No one has claimed that there's no dark matter or dark energy "in our neighborhood." In fact, the best understanding is that there should be both. The problem is detecting it. On large scales where you're dealing with large quantities of any kind of matter, it's not too hard to see the effect. But, on the scale of Earth or the solar system, even, the concetrations of dark matter (or dark energy) shouldn't be enough, compared to those of the massive bodies present, for us to see them through their effect on gravity. Instead, we would need some other means of detection. This is where dark matter being dark becomes a problem.
As I'm sure you've heard, there are four fundamental interactions between physical objects - gravity, electromagnetism, and the weak and strong interactions. We've already said that gravity is not a way we can directly detect local dark matter. So, we need to consider the other three. However, for any of these, we know of particles that don't couple to the interaction. For example, electrons don't interact through the strong force and neutrinos don't interact through electromagnetism.
The defining property of dark matter is its "darkness," which means that it doesn't couple to electromagnetism - it can't absorb or emit light. Further, it is extremely unlikely that it couples to the strong force, as particles that couple directly to the strong force can usually only exist bound together with each other. Also, we would expect strong coupled dark matter to interact with nuclei. So, the only thing we can hope to look at is a coupling to the weak interaction, which is already how we detect neutrinos. This raises a new problem - neutrinos are extremely common in the solar system, but actual detected events from weak interactions with neutrinos are rare. If dark matter particles are significantly scarcer than neutrinos in the solar system, interactions with them might be so rare as to be for all practical purposes undetectable.
As for "real equations" describing the universe, we already know that whatever they are they are far more complicated than F=ma. Look up the Einstein field equation, which is relativistic description of gravity.
First, this is all wholly irrelevent to the point I was making. What I said was that if physical constants of the universe are changing quickly enough or over short enough distances that we can measure the effect on manmade probes that are still within light hours of earth, we should be able to clearly make out such effect just from observing the stars nearest to us, which we don't. Your discussion seems to be focusing on much larger (extragalactic) scales.
While there is some discussion in the general physics community of the idea that the basic physical constants have changed over the history of the universe, and there are experimental programs working to measure such effects if they exist, there is currently no hard evidence to suggest such change. The "quantized red shift" you cite has already been thoroughly debunked (see, for example, http://xxx.lanl.gov/abs/astro-ph/0208117) as an artifact of small sample size in the earlier studies. This is not to say that we don't see groups of galaxies close together with similar redshifts; but that is thought to be the effect of gravitational binding leading to large scale structures in the universe.
Finally, the standard interpretation of the redshifts of light from distant galaxies is not as a doppler shift, which has to do with objects moving apart from each other through space, but with space itself expanding. Imagine that you have pieces of confetti sprinkled about on a sheet of rubber. If you stretch the rubber, the pieces of confetti will move apart from each other without moving across the sheet. In much the same way, as space expands, galaxies move apart from each other simply by staying at the same place in space. The reason this leads to light being redshifted is that space expands pretty much uniformly everywhere, even between subsequent peaks of a light wave. As the peaks of the wave are stretched apart, the wavelength increases, meaning that the light will appear redder.
If the physical constants of the universe were changing on time and distance scales small enough to be affecting either the Pioneer probes themselves or the signals sent to and from them, we would be able to detect such changes extremely easily, just by observing the few stars closest to us (not to mention the 200 billion or so other stars in the galaxy, and so on).
Relativity, while requiring some radical changes to theories of mechanics does not in any way violate determinism. The problems with classical determinism arise from quantum mechanics, which includes probabalistic elements at a fundamental level. However, even quantum mechanics does not totally abandon determinism - in fact, to do so would make the systematic study of physics quite impossible. In quantum mechanics, the wave function obeys perfectly deterministic laws. However, since the physical information carried by the wave function is interpreted to be the probability distribution of one or more particles, the results of any given observation cannot be predicted; but the results of a large number of measurements, when considered together, are.
There is no canonical conception of hell in Judaism. However, at various times and in various places there have been quite a few different ideas of hell in folk Judaism.
In this case, it doesn't matter whether the nucleus is a boson or a fermion. It matters whether the atom as a whole is. Since BECs are created at very low temperatures, it is pretty much assured that every atom has all its electrons, and, for the purposes of interactions with other atoms, acts as a single particle.
I bring this up because it is quite possible to have a fermionic atom with a bosonic nucleus. Take, for example, Nitrogen-14. The 14, or course, means it must have 14 nucleons, making the nucleus a boson. However, Nitrogen has 7 protons. Thus, an N-14 atom will have 7 electrons, for a grand total of 21 fermions. With an odd number of fermions, the atom is a fermion, as well.
And, of course, there are also atoms with fermionic nuclei that are, themselves, bosons (Hydrogen comes to mind).
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No one has claimed that there's no dark matter or dark energy "in our neighborhood." In fact, the best understanding is that there should be both. The problem is detecting it. On large scales where you're dealing with large quantities of any kind of matter, it's not too hard to see the effect. But, on the scale of Earth or the solar system, even, the concetrations of dark matter (or dark energy) shouldn't be enough, compared to those of the massive bodies present, for us to see them through their effect on gravity. Instead, we would need some other means of detection. This is where dark matter being dark becomes a problem. As I'm sure you've heard, there are four fundamental interactions between physical objects - gravity, electromagnetism, and the weak and strong interactions. We've already said that gravity is not a way we can directly detect local dark matter. So, we need to consider the other three. However, for any of these, we know of particles that don't couple to the interaction. For example, electrons don't interact through the strong force and neutrinos don't interact through electromagnetism. The defining property of dark matter is its "darkness," which means that it doesn't couple to electromagnetism - it can't absorb or emit light. Further, it is extremely unlikely that it couples to the strong force, as particles that couple directly to the strong force can usually only exist bound together with each other. Also, we would expect strong coupled dark matter to interact with nuclei. So, the only thing we can hope to look at is a coupling to the weak interaction, which is already how we detect neutrinos. This raises a new problem - neutrinos are extremely common in the solar system, but actual detected events from weak interactions with neutrinos are rare. If dark matter particles are significantly scarcer than neutrinos in the solar system, interactions with them might be so rare as to be for all practical purposes undetectable. As for "real equations" describing the universe, we already know that whatever they are they are far more complicated than F=ma. Look up the Einstein field equation, which is relativistic description of gravity.
I'm afraid that paper's already been debunked. It seems they accidentally included a thin disk of mass by using an incorrect solution to (of all things) Laplace's equation. See: http://arxiv.org/abs/astro-ph/0508377 http://arxiv.org/abs/astro-ph/0510750 http://arxiv.org/abs/astro-ph/0601191
First, this is all wholly irrelevent to the point I was making. What I said was that if physical constants of the universe are changing quickly enough or over short enough distances that we can measure the effect on manmade probes that are still within light hours of earth, we should be able to clearly make out such effect just from observing the stars nearest to us, which we don't. Your discussion seems to be focusing on much larger (extragalactic) scales. While there is some discussion in the general physics community of the idea that the basic physical constants have changed over the history of the universe, and there are experimental programs working to measure such effects if they exist, there is currently no hard evidence to suggest such change. The "quantized red shift" you cite has already been thoroughly debunked (see, for example, http://xxx.lanl.gov/abs/astro-ph/0208117) as an artifact of small sample size in the earlier studies. This is not to say that we don't see groups of galaxies close together with similar redshifts; but that is thought to be the effect of gravitational binding leading to large scale structures in the universe. Finally, the standard interpretation of the redshifts of light from distant galaxies is not as a doppler shift, which has to do with objects moving apart from each other through space, but with space itself expanding. Imagine that you have pieces of confetti sprinkled about on a sheet of rubber. If you stretch the rubber, the pieces of confetti will move apart from each other without moving across the sheet. In much the same way, as space expands, galaxies move apart from each other simply by staying at the same place in space. The reason this leads to light being redshifted is that space expands pretty much uniformly everywhere, even between subsequent peaks of a light wave. As the peaks of the wave are stretched apart, the wavelength increases, meaning that the light will appear redder.
If the physical constants of the universe were changing on time and distance scales small enough to be affecting either the Pioneer probes themselves or the signals sent to and from them, we would be able to detect such changes extremely easily, just by observing the few stars closest to us (not to mention the 200 billion or so other stars in the galaxy, and so on).
Relativity, while requiring some radical changes to theories of mechanics does not in any way violate determinism. The problems with classical determinism arise from quantum mechanics, which includes probabalistic elements at a fundamental level. However, even quantum mechanics does not totally abandon determinism - in fact, to do so would make the systematic study of physics quite impossible. In quantum mechanics, the wave function obeys perfectly deterministic laws. However, since the physical information carried by the wave function is interpreted to be the probability distribution of one or more particles, the results of any given observation cannot be predicted; but the results of a large number of measurements, when considered together, are.
There is no canonical conception of hell in Judaism. However, at various times and in various places there have been quite a few different ideas of hell in folk Judaism.
In this case, it doesn't matter whether the nucleus is a boson or a fermion. It matters whether the atom as a whole is. Since BECs are created at very low temperatures, it is pretty much assured that every atom has all its electrons, and, for the purposes of interactions with other atoms, acts as a single particle.
I bring this up because it is quite possible to have a fermionic atom with a bosonic nucleus. Take, for example, Nitrogen-14. The 14, or course, means it must have 14 nucleons, making the nucleus a boson. However, Nitrogen has 7 protons. Thus, an N-14 atom will have 7 electrons, for a grand total of 21 fermions. With an odd number of fermions, the atom is a fermion, as well.
And, of course, there are also atoms with fermionic nuclei that are, themselves, bosons (Hydrogen comes to mind).