{"id":963,"date":"2015-08-29T18:52:02","date_gmt":"2015-08-29T17:52:02","guid":{"rendered":"http:\/\/quantum-bits.org\/?p=963"},"modified":"2022-08-12T17:31:02","modified_gmt":"2022-08-12T16:31:02","slug":"on-hidden-realities-part-2","status":"publish","type":"post","link":"https:\/\/www.quantum-bits.org\/?p=963","title":{"rendered":"On hidden realities (part 2)"},"content":{"rendered":"<p>This is the second part of&nbsp;a series of posts on (a few selected) hidden realities : m<span id=\"Level_III:_Many-worlds_interpretation_of_quantum_mechanics\" class=\"mw-headline\">any-worlds interpretation of quantum mechanics, m<\/span>ultiverse linked to the space-time geometries and dynamics, higher dimensional multiverse, holographic multiverse and simulated multiverse.<\/p>\n<p>For the previous posts, please see:<\/p>\n<ul>\n<li>On hidden realities (part 1) &#8211; <a href=\"http:\/\/quantum-bits.org\/?p=896\" target=\"_blank\" rel=\"noopener noreferrer\">Many-worlds interpretation of quantum mechanics<\/a><\/li>\n<\/ul>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-994\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/multiverse.jpg\" alt=\"multiverse\" width=\"768\" height=\"375\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/multiverse.jpg 768w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/multiverse-300x146.jpg 300w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/p>\n<p><strong>Space-time geometry<\/strong><\/p>\n<p>General relativity (see this old post for a <a href=\"http:\/\/quantum-bits.org\/?p=116\" target=\"_blank\" rel=\"noopener noreferrer\">very brief introduction<\/a>) is a geometric theory of gravitation. From what we know, and even if many unanswered questions remain (the most fundamental being how to reconcile general relativity with quantum physics),&nbsp;it is the simplest theory&nbsp;consistent with experimental data.<\/p>\n<p>At the heart of general relativity lies the notion of space-time. It is a&nbsp;mathematical model that combines space and time into an interwoven continuum. Technically speaking, Einstein&#8217;s theory describes space-time as a a (<a href=\"http:\/\/en.wikipedia.org\/wiki\/Pseudo-Riemannian_manifold\" target=\"_blank\" rel=\"noopener noreferrer\">pseudo-riemannian<\/a>) <a href=\"http:\/\/en.wikipedia.org\/wiki\/Manifold\" target=\"_new\" rel=\"noopener noreferrer\">manifold<\/a>.<\/p>\n<p>Einstein&#8217;s field equation links the density and flux of matter-energy (<img decoding=\"async\" class=\"latex\" title=\"T^{\\mu\\nu} \" src=\"http:\/\/s0.wp.com\/latex.php?latex=T%5E%7B%5Cmu%5Cnu%7D+&amp;bg=ffffff&amp;fg=000000&amp;s=0\" alt=\"T^{\\mu\\nu} \">&nbsp;<a href=\"http:\/\/en.wikipedia.org\/wiki\/Stress-energy_tensor\" target=\"_new\" rel=\"noopener noreferrer\">stress-energy tensor<\/a>) and the curvature of space-time:<\/p>\n<p style=\"text-align: left;\"><img decoding=\"async\" class=\"latex aligncenter\" title=\"G_{\\mu\\nu} + \\Lambda g_{\\mu\\nu} = \\frac{8\\pi G}{c^4} T_{\\mu\\nu} \" src=\"http:\/\/s0.wp.com\/latex.php?latex=G_%7B%5Cmu%5Cnu%7D+%2B+%5CLambda+g_%7B%5Cmu%5Cnu%7D+%3D+%5Cfrac%7B8%5Cpi+G%7D%7Bc%5E4%7D+T_%7B%5Cmu%5Cnu%7D+&amp;bg=ffffff&amp;fg=000000&amp;s=0\" alt=\"G_{\\mu\\nu} + \\Lambda g_{\\mu\\nu} = \\frac{8\\pi G}{c^4} T_{\\mu\\nu} \"><\/p>\n<p style=\"text-align: left;\">where <img src='https:\/\/s0.wp.com\/latex.php?latex=G_%7B%5Cmu%5Cnu%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='G_{\\mu\\nu}' title='G_{\\mu\\nu}' class='latex' \/> is <a href=\"https:\/\/en.wikipedia.org\/wiki\/Einstein_tensor\" target=\"_blank\" rel=\"noopener noreferrer\">Einstein&#8217;s curvature tensor<\/a> and <img src='https:\/\/s0.wp.com\/latex.php?latex=%5CLambda&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\Lambda' title='\\Lambda' class='latex' \/> is the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Cosmological_constant\" target=\"_blank\" rel=\"noopener noreferrer\">cosmological constant<\/a>&nbsp;(which was at first omitted by Einstein in what he later called the &#8220;greatest mistake of his life&#8221;).<\/p>\n<p>In absence of matter-energy, space-time is described by a flat pseudo-euclidean manyfold. More precisely, it is describe by <a href=\"https:\/\/en.wikipedia.org\/wiki\/Minkowski_space\" target=\"_blank\" rel=\"noopener noreferrer\">Minkowski&#8217;s space-time <\/a>from&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Special_relativity\" target=\"_blank\" rel=\"noopener noreferrer\">special relativity<\/a>).<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-974\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/flat-space-time.png\" alt=\"flat-space-time\" width=\"700\" height=\"296\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/flat-space-time.png 700w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/flat-space-time-300x127.png 300w\" sizes=\"(max-width: 700px) 100vw, 700px\" \/><\/p>\n<p>In such space-time, the trajectory of a free (i.e. non-accelerating) particle is a straight line : the shortest path between two points.<\/p>\n<p>In presence of a source of gravity, space-time is described by a curved pseudo-riemanian manifold, which <a href=\"https:\/\/en.wikipedia.org\/wiki\/Solutions_of_the_Einstein_field_equations\" target=\"_blank\" rel=\"noopener noreferrer\">solves Einstein&#8217;s field equation<\/a>:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-975\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/curved-space-time.png\" alt=\"curved-space-time\" width=\"700\" height=\"310\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/curved-space-time.png 700w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/curved-space-time-300x133.png 300w\" sizes=\"(max-width: 700px) 100vw, 700px\" \/><\/p>\n<p>In curved spaces, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Geodesic\" target=\"_blank\" rel=\"noopener noreferrer\">geodesics<\/a>&nbsp;are the generalization of the notion of straight line in flat spaces. Timelike <a title=\"Geodesics in general relativity\" href=\"https:\/\/en.wikipedia.org\/wiki\/Geodesics_in_general_relativity\">geodesics in general relativity<\/a> describe the motion of a inertial particles. In the above illustration, the rockets&#8217; paths are &#8220;straight lines&#8221; in a curved space-time.<\/p>\n<p><strong>Geometry of Einstein&#8217;s field equation<\/strong><\/p>\n<p>There are many solutions to Einstein&#8217;s field equation, corresponding to different sets of conditions (assumptions on the distribution of matter-energy for example). Each solution describes a particular geometry of space-time. Their dynamics is the cornerstone of relativistic <a href=\"https:\/\/en.wikipedia.org\/wiki\/Physical_cosmology\" target=\"_blank\" rel=\"noopener noreferrer\">cosmology<\/a>.<\/p>\n<p>Einstein&#8217;s field equation can be written in terms of tensors, or developed as a system of 10 nonlinear partial differential equations in 4 independent variables. Such a system is very difficult solve. Finding exact solution usually requires specific physical conditions, sometimes with simplifying assumptions.<\/p>\n<p>There are two ways to search for these solutions:<\/p>\n<ul>\n<li>fixing the form of the stress\u2013energy tensor and studying the solutions&nbsp;(i.e. space-time geometries)<\/li>\n<li>fixing some geometrical properties of a given space-time and finding a matter source that could provide these properties<\/li>\n<\/ul>\n<p>In&nbsp;the first case, one usually assumes physical conditions, either observed or simplified ones.<\/p>\n<p>In&nbsp;the second&nbsp;case, there is a wide liberty. For example, one can assume that the universe is homogeneous, isotropic, and accelerating and try to realize what matter can support such a structure (<a title=\"Dark energy\" href=\"https:\/\/en.wikipedia.org\/wiki\/Dark_energy\">dark energy<\/a>).<\/p>\n<p>Let&#8217;s point out a few Einstein&#8217;s field equation exact solutions:<\/p>\n<ul>\n<li><a class=\"mw-redirect\" title=\"Minkowski spacetime\" href=\"https:\/\/en.wikipedia.org\/wiki\/Minkowski_spacetime\" target=\"_blank\" rel=\"noopener noreferrer\">Minkowski solution<\/a>&nbsp;&#8211;&nbsp;which describes an empty space-time with no cosmological constant<\/li>\n<li><a class=\"mw-redirect\" title=\"Schwarzschild vacuum\" href=\"https:\/\/en.wikipedia.org\/wiki\/Schwarzschild_vacuum\" target=\"_blank\" rel=\"noopener noreferrer\">Schwarzschild solution<\/a>&nbsp;&#8211; which describes the geometry of space-time around a spherical mass<\/li>\n<li><a class=\"mw-redirect\" title=\"Kerr vacuum\" href=\"https:\/\/en.wikipedia.org\/wiki\/Kerr_vacuum\" target=\"_blank\" rel=\"noopener noreferrer\">Kerr solution<\/a>&nbsp;&#8211; which describes the geometry of space-time around a rotating object<\/li>\n<li><a title=\"Reissner\u2013Nordstr\u00f6m metric\" href=\"https:\/\/en.wikipedia.org\/wiki\/Reissner%E2%80%93Nordstr%C3%B6m_metric\" target=\"_blank\" rel=\"noopener noreferrer\">Reissner\u2013Nordstr\u00f6m<\/a>&nbsp;solution&nbsp;&#8211; which describes the geometry around a charged spherical mass<\/li>\n<li><a title=\"Kerr\u2013Newman metric\" href=\"https:\/\/en.wikipedia.org\/wiki\/Kerr%E2%80%93Newman_metric\" target=\"_blank\" rel=\"noopener noreferrer\">Kerr\u2013Newman solution<\/a>&nbsp;&#8211; which describes the geometry around a charged, rotating object<\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric\" target=\"_blank\" rel=\"noopener noreferrer\">Friedmann\u2013Lema\u00eetre\u2013Robertson\u2013Walker solution<\/a>&nbsp;(or FLRW) &#8211; which describes the universe an&nbsp;homogeneous, isotropic expanding or contracting fluid. In&nbsp;<a title=\"Physical cosmology\" href=\"https:\/\/en.wikipedia.org\/wiki\/Physical_cosmology\">cosmology<\/a>, these fluid solutions are&nbsp;often used as <a class=\"mw-redirect\" title=\"Cosmological model\" href=\"https:\/\/en.wikipedia.org\/wiki\/Cosmological_model\">cosmological models<\/a>. Indeed, this&nbsp;model is sometimes called the<em>&nbsp;<\/em>Standard Model of cosmology<\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/De_Sitter_universe\" target=\"_blank\" rel=\"noopener noreferrer\">De Sitter<\/a> solution &#8211; which&nbsp;describes as spatially flat universe and neglects ordinary matter. In this solution, the universe is dominated by the cosmological constant. It is&nbsp;thought to correspond to dark energy in our universe or the <a class=\"mw-redirect\" title=\"Inflaton field\" href=\"https:\/\/en.wikipedia.org\/wiki\/Inflaton_field\" target=\"_blank\" rel=\"noopener noreferrer\">inflaton field<\/a> in the <a class=\"mw-redirect\" title=\"Early universe\" href=\"https:\/\/en.wikipedia.org\/wiki\/Early_universe\" target=\"_blank\" rel=\"noopener noreferrer\">early universe<\/a>&nbsp;(seen the &#8220;Inflation&#8221; paragraph later on)<\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Anti-de_Sitter_space\" target=\"_blank\" rel=\"noopener noreferrer\">Anti-De Sitter<\/a> solution &#8211; which describes&nbsp;a universe with&nbsp;a negative (attractive) cosmological constant, corresponding to a negative energy density and positive pressure of the vacuum. Anti-De Sitter (AdS) is best known in for its role in string and quantum gravity theories, namely through the <a title=\"AdS\/CFT correspondence\" href=\"https:\/\/en.wikipedia.org\/wiki\/AdS\/CFT_correspondence\" target=\"_blank\" rel=\"noopener noreferrer\">AdS\/CFT correspondence<\/a>&nbsp;and the <a title=\"Holographic principle\" href=\"https:\/\/en.wikipedia.org\/wiki\/Holographic_principle\" target=\"_blank\" rel=\"noopener noreferrer\">holographic principle<\/a>&nbsp;(we&#8217;ll get on this subject in a later post of this series on &#8220;hidden realities&#8221;)<\/li>\n<\/ul>\n<p>In fact imagination (also called mathematics) is only limited by physics: one has to ask oneself whether such solution (universe) corresponds to actually possible physical conditions or not.<\/p>\n<p>Solutions can indeed&nbsp;exhibit causally &#8220;suspect&#8221; features such as <a title=\"Closed timelike curve\" href=\"https:\/\/en.wikipedia.org\/wiki\/Closed_timelike_curve\" target=\"_blank\" rel=\"noopener noreferrer\">closed timelike curves<\/a> or universes&nbsp;with points of separation (&#8220;trouser-worlds&#8221;, which are usually ruled out).<\/p>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/G%C3%B6del_metric\" target=\"_blank\" rel=\"noopener noreferrer\">G\u00f6del<\/a> universe is one of them. It describes a universe with a privileged direction (roughly speaking, a universe with a rotating axis). Among many strange properties, G\u00f6del&#8217;s universe exhibits (a lot of)&nbsp;closed timelike curves, which would allow some forms of time travel :<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-999\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/ctc.png\" alt=\"ctc\" width=\"432\" height=\"355\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/ctc.png 432w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/ctc-300x247.png 300w\" sizes=\"(max-width: 432px) 100vw, 432px\" \/><\/p>\n<p>In this universe, &nbsp;there is actually no physical way to define whether a given event happened &#8220;earlier&#8221; or &#8220;later&#8221; than another event. Einstein himself (who knew G\u00f6del very well) wrote: &#8220;<em>Such cosmological solutions<\/em> [ &#8230; ] <em>have been found by Mr. G\u00f6del. It will be interesting to weigh whether these are not to be excluded on physical grounds.<\/em>&#8221;<\/p>\n<p>Thus, some physicists add &#8220;good-sense&#8221; conditions. For example, we should mention <a href=\"https:\/\/en.wikipedia.org\/wiki\/Igor_Dmitriyevich_Novikov\" target=\"_blank\" rel=\"noopener noreferrer\">Igor Novikov<\/a>&#8216;s <a href=\"https:\/\/en.wikipedia.org\/wiki\/Novikov_self-consistency_principle\" target=\"_blank\" rel=\"noopener noreferrer\">consistency principle<\/a>.&nbsp;This principle aims to solve time-travel paradoxes. It assumes either that there is only one timeline, or that any alternative timelines (such as those postulated by the many-worlds interpretation of quantum mechanics) are not accessible (event with null probability).<\/p>\n<p>One could also assume that solutions should&nbsp;be a Lorentzian manifolds, i.e. <a class=\"mw-redirect\" title=\"Smooth manifold\" href=\"https:\/\/en.wikipedia.org\/wiki\/Smooth_manifold\" target=\"_blank\" rel=\"noopener noreferrer\">smooth manifolds<\/a>. But it turns out that&nbsp;solutions which are not everywhere smooth can&nbsp;also be very fruitful. Which leads to our next paragraph on singularities.<\/p>\n<p><strong>Singularities<\/strong><\/p>\n<p>A singularity is a location where the curvature of space-time becomes infinite (for all coordinate systems). In this place, space-time even stops being a manifold. But infinity is one of the things physicists dislike most: they usually don&#8217;t exist in the <em>observable<\/em> world. Most of the time, this is a sign for a missing piece in the theory. Indeed, singularities occur in extreme conditions, where quantum effects dominate. This is somehow general relativity crying for help and stopping being relevant. It&#8217;s a call for quantum gravity, a theory we barely have clues about.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-1010\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/blackhole-simulation.jpg\" alt=\"blackhole-simulation\" width=\"1875\" height=\"823\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/blackhole-simulation.jpg 1875w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/blackhole-simulation-300x132.jpg 300w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/blackhole-simulation-1024x449.jpg 1024w\" sizes=\"(max-width: 1875px) 100vw, 1875px\" \/><\/p>\n<p>This doesn&#8217;t stop physicist to tackle this problem. Either in making <a href=\"https:\/\/en.wikipedia.org\/wiki\/Semiclassical_gravity\" target=\"_blank\" rel=\"noopener noreferrer\">semi-classical calculations<\/a>, building (hopefully consistent) theories from the ground up &#8230; or observing Mother Nature under extreme conditions and looking for new physics.<\/p>\n<p>Let&#8217;s get back first to general relativity and see how it behaves. Singularities can be found in the Schwarzschild metric, the Reissner\u2013Nordstr\u00f6m metric, the Kerr metric, the Kerr\u2013Newman metric, &#8230;<\/p>\n<p>The first step towards a mathematical characterization under which circumstances general relativity breaks down was achieved in the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Penrose%E2%80%93Hawking_singularity_theorems\" target=\"_blank\" rel=\"noopener noreferrer\">Penrose-Hawking singularity theorems<\/a>. In this set of theorems, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Roger_Penrose\" target=\"_blank\" rel=\"noopener noreferrer\">Roger Penrose<\/a> and <a href=\"https:\/\/en.wikipedia.org\/wiki\/Stephen_Hawking\" target=\"_blank\" rel=\"noopener noreferrer\">Steven Hawking<\/a>&nbsp; proved that, under very general conditions, singularities in any general relativity-like theories are ineluctable.<\/p>\n<p>Penrose theorem mostly deals with <a href=\"https:\/\/en.wikipedia.org\/wiki\/Black_hole\" target=\"_blank\" rel=\"noopener noreferrer\">black holes<\/a>, whereas Hawking&#8217;s deals with the universe as a whole (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Big_Bang\" target=\"_blank\" rel=\"noopener noreferrer\">Big Bang<\/a>) and works backwards in time (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Big_Crunch\" target=\"_blank\" rel=\"noopener noreferrer\">Big Crunch<\/a>). Of course, keep in mind that these theorems arose from general relativity alone and these results probably break down when quantum physics is somehow added. Hawking actually revised his own position later on, stating &#8220;<em>that there in fact no singularity at the beginning of the universe<\/em>&#8220;.<\/p>\n<p><strong>Singular objects and singular events<\/strong><\/p>\n<p>As we have seen, general relativity cannot be used solely to show a singularity. Because of this, I think we&#8217;d rather speak of &#8220;singular objects&#8221; and &#8220;singular events&#8221; &#8211; uncanny stellar objects and events &#8211; than &#8220;singularities&#8221;. These singular objects would be:<\/p>\n<ul>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Black_hole\" target=\"_blank\" rel=\"noopener noreferrer\">Black holes<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/White_hole\" target=\"_blank\" rel=\"noopener noreferrer\">White holes<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Wormhole\" target=\"_blank\" rel=\"noopener noreferrer\">Wormholes<\/a><\/li>\n<\/ul>\n<p>And singular events would be:<\/p>\n<ul>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Big_Bang\" target=\"_blank\" rel=\"noopener noreferrer\">Big bang<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Big_Rip\" target=\"_blank\" rel=\"noopener noreferrer\">Big rip<\/a><\/li>\n<li>Big freeze<\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Big_Crunch\" target=\"_blank\" rel=\"noopener noreferrer\">Big crunch<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Big_Bounce\" target=\"_blank\" rel=\"noopener noreferrer\">Big bounce<\/a><\/li>\n<\/ul>\n<p>We will deal with singular events later on, at the &#8220;Relativistic cosmology&#8221; paragraph.<\/p>\n<p>Let&#8217;s start with huge beasts: black holes. A black hole is usually defined as regions of space-time exhibiting extreme gravitational effects, caused by the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Gravitational_collapse\" target=\"_blank\" rel=\"noopener noreferrer\">collapse<\/a> of a huge stellar object:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-1018\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/gravitationnal-collapse.png\" alt=\"gravitationnal-collapse\" width=\"554\" height=\"310\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/gravitationnal-collapse.png 554w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/gravitationnal-collapse-300x168.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Stars are formed from the collapse of interstellar matter. The compression caused by this collapse raises the temperature until nuclear reactions ignite. The collapse comes then to a halt : the outward thermal pressure balances the gravitational forces and the star reaches a dynamic equilibrium. When all its energy sources reach exhaustion, the equilibrium is broken. The star &#8211; depending of its initial mass &#8211; will either expand or collapse (again), reaching <a href=\"https:\/\/en.wikipedia.org\/wiki\/Stellar_evolution\" target=\"_blank\" rel=\"noopener noreferrer\">new states of its evolution<\/a>. These &#8220;stellar remnants&#8221; could then be:<\/p>\n<ul>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/White_dwarf\" target=\"_blank\" rel=\"noopener noreferrer\">White dwarfs<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Neutron_star\" target=\"_blank\" rel=\"noopener noreferrer\">Neutron stars<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Red_giant\" target=\"_blank\" rel=\"noopener noreferrer\">Red giants<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Red_dwarf\" target=\"_blank\" rel=\"noopener noreferrer\">Red dwarfs<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Brown_dwarf\" target=\"_blank\" rel=\"noopener noreferrer\">Brown dwarfs<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Black_dwarf\" target=\"_blank\" rel=\"noopener noreferrer\">Black dwarfs<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Supernova\" target=\"_blank\" rel=\"noopener noreferrer\">Supernovae<\/a><\/li>\n<li>&#8230; and, of course, black holes<\/li>\n<\/ul>\n<p><strong>Black holes<\/strong><\/p>\n<p>The <a href=\"https:\/\/en.wikipedia.org\/wiki\/Schwarzschild_radius\" target=\"_blank\" rel=\"noopener noreferrer\">Schwarzschild radius<\/a> is the radius of a sphere such that, if all the mass of an object were to be compressed within it, the escape velocity from the surface of the sphere would equal the speed of light. Once a stellar remnant collapses below this radius, light cannot escape and the object is no longer directly visible, thereby forming a black hole. This radius defines a perimeter called the &#8220;event horizon&#8221; (more on this later):<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-1021\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/schwarzschild-radius.png\" alt=\"schwarzschild-radius\" width=\"364\" height=\"210\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/schwarzschild-radius.png 364w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/schwarzschild-radius-300x173.png 300w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><\/p>\n<p>The <a title=\"No-hair theorem\" href=\"https:\/\/en.wikipedia.org\/wiki\/No-hair_theorem\" target=\"_blank\" rel=\"noopener noreferrer\">no-hair theorem<\/a> states that a black hole has only three independent physical properties: mass, charge, and angular momentum. These properties are very special since they are visible from outside a black hole. A charged black hole would then repels or attracts other charges just like any other charged object.<\/p>\n<p>The simplest static black holes (also called&nbsp;Schwarzschild black holes) have mass but neither electric charge nor angular momentum. According to the no-hair theorem, this means that there is no observable difference between the gravitational field of such a black hole and that of any other spherical object of the same mass. The popular notion of a black hole &#8220;sucking in everything&#8221; in its surroundings is therefore only correct near the Schwarzchild radius. Far away, the external gravitational field is identical to that of any other body of the same mass (called quiet region). In between lies the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Ergosphere\" target=\"_blank\" rel=\"noopener noreferrer\">ergosphere<\/a>, where it would theoretically be possible to harness energy and mass from a (rotating) black hole.<\/p>\n<p>Just like space-time around a static black hole is described by a Schwarzchild metric<\/p>\n<ul>\n<li>charged black holes are described by the Reissner\u2013Nordstr\u00f6m metric<\/li>\n<li>rotating black holes are described by the Kerr metric<\/li>\n<li>black holes with both charge and angular momentum are described by Kerr\u2013Newman metric<\/li>\n<\/ul>\n<p>Now, let&#8217;s add a little quantum physics to this classical point of view. Even if nobody really knows how gravity can be incorporated into quantum mechanics, in the quiet zone, gravitational effects can be weak enough for calculations to be reliably performed in the framework of <a title=\"Quantum field theory in curved spacetime\" href=\"https:\/\/en.wikipedia.org\/wiki\/Quantum_field_theory_in_curved_spacetime\" target=\"_blank\" rel=\"noopener noreferrer\">quantum field theory in curved spacetime<\/a>.<\/p>\n<p>Hawking showed that quantum effects &#8211; and contrary to what classical general relativity predicts &#8211; can allow black holes to emit radiations. For this, one has to think first about the quantum vacuum.<\/p>\n<p>The quantum vacuum is the quantum state with the lowest possible energy. Contrary to one could expect, it all but a simple empty space. At the heart of quantum mechanics lies the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Werner_Heisenberg\" target=\"_blank\" rel=\"noopener noreferrer\">Werner Heisenberg<\/a>&#8216;s <a href=\"https:\/\/en.wikipedia.org\/wiki\/Uncertainty_principle\" target=\"_blank\" rel=\"noopener noreferrer\">uncertainty principle<\/a>. It is the formalization of the fact it is not possible to measure simultaneously the value of pairs of quantum variables with certainty. The <a href=\"https:\/\/en.wikipedia.org\/wiki\/Standard_deviation\" target=\"_blank\" rel=\"noopener noreferrer\">standard deviations<\/a> <img src='https:\/\/s0.wp.com\/latex.php?latex=%28%5Csigma_p+%2C+%5Csigma_q%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(\\sigma_p , \\sigma_q)' title='(\\sigma_p , \\sigma_q)' class='latex' \/> of such conjugated variables&nbsp;<img src='https:\/\/s0.wp.com\/latex.php?latex=%28p+%2C+q%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(p , q)' title='(p , q)' class='latex' \/> are connected through Heisenberg&#8217;s relations:<\/p>\n<p style=\"text-align: center;\"><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Csigma_p+%5Ctimes+%5Csigma_q+%5Csim+%5Cfrac%7B%5Chbar%7D%7B2%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\sigma_p \\times \\sigma_q \\sim \\frac{\\hbar}{2}' title='\\sigma_p \\times \\sigma_q \\sim \\frac{\\hbar}{2}' class='latex' \/><\/p>\n<p style=\"text-align: left;\">Applied to Energy and time, it gives : <img src='https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+E+%5Ctimes+%5CDelta+t+%5Csim+%5Cfrac%7B%5Chbar%7D%7B2%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\Delta E \\times \\Delta t \\sim \\frac{\\hbar}{2}' title='\\Delta E \\times \\Delta t \\sim \\frac{\\hbar}{2}' class='latex' \/><\/p>\n<p style=\"text-align: left;\">This means that during a very short period of times, there will be enough energy <img src='https:\/\/s0.wp.com\/latex.php?latex=E+%3D+m+c%5E2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='E = m c^2' title='E = m c^2' class='latex' \/> to create a particle-antiparticle pair that would annihilate shortly after. The quantum vacuum can then be pictured as being filled with virtual particles popping into and out of existence :<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1027 size-full\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/quantum-vaccuum.png\" alt=\"quantum-vaccuum\" width=\"233\" height=\"150\"><\/p>\n<p>Following <a class=\"mw-redirect\" title=\"Yakov Zeldovich\" href=\"https:\/\/en.wikipedia.org\/wiki\/Yakov_Zeldovich\" target=\"_blank\" rel=\"noopener noreferrer\">Yakov Zeldovich<\/a> and <a title=\"Alexei Starobinsky\" href=\"https:\/\/en.wikipedia.org\/wiki\/Alexei_Starobinsky\" target=\"_blank\" rel=\"noopener noreferrer\">Alexei Starobinsky<\/a>, Steven Hawking and&nbsp;<a title=\"Jacob Bekenstein\" href=\"https:\/\/en.wikipedia.org\/wiki\/Jacob_Bekenstein\" target=\"_blank\" rel=\"noopener noreferrer\">Jacob Bekenstein<\/a> imagined a particle-antiparticle (virtual) pair to appear close to the event horizon of a black hole. One of the virtual pair &#8220;falls into&#8221; the black hole while the other escapes:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-1024\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/hawking-radiation.png\" alt=\"hawking-radiation\" width=\"364\" height=\"234\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/hawking-radiation.png 364w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/hawking-radiation-300x193.png 300w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><\/p>\n<p>In order to preserve total energy, this causes the black hole to lose mass. For&nbsp; an outside observer, it would appear that the black hole has just emitted a particle : a real photon, produced via the annihilation of the remaining pair with another virtual (anti-)particle outside of the black hole. This process (which is in fact much more complex) is called <a href=\"https:\/\/en.wikipedia.org\/wiki\/Hawking_radiation\" target=\"_blank\" rel=\"noopener noreferrer\">Hawking radiation<\/a>.<\/p>\n<p>Through this process, a black hole would lose mass and eventually evaporate. The time for a black hole of mass <img src='https:\/\/s0.wp.com\/latex.php?latex=M_0+&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='M_0 ' title='M_0 ' class='latex' \/> to dissipate is:<\/p>\n<p style=\"text-align: center;\"><img src='https:\/\/s0.wp.com\/latex.php?latex=t+%3D+%5Cfrac%7B5120+%5Cpi+G%5E2+M%5E3_0%7D%7B%5Chbar+c%5E4%7D+&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='t = \\frac{5120 \\pi G^2 M^3_0}{\\hbar c^4} ' title='t = \\frac{5120 \\pi G^2 M^3_0}{\\hbar c^4} ' class='latex' \/><\/p>\n<p>This a slow process though, and black holes are huge. For a black hole of one solar mass, it would take more than current age of the universe&#8230;<\/p>\n<p>This radiation is somehow paradoxical, because, as the no-hair state, a black hole is solely characterized by three external parameters (mass, electric charge and angular momentum). It means than form the outside, any information entering inside the black hole is kept stored inside. But as the black hole eventually evaporates, this information is ultimately lost. This <a href=\"https:\/\/en.wikipedia.org\/wiki\/Black_hole_information_paradox\" target=\"_blank\" rel=\"noopener noreferrer\">information paradox<\/a> ignited a 40 years <a href=\"https:\/\/en.wikipedia.org\/wiki\/The_Black_Hole_War\">long and heated debate<\/a> (and <a href=\"https:\/\/en.wikipedia.org\/wiki\/Thorne%E2%80%93Hawking%E2%80%93Preskill_bet\" target=\"_blank\" rel=\"noopener noreferrer\">a bet lost by Hawking in 2004<\/a>) between renowned physicists Steven Hawking, <a title=\"John Preskill\" href=\"https:\/\/en.wikipedia.org\/wiki\/John_Preskill\" target=\"_blank\" rel=\"noopener noreferrer\">John Preskill<\/a>, Kip Thorne,&nbsp;<a title=\"Gerard 't Hooft\" href=\"https:\/\/en.wikipedia.org\/wiki\/Gerard_%27t_Hooft\" target=\"_blank\" rel=\"noopener noreferrer\">Gerard &#8216;t Hooft<\/a> and <a title=\"Leonard Susskind\" href=\"https:\/\/en.wikipedia.org\/wiki\/Leonard_Susskind\" target=\"_blank\" rel=\"noopener noreferrer\">Leonard Susskind. <\/a><\/p>\n<p>This battle between these friends and colleagues leaded to the <a title=\"Holographic principle\" href=\"https:\/\/en.wikipedia.org\/wiki\/Holographic_principle\" target=\"_blank\" rel=\"noopener noreferrer\">holographic principle<\/a> (and a later post will be dedicated to it), where the three dimensions of space could be reconstructed from a two-dimensional world without gravity \u2013 much like a hologram.<\/p>\n<p>A few days ago, Hawking made a <a href=\"http:\/\/www.sci-news.com\/physics\/science-stephen-hawking-black-holes-information-03172.html\" target=\"_blank\" rel=\"noopener noreferrer\">communication<\/a> on that particular subject at the <span id=\"intelliTXT\"><a href=\"http:\/\/www.kth.se\/en\" target=\"_blank\" rel=\"noopener noreferrer\">KTH Royal Institute of Technology<\/a><\/span>. His idea is that information never actually makes it inside the black hole :\u201c<em>I propose that the information is stored not in the interior of the black hole as one might expect, but on its boundary, the event horizon [&#8230;]<\/em>\u201d.&nbsp; His suggestion is that the information about particles passing through is translated into an hologram that would sit on the event horizon.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-1076\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/hawking-kth.png\" alt=\"hawking-kth\" width=\"1280\" height=\"853\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/hawking-kth.png 1280w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/hawking-kth-300x200.png 300w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/hawking-kth-1024x682.png 1024w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/hawking-kth-750x500.png 750w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/p>\n<p>Using the holographic principal, one can describe the evaporation of the black hole in the two-dimensional world without gravity, for which the usual rules of quantum mechanics apply. This process is deterministic, with small imperfections in the radiation encoding the history of the black hole. Holography tells us that information is not lost in black holes, <em>a priori<\/em> solving the information paradox.<\/p>\n<p>A paper will be published next month, fully describing the findings.<\/p>\n<p>Although I&#8217;m not a great fan of <a href=\"https:\/\/en.wikipedia.org\/wiki\/String_%28physics%29\" target=\"_blank\" rel=\"noopener noreferrer\">string<\/a> theories, one shall note that there are alternative descriptions of black holes which <em>a priori<\/em> solve the information paradox, like <a href=\"https:\/\/en.wikipedia.org\/wiki\/Superstring_theory\" target=\"_blank\" rel=\"noopener noreferrer\">superstring<\/a> <a href=\"https:\/\/en.wikipedia.org\/wiki\/Fuzzball_%28string_theory%29\" target=\"_blank\" rel=\"noopener noreferrer\">fuzzballs<\/a> &#8211; where singularity at the heart of a black hole is replaced by theorizing that the entire region within the black hole\u2019s event horizon is actually a ball of strings.<\/p>\n<p>As weird as they might be, black holes are not purely theoretical singular objects. By nature, black holes do not directly emit any signals other than the Hawking radiation, which is weak and difficult to measure. Nevertheless, indirect observation is possible because the interact of such massive objects with its environment (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Accretion_disc\" target=\"_blank\" rel=\"noopener noreferrer\">accretion of matter<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Gravitational_lens\" target=\"_blank\" rel=\"noopener noreferrer\">gravitational lenses<\/a>, &#8230;)<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-1040\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/BlackHole_Lensing.gif\" alt=\"Gravitationnal Lensing\" width=\"320\" height=\"256\"><\/p>\n<p>Although we do not fully understand black hole physics (absence or presence of singularities, Hawking radiation, evaporation, information paradox, &#8230;), <a href=\"https:\/\/en.wikipedia.org\/wiki\/List_of_black_holes\" target=\"_blank\" rel=\"noopener noreferrer\">there is a full list of candidates<\/a>.<\/p>\n<p><strong>White holes<\/strong><\/p>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/White_hole\" target=\"_blank\" rel=\"noopener noreferrer\">White holes<\/a> possible existence was put forward by Igor Novikov as part of a solution to the Einstein field equations. A white whole is, roughly speaking, the opposite of a black hole. According to <a href=\"http:\/\/preposterousuniverse.com\/\" target=\"_blank\" rel=\"noopener noreferrer\">Sean Carroll<\/a> : \u201c<em>A black hole is a place where you can go in but you can never escape; a white hole is a place where you can leave but you can never go back. Otherwise, [both share] exactly the same mathematics, exactly the same geometry.<\/em>\u201d<\/p>\n<p>White hole existence outside equations is nevertheless highly speculative, though some think the big bang is somehow a while hole.<\/p>\n<p>Some also have proposed that when a black hole forms, a big bang may occur at the core, which would create a new baby universe that would expands outside of the parent universe.<\/p>\n<p>There is no known observation corroborating the existence of white holes and white hole theories are shaky. All this has to be taken with a huge grain of salt.<\/p>\n<p><strong>Wormholes<\/strong><\/p>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Wormhole#Metrics\" target=\"_blank\" rel=\"noopener noreferrer\">Lorentzian wormholes<\/a> (Einstein-Rosen bridges) are other typical singular objects. They which describe &#8220;shortcuts&#8221; connecting two separate points in space-time&nbsp;(even&nbsp;many&nbsp;light-years&nbsp;apart), different universes, or even&nbsp;different points in time. In a 2-dimensional surface, a wormhole would appear as a hole in that surface, lead into a <a href=\"https:\/\/en.wikipedia.org\/wiki\/World_tube\" target=\"_blank\" rel=\"noopener noreferrer\">world-tube<\/a>, then re-emerge at another location on the 2-dimensional surface with a similar hole. An actual wormhole would be analogous to this, but with the 3 spatial dimensions. The entry and exit points would be visualized as spheres in 3-dimensional space.&nbsp;The possibility of traversable wormholes in general relativity was first demonstrated by <a title=\"Kip Thorne\" href=\"https:\/\/en.wikipedia.org\/wiki\/Kip_Thorne\" target=\"_blank\" rel=\"noopener noreferrer\">Kip Thorne<\/a>.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-1000\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/traversable-wormhole.png\" alt=\"traversable-wormhole\" width=\"501\" height=\"382\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/traversable-wormhole.png 501w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/traversable-wormhole-300x229.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><br \/>\nWormholes lead to many <a href=\"https:\/\/en.wikipedia.org\/wiki\/EPR_paradox\" target=\"_blank\" rel=\"noopener noreferrer\">paradoxes<\/a>&nbsp;and introduce non-linearities at the quantum level.&nbsp;David Deutsch nevertheless showed that time paradoxes&nbsp;can be solved within the many-world interpretation of quantum mechanics, where a particle returning from the future would&nbsp;not return to its universe of origination but to a another&nbsp;world. String theorist&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Joseph_Polchinski\" target=\"_blank\" rel=\"noopener noreferrer\">Joseph Polchinski <\/a>discovered an &#8220;Everett phone&#8221; (a theoretical universe-to-universe communicator) in <a href=\"https:\/\/en.wikipedia.org\/wiki\/Steven_Weinberg\" target=\"_blank\" rel=\"noopener noreferrer\">Steven Weinberg<\/a>\u2019s formulation of nonlinear quantum mechanics.&nbsp;Such a possibility (and a scientifically correct visualization of spherical 3-dimensional wormhole entrance) is depicted in <a href=\"https:\/\/en.wikipedia.org\/wiki\/Christopher_Nolan\" target=\"_blank\" rel=\"noopener noreferrer\">Christopher Nolan<\/a>&#8216;s remarkable&nbsp;film&nbsp;<a title=\"Interstellar (film)\" href=\"http:\/\/ww.imdb.com\/title\/tt0816692\" target=\"_blank\" rel=\"noopener noreferrer\">Interstellar<\/a>. But from what we know, there is no observation corroborating the existence of wormholes, which remains hypothetical.<\/p>\n<p><strong>Horizons<\/strong><\/p>\n<p>Horizons are boundaries in space-time beyond which events cannot affect an outside observer (and conversely, the observer cannot affect these events).<\/p>\n<p><a href=\"http:\/\/quantum-bits.org\/?p=116\" target=\"_blank\" rel=\"noopener noreferrer\">We have already seen<\/a> how Einstein&#8217;s special relativity defines a causal structure. If at a given event E (that will be called &#8220;present&#8221; for the observer) a flash of light is emitted, it will expend at the speed of light in the form of a growing sphere. Since nothing can go faster than the speed of light, this expanding sphere is a boundary beyond which nothing affects or can be affected by E.<\/p>\n<p>If one tries to visualize this sphere of light in a 3-space where two horizontal axes are chosen to be spatial dimensions and the vertical axis is chosen to be time, the expending light-sphere will be represented by an expending circle, which, as time go, will span a light-cone centered on the event E :<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2010\/05\/lightcone.png\" alt=\"\"><\/p>\n<p>Relatively to the event E, the light cone will classifies event into distinct areas:<\/p>\n<ul>\n<li>The green light cone defines the future: events affected by information emitted at E<\/li>\n<li>The red light cone defines the past: events than can affect the present<\/li>\n<li>All other events are in the absolute elsewhere: events that cannot effect or be affected by E<\/li>\n<\/ul>\n<p>The above classification holds true in any frame of reference. An event judged to be in the light cone by one observer, will also be judged to be in the same light cone by all other observers, no matter their frame of reference.<\/p>\n<p>Now let&#8217;s introduce gravity.<\/p>\n<p>The good old flat (pseudo)-minkowskian space-time will, under the influence of gravity, transforms into a curved (pseudo)-riemanian space-time.&nbsp; The curvature of space-time will be depicted by the tilting of the lightcones. The causal structure around a star will then be depicted as follows :<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1057 size-full\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/lightcone-star.png\" alt=\"lightcone-star\" width=\"485\" height=\"351\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/lightcone-star.png 485w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/lightcone-star-300x217.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/p>\n<p>When the star collapses into a black hole, the curvature of space-time becomes so severe that, for some region, there is no path out of that region that remains inside its own light-cones. That is, the causal structure of the space-time is such that one cannot escape from that region :<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1056 size-full\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/lightcone-collapse.png\" alt=\"lightcone-collapse\" width=\"466\" height=\"373\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/lightcone-collapse.png 466w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/lightcone-collapse-300x240.png 300w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><\/p>\n<p>The border of that region (in red in the above illustration) is called the black hole event horizon. The surface at the Schwarzschild radius acts as an event horizon in a non-rotating body that fits inside this radius (although a rotating black hole operates slightly differently).<\/p>\n<p>Black hole event horizons are often misunderstood. A common error is the idea that matter can be observed \u201cfalling into\u201d a black hole. This is not possible, precisely because no information exits from the horizon. Astronomers can only detect accretion disks around black holes, where material moves with such speed that friction creates high-energy radiation which can be detected, outside of the black hole.<\/p>\n<p>Black hole event horizons are not the single type of event horizons.<\/p>\n<p>Let&#8217;s introduce the notion of <a href=\"https:\/\/en.wikipedia.org\/wiki\/Hubble_volume\">Hubble sphere<\/a>. In cosmology, a <a href=\"https:\/\/en.wikipedia.org\/wiki\/Edwin_Hubble\" target=\"_blank\" rel=\"noopener noreferrer\">Hubble<\/a> sphere is a spherical region of the Universe surrounding an observer beyond which objects recede from that observer at a rate greater than the speed of light due to the expansion of the Universe (we will get into the universe expansion in the next paragraph).<\/p>\n<p>Objects at the Hubble limit have an average proper speed equal to the speed of light relative to the observer. In a universe with constant <a class=\"mw-redirect\" title=\"Hubble parameter\" href=\"https:\/\/en.wikipedia.org\/wiki\/Hubble_parameter\" target=\"_blank\" rel=\"noopener noreferrer\">Hubble parameter<\/a>, light emitted at the present time by objects outside the Hubble limit would never be seen by the observer. That is, Hubble limit would coincide with a <a href=\"https:\/\/en.wikipedia.org\/wiki\/Cosmological_horizon\" target=\"_blank\" rel=\"noopener noreferrer\">cosmological event horizon.<\/a><\/p>\n<p>Now that the notion of event horizon has been a little bit precised (there are actually other types of horizons, like the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Apparent_horizon\" target=\"_blank\" rel=\"noopener noreferrer\">apparent horizon<\/a>), let&#8217;s think about realities hidden beyond these horizons.<\/p>\n<p>As far as black hole horizons go, it would not be very interesting: if life or other worlds or universes would exist inside a black hole horizon, it would be hidden for good from what we know.<\/p>\n<p>But, this actually include the singularity predicted by general relativity (but which might be ruled out by quantum physics), which is completely enclosed by the black hole event horizon. Actually, Roger Penrose proposed in the late seventies the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Cosmic_censorship_hypothesis\" target=\"_blank\" rel=\"noopener noreferrer\">Cosmic Censorship hypothesis<\/a>: is postulates that no naked singularities (other than the Big Bang) exist. Nevertheless, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Loop_quantum_gravity\" target=\"_blank\" rel=\"noopener noreferrer\">loop quantum gravity<\/a> suggests that this hypothesis does not hold. ohn Preskill and Kip Thorne bet (again &#8230;) against Stephen Hawking that the hypothesis was false. The bet was conceded by Hawking. <ins><\/ins><\/p>\n<p>The cosmological event horizon is even funnier, because the Hubble parameter is not necessary constant. In many cosmological models, the Hubble limit does not coincide with a cosmological event horizon.<\/p>\n<p>For example in a decelerating universe, the Hubble sphere would expand faster than the universe and its boundary would overtake light emitted by receding galaxies. Light emitted at earlier times by objects outside the Hubble sphere would would eventually arrive inside the sphere and be seen by us. Unseen &#8220;universes&#8221; would then appear to us.<\/p>\n<p>Conversely, in an accelerating universe, the Hubble sphere expands more slowly than the Universe, and bodies move out of the Hubble sphere. And actually, observations indicate that the universe is accelerating. Thus, some objects that we can currently exchange signals with will one day cross our Hubble limit. They would disappear to us (or conversely, we would disappear to them).<\/p>\n<p><strong>Relativistic cosmology<\/strong><\/p>\n<p>Physical cosmology is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its origin, structure, evolution, and ultimate fate.<\/p>\n<p>Let&#8217;s start with the large-scale structure of space-time and consider a simple space-time model such as Friedmann&#8217;s. In this model, space-time is an homogeneous and isotropic expanding universe and the overall curvature of the universe is governed by the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Friedmann_equations#Density_parameter\" target=\"_blank\" rel=\"noopener noreferrer\">density parameter<\/a> <span class=\"texhtml\">\u03a9<\/span>:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1062\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/universe-shape-1024x950.jpg\" alt=\"universe-shape\" width=\"400\" height=\"371\"><\/p>\n<ul>\n<li>If <span class=\"texhtml\">\u03a9 &gt; 1<\/span>, the global curvature of the universe is positive<\/li>\n<li>if <span class=\"texhtml\">\u03a9 &lt; 1,<\/span> the global curvature of the universe is negative<\/li>\n<li>If <span class=\"texhtml\">\u03a9 = 1<\/span>, the universe is flat<\/li>\n<\/ul>\n<p>The density parameter <span class=\"texhtml\">\u03a9<\/span> can actually be experimentally measured. Data from the <a title=\"Wilkinson Microwave Anisotropy Probe\" href=\"https:\/\/en.wikipedia.org\/wiki\/Wilkinson_Microwave_Anisotropy_Probe\" target=\"_blank\" rel=\"noopener noreferrer\">Wilkinson Microwave Anisotropy<\/a> Probe (see below the image of the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Cosmic_microwave_background\" target=\"_blank\" rel=\"noopener noreferrer\">cosmic microwave background <\/a>measured by WMAP, from which is <span class=\"texhtml\">\u03a9<\/span> evaluated), the <a title=\"Planck (spacecraft)\" href=\"https:\/\/en.wikipedia.org\/wiki\/Planck_%28spacecraft%29\" target=\"_blank\" rel=\"noopener noreferrer\">Planck<\/a> spacecraft or the <a title=\"BOOMERanG experiment\" href=\"https:\/\/en.wikipedia.org\/wiki\/BOOMERanG_experiment\" target=\"_blank\" rel=\"noopener noreferrer\">BOOMERanG<\/a> experiment indicate that <span class=\"texhtml\">\u03a9 ~<\/span> 1.00<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-1065\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/wmap-9y-cosmic-bkg.png\" alt=\"wmap-9y-cosmic-bkg\" width=\"613\" height=\"336\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/wmap-9y-cosmic-bkg.png 613w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/wmap-9y-cosmic-bkg-300x164.png 300w\" sizes=\"(max-width: 613px) 100vw, 613px\" \/><\/p>\n<p>From these measured values, it seems that within experimental error, the universe is globally flat. Which is kind of boring. But kind of only, because observations do not say anything about how those volumes fit together to give the universe its overall shape &#8211; its <a href=\"https:\/\/en.wikipedia.org\/wiki\/Topology\" target=\"_blank\" rel=\"noopener noreferrer\">topology<\/a>.<\/p>\n<p>In a universe with zero curvature, the local geometry is flat. The most obvious global structure is that of Euclidean space, which is infinite in extent.<\/p>\n<p>In three dimensions, there are 10 finite closed flat 3-manifolds, of which 6 are orientable and 4 are non-orientable. Flat universes that are finite in extent include the torus and <a title=\"Klein bottle\" href=\"https:\/\/en.wikipedia.org\/wiki\/Klein_bottle\">Klein bottle<\/a>:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-1066\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/torus-bottle-klein-universe.png\" alt=\"torus-bottle-klein-universe\" width=\"635\" height=\"352\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/torus-bottle-klein-universe.png 635w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/torus-bottle-klein-universe-300x166.png 300w\" sizes=\"(max-width: 635px) 100vw, 635px\" \/><\/p>\n<p>Of course, other possible shapes have been proposed, like <a href=\"https:\/\/en.wikipedia.org\/wiki\/Jean-Pierre_Luminet\">Jean-Pierre Luminet<\/a>&#8216;s proposal that the shape of the Universe is a finite dodecahedron, attached to itself by each pair of opposite faces, forming a <a class=\"mw-redirect\" title=\"Poincar\u00e9 homology sphere\" href=\"https:\/\/en.wikipedia.org\/wiki\/Poincar%C3%A9_homology_sphere\" target=\"_blank\" rel=\"noopener noreferrer\">Poincar\u00e9 homology sphere<\/a>.&nbsp; As beautiful as this proposal may be, there is no strong support for the correctness of the model, as yet.<\/p>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Flatness_problem\" target=\"_blank\" rel=\"noopener noreferrer\">How comes the universe is so flat<\/a> ?<\/p>\n<p>The <a href=\"https:\/\/en.wikipedia.org\/wiki\/Inflation_(cosmology)\" target=\"_blank\" rel=\"noopener noreferrer\">inflationary<\/a> hypothesis was initially proposed by <a title=\"Alan Guth\" href=\"https:\/\/en.wikipedia.org\/wiki\/Alan_Guth\" target=\"_blank\" rel=\"noopener noreferrer\">Alan Guth<\/a> in the early 1980s. It explains the origin of the large-scale structure of the cosmos. The idea that the universe went through a brief period of exponential expansion in the first fraction of a second after the Big Bang; the flatness problem and the horizon problem (along with the along with the monopole problem, which is a different subject) are three principal motivations for inflationary theory.<\/p>\n<p>The detailed quantum mechanism responsible for inflation is not known, Nevertheless, the basic picture makes a number of predictions that have been confirmed by observation. The hypothetical field thought to be responsible for inflation is called the <a title=\"Inflaton\" href=\"https:\/\/en.wikipedia.org\/wiki\/Inflaton\" target=\"_blank\" rel=\"noopener noreferrer\">inflaton<\/a>. Some think it is related to the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Higgs_field_%28classical%29\">Higgs field<\/a>.<\/p>\n<p>The horizon problem is easy to understand. It points out that different regions of the universe have not &#8220;contacted&#8221; each other because of the great distances between them (as we&#8217;ve seen with the Hubble sphere), but nevertheless they have the same temperature and other physical properties. This should not be possible, given that the transfer of information (or energy, heat, etc.) can occur, at most, at the speed of light&#8230;<\/p>\n<p>Inflation answers this question by postulating that all the regions come from an earlier era with a cosmological constant (big vacuum energy). Space with a cosmological constant is qualitatively different: instead of moving outward, the cosmological horizon stays put. For any one observer, the distance to the cosmological horizon is constant. With exponentially expanding space, two nearby observers are separated very quickly; so much so, that the distance between them quickly exceeds the limits of communications. Things are constantly moving beyond the cosmological horizon, which is a fixed distance away, and everything becomes homogeneous very quickly.<\/p>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Dark_energy\" target=\"_blank\" rel=\"noopener noreferrer\">Dark energy<\/a> is the most accepted hypothesis to explain the observations since the 1990s indicating that the universe is <a title=\"Metric expansion of space\" href=\"https:\/\/en.wikipedia.org\/wiki\/Metric_expansion_of_space\" target=\"_blank\" rel=\"noopener noreferrer\">expanding<\/a> at an the accelerating rate astronomers are measuring when observing the light from distant galaxies and supernovae.<\/p>\n<p>In the absence of dark energy, a flat universe expands forever but at a continually decelerating rate, with expansion asymptotically approaching zero. With dark energy, the expansion rate of the universe initially slows down, due to the effect of gravity, but eventually increases. As the inflationary field slowly relaxes to the vacuum, the cosmological constant goes to zero, and space begins to expand normally. The new regions that come into view during the normal expansion phase are exactly the same regions that were pushed out of the horizon during inflation. Thus they are necessarily at nearly the same temperature and curvature, because they come from the same little patch of space.<\/p>\n<p>If the theory of inflation explains why the temperatures and curvatures of different regions are so nearly equal, it also predicts that the total curvature of a space-slice at constant global time is zero. Irrespective of the original geometry of the Universe, it would appear flat to us. The analogy will be to take a balloon; we can easily see it to be rounded; now blow the balloon to a very large volume and then put a small ant on its surface. The ant will think that it is on a sheet; it cannot detect the curvature.<\/p>\n<p>The <a href=\"https:\/\/en.wikipedia.org\/wiki\/Lambda-CDM_model\" target=\"_blank\" rel=\"noopener noreferrer\">\u039bCDM<\/a> (Lambda cold dark matter) has become the standard model of big bang cosmology.<\/p>\n<p>It assumes that general relativity is the correct theory of gravity on cosmological scales and is the simplest model that provides a reasonably good account of the following properties;<\/p>\n<ul>\n<li>the existence and structure of the cosmic microwave background<\/li>\n<li>the large-scale structure in the distribution of galaxies<\/li>\n<li>the abundances of hydrogen (including deuterium), helium, and lithium<\/li>\n<li>the accelerating expansion of the universe<\/li>\n<\/ul>\n<p>The following illustration pictures the evolution of the universe according to this model:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-1059\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/lcdm-evolution.jpg\" alt=\"lcdm-evolution\" width=\"1229\" height=\"749\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/lcdm-evolution.jpg 1229w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/lcdm-evolution-300x183.jpg 300w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/lcdm-evolution-1024x624.jpg 1024w\" sizes=\"(max-width: 1229px) 100vw, 1229px\" \/><\/p>\n<p><strong>Cyclic universe<\/strong><\/p>\n<p>Cyclic cosmological models theorize that the universe follows self-sustaining cycles. For example, the oscillating universe theory briefly considered by <a title=\"Albert Einstein\" href=\"https:\/\/en.wikipedia.org\/wiki\/Albert_Einstein\" target=\"_blank\" rel=\"noopener noreferrer\">Albert Einstein<\/a> in 1930 described a universe following series of oscillations, each beginning with a <a href=\"https:\/\/en.wikipedia.org\/wiki\/Big_Bang\" target=\"_blank\" rel=\"noopener noreferrer\">big bang<\/a> and ending with a <a href=\"https:\/\/en.wikipedia.org\/wiki\/Big_Crunch\" target=\"_blank\" rel=\"noopener noreferrer\">big crunch<\/a>. Between cycles, the universe would expand until gravitational attraction causes it to collapse back and undergo a <a href=\"https:\/\/en.wikipedia.org\/wiki\/Big_Bounce\" target=\"_blank\" rel=\"noopener noreferrer\">big bounce<\/a>.<\/p>\n<p>But these early attempts failed because of the cyclic problem: according to the <a class=\"mw-redirect\" title=\"Second Law of Thermodynamics\" href=\"https:\/\/en.wikipedia.org\/wiki\/Second_Law_of_Thermodynamics\" target=\"_blank\" rel=\"noopener noreferrer\">Second Law of Thermodynamics<\/a>, entropy can only increase. This implies that successive cycles grow longer and larger. If we go back in time, cycles before the present one would become shorter and smaller, culminating again in a &#8230; big bang and &#8230; thus not replacing it.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-1073\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/cyclic-universe.png\" alt=\"cyclic-universe\" width=\"711\" height=\"225\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/cyclic-universe.png 711w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/cyclic-universe-300x95.png 300w\" sizes=\"(max-width: 711px) 100vw, 711px\" \/><\/p>\n<p>Several alternative cyclic universe have since been proposed:<\/p>\n<ul>\n<li><a title=\"Conformal cyclic cosmology\" href=\"https:\/\/en.wikipedia.org\/wiki\/Conformal_cyclic_cosmology\" target=\"_blank\" rel=\"noopener noreferrer\">Conformal cyclic cosmology<\/a> &#8211; a general relativity based theory proposed by Roger Penrose. In this model, the universe expands until all the matter decays and is turned to light &#8211; so there is nothing in the universe that has any time or distance scale associated with it. This permits it to become identical with the Big Bang, so starting the next cycle.<\/li>\n<li><a title=\"Loop quantum cosmology\" href=\"https:\/\/en.wikipedia.org\/wiki\/Loop_quantum_cosmology\" target=\"_blank\" rel=\"noopener noreferrer\">Loop quantum cosmology<\/a> which predicts a &#8220;quantum bridge&#8221; between contracting and expanding cosmological branches.<\/li>\n<\/ul>\n<p><strong>Perpetual Inflation<\/strong><\/p>\n<p>In <a href=\"https:\/\/en.wikipedia.org\/wiki\/Eternal_inflation\" target=\"_blank\" rel=\"noopener noreferrer\">perpetual inflation<\/a> models proposed by physicists like Alan Guth&nbsp;or <a title=\"Andrei Linde\" href=\"https:\/\/en.wikipedia.org\/wiki\/Andrei_Linde\" target=\"_blank\" rel=\"noopener noreferrer\">Andrei Linde<\/a>, the inflationary phase of the universe&#8217;s expansion lasts forever in at least some regions of the universe. Because these regions expand exponentially rapidly, most of the volume of the universe at any given time is inflating. All models of eternal inflation produce an infinite (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Fractal\" target=\"_blank\" rel=\"noopener noreferrer\">fractal<\/a>) multiverse. In these interpretations, new universes would pop into existence (at unknown rate), creating a complex web of bubble universes within a larger multiverse.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-1074\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/perpetual-inflation.png\" alt=\"perpetual-inflation\" width=\"460\" height=\"424\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/perpetual-inflation.png 460w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/perpetual-inflation-300x277.png 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><\/p>\n<p>New inflation does not produce a perfectly symmetric universe: tiny quantum fluctuations in the inflaton are created. These tiny fluctuations form the primordial seeds for all structure created in the later universe. These fluctuations were calculated by four groups of physicist working separately (over the course of&nbsp; a workshop), including Stephen Hawking, Alan Guth. Even if&nbsp; these models turns out to be&nbsp;consistent with WMAP data adds weight to the idea that the universe could be created in such a way, many physicists agree it is possible, but needs further work and data support to be accepted.<\/p>\n<p><strong>Poetic ending<\/strong><\/p>\n<p>Let&#8217;s, once again, end this post on a poetic note. As mentioned above,&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Christopher_Nolan\" target=\"_blank\" rel=\"noopener noreferrer\">Christopher Nolan<\/a>&#8216;s film&nbsp;<a title=\"Interstellar (film)\" href=\"https:\/\/en.wikipedia.org\/wiki\/Interstellar_(film)\" target=\"_blank\" rel=\"noopener noreferrer\">Interstellar<\/a>&nbsp;is truly&nbsp;remarkable.<\/p>\n<p>From an artistic point of view the film &#8211; in its narration and its aesthetic &#8211; can be seen as a beautiful offspring of&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Stanley_Kubrick\" target=\"_blank\" rel=\"noopener noreferrer\">Stanley Kubrick<\/a>&#8216;s masterpiece <a title=\"2001: A Space Odyssey (film)\" href=\"http:\/\/www.imdb.com\/title\/tt0062622\/\" target=\"_blank\" rel=\"noopener noreferrer\">2001: A Space Odyssey<\/a>.<\/p>\n<p>From a scientific point of view, it is probably one of the most accurate film I have ever seen (depiction of black holes and wormholes, time stretching, naked singularities, &#8220;Everett phone&#8221;, &#8230;), thanks to <a href=\"https:\/\/www.youtube.com\/watch?v=z9tUFJG0lWA\" target=\"_blank\" rel=\"noopener noreferrer\">Kip Thorne&#8217;s implication in the making of the film<\/a>.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-983\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2015\/08\/interstellar-movie-chris-nolan.png\" alt=\"interstellar-movie-chris-nolan\" width=\"1200\" height=\"750\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/interstellar-movie-chris-nolan.png 1200w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/interstellar-movie-chris-nolan-300x188.png 300w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2015\/08\/interstellar-movie-chris-nolan-1024x640.png 1024w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is the second part of&nbsp;a series of posts on (a few selected) hidden realities : many-worlds interpretation of quantum mechanics, multiverse linked to the space-time geometries and dynamics, higher &#8230;<\/p>\n","protected":false},"author":1,"featured_media":3854,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[6],"tags":[],"_links":{"self":[{"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=\/wp\/v2\/posts\/963"}],"collection":[{"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=963"}],"version-history":[{"count":0,"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=\/wp\/v2\/posts\/963\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=\/wp\/v2\/media\/3854"}],"wp:attachment":[{"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=963"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=963"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}