BlackHole

General relativity does not seem to conserve energy, only energy-momentum because energy alone is frame dependent but general relativity treats all frames of reference as equivalent. I found this paper very helpful but it's rather advanced stuff. I really have problems to digest it.

Two entangled photons can be millions of miles apart and yet, if the polarity of one photon flips, the other will flip simultaneously. To a lot of classical physicists such as Einstein, the existence of nonlocal phenomena would mean that the two photons are communicating at superluminal speeds which is a no-no. Einstein called it "spooky action at a distance." Many have refused to accept the completeness and even the correctness of QM for this reason. But the superluminal objection is flawed in my opinion, because it assumes the physical existence of space. There is no space and therefore it is easy to see that there is no superluminal or any sort of communication taking place between the entangled photons. Particles do not exist in space, they just exist. There is no spooky action at a distance because there is no distance between particles. This is not the same as saying that the distance is zero; distance simply does not exist: it is abstract. More precisely, it is the abstract vector difference between two positional properties. The Big Bang predicts that no elements heavier than lithium would have been created, yet elements heavier than lithium are observed in quasars, which presumably are some of the oldest galaxies in the universe. The third problem is since the big bang nucleosynthesis produces no elements heavier than lithium, then we ought to see some long lived remnant stars which have no heavy elements in them. Up to now we don't see them.

String theory/M-theory is highly speculative. We have no evidence for extra-dimensions and D-branes. In fact we don't have evidence for the physical existence of space & time (see EPR paradox). I am convinced (and always were) that everything must draw upon a energy/power source. I think gravity is a quantum-dynamical effect. If we examine carefully we'll notice that electrodynamics, quantum mechanics, statistical thermodynamics, condensed matter physics, nuclear physics, plasma physics etc. do not agree with general relativity about the physical existence of space-time. The fact that gravitational singularities and non-baryonic dark matter have never been directly detected is not good a sign for the BBT. Another problem is that the BBT predicts a new class of stars, in which lithium should be abundant. Up to now we don't see it.

According to classical gravity, gravitation in the center of the earth should be zero. This means that if we could tunnel a cave to the center of the earth, there should be no gravitation there. The question is whether gravity depends only on mass & distance or also on density & pressure. See gravitoelectromagnetism. PS: Pressures and temperatures increase with depth inside the Earth, reaching maximum values of 364 gigapascals (GPa; 3,640,000 atmospheres) and about 6,000 kelvins at the centre. The interior temperatures are high enough to partially melt a small fraction of the crust and mantle and to completely melt the outer core. Most of the interior, however, including the inner core, is at a temperature below the melting point.

Gravity must draw upon some energy/power source in order to do work. It cannot draw upon 4-dimensional spacetime. I think it's the earth's core. I also think that a "force" which curves our vacuum cannot be weak. Einstein said that mass inside stars is converted into energy. I think there is a deeper reality to it.

Our predictions usually take longer than expected. Unfortunately, the only things which can be predicted very accurately are astronomical events. Quantum gravity predicts the existance of gravitons, the mediator of the gravitational force. Another thing, which is much more speculative i'd say, are new particles which could be the dark energy. I'm also skeptical about the Higgs boson. If the particle does not exist, this will be a setback for Lambda-CDM. I like to believe that what can't be measured does not exist. It's speculative but the gravitational phenomena could be generated by the earth's core, the most reliable atom smasher i'd say. The magnetic monopoles thought not to exist could be this. Another discovery, which i believe is consistent with this, is that stars really have a size limit quite below than was predicted. This is also consistent with what Einstein said (before he developed general relativity): mass inside stars is converted into energy. Regards

In general relativity the gravitational field energy-momentum 4-tensor is a pseudo-tensor. Basically GR conserves energy-momentum, which is generally different to energy conservation, which general relativity conserves only in asymptotically flat space-times. Energy is a frame dependent concept, and as there are no preferred frames in GR there is no clear definition of energy or whether it is conserved or not. http://arxiv.org/PS_cache/gr-qc/pdf/0410/0410004.pdf http://arxiv.org/PS_cache/hep-th/pdf/0308/0308070.pdf http://www.pma.caltech.edu/Courses/ph136/yr2002/chap01/0201.2.pdf In order for energy to be conserved, the matter energy-momentum 4-tensor must satisfy the requirement that the covariant 4-divergence must be 0. However,though this is the natural covariant extension of the flat-case conservation law [math] \mbox{SR}:\partial^{\mu} \Theta_{\mu\nu}^{\mbox{matter}} =0\rightarrow \mbox{GR} :\nabla^{\mu} \Theta_{\mu\nu}^{\mbox{matter}} =0 [/math]

In 2008, the LHC should confirm the existence of the Higgs boson. The accelerator is a circular type. The accelerated particles move in a circle until they reach sufficient energy. The particle track is bent into a circle using dipole magnets. The advantage of circular accelerators over linacs is that components can be reused to accelerate the particles further, as the particle passes a given point many times. However they suffer a disadvantage in that the particles emit synchrotron radiation. However the machine will barely touch the lower-limit that is placed on the decoupling energy associated with gravitons & dark energy particles. In order to test for future theories of gravitation we'll have to reach energies 1,000 to 1,000,000 times higher than the LHC can, that is 10 PeV to 10 EeV. For the very difficult task, new technologies will have to be developed over particle accelerators. Currently it's not possible to make such a difficult prediction but what kind of technology do you think could be used?

I think that light (or any other form of electromagnetic radiation) may possess other properties we don't understand. It remains to be seen whether non-baryonic matter really exists. Could light be the mediator of gravity? There may be a connection between photons and neutrinos but this is still speculative.

Many physicists start to believe that cosmic inflation can explain the acceleration without the need for dark energy. Other believe it's an experimental error. Viable exact model universe without dark energy from primordial inflation David L. Wiltshire http://www.arxiv.org/abs/gr-qc/0503099 Primordial inflation explains why the universe is accelerating today http://arxiv.org/hep-th/0503117 Effect of inhomogeneities on the expansion rate of the Universe http://arxiv.org/hep-ph/0409038 The Effect of Inhomogeneities on the Luminosity Distance-Redshift Relation: is Dark Energy Necessary in a Perturbed Universe? http://arxiv.org/abs/astro-ph/0501152 Exact model universe fits type IA supernovae data with no cosmic acceleration http://www.arxiv.org/abs/astro-ph/0504192 Primordial inflation explains why the universe is accelerating today http://arxiv.org/hep-th/0503117 Do Large-Scale Inhomogeneities Explain Away Dark Energy? http://arxiv.org/abs/astro-ph/0503553 Can superhorizon cosmological perturbations explain the acceleration of the universe? http://arxiv.org/abs/astro-ph/0503582 Here's a paper by Halton Arp: The Discovery of a High Redshift X-ray Emitting QSO Very Close to the Nucleus of NGC 7319 http://arxiv.org/abs/astro-ph/0409215

Marc McCutcheon believes that matter expands with the space around it, therefore we don't feel any expansion. This is called the expansion theory. I also think that 'expansion of space' is wrong. This could be an optical illusion. I think that the universe is like a blackbody radiator and that the CMBR is basically what's prevents all matter from collapsing into a gravitational singularity (which is also impossible). Maybe future understanding of the CMBR would give better explanations for all what's going on. Another explanation is that our understanding of redshifts is incomplete or/and that the Friedmann equation is not correct at late times.

Yes measuring Planck's constant can be done in laboratories provided the right equipment is available. By looking at the blackbody radiation data it's possible to measure Planck's constant. Here's another paper which explains it well. More difficult questions are: Do blackbodies really exist as we think of them? Could the universe be one? I'm sure that future X-ray missions will answer these questions.

Thanks Martin. But how did Max Planck arrive at h = 6.626196 x 10-34 J s? Could it be wrong? How do we know these units are true? Planck's constant has units of energy multiplied by time, but doesn't it speak for itself? Isn't time also energy (because we measure time by seconds)? If Planck's law is true than type III civilizations could be able to get to Planck tempertures, and type IV civilizations must, in order to fit the requirements. We are between Type 0.3 and Type 0.8. Astronomer Don Goldsmith reminds us that the earth receives about one billionth of the suns energy, and that humans utilize about one millionth of that. So we consume about one million billionth of the suns total energy. At present, our entire planetary energy production is about 10 billion billion ergs per second. Planck's temperature implies that the universe will at some point in time run out of energy and collapse under itself to form an enormous black hole. I don't believe this will ever happen.

We know that there're no physically meaningful temperatures below absolute zero or zero-point energy. At the zero-point energy there is a singularity. It can be shown from the laws of thermodynamics that the temperature can never be exactly absolute zero; this is the same principle that ensures no system may be 100% efficient, although it is possible to achieve temperatures arbitrarily close to it. I was wondering whether the same laws apply to high temperatures. Basically temperatures becomes physically meaningless higher than Planck's temperature at 1.41679 × 1032 K (that's a very high temperature we'll never reach). In fact we have discovered the quark-gluon plasma, a superheated, high-density mass of quarks and gluons which is believed to have existed during the first 20 or 30 microseconds of the Universe's existence. Could there be a singular point much before Planck's temperature?

Do you think it is possible, in principle at least, to build a particle accelerator which will collide protons at super-high energies of up to 10 PeV? In order to test superstring theory we'll probably need to 're-create the creation'. This is not possible with current technology because the energies required are trillions of trillions of times larger than the hydrogen bomb. Although such a complex design will probably not be finished in my lifetime (and probably not before 2100), i believe this is achievable. Also the problem is that the structure might take the size of half the solar system. The greatest mystery is what really happenes at temperatures of up to 100 quadrillion kelvins. Maybe the problem is not practical but theoretical. In other words, although the string equations are perfectly well-defined, no one can solve them yet. Maybe Quantum computers and new numerical algorithms will solve the problem. What we need is new math to solve it... PS: See also the final theory with a heated discussion on physics.com.

Halton Arp says that redshift is not a reliable distance indicator and that some redshifts might be intrinsic. Arp discovered, from photographs and spectra with the big telescopes, that many pairs of quasars ("quasi-stellar objects") which have extremely high redshift z values (and are therefore thought to be receding from us very rapidly - and thus must be located at a great distance from us) are physically connected to galaxies that have low redshift and are known to be relatively close by. Allessio Notari believes that Friedman's equation is not suitable at very great distances (or at late times). http://arxiv.org/PS_cache/astro-ph/pdf/0503/0503715.pdf I think the CMB could be: 1) the local ground-state of the quantum vacuum 2) the polar opposite of gravity I hope the 2nd year WMAP data will be released until 2006. The longer the release is delayed, the more I suspect that the delay is due to a "problem" with the magnitude of the small angle anisotropies.

The question "how is space expanding?" or "what is space expanding into?" is not only sophisticated but also tricky because it depends on two things: 1) what is meant by space and 2) how we measure distances. Generally, a space is a set with some additional structure. Important is to realize that the distance in the Riemannian metric is the one which is growing.

I just copied the sign. Basically it can be written as Lambda-CDM. I didn't like Alec MacAndrew's darwinistic approach. Here's a friendlier correction to plama cosmology by Edward L. Wright.

Here's some very useful paper i found which corrects the mistakes made in Lerner's plasma cosmology in favor of the ΛCDM model and standard big bang cosmology. http://www.evolutionpages.com/big_bang_no_myth.htm I guess the ΛCDM will remain of top until 2007-2008 LHC experiment which should confirm the existence of the Higgs boson and other supersymmetric particles. I guess that the only good argument against the big bang cosmology is that some redshifts might be intrinsic or that the Friedmann equation might not be reliable at late times.

It's highly unlikely that something physical will ever breach the speed of light because there is no known energy to carry it. This will require some unknown force (extra-dimensional) we don't know about. What was observed in quantum tunneling was an illusion. There was no particle that really went faster than light because of the uncertainty principle.

No, i believe that what you did was correct. The integration by parts was correct but first we need to find the antiderivative because elliptic functions are inverse to elliptic integrals. Jacobi's elliptic functions (which are the closest to elliptic integrals) arise as solutions to the form: [math] \frac{d^{2x}}{dt^2} = A + Bx + Cx^2 + Dx^3 [/math]

Elliptic functions are beyond me. I don't know whether that's required for QM and especially GR though. Edit: An EllipticF is the eliptic integral of the first (F) kind defined as: [math]F(x,k)=\int_0^x\frac{dx}{\sqrt{(1-x^2)(1-k^2x^2)}}[/math]. Mathematica gave this answer: [math]\int \cos^{3/2}x \ dx = \frac{2}{3} (EllipticF[\frac{x}{2}, 2]) + \sqrt {cos x} \ sin x[/math] Elliptic functions are not widely used in physics (except maybe dynamics) but anyway.

From integration by parts i got: [math]\cos^{3/2}x = \cos x (cos^{1/2})[/math] [math]u = \cos^{1/2}x ; dv = \cos x ; v = \sin x[/math] [math]\cos^{1/2}x (\sin x - {1/2}) \int \sin x^{3/2}x dx[/math] That's a problem in itself... I think we need to use [math]F(x,k)=\int_0^x\frac{dx}{\sqrt{(1-x^2)(1-k^2x^2)}}[/math].

Does anyone have any idea how i can find the antiderivative of cos3/2x in terms of simple functions? The result is [math]\frac{\sqrt \cos{x}}{1/2}[/math]. Ive been playing with it, cant really get anywhere. I was trying to figure out a way with trig identities to simplify it, but I can't get rid of the square root. Maybe using Jacobi's elliptic functions will solve the problem.