Astronomy Bizarre Wheeler309N, Fall 2004 Dec. 3, 2004(47855)Review Sheet 5Quantum Gravity, Strings, Branes, and HyperspaceConflict between Gravity and Quantum Theory – Need quantum gravity to understand the singularity at the birthof Big Bang and in black holes, worm hole time machines, and quantum foam.Planck scale – the tiny scale (10-33 cm, 10-43 s, 1093 gm/cm3) where Einstein’s theory and quantum theory arepredicted to collide, the implied “size” of the singularity. Strings are somewhat larger than this.“Quantum Foam” – word description (in absence of quantitative mathematical theory) of the expected nature ofspace-time on the smallest level (Planck scale) where quantum effects compete with space-time curvature.At the quantum foam level it is not just the position of an object in otherwise uniform space that is uncertain (theclassic quantum view), but the nature of space itself must be quantum uncertain.Carl Sagan's "Contact" - Catalyst of work on wormholes and time machines.Exotic matter - like the tension in a rubber band only with an energy greater than the mass energy, mc2. Ratherthan adding to the weight of gravity like ordinary pressure/energy, the "negative pressure" of exotic matter repelsagainst gravity (related in principle to Dark Energy).Worm holes - exotic matter could, in principle, be used to hold off the effects of gravity and maintain the openingof a worm hole to connect two distant places in the Universe.Shape of a wormhole - a three dimensional worm hole is not a "tube" as it appears in its two-dimensionalembedding diagram, but rather a spherical space that can be approached from any direction.Travel through a worm hole - one would proceed "straight" along a radius toward the center of the sphericalspace, but eventually find oneself moving away from the center and out into normal space, without ever changingdirection.View inside a wormhole - one should be able to see through a worm hole looking along the radius toward thecenter of the spherical space, but if one looks "sideways," perpendicular to the radius, one would see light thattraveled around the highly curved space and returned to its origin.Time and Special Relativity - if two observers are in uniform motion, each will see the other aging more slowly.The twin paradox - if one twin remains stationary, and the other is subjected to an acceleration, either by travelingout and back or by venturing in a stronger gravity, then the twin who has experienced the acceleration, notuniform motion, will be absolutely younger.Time machines - if worm holes exist, then they can, in principle, be used to make a time machine through the twinparadox mechanism. After one end of the worm hole is accelerated and returned, it will thereafter be absolutelyyounger than the mouth of the worm hole that remained at rest or in uniform motion.Grandfather paradox - the notion that since time machines can violate causality (“cause” before “effect”) asituation, like traveling back in time to kill your Grandfather, can arise that can be neither true or not true.Novikov consistency conjecture - the conjecture that physics must be self-consistent and simply does not allowparadoxes even if time travel exists.The pool ball crisis - the idea that a simple mechanical example could be invented to show that time machineswill always come with paradoxes. A pool ball rolling into one end of a worm hole can come out in the past andhit itself before it goes in, thereby preventing it from entering the worm hole in the first place.Resolution of pool ball crisis - Novikov and Thorne and associates showed that the pool ball problem satisfies theconsistency conjecture. No case was found that gave rise to a paradox. The past and future pool balls could just"kiss" with a slight deflection of the trajectory, but a "hard" collision with the first pool ball being knocked awayfrom the worm hole, thus giving a paradox, simply did not and cannot arise.Free will and time machines - if time machines exist and the consistency conjecture holds, then is everything pre-ordained, and there is no free will?Changing the future - if the consistency conjecture is true, then the future cannot be "altered" by the acts of a timetraveler who went back in time.Vacuum energy and time machines - vacuum quantum energy could travel into the past, pile up, and create such ahigh gravity that any worm hole would be quickly sealed. This issue cannot be resolved without a completetheory of quantum gravity.Classic quantum theory – particles are points (electrons) that also have quantum wave-like properties, or are madeup of point particles (protons are made of three quarks). The notion of particles as strings changes that picture in afundamental way.String Theory – “particles” are actually strings in a space of 10 dimensions plus time. The theory “contains”Einstein’s General Relativity and has been used to compute the entropy and temperature of a black hole frombasic theory.Fundamental forces – according to string theory all the basic forces, electricity, magnetism, strong force, weakforce – are confined to regular three-dimensional space. Gravity – the creature of space-time – can "leak" intohigher dimensions, if they exist.Early history of string theory – recognition that equations that corresponded to the strong nuclear force alsodescribed entities, strings, that could stretch and wiggle.Quantum View of Forces – the quantum theory views (mathematically) all forces as resulting from an exchangeof particles, with different particles representing different forces (electromagnetic, weak, strong).Strings and space – the shape of the wrapped-up spaces determine how the strings can vibrate and hence whatparticle they represent.Extra dimensions – in the first version of string theory, all the extra dimensions were "wrapped up" on a scalecomparable to the Plank Scale. Thought to be necessary so that gravity would have inverse-with-distance-squaredbehavior.Calabi Yau – a space – special 6-dimensional geometry that could be the shape of the wrapped-up dimensions.Finite extra dimensions – the realization, guided by string theory, that some of the extra dimensions could be"large." Experimental limits would not rule out one millimeter. Only gravity could go there.Branes – surfaces