coldcreation Posted January 26, 2008 Report Posted January 26, 2008 This thread is temprarily on hold. Please refer to SNe Ia, Implications, Interpretations, Lambda-CDM to continue the discussion of lambda. No one really knows if dark energy exists or not. Astronomers do not "know it is there." You can take lambda out of the trash, but you can't take the trash out of lambda! If you subscribe to quantum field theory, the Casimir effect is direct evidence that vacuum energy is real or that the vacuum expectation value is not necessarily zero. [...] my point being: We would have a hard time saying it doesn't exist. There is a huge difference, both conceptually and physically, between energy (zero-point energy, ground state energy, or energy in general) and "dark" energy. You seem to be implying that they are one and the same thing. This is obviously not the case. They are very, very related. Any "zero point energy" should be a source of gravity- hence a source of "dark energy." It may not be the ONLY source of dark energy but it certainly is one source that should exist. That ZPE gravitates is not the problem. The problem occurs when dark energy is treaded as if it were negative energy (or negative pressure). ZPE is not negative energy, nor is it a negative absolute pressure, or negative gauge pressure). It is non-zero and positive. Though ZPE gravitates, it does not follow that ZPE is a source of dark energy. Zero point energy is the lowest possible energy state of a system. It cannot be removed from the system. Nor could it be a zero-point field; the lowest energy state of a field (also called the ground state). I am, by the way, a fervent believer in Einstein's cosmological term. I believe that its value is not just close to zero, but is precisely zero. This implies that the vacuum energy should be exactly 0 as well. I know of no way to do this except unbroken super-symmetry which is experimentally ruled out. That would be the case if (and only if) the cosmological constant was in fact vacuum energy. Unfortunately that is not fact. I argue that it is possible to have lambda equal to zero and vacuum energy non-zero, i.e., positive. So, as energy tends to zero, the vacuum state described by lambda is approached, but not attained (since there will always remain a residual ground energy). The stress-energy tensor of the vacuum does not obligatorily (or, at all) lead to a negative energy state, as long as lambda is thought of as a vacuum state that induces a 'tension' (rather than a kind of energy with a plus or minus sign). It can then be shown that lambda acts as a repulsive force without actually being one. It follows that because we live in a universe with matter (as opposed to one that is empty), the gravitational field curvature is implicitly and explicitly a result of the tension associated with lambda in the presence of matter. There is no fine-tunning problem since lambda and gravity are not opposite forces (energies or pressures). They are simply part of the same field, where lambda represents the ultra-high vacuum minima. In geometrical terms, lambda describes the special relativistic gravity-free vacuum state with a Minkowski spacetime signature, while the field equations of general relativity describe the deviation-from-linearity (the curvature) of the manifold obtained by measurements of the metric properties internal to the manifold. A non-zero lambda is the most straightforward way to understand dark energy. How does treating 'something' as non-zero provide a clue as to the nature of 'something.' With the description above, a "non-zero" lambda is simply called gravity. This may appear, at first glance, to be a non-conventional precept of spacetime, or at least a non-conventional interpretation of lambda. But it actually is not, since there is no new physics involved, and since lambda still represents (or describes) the state of empty space in relation that which gravitates, i.e., in interaction with the gravitational field (in semi-accord with Einstein's initial version of lambda). However it is no longer a parameter that can be tweaked, since its value must remain constant and equal to zero at all times. And so it does not increase with distance opposite to the inverse square reduction of the gravitational potential with distance. Curvature varies, lambda would not. The good news: we rid ourselves of the "tendentious tenebrous speculation that the cosmological constant is different from zero" (see Sandage 1993). ... Move Einstein's constant to the other side (the stress energy tensor side), and we can recognize it as the energy density of empty space, i.e. what you called "zero-point energy." The difference here is that you describe lambda (in accord with the standard contemporary interpretation) as the energy density of empty space, or ZPE as you wrote above, whereas I describe it as the minima of curvature upon which (or within which) ZPE and other forms of mass-energy; galaxies, stars, planets, people, etc., subsist. The explosion of 1998 seemed capable of blowing-up the bureaucratic shell of expansionists. But the regenerative capacity of the cosmological constant has once again played its role. In the long run, the only good deed introduced by the resurrected trepidation could be that it may unwittingly have set in motion the forces that will end the Great Cosmological Slump of the twentieth century. But that is a distant threat, for now. There are no reasons yet (or, perhaps there is one) to shrug off the disturbing evidence of gravity’s weakness (failure) to slow down the runaway universe. We humans naturally reach for transcendence (not transhumance), seeking symbols with which to make it real. Science and religion have always worked that way. So, for that matter, has art. But transcendence, by definition, transcends. We should be reticent, consequently, in the claims we make on the unlimited—the existence of a force above and apart from the material world. And equally reticent, yes, in claims we make on absolutes. CC Quote
Erasmus00 Posted January 26, 2008 Report Posted January 26, 2008 That ZPE gravitates is not the problem. The problem occurs when dark energy is treaded as if it were negative energy (or negative pressure). ZPE is not negative energy, nor is it a negative absolute pressure, or negative gauge pressure). It is non-zero and positive. Though ZPE gravitates, it does not follow that ZPE is a source of dark energy. Zero point energy is the lowest possible energy state of a system. It cannot be removed from the system. Nor could it be a zero-point field; the lowest energy state of a field (also called the ground state). A brief example of how gravitating zero point energy can cause "dark energy." Consider a universe that has real scalar particles in it, described by a field [imath]\phi[/imath] with action [math] S = \int \sqrt{-g} d^4x \frac{1}{2}g^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi - V\left({\phi}\right) [/math] This has a stress energy tensor [math] T_{\mu\nu} = \frac{1}{2}\partial_{\mu}\phi\partial_{\nu}\phi +\frac{1}{2}g^{\rho\sigma}\partial_{\rho}\phi\partial_{\sigma}\phi g_{\nu\mu} -V\left(\phi\right)g_{\mu\nu} [/math] Now, lets assume that we have a vacuum, the state of lowest energy of our system. [math] T_{\mu\nu} = -V\left(\phi_o\right)g_{\mu\nu} = -\rho_{vac}g_{\mu\nu}[/math] Here I identified the lowest value of V as the energy density of the vacuum. Lets go to a local lorentz frame and look at this. [math] T_{\mu\nu} = \rho_{vac} \left(\begin{array}{cccc} 1&0&0&0\\ 0&-1&0&0\\0&0&-1&0\\0&0&0&-1 \end{array}\right) [/math] Now compare this to the stress energy tensor of a perfect fluid with energy [imath] \rho[/imath] and pressure P. [math] T_{\mu\nu} = \left(\begin{array}{cccc} \rho&0&0&0\\ 0&P&0&0\\0&0&P&0\\0&0&0&P \end{array}\right) [/math] We see right away that the energy of a vacuum (the positive energy density) can be thought of as a perfect fluid with [imath] P = -\rho_{vac} [/imath]. While I have shown this for one specific case, it is a general result. Vacuum energy behaves as a fluid WITH NEGATIVE PRESSURE. Now, can we identify this with a cosmological constant? Consider Einstein's equations with cosmological constant (as Einstein wrote it) [math] G_{\mu\nu} +\Lambda g_{\mu\nu} = 8\pi T^{matter}_{\mu\nu}[/math] If we move lambda to the other side, we see that the right side can be written [math] 8\pi\left(T^{matter}_{\mu\nu} -\frac{\Lambda}{8\pi} g_{\mu\nu}\right)[/math] Comparing this to our above expression for the stress energy tensor, we see that [math] \frac{\Lambda}{8\pi} = \rho_{vac}[/math] Hence, the cosmological constant is completely equivalent to vacuum energy! So, to recap- I have demonstrated that 1. Vacuum energy (what you call zero point energy) gravitates as a fluid with negative pressure. 2. This vacuum energy/pressure whatever you want to call it is exactly equivalent to a cosmological constant as Einstein introduced it. Care to comment? -Will Quote
coldcreation Posted January 26, 2008 Author Report Posted January 26, 2008 This thread is temporarily on hold. I will re-open it at a later date. Please refer, for now, to SNe Ia, Implications, Interpretations, Lambda-CDM... for a continued discussion on the cosmological constant. Will, could you re-post the above in that thread? Sorry for the inconvenience. Modest is right. Lambda needs to be discussed in the context of the latest evidence, viz, the SNe Ia data, not in the context of a stationary universe model, where I was headed.:) CC Quote
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