Relativity Lite

80 | Relativity Lite effect on the early expansion of the universe: * the negative pressure of the Higgs field would produce a repulsive gravitational force that would overpower its own inward tugging on spacetime once the density of the universe became low enough. Within 10 −35 seconds the universe would double 100 times to become 10 30 times its original size! † Andreas Albrecht with Paul Steinhardt and Andrei Linde, proposed modifications that account better for the production of a hot fireball at the end of this inflationary expansion that would look very much like the standard Big Bang. ‡ WHY WOULD THE HIGGS FIELD PRODUCE A NEGATIVE PRESSURE, AND WHY WOULD THIS OPPOSE GRAVITY? One of the fascinating facets of quantum mechanics is Heisenberg’s uncertainty principle , which says that one cannot know both a particle’s position and its momentum with absolute certainty. Imagine, for instance, shining light on a tiny particle so that one may see it in a microscope. One would like to use light with a short wavelength, since objects have to be bigger than, or roughly the same size as, the distance between light wave crests in order to be seen. But unfortunately, short wavelength light, such as ultraviolet (UV) radiation, has higher energy and momentum § than long wavelength light, such as infrared (IR) light. So imaging the particle with UV would allow one to see where the particle is more easily, except that UV will also kick it away from the light source so that one has less of an idea of where it is after the attempt. On the other hand, imaging the tiny particle with IR would help keep the particle more in place while we image it, but IR waves are so long that we can- not use them to see the particle if that particle is small enough. This difficulty is a physical manifestation of the uncertainty principle. Given that energy and time are related in relativity to momentum and position, one should not be surprised that an uncertainty principle involving time and energy also ap- pears in quantum mechanics. One of the most interesting manifestations of this is that one may violate our certainty that energy is conserved as long as one does so for a very short time. It turns out that what we think about as the emptiness of spacetime constantly has pairs of electrons and their antimatter partners, called positrons, springing into existence, existing for a very short time, and then annihilating each other, giving back the energy they “borrowed” from the universe in order to come into being. Virtual protons and antiprotons likewise spring into existence in empty space, in the room before us, and in between our * Alan H. Guth, Phys. Rev. 23 , 347 (1981). † Alan H. Guth, The Inflationary Universe: The Quest for a New Theory of Cosmic Origins (Addison Wesley, Reading, MA, 1997), p. 171–77. ‡ Andreas Albrecht and Paul J. Steinhardt, Phys. Rev. Lett. 48 , 1220 (1982); Andrei D. Linde, Phys. Lett. B 175 , 395 (1986). § Yes, massless particles have momentum. In general, the ratio of momentum to energy is, from figure 3 of chapter 2, p E mv mc v c = = γ γ 2 2 . For light, v = c so p E c c c = = 2 1 , or p = E/c .