The expansion rate averaged over the observer’s world line is: and using the first equation, it follows that.
1, No. You can help our author matching system! Such geodesics are incomplete. Regions like ours are constantly being formed. Its only purpose is for us to contact you about your account.
Penrose showed that a space-time satisfying the null convergence condition (and some additional mild assumptions) must contain incomplete geodesics. The answer to the question, “Did the universe have a beginning?” is, “It probably did.” We have no viable models of an eternal universe. If inflation goes on and on into the future, could it also have gone on and on into the past?7 A universe without a beginning would make it unnecessary to ask how it began. A theoretical physicist who has been working in the field of cosmology for 35 years, Vilenkin has written over 150 papers and is responsible for introducing the ideas of eternal inflation and quantum creation of the universe from The expansion is driven by a false vacuum. And according to quantum mechanics, any process which is not strictly forbidden by the conservation laws will happen with some probability.18. For any isolated system, energy is proportional to mass and must be positive. George Ellis and his collaborators have suggested that a finite, closed universe, in which space closes upon itself like the surface of a sphere, could have existed forever in a static state and then burst into inflationary expansion.9 Averaged over infinite time, the expansion rate would then be zero, and the BGV theorem would not apply. As quoted in Carl Friedrich von Weizsacker, William Craig, “Theistic Critiques of Atheism,” in.
For a homogeneous and isotropic universe, this definition reduces to the Hubble parameter. It is nonetheless the first attempt to formulate the problem of cosmic origin and to address it in a quantitative way.19. At that point, the mathematical expressions appearing in the equations of general relativity become ill defined, and evolution cannot be continued. No cause is needed for the quantum creation of the universe. If you have a radioactive atom, it will decay, and quantum mechanics gives the decay probability in a given interval of time, say, a minute. In fact, the geodesic congruence needs to be defined only along the observer’s worldline.
The most probable universes are the ones with the smallest initial size and the highest vacuum energy. Vacuum decay is similar to the boiling of water. The idea of a cyclic universe was recently revived by Paul Steinhardt and Neil Turok.11 They suggested that in each cycle expansion is greater than contraction, so that the volume of the universe is increased. [1][3][4], The theorem does not assume any specific mass content of the universe and it does not require gravity to be described by Einstein field equations. Alexander Vilenkin is Director of the Institute of Cosmology at Tufts University. In this essay, I focus on models in which it occurs through bubble nucleation. (Don't worry, your e-mail will not be distributed or made public.
where γ=1/1-νrel2 is the Lorentz factor, and νrel=p/E is the observer’s speed relative to the comoving particles. [2][1] The BGV theorem is also popular outside physics, especially in religious and philosophical debates. Roger Penrose, “Gravitational Collapse and Space-time Singularities,”, Mathematically, the null convergence condition requires that the Ricci curvature tensor, Lawrence Ford, “Negative Energy Densities in Quantum Field Theory,”. There is no reason why the atom decayed at this particular moment and not another. Imagine a two-dimensional closed universe, which we can picture as a surface of a globe. We do not find ourselves in such a state.
The BGV theorem is sweeping in its generality. http://cosmos2.phy.tufts.edu/vilenkin.html, http://humbleapproach.templeton.org/Multiverse_and_String_Theory/vilenkin.htm, http://adsabs.harvard.edu/abs/1978PhDT........45V. For an observer of mass m, the 4-momentum is Pμ=m dxμ/dτ, so that dτ=(m/E)dt, where E=P0=p2+m2 denotes the energy, and p, the magnitude of the 3-momentum. “As to the first cause of the universe,” wrote the British astrophysicist Edward Milne, “this is left for the reader to insert, but our picture is incomplete without Him.”13 Some scientists feared that a cosmic beginning could not be described in scientific terms. A deep mystery remains. When physicists or theologians ask me about the BGV theorem, I am happy to oblige.
We live in the aftermath of a great explosion—the big bang—that occurred 13.7 billion years ago. Both kinetic and gravitational energies are then equal to zero, so the total energy is zero. In the 1920s, the Russian mathematician Alexander Friedmann provided a mathematical description of an expanding universe by solving Albert Einstein’s equations of general relativity. In 2003, Tufts cosmologist Alexander Vilenkin and his colleagues, Arvind Borde, now a senior professor of mathematics at Long Island University, and Alan Guth, a professor of physics at MIT, proved a mathematical theorem showing that, under very general assumptions, the universe must, in fact, have had a … 4. everything that begins to exist has a cause; In general relativity, space and time are unified in a single four-dimensional entity, called space-time. Alexander Vilenkin is the Leonard and Jane Bernstein Professor and Director of the Institute of Cosmology at Tufts University. Richard Dawkins, Lawrence Krauss and Victor Stenger have argued that modern science leaves no room for the existence of God. The Borde–Guth–Vilenkin theorem, or the BGV theorem, is a theorem in physical cosmology which deduces that any universe that has, on average, been expanding throughout its history cannot be infinite in the past but must have a past spacetime boundary.
Inflationary theory predicted that Euclidean geometry describes the universe on the largest scales. And why are these laws the ones we have? (2016) Black holes and the multiverse Journal of Cosmology and Astroparticle Physics. If space-time is free of singularities, all geodesics should have infinite extent. I would now like to take issue with the first part of the argument. This can be illustrated by the following Newtonian example. The distinction between the dimensions of time and space disappears.
Imagine that the universe is filled with a congruence of comoving geodesics, representing test particles and consider a non-comoving geodesic observer described by a world line xμ(τ).20 Let uμ and νμ designate the 4-velocities of test particles and the observer. Both quantities are computed in the rest frame of one of the particles. sign in and mark matches as correct or incorrect. There is a loophole in this reasoning. The entropy of the universe we can now observe could be the same as the entropy of some similar region in an earlier cycle; nonetheless, the total entropy of the universe would have increased because the volume of the universe is now greater than it was before. Then the Lorentz factor of the observer relative to the particles is. Alexander Vilenkin. Inflation does not come to an end everywhere at once. A singularity appears to be unavoidable. As is usual in quantum theory, we cannot tell which of these possibilities is actually realized, but we can calculate their probabilities. There remains the null observer described by a null geodesic. The volume of the universe increases with time. See Alexander Vilenkin, “Creation of Universes from Nothing,”. Physics / Critical Essay / Vol. The bubbles are then driven apart by inflationary expansion, making room for more bubbles. If the universe had already completed an infinite number of cycles, it would have reached a state of thermal equilibrium, and so a state of maximum entropy. No matter its initial size, the universe very quickly becomes huge. Time is expressed using imaginary numbers, introduced only for computational convenience.
Caused by what? Arvind Borde, Alan Guth and Alexander Vilenkin, “Inflationary Spacetimes are Incomplete in Past Directions,”, George Ellis, Jeff Murugan and Christos Tsagas, “The Emergent Universe: An Explicit Construction,”, Audrey Mithani and Alexander Vilenkin, “Instability of an Emergent Universe,”, Paul Steinhardt and Neil Turok, “A Cyclic Model of the Universe,”. As is so often the case in physics, an irresistible force is now about to encounter an immovable obstruction. The conclusion holds for all familiar forms of classical matter. Ellis constructed a classical model of a stable closed universe and provided a mechanism triggering the onset of expansion. The laws of physics that describe the quantum creation of the universe also describe its evolution. This suggests that there could be a multitude of other universes. The energy of the gravitational field is negative;17 it is conceivable that this negative energy could compensate for the positive energy of matter, making the total energy of the cosmos equal to zero.
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