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    Not Afraid Of The Dark: Dark Energy As The Ultimate Sisyphus
    By Sascha Vongehr | November 15th 2010 06:11 AM | Print | E-mail | Track Comments
    About Sascha

    Dr. Sascha Vongehr [风洒沙] studied phil/math/chem/phys in Germany, obtained a BSc in theoretical physics (electro-mag) & MSc (stringtheory)...

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    Many are troubled by dark energy. I will tell you first why dark energy is really crazy. Then I tell you that the crazy part is not actually the problem of dark energy, but one of basic general relativity. Many educated people are proudly critical of dark stuff, but when it comes to relativity, they do not want to be found hanging out in the crack-pot corner. In other words, my post is directed at the guys who go: “I know about relativity and agree it is more or less fine what those cosmologists did then, but this dark stuff now is going too far! Stop the wild guessing and go back to doing proper science.”


    One aside: The main reason for dark stuff being widely rejected is a psychological one, of course: the “dark” scares daytime hunting animals like us. People do not care much about something called “cosmological constant”, which is constant dark energy. Same with “dark matter”: “dark” merely implies that the matter is not as visible as that inside blindingly bright stars that shine in skies gazillions of light years away. Cold brown dwarf stars and other entirely mundane things belong to dark matter.

    Some comments on the space plunger and on energy non-conservation illustrate a big difficulty with dark energy. I will let Straw-man give his version:

    Straw-man: “Imagine a gas with a pressure P that pushes on the walls of a box. Now add gravity: Either make the gas molecules heavier, or add a big mass in the middle of the box, or just consider that the pressure itself actually leads to gravity, as it does in general relativity. This “added” gravity will pull the particles towards each other, and it pulls on the walls, and these two each imply that the added gravity is a negative contribution to the pressure. Thus, gravity is negative pressure, because it pulls, and positive pressure implies expansion. Pressure is the opposite of gravity: repulsion, not attraction! However, cosmologists tell us that dark energy has negative pressure and leads to expansion of space. If it is negative pressure, it should contract, not expand!”


    All this is correct up until “the added gravity is a negative contribution to the pressure”. Gravity may pull on the walls, but that pull is proportional to the mass of the walls. Gravity also pulls on the gas particles, thus they are more numerous in the center of the box, but that may even increase the pressure: although the particles collide less often with the walls of the box, they collide more often with each other in the center of the box. If the mass is so large that all the gas is clumped into a hot sun in the middle of the box, the walls feel little pressure. The pressure in the box is nevertheless large if you sum it all up, because the pressure in the sun is large. With gravity, pressure becomes inhomogeneous, and all the pressure of a system, just like all the energy, contributes to the system’s gravity.

    All pressures here are positive. There are no negative pressures in Straw-man’s box of gas. Gravity is not pressure. In Einstein’s equation Guv + Λ guv = Tuv, pressure is in the pressure-energy density tensor T on the right hand side. It is the physical source of what happens. Gravity, the Guv, is on the left side. Its essence is curvature of space-time. Gravity is non-linear and so on, meaning gravity self-interacts and it seems in this sense that it is its own source. Still, G is curvature of space-time, not a force; T is what includes pressure as a source.


    Straw-man: “Dark energy has negative pressure. So how can it lead to expanding space? Internal pressure expands stuff! Internal negative pressure contracts.”


    Dark energy is not expanding stuff. Space itself expands. Dark energy has negative pressure. It wants to contract. It tries to pull itself together. However, because its pressure is more negative than its energy density can contribute positively, space-time is curved in such a way that space expands. So there is more and more space, and thus there is more and more dark energy, too. Dark energy is the ultimate Sisyphus. It is shy; it wants to disappear into a point, but trying to do so, space-time blows it up onto a bigger and bigger stage. Pure Buddhism: The very act of trying to relieve the suffering increases it.


    Straw-man: “If it pulls to contract, space should contract. Something here is fishy with those cosmologists’ ad hoc solutions. They did fine using Einstein’s formulas and all, but now adding this dark stuff, enough already, it is going too far.”


    Wait a minute! The crazy point is that something that pulls itself together expands, right? But that is not the contribution of dark energy. That part is usual general relativity. It has been accepted for almost a century by now: Pressure, although it pushes and "wants to expand", contributes to gravity, which pulls and leads to contraction. It is the contribution of the internal pressure that makes a neutron star collapse to a black hole. If you do not accept that, why blame today’s researchers? Have the guts to doubt Einstein.


    For other entries in the demystifying “the boring universe” series:

    Black Holes Demystified

    The Lameness of Inflation