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In General Relativity Einstein's equations talk to relationship between curved space-time and the energy Tensor that represents matter. In simple mathematics, if you want to apply a constant to an equation, you can do so without skewing the results. This kind of whimsy doesn’t work when you are painting the essential equations of space time for this reason – if you begin with a value for energy of zero (0) you cannot add a constant to it without changing the resulting curve. Since zero is the value assigned to the base tensor curve of space-time the addition or subtraction to it of a constant changes (among other things) the force and nature of gravitation results. The physics of Newtonian mechanics dealing with large bodies that comprise macronic units call for arbitrary conditions of energy tensors describing matter that are unusual. For example, in the “Weak Energy” condition you have to contrive at the outset that the energy density measured by any observer in their frame is always a positive value. These artificial standards are called inequalities. Now contrast that with the micronic world of matter, especially below the ceiling of the arrow in time – otherwise known as the quantum world. This is the region well below the level of Newtonian mechanics where masses of matter rule and instead the probabilistic nature of quantum reality applies. In this quantum world the inequalities do not apply as neatly. For example, the “Weak Energy” tensor can be positive or negative at any given point. This gives us a really interesting place to be since a negative value essentially means negative energy; in this way negative energy seems to be allowed which provided for several variations of “warping” space time such as the class="copylinks">[[Alcubierre Warp drive ] that requires increasing the space- time curvature behind and decreasing the space-time curvature in front of a craft to travel faster than light. The ability to decrease curve ahead of the craft means that negative energy value is required. This freedom from inequalities was too much for some and they retreated behind the need to limit their worlds and get back to the comforts of nice rules that fit back inside the inequalities that prevail in the large mass universe. As a result they developed something called Quantum inequalities, a disciplined, but unimaginative thing to do. How did they perform this progeny? Essentially, they mathematically expanded the terrain, reaching back to build a bigger unit of space-time. The task was to move away from a single point of space-time and instead measure a weighted average of energy density in a region; in this case, the region of space-time where the observer resides. The result was to limit the durations and strength of energy density to a narrow range and, perhaps equally predictably, to reestablish inequalities as a part of even quantum mechanics. So much for romance… FOR MORE INFORMATION: Websites: {Link without Title} {Link without Title} {Link without Title} {Link without Title} Papers: Averaged Energy Conditions and Quantum Inequalities Authors: L.H. Ford, Thomas A. Roman Comments: 20pp, plain LATEX, TUTP-94-16 Journal-ref: Phys.Rev. D51 (1995) 4277-4286 A general worldline quantum inequality Authors: C.J. Fewster (Dept. of Mathematics, University of York, U.K.) Comments: 19pp, LaTeX2e. The statement of the main result is changed slightly. Several typos fixed, references added. To appear in Class Quantum Grav Subj-class: General Relativity and Quantum Cosmology; Mathematical Physics Journal-ref: Class.Quant.Grav. 17 (2000) 1897-1911 Books: Inequalities by Elliott H Lieb - Mathematics - 2002 - 721 pages Page 3 - The subject of ‘inequalities' was first systematically established by Hardy, ... the deepest formulation of the uncertainty principle in quantum mechanics. ... Quantum Mechanics: A Modern Development by Leslie E Ballentine - Science - 1998 - 672 pages Page 602 - ... Bell's theorem has been obtained as inequalities restricting correlations or probabilities, and the violation of these inequalities by quantum mechanics ... |
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