The present is the period of time that is occurring now. The present is contrasted with the past , the period of time that has already occurred, and the future , the period of time that has yet to occur.
76-438: It is sometimes represented as a hyperplane in space-time , typically called "now", although modern physics demonstrates that such a hyperplane cannot be defined uniquely for observers in relative motion. The present may also be viewed as a duration . Contemporary history describes the historical timeframe immediately relevant to the present time and is a certain perspective of modern history . You shouldn't chase after
152-400: A Euclidean space or more generally an affine space , or a vector space or a projective space , and the notion of hyperplane varies correspondingly since the definition of subspace differs in these settings; in all cases however, any hyperplane can be given in coordinates as the solution of a single (due to the "codimension 1" constraint) algebraic equation of degree 1. If V
228-478: A galaxy exchange kinetic energy in a process called dynamical relaxation , making their velocity distribution approach the Maxwell–Boltzmann distribution . Dynamical relaxation can proceed either by close encounters of two stars or by less violent but more frequent distant encounters. In the case of a close encounter, two brown dwarfs or stellar remnants will pass close to each other. When this happens,
304-409: A quasar , as long as enough matter is present there. In an expanding universe with decreasing density and non-zero cosmological constant , matter density would reach zero, resulting in most matter except black dwarfs , neutron stars , black holes , and planets ionizing and dissipating at thermal equilibrium . The following timeline assumes that protons do decay. The subsequent evolution of
380-445: A subspace whose dimension is one less than that of the ambient space . Two lower-dimensional examples of hyperplanes are one-dimensional lines in a plane and zero-dimensional points on a line. Most commonly, the ambient space is n -dimensional Euclidean space , in which case the hyperplanes are the ( n − 1) -dimensional "flats" , each of which separates the space into two half spaces . A reflection across
456-618: A combined mass of more than the Chandrasekhar limit of about 1.4 solar masses happen to merge. The resulting object will then undergo runaway thermonuclear fusion, producing a Type Ia supernova and dispelling the darkness of the Degenerate Era for a few weeks. Neutron stars could also collide , forming even brighter supernovae and dispelling up to 6 solar masses of degenerate gas into the interstellar medium. The resulting matter from these supernovae could potentially create new stars. If
532-411: A different associated light cone. One has to conclude that in relativistic models of physics there is no place for "the present" as an absolute element of reality, and only refers to things that are close to us. Einstein phrased this as: "People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion" . In physical cosmology ,
608-502: A false vacuum ; 95% confidence interval is 10 to 10 years due in part to uncertainty about the top quark mass. In 10 years, cold fusion occurring via quantum tunneling should make the light nuclei in stellar-mass objects fuse into iron-56 nuclei (see isotopes of iron ). Fission and alpha particle emission should make heavy nuclei also decay to iron, leaving stellar-mass objects as cold spheres of iron, called iron stars . Before this happens, however, in some black dwarfs
684-436: A finite scale factor. If the current vacuum state is a false vacuum , the vacuum may decay into an even lower-energy state. Presumably, extreme low- energy states imply that localized quantum events become major macroscopic phenomena rather than negligible microscopic events because even the smallest perturbations make the biggest difference in this era, so there is no telling what will or might happen to space or time. It
760-470: A given event, can not be in direct cause-effect relationship . Such collections of events are perceived differently by different observers. Instead, when focusing on "now" as the events perceived directly, not as a recollection or a speculation, for a given observer "now" takes the form of the observer's past light cone . The light cone of a given event is objectively defined as the collection of events in causal relationship to that event, but each event has
836-421: A half-life comparable to that of protons. Planets (substellar objects) would decay in a simple cascade process from heavier elements to hydrogen and finally to photons and leptons while radiating energy. If the proton does not decay at all, then stellar objects would still disappear, but more slowly. See § Future without proton decay below. Shorter or longer proton half-lives will accelerate or decelerate
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#1732843925343912-399: A hyperplane does not divide the space into two parts; rather, it takes two hyperplanes to separate points and divide up the space. The reason for this is that the space essentially "wraps around" so that both sides of a lone hyperplane are connected to each other. In convex geometry , two disjoint convex sets in n-dimensional Euclidean space are separated by a hyperplane, a result called
988-413: A hyperplane is a kind of motion ( geometric transformation preserving distance between points), and the group of all motions is generated by the reflections. A convex polytope is the intersection of half-spaces. In non-Euclidean geometry , the ambient space might be the n -dimensional sphere or hyperbolic space , or more generally a pseudo-Riemannian space form , and the hyperplanes are
1064-502: A process called 'stellar ignition' occurs, and its lifetime as a star will properly begin. Stars of very low mass will eventually exhaust all their fusible hydrogen and then become helium white dwarfs . Stars of low to medium mass, such as our own sun , will expel some of their mass as a planetary nebula and eventually become white dwarfs ; more massive stars will explode in a core-collapse supernova , leaving behind neutron stars or black holes . In any case, although some of
1140-405: A smaller, denser galaxy. Since encounters are more frequent in this denser galaxy, the process then accelerates. The result is that most objects (90% to 99%) are ejected from the galaxy, leaving a small fraction (maybe 1% to 10%) which fall into the central supermassive black hole . It has been suggested that the matter of the fallen remnants will form an accretion disk around it that will create
1216-412: A state in which the temperature approaches a uniform value, no further work will be possible, resulting in a final heat death of the universe. Infinite expansion does not constrain the overall spatial curvature of the universe . It can be open (with negative spatial curvature), flat, or closed (positive spatial curvature), although if it is closed, sufficient dark energy must be present to counteract
1292-400: A vector space, a vector hyperplane is a subspace of codimension 1, only possibly shifted from the origin by a vector, in which case it is referred to as a flat . Such a hyperplane is the solution of a single linear equation . Projective hyperplanes , are used in projective geometry . A projective subspace is a set of points with the property that for any two points of the set, all
1368-420: Is an affine subspace of codimension 1 in an affine space . In Cartesian coordinates , such a hyperplane can be described with a single linear equation of the following form (where at least one of the a i {\displaystyle a_{i}} s is non-zero and b {\displaystyle b} is an arbitrary constant): In the case of a real affine space, in other words when
1444-621: Is a vector space, one distinguishes "vector hyperplanes" (which are linear subspaces , and therefore must pass through the origin) and "affine hyperplanes" (which need not pass through the origin; they can be obtained by translation of a vector hyperplane). A hyperplane in a Euclidean space separates that space into two half spaces , and defines a reflection that fixes the hyperplane and interchanges those two half spaces. Several specific types of hyperplanes are defined with properties that are well suited for particular purposes. Some of these specializations are described here. An affine hyperplane
1520-480: Is defined to be a "face" of the polyhedron. The theory of polyhedra and the dimension of the faces are analyzed by looking at these intersections involving hyperplanes. Stelliferous Era Current observations suggest that the expansion of the universe will continue forever. The prevailing theory is that the universe will cool as it expands, eventually becoming too cold to sustain life. For this reason, this future scenario once popularly called " Heat Death "
1596-515: Is no concept of half-planes. In greatest generality, the notion of hyperplane is meaningful in any mathematical space in which the concept of the dimension of a subspace is defined. The difference in dimension between a subspace and its ambient space is known as its codimension . A hyperplane has codimension 1 . In geometry , a hyperplane of an n -dimensional space V is a subspace of dimension n − 1, or equivalently, of codimension 1 in V . The space V may be
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#17328439253431672-420: Is not a hyperplane, and does not separate the space into two parts (the complement of such a line is connected). Any hyperplane of a Euclidean space has exactly two unit normal vectors: ± n ^ {\displaystyle \pm {\hat {n}}} . In particular, if we consider R n + 1 {\displaystyle \mathbb {R} ^{n+1}} equipped with
1748-436: Is now an almost pure vacuum (possibly accompanied with the presence of a false vacuum ). The expansion of the universe slowly causes itself to cool down to absolute zero . The universe now reaches an even lower energy state than the earlier one mentioned. Whatever event happens beyond this era is highly speculative. It is possible that a Big Rip event may occur far off into the future. This singularity would take place at
1824-638: Is now known as the "Big Chill" or "Big Freeze". If dark energy —represented by the cosmological constant , a constant energy density filling space homogeneously, or scalar fields , such as quintessence or moduli , dynamic quantities whose energy density can vary in time and space—accelerates the expansion of the universe, then the space between clusters of galaxies will grow at an increasing rate. Redshift will stretch ancient ambient photons (including gamma rays) to undetectably long wavelengths and low energies. Stars are expected to form normally for 10 to 10 (1–100 trillion) years, but eventually
1900-490: Is possible that the dark energy equation of state could change again resulting in an event that would have consequences which are extremely difficult to parametrize or predict. In the 1970s, the future of an expanding universe was studied by the astrophysicist Jamal Islam and the physicist Freeman Dyson . Then, in their 1999 book The Five Ages of the Universe , the astrophysicists Fred Adams and Gregory Laughlin divided
1976-469: The Adler–Bell–Jackiw anomaly , virtual black holes , or higher-dimension supersymmetry possibly with a half-life of under 10 years. 2018 estimate of Standard Model lifetime before collapse of a false vacuum ; 95% confidence interval is 10 to 10 years due in part to uncertainty about the top quark mass. Although protons are stable in standard model physics, a quantum anomaly may exist on
2052-655: The Big Bang , the Milky Way and the Andromeda galaxy will collide with one another and merge into one large galaxy based on current evidence. Up until 2012, there was no way to confirm whether the possible collision was going to happen or not. In 2012, researchers came to the conclusion that the collision is definite after using the Hubble Space Telescope between 2002 and 2010 to track the motion of Andromeda. This results in
2128-414: The Big Bang , the first star formed. Since then, stars have formed by the collapse of small, dense core regions in large, cold molecular clouds of hydrogen gas. At first, this produces a protostar , which is hot and bright because of energy generated by gravitational contraction . After the protostar contracts for a while, its core could become hot enough to fuse hydrogen, if it exceeds critical mass,
2204-647: The Local Supercluster will be redshifted to such an extent that even gamma rays they emit will have wavelengths longer than the size of the observable universe of the time. Therefore, these galaxies will no longer be detectable in any way. By 10 (100 trillion) years from now, star formation will end, leaving all stellar objects in the form of degenerate remnants . If protons do not decay , stellar-mass objects will disappear more slowly, making this era last longer . By 10 (100 trillion) years from now, star formation will end. This period, known as
2280-538: The Local Supercluster will pass behind the cosmological horizon . It will then be impossible for events in the Local Supercluster to affect other galaxies. Similarly, it will be impossible for events after 150 billion years, as seen by observers in distant galaxies, to affect events in the Local Supercluster. However, an observer in the Local Supercluster will continue to see distant galaxies, but events they observe will become exponentially more redshifted as
2356-654: The accelerating expansion of the universe has removed the local supercluster beyond the cosmological horizon (at about 150 billion years). In radiocarbon dating , the "present" is defined as AD 1950 . In English grammar , actions are classified according to one of the following twelve verb tenses: past ( past , past continuous , past perfect , or past perfect continuous ), present (present, present continuous , present perfect , or present perfect continuous ), or future ( future , future continuous , future perfect , or future perfect continuous ). The present tense refers to things that are currently happening or are always
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2432-595: The concordance model of physical cosmology (Lambda-cold dark matter or ΛCDM), dark energy is in the form of a cosmological constant , the expansion will eventually become exponential, with the size of the universe doubling at a constant rate. If the theory of inflation is correct, the universe went through an episode dominated by a different form of dark energy in the first moments of the Big Bang; but inflation ended, indicating an equation of state much more complicated than those assumed so far for present-day dark energy. It
2508-512: The electroweak level, which can cause groups of baryons (protons and neutrons) to annihilate into antileptons via the sphaleron transition. Such baryon/lepton violations have a number of 3 and can only occur in multiples or groups of three baryons, which can restrict or prohibit such events. No experimental evidence of sphalerons has yet been observed at low energy levels, though they are believed to occur regularly at high energies and temperatures. After 10 years, black holes will dominate
2584-424: The hyperplane separation theorem . In machine learning , hyperplanes are a key tool to create support vector machines for such tasks as computer vision and natural language processing . The datapoint and its predicted value via a linear model is a hyperplane. The dihedral angle between two non-parallel hyperplanes of a Euclidean space is the angle between the corresponding normal vectors . The product of
2660-413: The "Degenerate Era", will last until the degenerate remnants finally decay. The least-massive stars take the longest to exhaust their hydrogen fuel (see stellar evolution ). Thus, the longest living stars in the universe are low-mass red dwarfs , with a mass of about 0.08 solar masses ( M ☉ ), which have a lifetime of over 10 (10 trillion) years. Coincidentally, this is comparable to
2736-425: The Local Supercluster becomes causally impossible. 8 × 10 (800 billion) years from now, the luminosities of the different galaxies, approximately similar until then to the current ones thanks to the increasing luminosity of the remaining stars as they age, will start to decrease, as the less massive red dwarf stars begin to die as white dwarfs . 2 × 10 (2 trillion) years from now, all galaxies outside
2812-464: The Milky Way and the Andromeda Galaxy, are gravitationally bound to each other. It is expected that between 10 (100 billion) and 10 (1 trillion) years from now, their orbits will decay and the entire Local Group will merge into one large galaxy. Assuming that dark energy continues to make the universe expand at an accelerating rate, in about 150 billion years all galaxies outside
2888-565: The black hole's mass decreases, its temperature increases, becoming comparable to the Sun 's by the time the black hole mass has decreased to 10 kilograms. The hole then provides a temporary source of light during the general darkness of the Black Hole Era. During the last stages of its evaporation, a black hole will emit not only massless particles, but also heavier particles, such as electrons , positrons , protons , and antiprotons . After all
2964-489: The black holes have evaporated (and after all the ordinary matter made of protons has disintegrated, if protons are unstable), the universe will be nearly empty. Photons , leptons , baryons , neutrinos , electrons , and positrons will fly from place to place, hardly ever encountering each other. Gravitationally , the universe will be dominated by dark matter , electrons , and positrons (not protons ). By this era, with only very diffuse matter remaining, activity in
3040-511: The case and no easy answer to the question. Buddhism and many of its associated paradigms emphasize the importance of living in the present moment—being fully aware of what is happening, and not dwelling on the past or worrying about the future . This does not mean that they encourage hedonism , but merely that constant focus on one's current position in space and time (rather than future considerations, or past reminiscence) will aid one in relieving suffering. They teach that those who live in
3116-399: The case. For example, in the sentence, "she walks home everyday," the verb "walks" is in the present tense because it refers to an action that is regularly occurring in the present circumstances. Verbs in the present continuous tense indicate actions that are currently happening and will continue for a period of time. In the sentence, "she is walking home," the verb phrase "is walking" is in
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3192-670: The combined mass is not above the Chandrasekhar limit but is larger than the minimum mass to fuse carbon (about 0.9 M ☉ ), a carbon star could be produced, with a lifetime of around 10 (1 million) years. Also, if two helium white dwarfs with a combined mass of at least 0.3 M ☉ collide, a helium star may be produced, with a lifetime of a few hundred million years. Finally, brown dwarfs could form new stars by colliding with each other to form red dwarf stars, which can survive for 10 (10 trillion) years, or by accreting gas at very slow rates from
3268-862: The conventional inner product ( dot product ), then one can define the affine subspace with normal vector n ^ {\displaystyle {\hat {n}}} and origin translation b ~ ∈ R n + 1 {\displaystyle {\tilde {b}}\in \mathbb {R} ^{n+1}} as the set of all x ∈ R n + 1 {\displaystyle x\in \mathbb {R} ^{n+1}} such that n ^ ⋅ ( x − b ~ ) = 0 {\displaystyle {\hat {n}}\cdot (x-{\tilde {b}})=0} . Affine hyperplanes are used to define decision boundaries in many machine learning algorithms such as linear-combination (oblique) decision trees , and perceptrons . In
3344-405: The coordinates are real numbers, this affine space separates the space into two half-spaces, which are the connected components of the complement of the hyperplane, and are given by the inequalities and As an example, a point is a hyperplane in 1-dimensional space, a line is a hyperplane in 2-dimensional space, and a plane is a hyperplane in 3-dimensional space. A line in 3-dimensional space
3420-399: The diagram on the right was to portray a 3-dimensional object having access to the past, present, and future in the present moment (4th dimension). It follows from Albert Einstein 's Special Theory of Relativity that there is no such thing as absolute simultaneity . When care is taken to operationalise "the present", it follows that the events that can be labeled as "simultaneous" with
3496-556: The formation of Milkdromeda (also known as Milkomeda ). 22 billion years in the future is the earliest possible end of the Universe in the Big Rip scenario, assuming a model of dark energy with w = −1.5 . False vacuum decay may occur in 20 to 30 billion years if the Higgs field is metastable. The galaxies in the Local Group , the cluster of galaxies which includes
3572-439: The future without us being determined to do it) since at least Boethius . Thomas Aquinas offers the metaphor of a watchman, representing God, standing on a height looking down on a valley to a road where past, present and future, represented by the individuals and their actions strung out along its length, are all visible simultaneously to God. Therefore, God's knowledge is not tied to any particular date. The original intent of
3648-405: The galaxy approaches the horizon until time in the distant galaxy seems to stop. The observer in the Local Supercluster never observes events after 150 billion years in their local time, and eventually all light and background radiation lying outside the Local Supercluster will appear to blink out as light becomes so redshifted that its wavelength has become longer than the physical diameter of
3724-662: The gravitational forces or else the universe will end in a Big Crunch . Observations of the Cosmic microwave background by the Wilkinson Microwave Anisotropy Probe and the Planck mission suggest that the universe is spatially flat and has a significant amount of dark energy . In this case, the universe might continue to expand at an accelerating rate. The acceleration of the universe's expansion has also been confirmed by observations of distant supernovae . If, as in
3800-446: The horizon. Technically, it will take an infinitely long time for all causal interaction between the Local Supercluster and this light to cease. However, due to the redshifting explained above, the light will not necessarily be observed for an infinite amount of time, and after 150 billion years, no new causal interaction will be observed. Therefore, after 150 billion years, intergalactic transportation and communication beyond
3876-406: The hypersurfaces consisting of all geodesics through a point which are perpendicular to a specific normal geodesic. In other kinds of ambient spaces, some properties from Euclidean space are no longer relevant. For example, in affine space , there is no concept of distance, so there are no reflections or motions. In a non-orientable space such as elliptic space or projective space , there
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#17328439253433952-595: The length of time over which star formation takes place. Once star formation ends and the least-massive red dwarfs exhaust their fuel, nuclear fusion will cease. The low-mass red dwarfs will cool and become black dwarfs . The only objects remaining with more than planetary mass will be brown dwarfs , with mass less than 0.08 M ☉ , and degenerate remnants ; white dwarfs , produced by stars with initial masses between about 0.08 and 8 solar masses; and neutron stars and black holes , produced by stars with initial masses over 8 M ☉ . Most of
4028-417: The mass of this collection, approximately 90%, will be in the form of white dwarfs. In the absence of any energy source, all of these formerly luminous bodies will cool and become faint. The universe will become extremely dark after the last stars burn out. Even so, there can still be occasional light in the universe. One of the ways the universe can be illuminated is if two carbon – oxygen white dwarfs with
4104-513: The past and future history of an expanding universe into five eras. The first, the Primordial Era , is the time in the past just after the Big Bang when stars had not yet formed. The second, the Stelliferous Era , includes the present day and all of the stars and galaxies now seen. It is the time during which stars form from collapsing clouds of gas . In the subsequent Degenerate Era ,
4180-455: The past and is finished as of the current reference to the action. Finally, verbs in the present perfect continuous tense refer to actions that have been continuing up until the current time, thus combining the characteristics of both the continuous and perfect tenses. An example of a present perfect continuous verb phrase can be found in the sentence, "she has been walking this route for a week now," where "has been walking" indicates an action that
4256-415: The past or place expectations on the future. What is past is left behind. The future is as yet unreached. Whatever quality is present you clearly see right there, right there. What we perceive as present is the vivid fringe of memory tinged with anticipation. "The present" raises the question: "How is it that all sentient beings experience now at the same time?" There is no logical reason why this should be
4332-453: The points on the line determined by the two points are contained in the set. Projective geometry can be viewed as affine geometry with vanishing points (points at infinity) added. An affine hyperplane together with the associated points at infinity forms a projective hyperplane. One special case of a projective hyperplane is the infinite or ideal hyperplane , which is defined with the set of all points at infinity. In projective space,
4408-415: The present continuous tense because it refers to a current action that will continue until a certain endpoint (when "she" reaches home). Verbs in the present perfect tense indicate actions that started in the past and is completed at the time of speaking. For example, in the sentence, "She has walked home," the verb phrase "has walked" is in the present perfect tense because it describes an action that began in
4484-428: The present moment are the happiest. A number of meditative techniques aim to help the practiser live in the present moment. Christianity views God as being outside of time and, from the divine perspective past, present and future are actualized in the now of eternity . This trans-temporal conception of God has been proposed as a solution to the problem of divine foreknowledge (i.e. how can God know what we will do in
4560-489: The present time in the chronology of the universe is estimated at 13.8 billion years after the singularity determining the arrow of time . In terms of the cosmic expansion history , it is in the dark-energy-dominated era , after the universe's matter content has become diluted enough for dark energy to dominate the total energy density. It is also in the universe's Stelliferous Era , after enough time for superclusters to have formed (at about 5 billion years), but before
4636-729: The process is expected to lower their Chandrasekhar limit resulting in a supernova in 10 years. Non-degenerate silicon has been calculated to tunnel to iron in approximately 10 years. Quantum tunneling should also turn large objects into black holes , which (on these timescales) will instantaneously evaporate into subatomic particles. Depending on the assumptions made, the time this takes to happen can be calculated as from 10 years to 10 years. Quantum tunneling may also make iron stars collapse into neutron stars in around 10 years. With black holes having evaporated, nearly all baryonic matter will have now decayed into subatomic particles (electrons, neutrons, protons, and quarks). The universe
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#17328439253434712-537: The process. This means that after 10 years (the maximum proton half-life used by Adams & Laughlin (1997)), one-half of all baryonic matter will have been converted into gamma ray photons and leptons through proton decay. Given our assumed half-life of the proton, nucleons (protons and bound neutrons) will have undergone roughly 1,000 half-lives by the time the universe is 10 years old. This means that there will be roughly 0.5 (approximately 10 ) as many nucleons; as there are an estimated 10 protons currently in
4788-485: The proton does not decay according to the theories described above, then the Degenerate Era will last longer, and will overlap or surpass the Black Hole Era. On a time scale of 10 years solid matter is theorized to potentially rearrange its atoms and molecules via quantum tunneling , and may behave as liquid and become smooth spheres due to diffusion and gravity. Degenerate stellar objects can potentially still experience proton decay, for example via processes involving
4864-427: The remaining interstellar medium until they have enough mass to start hydrogen burning as red dwarfs. This process, at least on white dwarfs, could induce Type Ia supernovae. Over time, the orbits of planets will decay due to gravitational radiation , or planets will be ejected from their local systems by gravitational perturbations caused by encounters with another stellar remnant . Over time, objects in
4940-587: The star's matter may be returned to the interstellar medium , a degenerate remnant will be left behind whose mass is not returned to the interstellar medium. Therefore, the supply of gas available for star formation is steadily being exhausted. The Andromeda Galaxy is approximately 2.5 million light years away from our galaxy, the Milky Way galaxy, and they are moving towards each other at approximately 300 kilometers (186 miles) per second. Approximately five billion years from now, or 19 billion years after
5016-547: The stars will have burnt out, leaving all stellar-mass objects as stellar remnants — white dwarfs , neutron stars , and black holes . In the Black Hole Era , white dwarfs, neutron stars, and other smaller astronomical objects have been destroyed by proton decay , leaving only black holes. Finally, in the Dark Era , even black holes have disappeared, leaving only a dilute gas of photons and leptons . This future history and
5092-448: The supply of gas needed for star formation will be exhausted. As existing stars run out of fuel and cease to shine, the universe will slowly and inexorably grow darker. According to theories that predict proton decay , the stellar remnants left behind will disappear, leaving behind only black holes , which themselves eventually disappear as they emit Hawking radiation . Ultimately, if the universe reaches thermodynamic equilibrium ,
5168-559: The timeline below assume the continued expansion of the universe. If space in the universe begins to contract, subsequent events in the timeline may not occur because the Big Crunch , the collapse of the universe into a hot, dense state similar to that after the Big Bang, will prevail. The observable universe is currently 1.38 × 10 (13.8 billion) years old. This time lies within the Stelliferous Era. About 155 million years after
5244-423: The trajectories of the objects involved in the close encounter change slightly, in such a way that their kinetic energies are more nearly equal than before. After a large number of encounters, then, lighter objects tend to gain speed while the heavier objects lose it. Because of dynamical relaxation, some objects will gain just enough energy to reach galactic escape velocity and depart the galaxy, leaving behind
5320-496: The transformations in the two hyperplanes is a rotation whose axis is the subspace of codimension 2 obtained by intersecting the hyperplanes, and whose angle is twice the angle between the hyperplanes. A hyperplane H is called a "support" hyperplane of the polyhedron P if P is contained in one of the two closed half-spaces bounded by H and H ∩ P ≠ ∅ {\displaystyle H\cap P\neq \varnothing } . The intersection of P and H
5396-463: The universe are predicted to continue to grow. Larger black holes of up to 10 (100 trillion) M ☉ may form during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of 10 to 10 years. Hawking radiation has a thermal spectrum . During most of a black hole's lifetime, the radiation has a low temperature and is mainly in the form of massless particles such as photons and hypothetical gravitons . As
5472-746: The universe depends on the possibility and rate of proton decay . Experimental evidence shows that if the proton is unstable, it has a half-life of at least 10 years. Some of the Grand Unified theories (GUTs) predict long-term proton instability between 10 and 10 years, with the upper bound on standard (non-supersymmetry) proton decay at 1.4 × 10 years and an overall upper limit maximum for any proton decay (including supersymmetry models) at 6 × 10 years. Recent research showing proton lifetime (if unstable) at or exceeding 10 –10 year range rules out simpler GUTs and most non-supersymmetry models. Neutrons bound into nuclei are also suspected to decay with
5548-872: The universe will eventually tail off dramatically (compared with previous eras), with very low energy levels and very large time scales, with events taking a very long time to happen if they ever happen at all. Electrons and positrons drifting through space will encounter one another and occasionally form positronium atoms. These structures are unstable, however, and their constituent particles must eventually annihilate. However, most electrons and positrons will remain unbound. Other low-level annihilation events will also take place, albeit extremely slowly. The universe now reaches an extremely low-energy state. If protons do not decay, stellar-mass objects will still become black holes , although even more slowly. The following timeline that assumes proton decay does not take place. 2018 estimate of Standard Model lifetime before collapse of
5624-458: The universe, none will remain at the end of the Degenerate Age. Effectively, all baryonic matter will have been changed into photons and leptons . Some models predict the formation of stable positronium atoms with diameters greater than the observable universe's current diameter (roughly 6 × 10 metres) in 10 years, and that these will in turn decay to gamma radiation in 10 years. If
5700-437: The universe. They will slowly evaporate via Hawking radiation . A black hole with a mass of around 1 M ☉ will vanish in around 2 × 10 years. As the lifetime of a black hole is proportional to the cube of its mass, more massive black holes take longer to decay. A supermassive black hole with a mass of 10 (100 billion) M ☉ will evaporate in around 2 × 10 years. The largest black holes in
5776-406: Was happening continuously in the past and continues to happen continuously in the present. [REDACTED] Quotations related to present at Wikiquote Hyperplane In geometry , a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension . Like a plane in space , a hyperplane is a flat hypersurface ,
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