A new ‘Einstein’ equation suggests wormholes hold key to quantum gravity |
ER=EPR summarizes new clues to understanding entanglement and spacetimeContext stockernumber2/Shutterstock There’s a new equation floating around the world of physics these days that would make Einstein proud. It’s pretty easy to remember: ER=EPR. You might suspect that to make this equation work, P must be equal to 1. But the symbols in this equation stand not for numbers, but for names. E, you probably guessed, stands for Einstein. R and P are initials — for collaborators on two of Einstein’s most intriguing papers. Combined in this equation, these letters express a possible path to reconciling Einstein’s general relativity with quantum mechanics. Quantum mechanics and general relativity are both spectacularly successful theories. Both predict bizarre phenomena that defy traditional conceptions of reality. Yet when put to the test, nature always complies with each theory’s requirements. Since both theories describe nature so well, it’s hard to explain why they’ve resisted all efforts to mathematically merge them. Somehow, everybody believes, they must fit together in the end. But so far nature has kept the form of their connection a secret. ER=EPR, however, suggests that the key to their connection can be found in the spacetime tunnels known as wormholes. These tunnels, implied by Einstein’s general relativity, would be like subspace shortcuts physically linking distant locations. It seems that such tunnels may be the alter ego of the mysterious link between subatomic particles known as quantum entanglement. For the last 90 years or so, physicists have pursued two main quantum issues separately: one, how to interpret the quantum math to make sense of its weirdness (such as entanglement), and two, how to marry quantum mechanics to gravity. It turns out, if ER=EPR is right, that both questions have the same answer: Quantum weirdness can be understood only if you understand its connection to gravity. Wormholes may forge that link. Wormholes are technically known as Einstein-Rosen bridges (the “ER” part of the equation). Nathan Rosen collaborated with Einstein on a paper describing them in 1935. EPR refers to another paper Einstein published with Rosen in 1935, along with Boris Podolsky. That one articulated quantum entanglement’s paradoxical puzzles about the nature of reality. For decades nobody seriously considered the possibility that the two papers had anything to do with one another. But in 2013, physicists Juan Maldacena and Leonard Susskind proposed that in some sense, wormholes and entanglement describe the same thing. In a recent paper, Susskind has spelled out some of the implications of this realization. Among them: understanding the wormhole-entanglement equality could be the key to merging quantum mechanics and general relativity, that details of the merger would explain the mystery of entanglement, that spacetime itself could emerge from quantum entanglement, and that the controversies over how to interpret quantum mechanics could be resolved in the process. “ER=EPR tells us that the immensely complicated network of entangled subsystems that comprises the universe is also an immensely complicated (and technically complex) network of Einstein-Rosen bridges,” Susskind writes. “To me it seems obvious that if ER=EPR is true it is a very big deal, and it must affect the foundations and interpretation of quantum mechanics.” Entanglement poses one of the biggest impediments to understanding quantum physics. It happens, for instance, when two particles are emitted from a common source. A quantum description of such a particle pair tells you the odds that a measurement of one of the particles (say, its spin) will give a particular result (say, counterclockwise). But once one member of the pair has been measured, you instantly know what the result will be when you make the same measurement on the other, no matter how far away it is. Einstein balked at this realization, insisting that a measurement at one place could not affect a distant experiment (invoking his famous condemnation of “spooky action at a distance”). But many actual experiments have confirmed entanglement’s power to defy Einstein’s preference. Even though (as Einstein insisted) no information can be sent instantaneously from one particle to another, one of them nevertheless seems to “know” what happened to its entangled partner. Ordinarily, physicists speak of entanglement between two particles. But that’s just the simplest example. Susskind points out that quantum fields — the stuff that particles are made from — can also be entangled. “In the vacuum of a quantum field theory the quantum fields in disjoint regions of space are entangled,” he writes. It has to do with the well-known (if bizarre) appearance of “virtual” particles that constantly pop in and out of existence in the vacuum. These particles appear in pairs literally out of nowhere; their common origin ensures that they are entangled. In their brief lifetimes they sometimes collide with real particles, which then become entangled themselves. Now suppose Alice and Bob, universally acknowledged to be the most capable quantum experimenters ever imagined, start collecting these real entangled particles in the vacuum. Alice takes one member of each pair and Bob takes the other. They fly away separately to distant realms of space and then each smushes their particles so densely that they become a black hole. Because of the entanglement these particles started with, Alice and Bob have now created two entangled black holes. If ER=EPR is right, a wormhole will link those black holes; entanglement, therefore, can be described using the geometry of wormholes. “This is a remarkable claim whose impact has yet to be appreciated,” Susskind writes. Even more remarkable, he suggests, is the possibility that two entangled subatomic particles alone are themselves somehow connected by a sort of quantum wormhole. Since wormholes are contortions of spacetime geometry — described by Einstein’s gravitational equations — identifying them with quantum entanglement would forge a link between gravity and quantum mechanics. In any event, these developments certainly emphasize the importance of entanglement for understanding reality. In particular, ER=EPR illuminates the contentious debates about how quantum mechanics should be interpreted. Standard quantum wisdom (the Copenhagen interpretation) emphasizes the role of an observer, who when making a measurement “collapses” multiple quantum possibilities into one definite result. But the competing Everett (or “many worlds”) interpretation says that the multiple possibilities all occur — any observer just happens to experience only one consistent branching chain of the multiple possible events. In the Everett picture, collapse of the cloud of possibilities (the wave function) never happens. Interactions (that is, measurements) just cause the interacting entities to become entangled. Reality, then, becomes “a complicated network of entanglements.” In principle, all those entangling events could be reversed, so nothing ever actually collapses — or at least it would be misleading to say that the collapse is irreversible. Still, the standard view of irreversible collapse works pretty well in practice. It’s never feasible to undo the multitude of complex interactions that occur in real life. In other words, Susskind says, ER=EPR suggests that the two views of quantum reality are “complementary.” Susskind goes on to explore in technical detail how entanglement functions with multiple participants and describes the implications for considering entanglement to be equivalent to a wormhole. It remains certain, for instance, that wormholes cannot be used to send a signal through space faster than light. Alice and Bob cannot, for instance, send messages to each other through the wormhole connecting their black holes. If they really want to talk, though, they could each jump into their black hole and meet in the middle of the wormhole. Such a meeting would provide strong confirmation for the ER=EPR idea, although Alice and Bob would have trouble getting their paper about it published. In the meantime, a great many papers are appearing about ER=EPR and other work relating gravity — the geometry of spacetime — to quantum entanglement. In one recent paper, Caltech physicists ChunJun Cao, Sean M. Carroll and Spyridon Michalakis attempt to show how spacetime can be “built” from the vast network of quantum entanglement in the vacuum. “In this paper we take steps toward deriving the existence and properties of space itself from an intrinsically quantum description using entanglement,” they write. They show how changes in “quantum states” — the purely quantum descriptions of reality — can be linked to changes in spacetime geometry. “In this sense,” they say, “gravity appears to arise from quantum mechanics in a natural way.” Cao, Carroll and Michalakis acknowledge that their approach remains incomplete, containing assumptions that will need to be verified later. “What we’ve done here is extremely preliminary and conjectural,” Carroll writes in a recent blog post. “We don’t have a full theory of anything, and even what we do have involves a great deal of speculating and not yet enough rigorous calculating.” Nevertheless there is a clear sense among many physicists that a path to unifying quantum mechanics and gravity has apparently opened. If it’s the right path, Carroll notes, then it turns out not at all to be hard to get gravity from quantum mechanics — it’s “automatic.” And Susskind believes that the path to quantum gravity — through the wormhole — demonstrates that the unity of the two theories is deeper than scientists suspected. The implication of ER=EPR, he says, is that “quantum mechanics and gravity are far more tightly related than we (or at least I) had ever imagined.” Follow me on Twitter: @tom_siegfried |
Draven Star is bound down |
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Approximate Quantum Error Correction Revisited: Introducing the Alphabit. (arXiv:1706.09434v1 [quant-ph]) |
Authors: Patrick Hayden, Geoffrey Penington We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap between them; replacing classical bits by zero-bits makes teleportation asymptotically reversible. The decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. We study the effect of a constraint on the dimension of the reference system when considering information leakage. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. The size of the reference can be characterized by a parameter $\alpha$; we call the associated resource an $\alpha$-bit. Changing $\alpha$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. We develop the theory of $\alpha$-bits, including the applications above, and determine the $\alpha$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants. |
Equivariant control data and neighborhood deformation retractions. (arXiv:1706.09539v1 [math.SG]) |
Authors: Markus J. Pflaum, Graeme Wilkin In this article we study Whitney (B) regular stratified spaces with the action of a compact Lie group $G$ which preserves the strata. We prove an equivariant submersion theorem and use it to show that such a $G$-stratified space carries a system of $G$-equivariant control data. As an application, we show that if $A \subset X$ is a closed $G$-stratified subspace which is a union of strata of $X$, then the inclusion $i : A \hookrightarrow X$ is a $G$-equivariant cofibration. In particular, this theorem applies whenever $X$ is a $G$-invariant analytic subspace of an analytic $G$-manifold $M$ and $A \hookrightarrow X$ is a closed $G$-invariant analytic subspace of $X$. |
Discontinuous Skeletal Gradient Discretisation Methods on polytopal meshes. (arXiv:1706.09683v1 [math.NA]) |
Authors: Daniele A. Di Pietro, Jérôme Droniou, Gianmarco Manzini In this work we develop arbitrary-order Discontinuous Skeletal Gradient Discretisations (DSGD) on general polytopal meshes. Discontinuous Skeletal refers to the fact that the globally coupled unknowns are broken polynomial on the mesh skeleton. The key ingredient is a high-order gradient reconstruction composed of two terms: (i) a consistent contribution obtained mimicking an integration by parts formula inside each element and (ii) a stabilising term for which sufficient design conditions are provided. An example of stabilisation that satisfies the design conditions is proposed based on a local lifting of high-order residuals on a Raviart-Thomas-N\'ed\'elec subspace. We prove that the novel DSGDs satisfy coercivity, consistency, limit-conformity, and compactness requirements that ensure convergence for a variety of elliptic and parabolic problems. Links with Hybrid High-Order, non-conforming Mimetic Finite Difference and non-conforming Virtual Element methods are also studied. Numerical examples complete the exposition. |
Real spectrum versus {\ell}-spectrum via brumfiel spectrum. (arXiv:1706.09802v1 [math.RA]) |
Authors: Friedrich Wehrung (LMNO) It is well known that the real spectrum of any commutative unital ring, and the {\ell}-spectrum of any Abelian lattice-ordered group with order-unit, are all completely normal spectral spaces. We prove the following results: (1) Every real spectrum can be embedded, as a spectral subspace, into some {\ell}-spectrum. (2) Not every real spectrum is an {\ell}-spectrum. (3) A spectral subspace of a real spectrum may not be a real spectrum. (4) Not every {\ell}-spectrum can be embedded, as a spectral subspace, into a real spectrum. (5) There exists a completely normal spectral space which cannot be embedded , as a spectral subspace, into any {\ell}-spectrum. The commutative unital rings and Abelian lattice-ordered groups in (2), (3), (4) all have cardinality $\aleph 1 , while the spectral space of (4) has a basis of car-dinality $\aleph 2. Moreover, (3) solves a problem by Mellor and Tressl. |
Fundamental irreversibility of the classical three-body problem. New approaches and ideas in the study of dynamical systems. (arXiv:1706.09827v1 [math-ph]) |
Authors: A. S. Gevorkyan The three-body general problem is formulated as a problem of geodesic trajectories flows on the Riemannian manifold. It is proved that a curved space with local coordinate system allows to detect new hidden symmetries of the internal motion of a dynamical system and reduce the three-body problem to the system of 6\emph{th} order. It is shown that the equivalence of the initial Newtonian three-body problem and the developed representation provides coordinate transformations in combination with the underdetermined system of algebraic equations. The latter makes a system of geodesic equations relative to the evolution parameter, i.e., to the arc length of the geodesic curve, irreversible. Equations of deviation of geodesic trajectories characterizing the behavior of the dynamical system as a function of the initial parameters of the problem are obtained. To describe the motion of a dynamical system influenced by the external regular and stochastic forces, a system of stochastic equations (SDE) is obtained. Using the system of SDE, a partial differential equation of the second order for the joint probability distribution of the momentum and coordinate of dynamical system in the phase space is obtained. A criterion for estimating the degree of deviation of probabilistic current tubes of geodesic trajectories in the phase and configuration spaces is formulated. The mathematical expectation of the transition probability between two asymptotic subspaces is determined taking into account the multichannel character of the scattering. |
Hausdorff dimension of union of affine subspaces. (arXiv:1701.02299v2 [math.MG] UPDATED) |
Authors: K. Héra, T. Keleti, A. Máthé We prove that for any $1 \le k<n$ and $s\le 1$, the union of any nonempty $s$-Hausdorff dimensional family of $k$-dimensional affine subspaces of ${\mathbb R}^n$ has Hausdorff dimension $k+s$. More generally, we show that for any $0 < \alpha \le k$, if $B \subset {\mathbb R}^n$ and $E$ is a nonempty collection of $k$-dimensional affine subspaces of ${\mathbb R}^n$ such that every $P \in E$ intersects $B$ in a set of Hausdorff dimension at least $\alpha$, then $\dim B \ge 2 \alpha - k + \min(\dim E, 1)$, where $\dim$ denotes the Hausdorff dimension. As a consequence, we generalize the well known Furstenberg-type estimate that every $\alpha$-Furstenberg set has Hausdorff dimension at least $2 \alpha$, we strengthen a theorem of Falconer and Mattila, and we show that for any $0 \le k<n$, if a set $A \subset {\mathbb R}^n$ contains the $k$-skeleton of a rotated unit cube around every point of ${\mathbb R}^n$, or if $A$ contains a $k$-dimensional affine subspace at a fixed positive distance from every point of ${\mathbb R}^n$, then the Hausdorff dimension of $A$ is at least $k + 1$. |
Eldan's stochastic localization and tubular neighborhoods of complex-analytic sets. (arXiv:1702.02315v3 [math.MG] UPDATED) |
Authors: Bo'az Klartag Let Z be the zero set of a holomorphic map from C^n to C^k. Assume that Z is non-empty. We prove that for any r > 0, the Gaussian measure of the Euclidean r-neighborhood of Z is at least as large as the Gaussian measure of the Euclidean r-neighborhood of E, where E is any (n-k)-dimensional, affine, complex subspace whose distance from the origin is the same as the distance of Z from the origin. |
quadratic form |
> Write a function in Sage that accepts as input a symmetrical bilinear (not trivial) form B [caracterized by the associated matrix respect to the canonical base in R^n] and gives in output a vector subspace W ⊆ R^n such that:
- Dim W is maximal
- the restriction B|wxw has maximum rank |
Bilinear form |
Write a function in Sage that accepts as input a symmetrical bilinear (not trivial) form B [caracterized by the associated matrix respect to the canonical base in R^n] and gives in output a vector subspace W ⊆ R^n such that:
- Dim W=n
- the restriction of B to WxW has maximum rank |
Approximate Quantum Error Correction Revisited: Introducing the Alphabit. (arXiv:1706.09434v1 [quant-ph]) |
Authors: Patrick Hayden, Geoffrey Penington We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap between them; replacing classical bits by zero-bits makes teleportation asymptotically reversible. The decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. We study the effect of a constraint on the dimension of the reference system when considering information leakage. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. The size of the reference can be characterized by a parameter $\alpha$; we call the associated resource an $\alpha$-bit. Changing $\alpha$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. We develop the theory of $\alpha$-bits, including the applications above, and determine the $\alpha$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants. |
Toothpaste fixes all! |
Ok, so I haven't exactly been active lately here. But hell, there's probably 3 people reading this, so whatever. Anyway, I picked up Brawl yesterday (Friday) and I was like: "Sweet! FIN-FRICKIN-LY"* After about 5 months, we finally get one of the Wii's greatest games and I'm loving every minute of it. I've already unlocked Sonic, Captain Falcon, Luigi and some other dudes; but I've hardly played Subspace Emissary because there have been 4 people playing all the time. Oh well, I'm looking forward to getting R.O.B. too. So, all was well. Until my sister knocked the Wii over accidentally. It wasn't her fault really, it was just a particularly heated battle and the Game Cube controller wires were particularly short. Damn controller wires. But, long story short, the disc was scratched. Some things didn't work and it just said "Disc cannot be read." Anyone who hasn't been living under a secluded rock under the lost City of Atlantis should understand my pain and frustration here. The scratch was minimal! And yet it's managed to make me unable to play like 4 stages and so many characters. Understandably, I raged. And I mean full-fledged psychotic LCD-inducing rage. Yea... it was pretty bad. After a while of general sulking and tantrums; I remembered something from my young days. Toothpaste. No no no, I wasn't trying to remember whether or not I had brush my teeth this morning (which I had, mind you). I was going to put toothpaste on the disc to clear out the scratch marks. Ludicrous, some of you might say (particularly the portion of people who haven't tried this before). But I tempted fate and kicked it's ass! After about 10 minutes of general rubbing and scrubbing; it was practically as good as new. After a quick rinse under the tap (yes, I used water on the CD). It worked beautifully. Immaculately even. WJUK: 1. Er... Scratched disc: 0. Well, my sisters are still playing Brawl upstairs while I'm grabbing a bite to eat. It seems they've become quite addicted to the game, and rightly so. Kicking someone's ass while trash-talking to them is totally what SSBB is about. It's the core essence of it, and I think I do both parts really well. And there's always the annoyance factor, I was getting my ass handed to me while playing Yoshi (random selection FTL) in a 5-stock match. When the smash ball came, I just kept shouting: "YOSHI'S TURN!" In as weird a voice as possible, and the tactic seems to have worked. I turned the match on it's head as I KO'ed everyone twice without taking a single hit (the smash ball helped too). And I actually managed to win... with YOSHI (and frankly, I suck ass as Yoshi). *ahem* Anyway, I think I've babbled on for quite some time now. And I live you with this: WHY DON'T YOU HAVE BRAWL YET?**
*More swearing may have been involved. **Doesn't apply to anyone who has Brawl.
Cast your eyes on the awesomeness: |
Supplemental 30 - Gene Roddenberry Versus Star Trek |
John, Ken, and Mission Log Executive Producer Rod Roddenberry talk over Star Trek with and without its creator - Gene Roddenberry. Plus questions from panel attendees. Once more from the Rio, we put Gene Roddenberry Versus Star Trek in the Mission Log. Subspace channels are open: On Facebook: facebook.com/missionlogpod On Twitter: @missionlogpod On Skype: missionlogpod On the phone: (323) 522-5641 Online: missionlogpodcast.com We may use your comments on a future episode of Mission Log. |
Supplemental 29 - Ten Essential TOS from STLV50 |
Ken and John return to the Rio. From the Roddenberry Interactive Stage and Lounge, Mission Log presents the 10 to 20 best or essential episodes of Star Trek: TOS, plus a few episodes of the animated series and one mention of Next Gen. But mostly TOS. Subspace channels are open: On Facebook: facebook.com/missionlogpod On Twitter: @missionlogpod On Skype: missionlogpod On the phone: (323) 522-5641 Online: missionlogpodcast.com We may use your comments on an upcoming episode of Mission Log |
198 - Disaster |
Everything is going so well, right until it does not. A student tour turns into a deadly turbo lift ride! A chair on the bridge turns into a hot seat! An impromptu audition turns into a radioactive fire! And there is still more trouble. Yet, despite the various issues, the title is singular. See what happens when we put Disaster in the Mission Log. Subspace channels are open: On Facebook: facebook.com/missionlogpod On Twitter: @missionlogpod On Skype: missionlogpod On the phone: (323) 522-5641 Online: missionlogpodcast.com We may use your comments on a future episode of Mission Log. |
197 - Silicon Avatar |
The Enterprise says “hello” to an old enemy. Or tries to say “hello.” And tries to figure out whether it is an enemy. Along to help is Dr. Kila Marr. Or is it help she is offering? She is getting to know her son, and will not let a little thing like his dying a few years ago stand in her way. Shields up for safety as we put Silicon Avatar in the Mission Log. Subspace channels are open: On Facebook: facebook.com/missionlogpod On Twitter: @missionlogpod On Skype: missionlogpod On the phone: (323) 522-5641 Online: missionlogpodcast.com We may use your comments on a future episode of Mission Log. |
196 - Ensign Ro |
A Bajoran terrorist attack on a Federation colony has got everyone a little jumpy. Enter Ensign Ro Laren, Starfleet officer and Bajoran herself, who has been released from prison to help find the attackers. But what do the Cardassians have to do with all this? And why does Starfleet's Admiral Kennelly seem to be keeping secrets? This week, Ensign Ro and "Ensign Ro" go into the Mission Log. Subspace channels are open: On Facebook: facebook.com/missionlogpod On Twitter: @missionlogpod On Skype: missionlogpod On the phone: (323) 522-5641 Online: missionlogpodcast.com We may use your comments on a future episode of Mission Log. |
Busty blonde tightly tied and assfucked without mercy by huge black cock |
Release Year: 2015 Genres: BDSM, Anal Bondage Fucking, Anal Sex, Big Breasts, Big Dick, Black Cock, Blonde, Blonde Slave Training, Blue Eyes, Box Tie, Deep Throat, Double Penetration, Drool, Interracial, Long Hair, Shaved In the final part of Holly Heart’s live BaRS show, we pull out the big guns. It is DP time. This BBC loving whore loves getting her ass royally plowed by huge dick and we are here to oblige. The bondage, orgasms and relentless facefucking have already blasted our big breast MILF into sexual subspace. Assfucking will be the rocket to take her into the universe of Sexuallybroken. After binding up our pet in a strict chest harness and letting her pee in a bucket so she does not spoil our nice dungeon floors, we throw Holly onto the fuckbed. What follows is an epic dicking down in every single hole by two hard relentless cocks. Holly is ragdoll fucked all over the bed in every angle and position we so desire. This is what she was born for. Her hair and makeup are destroyed, giving her the look of a sad eyed messy panda. Drool pours out as the cocks pour in. Holly’s eyes roll up into the back of her skull as 10 inches of black thunder own her ass and reshape it to be custom fitted. When we follow that up with a DP, Holly loses her mind. And who can blame her? We fuck until we have had our fill. Our drained and well fucked pet is left twitching on the bed, reduced to a sticky bag of holes. Quick, did someone get the number of the cock truck that just hit her? Format: mp4 Duration: 29:33 Video: 1280x720, AVC (H.264), 7286kbps Audio: 105kbps File size: 1.6 GB http://svalka.ws/ |
Little Chastity Lynn Is Suspended, Fucked To Orgasm, Skull Fucked To Subspace , HD 720p |
Year : 2016 Genre : PAIN PLAY, Device, Domination, Canning, Torture, Spanking, Hummulation Country : USA Studio : SB Duration : 18 min [...] |