という概念について、2つの劇的に異なるものがあってはなりません。全てを支配する1つの巨大な理論がなければならないのです」と、ペンシルベニア州立大学(米国ユニバーシティーパーク)の物理学者Abhay Ashtekarは言う。







    1974年、ケンブリッジ大学(英国)のStephen Hawkingは、ブラックホールの周りの空間の量子効果により、あたかもブラックホールが高温であるかのように、そこから放射が飛び出すことを示した。この有名な発見後すぐに、他の物理学者たちが、この現象が極めて一般的なものであることを明らかにした。例えば、加速中の宇宙船に乗っている人は、完全に空っぽの空間にいるときでさえ、自分が熱浴に囲まれていることを知覚するのだ。ただ、その効果は非常に小さいので、ロケットで実現できる程度の加速では知覚できないだろうが、現象自体は極めて基本的なものと考えられる。量子論と一般相対性理論が正しいなら(実際、どちらも実験により十分によく裏付けられている)、Hawking放射の存在は避けられないようにみえる。

    第2のカギとなる発見は、これと密接に関連したものだ。標準的な熱力学では、天体はエントロピー(その内部にある量子状態の個数の尺度)を減らすことによってのみ熱を放射することができる。ブラックホールについても同じである。現在エルサレム・ヘブライ大学(イスラエル)に所属しているJacob Bekensteinは、Hawkingが1974年の論文を発表するより前に、ブラックホールもエントロピーを持つことを明らかにした。ただ、普通の天体と違っている点もあった。ほとんどの天体のエントロピーは、そこに含まれる原子の個数(ゆえに、その体積)に比例しているのに対して、ブラックホールのエントロピーは、その事象の地平線(光さえ逃げ出すことができない境界線)の表面積に比例していることが分かったのだ。それはあたかも、ブラックホールの表面が、何らかの方法で、内部にあるものに関する情報を符号化しているようにみえた。これは、二次元のホログラムが、三次元の画像を符号化しているのと全く同じことだ。

    1995年には、メリーランド大学カレッジパーク校(米国)の物理学者Ted Jacobsonが、この2つの知見を組み合わせて、空間内の全ての点が、エントロピーと表面積との関係を満たす微小な「ブラックホールの地平線」上にあると仮定した。そしてそこから、時空の曲がりの概念は用いずに、熱力学の概念のみを用いて、数学的にアインシュタインの一般相対性理論の方程式を導き出せることを発見したのだ1


    2010年、この仮説はアムステルダム大学(オランダ)のひも理論研究者Eric Verlindeによって、一歩前進した。彼は、時空の基本構成要素(それがどんなものであるかは問わない)の統計熱力学から、自動的にニュートンの重力法則が導かれることを示したのだ2

    これとは別の研究で、天文学・天体物理学大学間センター(インド・プーナ)の宇宙論学者Thanu Padmanabhanは、他の多くの代替重力理論と同じように、アインシュタインの方程式を書き換えて、熱力学の法則と同じ形にできることを示した3。Padmanabhanは現在、熱力学的アプローチを拡張して、宇宙全体に広がり、その膨張を加速している謎めいた力である「ダークエネルギー」の起源と強さを説明しようとしている。



    ローマ大学(イタリア)の量子重力研究者Giovanni Amelino-Cameliaとその同僚らは、2013年4月に記録されたγ線バーストからの光子にそのような遅れを示唆する証拠を発見した4。その結果は最終結論ではないとAmelino-Cameliaは言うが、研究チームは研究を拡大して、宇宙で起こる事象により生成する高エネルギーニュートリノの飛行時間を調べようと計画している。理論が検証できないとしたら、「私にとって、それは科学ではありません。宗教上の教義と同じですから興味ありませんね」と彼は言う。

    実験室で検証を進めている物理学者もいる。例えば2012年には、ウィーン大学(オーストリア)とインペリアル・カレッジ・ロンドンの研究者が、レーザーを使って極小の鏡を動かす卓上実験を提案した5。彼らは、プランク長での時空の粒状性により、鏡が反射する光に検出可能な変化が生じると主張している(Nature http://doi.org/njf; 2012参照)。







    今年、ウルグアイ共和国大学(モンテビデオ)の物理学者Rodolfo Gambiniとルイジアナ州立大学(バトンルージュ)のJorge Pullinは、ブラックホールについて同様のシミュレーションを行い、その結果を報告した8。彼らは、ブラックホールの中心に向かって落ちてゆく観察者は、特異点ではなく、空間の別の場所につながっている薄い「時空のトンネル」に遭遇することを見いだした。「特異点問題を取り除いたことは重要な業績です」とAshtekarは言う。彼は他の研究者と共同で、ビッグバン(大きな爆発)ならぬビッグバウンス(大きな跳ね返り)が、宇宙マイクロ波背景放射(生まれて間もない宇宙が急激に膨張したときの名残りの放射)に刻み込んだサインを探している。

    ループ量子重力理論には他の力が含まれていないため、完全な統一理論ではない。さらに、物理学者たちはまだそうした情報の蜘蛛の巣から普通の時空が現れてくる仕組みを明らかにしていない。マックス・プランク重力物理学研究所(ドイツ・ゴルム)の物理学者Daniele Oritiは、物性物理学研究からヒントを得たいと考えている。物性物理学者は、場の量子論によって記述される相転移を起こす、奇妙な物質相を作り出してきた。Oritiらは、宇宙がこれと同じように、離散的なループの集合から滑らかで連続的な時空へと相転移する方法を定式化しようとしている。「私たちが宇宙を理解しようとすることは、水の中を泳ぐ魚が水を理解しようとするのと同じです。研究は始まったばかりで、非常に難しいのです」とOritiは言う。


    なかなか成果が出ないいら立ちから、一部の研究者は、因果集合理論として知られるアプローチをとるようになった。これは簡素化を良しとするアプローチだ。ペリメーター研究所(カナダ・ウォータールー)の物理学者Rafael Sorkinが先鞭をつけたこの理論は、時空の基本構成要素は単純な数学的な点であり、これらの点が過去から未来に向かうリンクによって連結されると仮定する。このリンクは、前の点は後の点に影響を及ぼしうるが、その逆はないとする「因果律」の要点を表現している。点どうしをリンクで連結してできるネットワークは、時空の中で徐々に成長する木のようなものである。「原子から温度が創発するように、点から空間が創発すると考えることができます」とSorkinは言う。「原子1個の温度を問うことは無意味です。温度の概念が意味を持つためには、原子がたくさん集まっている必要があるのです」。

    1980年代の末に、Sorkinはこの枠組みを用いて、観測可能な宇宙に存在する点の個数を見積もり、これらの点は宇宙の膨張を加速させるような小さな固有エネルギーを生じるはずだと推測した9。数年後にダークエネルギーが発見されたことは、彼の推測の正しさを裏付けた。インペリアル・カレッジ・ロンドンの量子重力研究者Joe Hensonは、「量子重力理論は検証可能な予測をすることはできないと考える人が多いのですが、これはその反例です」と言う。「ダークエネルギーの値がもっと大きいか、ゼロだったなら、因果集合理論は否定されていたはずです」。



    ラドバウド大学ナイメーヘン校(オランダ)の物理学者Renate Lollによると、初期の試みはがっかりするような結果になったという。時空の基本構成単位は単純な超錐体(三次元の四面体に相当する四次元の形)で、これらを自由に組み合わせてよいという接着規則の下でシミュレーションを行った。その結果できた宇宙は奇妙なものばかりで、次元が多過ぎたり少な過ぎたりし、折りたたまれてしまったり、ばらばらになってしまったりした。「それはまさに何でもありの状況で、私たちが知っている宇宙とは似ても似つかないものでした」と彼女は言う。

    けれどもSorkinと同様、Lollらも、因果律を加えることで全てが変わることを見いだした。結局 、時間の次元は3つの空間次元とはあまり似ていないようだとLollは言う。「私たちは時間の中を前後に移動することはできないからです」。そこでチームはシミュレーションを変えて、原因より先に結果が来ないようにしたところ、時空の塊はしっかりと組み上がり始め、私たちの宇宙に似た性質を持つ、滑らかな四次元宇宙を形成したのだった10



    時空の創発について、Van Raamsdonkは、これらの仮説とは大きく異なるホログラフィック原理を提唱している。ホログラフィック原理は、ブラックホールがホログラムのように表面に全エントロピーを貯蔵していることをヒントにしたもので、プリンストン高等研究所(米国ニュージャージー州)のひも理論研究者Juan Maldacenaによって、最初に明確な数学的形式を与えられた。彼のホログラフィック宇宙モデルは1998年に発表され、多くの影響を及ぼした11。このモデルでは、宇宙の三次元の内部には、重力のみに支配されるひもとブラックホールが含まれているのに対して、その二次元の境界面には、重力なしの普通の量子法則に従う素粒子と場が含まれている。


    2010年にVan Raamsdonkは、境界面上にある量子的粒子が「もつれて」いて、一方の粒子の観測が不可避的に他方の粒子に影響を及ぼすとき、それが何を意味するかを調べた12。彼は、境界面の2つの離れた領域の間にある全ての「粒子もつれ」が徐々に小さくなってゼロになり、両者の間の量子的結びつきが消滅するとき、三次元の空間は、分裂する細胞のように徐々に分割され、ついには、2分割された空間の間にある最後の薄い接続がパチンと消滅することを見いだした。

    このプロセスを繰り返すと、三次元の空間は何度も再分割されるが、二次元の境界面はつながったままである。だから実質的に、三次元の宇宙は境界面上の量子もつれによって保たれているといえる、とVan Raamsdonkは結論付ける。それはある意味、量子もつれと時空が同じものだということになる。


  3. Balance

    In search for balance
    Learn how to?
    Everything is so unbalanced
    or balanced?
    from rich to poor
    from peace to war
    from birth to death
    How much can be called balanced ?
    Goodness shine because evil
    good and evil are balanced?
    without evil or destroy evil
    goodness can transform to nuture I hope!
    Natural in balance to protect planet
    if planet destroyed
    then something new start right?
    politics in balance to benefit nation
    What kind of balance can stop war?
    Too much to comprehend
    People don’t learn their history’ lessons
    Tragedy repeats everywhere
    Mind our own business and Just learn to
    Balance the daily habits that will
    lead a happier and healthier life


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