The greatest story ever told so var

WHY ARE WE HERE? Lawrence M Krauss BONUS MATERIAL NEW YORK 3P_GreatestStoryEverTold_AC.indd • LONDON • TORON TO • SYDNEY • NEW DELHI 1/4/17 3:11 PM From the Armoire to the Cave 11 Figure 1A 3P_GreatestStoryEverTold_AC.indd 11 1/4/17 3:11 PM From the Armoire to the Cave 15 Figure 1B: Cave Shadows This shadow displays both length and directionality, two concepts that we, who are not confined to the cave, take for granted However, as the prisoners watch, this shadow changes: Later it looks like this: And again later like this: And later still, like this: 3P_GreatestStoryEverTold_AC.indd 15 1/4/17 3:11 PM 16 THE GRE ATEST STORY EVER TOLD—SO FAR The Rotating Weather Vane What will the natural philosopher, who has escaped to the surface to explore the richer world beyond the shadows, discover? He will see that the shadow is first of all just a shadow: a two-dimensional image on the wall cast from a real, three-dimensional object located behind the prisoners He will see that the object has a fixed length that never changes, and that it’s accompanied by an arrow that is always on the same side of the object From a vantage point slightly above the object, he sees that the series of images results from the projection of a rotating weather vane onto the wall: Figure 1C 3P_GreatestStoryEverTold_AC.indd 16 1/4/17 3:11 PM Faraday's Electrical Fields Faraday imagined that each electric charge would be surrounded by an electric “field,” which he could picture in his head He saw the field as a bunch of lines emanating radially outward from the charge T he field lines would have arrows on them, pointing outward if the charge was positive, and inward if it was negative: Figure 2A He further imagined that the number of field lines increased as the magnitude of the charge increased: Figure 2B A B C The utility of this mental picture was that Faraday could now intuitively understand both what would happen when another test charge 3P_GreatestStoryEverTold_AC.indd 28 1/4/17 3:11 PM was put near the first charge and why (Whenever I use the colloquial why, I mean “how.”) T h e test charge would feel the “field” of the first charge wherever the second charge was located, with the strength of the force being proportional to the number of field lines in the region, and the direction of the force being along the direction of the field lines T h us, for example, the test charge in question would be pushed outward in the direction shown: Figure 2C One can more than this with Faraday’s pictures Imagine placing two charges near each other Since field lines begin at a positive charge and end on a negative charge and can never cross, it is almost intuitive that the field lines in between two positive charges should appear to repel each other and be pushed apart, whereas between a positive and a negative charge they should connect together: Figure 2D Once again, if a test charge is placed anywhere near these two charges, it would feel a force in the direction of the field lines, with a strength proportional to the number of field lines in that region 3P_GreatestStoryEverTold_AC.indd 29 1/4/17 3:11 PM Maxwell's Principles of Electromagnetism Experiment Consider the following thought experiment Take an electrically charged object and jiggle it up and down What happens as you this? Figure 3A Well, an electric field surrounds the charge, and when you move the charge, the position of the field lines changes But, according to Maxwell, this changing electric field will produce a magnetic field, which will point in and out of the paper as shown below: Figure 3B 3P_GreatestStoryEverTold_AC.indd 39 1/4/17 3:11 PM Here the field line pointing into the paper has a cross (the back of an arrow), and that pointing out of the paper has a dot (the tip of an arrow) T h is field will flip direction as the charge changes the direction of its motion from upward to downward But we should not stop there If I keep jiggling the charged object, the electric field will keep changing, and so will the induced magnetic field But a changing magnetic field will produce an electric field T h us there are new induced electric field lines, which point vertically, changing from up to down as the magnetic field reverses its sign I display the electric field line to the right only for lack of space, but the mirror image will be induced on the left-hand side Figure 3C But that changing electric field will in turn produce a changing magnetic field, which would exist farther out to the right and left of the diagram, and so on Jiggling a charge produces a succession of disturbances in both electric and magnetic fields that propagate outward, with the change in each field acting as a source for the other, due to the rules of electromagnetism as Maxwell defined them We can extend the picture shown above to a 3-D image that captures the full nature of the changing as shown below: 3P_GreatestStoryEverTold_AC.indd 40 1/4/17 3:11 PM Figure 3D E B c 3P_GreatestStoryEverTold_AC.indd 41 1/4/17 3:11 PM Space and Time Illustrations Einstein, Minkowski and Lorentz Figure 5A lightning hits B A 3P_GreatestStoryEverTold_AC.indd 57 a little while later v B v A 1/4/17 3:11 PM Even before completing this work, however, Feynman described an intuitive physical reason why relativity, when combined with quantum mechanics, requires the existence of antiparticles Consider an electron moving along on a possible “quantum” trajectory What does this mean? An electron takes all possible trajectories between two points as long as I am not measuring it while it travels Among these are trajectories that are classically not allowed because they would violate rules such as the limitation that objects cannot travel faster than light (arising from relativity) Now the Heisenberg uncertainty principle says that even if I try to measure the electron along its trajectory over some short time interval, some intrinsic uncertainty in the velocity of the electron remains that can never be overcome Thus even if I measure the trajectory at various points, I cannot rule out some weird nonclassical behavior during these intervals Now, imagine the trajectory shown below: Figure 8A time For the short time in the middle of the time interval shown the electron is traveling faster than the speed of light But Einstein tells us that time is relative, and different observers will measure different intervals between events And if a particle is traveling faster than light in one reference frame, in another reference frame it will appear to be traveling backward in time, as shown below (this is one of the reasons relativity restricts all observed particles to travel at speeds less than or equal to the speed of light: 3P_GreatestStoryEverTold_AC.indd 100 1/4/17 3:11 PM Figure 8B Feynman recognized that in the latter frame this would look like an electron moving forward in time for a little while, then moving backward in time, then moving forward in time But what does an electron moving backward in time appear like? Since the electron is negatively charged, a negative charge moving backward in time to the right is equivalent to a positive charge moving forward in time to the left Thus, the picture is equivalent to the following: Figure 8C time In this picture one starts with an electron moving forward in time, and then sometime later an electron and a particle that appears like an electron but has the opposite charge suddenly appear out of empty space, and the positively charged particle moves to the left, again forward in time, until it encounters the original electron and the two annihilate, leaving only one electron left over to continue moving All of this happens on a timescale that cannot be observed directly, for if it could be, then this strange behavior, violating the tenets of relativity, would be impossible Nevertheless, you can be assured that inside 3P_GreatestStoryEverTold_AC.indd 101 1/4/17 3:11 PM But the agreement between theory and observation is only possible if the effects of virtual particles are included Indeed, the very phenomenon of virtual particles implies that, in quantum theory, forces between particles are always conveyed by the exchange of virtual particles, in a way I shall now describe In quantum electrodynamics, electromagnetic interactions occur by the absorption or emission of the quanta of electromagnetism, namely photons Following Feynman, we can diagram this interaction as an electron emitting a wavy “virtual” photon (γ) and changing direction: Figure 8D time e e Th en, the electric interaction between two electrons can be diagrammed as: Figure 8E e time e e 3P_GreatestStoryEverTold_AC.indd 103 e 1/4/17 3:11 PM Neutron Decay T h e starting point of Fermi’s thinking involved light, as did almost all of modern physics, and in this case the modern quantum theory of light inter-acting with matter Recall that Feynman developed a pictorial framework to think about fundamental processes in space and time, when he argued that antimatter should exist T h e space-time picture of an electron emitting a photon is reproduced here, but with the electron replaced by a proton, p: Figure 10A time p p 3P_GreatestStoryEverTold_AC.indd 130 1/4/17 3:11 PM Fermi imagined the decay of a neutron in a similar fashion, but instead of the neutron emitting a photon and remaining the same particle, the neutron, n, would emit a pair of particles—an electron, e, and a neu-trino, ν, and would be converted into a proton, p: Figure 10b e time p n 3P_GreatestStoryEverTold_AC.indd 131 1/4/17 3:11 PM Neutron Decay with Intermediate Particle Figure 11A e e p time time p n 3P_GreatestStoryEverTold_AC.indd 145 n 1/4/17 3:11 PM Figure 12A right-handed left-handed 3P_GreatestStoryEverTold_AC.indd 165 1/4/17 3:11 PM Figure 14A: Ice Crystals Photograph by Helen Filatova 3P_GreatestStoryEverTold_AC.indd 181 1/4/17 3:11 PM Figure 15A: Levitating Magnet Photograph by Mai-Linh Doan 3P_GreatestStoryEverTold_AC.indd 195 1/4/17 3:11 PM Recall that in an electromagnetic wave the electric (E) and magnetic (B) fields oscillate back and forth in directions that are perpendicular to the direction of the wave, as shown: Figure 15B E B C 3P_GreatestStoryEverTold_AC.indd 198 1/4/17 3:11 PM Figure 19A: New Quark-Antiquark Pair quark antiquark It would be like stretching a rubber band Eventually the band will snap into two pieces instead of stretching forever Each piece in this case would then represent a new bound quark-antiquark pair 3P_GreatestStoryEverTold_AC.indd 242 1/4/17 3:11 PM Higgs Particles By this I mean that if we can focus enough energy at a single point in space, we can excite real Higgs particles to emerge and be measured One can picture this as follows In the language of elementary particle physics, using Feynman diagrams, we can think of a virtual Higgs particle emerging from the background Higgs field, giving mass to other particles T h e left diagram corresponds to particles such as quarks and electrons scattering off a virtual Higgs particle and being deflected, thus experiencing resistance to their forward motion T h e right diagram rep-resents the same effect for particles such as the W and the Z Figure 20A We can then simply turn this picture around: Figure 20B 3P_GreatestStoryEverTold_AC.indd 256 1/4/17 3:11 PM Figure 21A 3P_GreatestStoryEverTold_AC.indd 265 1/4/17 3:11 PM Figure 21B 3P_GreatestStoryEverTold_AC.indd 267 1/4/17 3:11 PM Figure 21C 3P_GreatestStoryEverTold_AC.indd 268 1/4/17 3:11 PM ... 3P_GreatestStoryEverTold_AC.indd 256 1/4/17 3:11 PM Figure 21A 3P_GreatestStoryEverTold_AC.indd 265 1/4/17 3:11 PM Figure 21B 3P_GreatestStoryEverTold_AC.indd 267 1/4/17 3:11 PM Figure 21C 3P_GreatestStoryEverTold_AC.indd... 1/4/17 3:11 PM 16 THE GRE ATEST STORY EVER TOLD? ? ?SO FAR The Rotating Weather Vane What will the natural philosopher, who has escaped to the surface to explore the richer world beyond the shadows, discover?... region around the center of the figure, and at faraway places where all the peaks might again line up: 3P_GreatestStoryEverTold_AC.indd 88 1/4/17 3:11 PM Figure 7F 3P_GreatestStoryEverTold_AC.indd