BlackHole

Your velocity can be deduced from Classical Mechanics. Also the speed of light [math]c[/math] in vacuum is constant; [math]$c = 186,000 miles/sec$[/math].

This is Special Relativity's equation for time dilation, where t' is the fraction of t that is dilated, v is velocity and c is the speed of light. [math]t' = {t\over\sqrt{1-{(v^2/c^2)}}[/math] In this case, plugging numbers for [math]v[/math] higher than [math]c[/math] return an undefined solution.

The two basic problems with the hot big bang theory are: 1. The singularity 2. dark matter, dark energy and inflation Yes the theory is flawed but that's the best we have so far.

The standard big-bang cosmology is based on the cosmological principle, which assumes that the universe is homogenous and isotropic on large distances. We use the FRW metric. Since cosmic inflation is getting slight support, why do cosmologists estimate that the acceleration began roughly 5 billion years ago? If so, what hapanned before that which caused the universe to decelerate?

Basically it's possible that entangled quantum states in the universe may change interpretations of observations and even revise the concept of dark matter. Better theories to explain dark energy could be subtle modifications to Einstein-Hilbert equation. Also evidence for comsic inflation is increasing.

Black holes were deduced from Einstein's theory of gravitation. Basically the geometrical structure of a black hole is calculated from GR. A “singularity” of zero volume and infinite density (probably also infinite temperature) pulls in all matter and energy that comes within an event horizon, defined by the Schwarzschild radius, around it. Here is the solution: [math]ds^2 = - (1 - \frac{2M}{r})dt^2 + (1 - \frac{2M}{r})^{-1} dr^2 + r^2d\Omega^2[/math], [math]c=G=1[/math] and [math]d\Omega^2 = d\theta + \sin^2\theta; d\phi^2[/math]. In 1965, Roger Penrose proved the singularity theorem, which says that a singularity must reside inside every imploding star, and therefore every black hole. At the singularity, though, the laws of physics, including GR, break down. We don't know what happens at and beyond the singularity. The problem is that GR incompletely describes gravity. Inflationary models are becomming the leading candidates now. Like GR, cosmic inflation also predicts that a characteristic pattern of long-wavelength gravitational waves would have been created in the early universe. These waves are literally gravitons - the hypothetical particles that carry the gravitational force - that have been stretched to macroscopic lengths by the cosmic expansion. The detection of these waves would provide a unique signature of inflation.

Yes there was an article in Science about this. Basically there are two leading candidates for the particles that may make up this mysterious form of matter: weakly interacting massive particles (WIMPs) and axions. Check also Einstein's legacy

I believe that it's very difficult to understand the application of mathematics to physical situations in quantum mechanics without knowing elementary physics first (and of course one has to know it very well).

I think you are referring to supersymmetry (in higher physics) which is highly complicated. However, if strings really exist they will replace the notion of elementary particles in quantum field theory (e.g. the standard model is a quantum field theory). If i understood correctly, the deepest problem in current physics is that general relativity and quantum mechanics cannot both be right. General relativity explains the behavior of the universe at large scales, while quantum mechanics describes the behavior of subatomic particles. Yet the theories collide horribly under extreme conditions such as black holes or times close to the big bang. Since both theories are highly successful, theoretical physicists search for a theory of everything (a unified framework for all fundamental forces). Here's where string theory comes in. The most self-consistent superstring theories propose 10 dimensions; 4 correspond to the 3 ordinary spatial dimensions and time (a continuum which lacks spatial dimensions), while the rest are curled up and not perceptible. Even if strings exist, right now we don't have the technology to observe them (strings are said to be roughly of Planck length, about 10-35 meters across). The problem is that sound waves are compression waves (and i believe, compression requires energy). All we know is that sound waves cannot be propagated in vacuum. Mechanical waves such as sound waves require a medium through which to travel, while electromagnetic waves do not require a medium and can be propagated through a vacuum. Strictly speaking, only compression waves occurring in air should be called sound waves, unless the eardrum is actually in contact with another medium such as water (as for skin diver). The term sound is often used for any compression wave, in any medium. Also as we currently know, it's only possible for light to go faster-than-light. A wave front, e.g., can go faster than light but without carrying energy. I believe that general relativity is just not complete. I mean general relativity sees gravity as geometrical and not as a force. This is not the case in quantum mechanics. Maybe quantum mechanics would have to replace some parts in general relativity. Otherwise it seems to be consistent with special relativity.

Looks complicated but it should be impossible. I mean electromagnetic radiation is basically the fastest way for the trasmission of information in a vacuum (the speed of light). Sound is a P-wave (pressure wave). Unlike electromagnetic waves, sound waves cannot be propogated in a vacuum, only through a medium (such as air).

True. Neutrinos have positive mass (slighly above zero) but tachyons do not have a real mass. If they have an imaginary mass, they cannot interact with time-like matter. As to proving theie existence, one basically has to discover a particle interaction which can only be explained by the presence of one or more tachyons. High-enery physicists have searched through some experimental records and so far none of the high-energy accelerator labs have detected an interaction which can only be explained by tachyons. This means that tachyons must be far more weakly interacting than neutrinos. Even if they do exist, tachyons would be extremely difficult to utilize under our current understanding of physics. Basically, the existence of tachyons will violate both special relativity and causality.

Let me start by saying i'm neither a particle physicist nor do i know anything about modern quantum physics but some believe that neutrinos could be tachyons, others are convinced that they can't exist. Tachyons are a putative class of particles which are able to travel faster than the speed of light. Tachyons were first proposed by physicist Arnold Sommerfeld (1961), and named by Gerald Feinberg. The word tachyon derives from the Greek (tachus), meaning "speedy particle" Tachyons have the strange properties that, when they lose energy, they gain speed. Consequently, when tachyons gain energy, they slow down. The slowest speed possible for tachyons is the speed of light. http://physics.gmu.edu/~e-physics/bob/y.htm Another site seems to contradict them by saying that faster than light communication is impossible. http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html I guess that if these particles really exist, probably we will not be able to see them. Actually this is a complicated topic that I never really unterstood much. The part that I am still a bit confused about is how it is believed that travelling faster than the speed of light will actually result in reversal of time. I believe time and space are not a physical entities so is it because we mark time based on what we are able to see or is it just because how our brain works? Basically, tachyons would violate both: a) theory of special relativity b) causality (also known as cause-and-effect). It seems unavoidable that if tachyons exist, the principle of special relativity must be false, and there exists a unique time order for all observers in the universe independent of their state of motion. In fact plenty experiments show that some things (which are not matter or a physical object) can travel faster than the speed of light. But the universe always manages to ensure that we can never use the effect for anything useful, like building a FTL starship or travelling back in time. Of course there are other theories of time-travel besides tachyons such as: a) wormholes b) cosmic strings c) inflation theory a) A wormhole is a theoretical opening in space-time that one could use to travel to far away places very quickly. The wormhole itself is two copies of the black hole geometry connected by a throat - the throat, or passageway, is called an Einstein-Rosen bridge. It has never been proved that wormholes exist and there is no experimental evidence for them, but it is fun to think about the possibilities their existence might create. b) A cosmic string is basically a disruption in space with a linear form, which has to do with the fact that space can have different phases, and therefore you can disrupt space by making walls, or solid objects, or planar objects, or even straight lines. I believe that the absurtidy of this theory is that it assumes the number of dimensions our universe can have in the first place. Currently we know just of four dimensions in our universe (including spacetime which is fully based on geometry). c) Cosmic inflation is a theory proposed by Alan Guth (1981). According to cosmic inflation the nascent universe passed through a phase of exponential expansion (the inflationary epoch) that was driven by a negative pressure vacuum energy density (positive vacuum pressure). I think it's also called false vacuum. The contraction is how could vacuum ever contain pressure? Pressure requires force (and force requires energy). Actually density is caused by pressure. Not that i know what all this means but i think it has to do with Einstein's general theory of gravity. Einstein said that space-time has an energy which is always positive (meaning non-zero). According to his theory, bodies create the space around them (differential geometry which is the study of geometry using calculus) and therefore true space or emptiness does not exist. The way i see it, space-time is not a dimension, unless you believe that cosmic strings and wormholes are possible, which would also allow time-travel, which i believe is not possible. I also disagree with him about the concept of singularity which is mathematically impossible (it's like division by zero). Maybe quantum theory and string theory would have to be revised and enhanced in the future (we don't know yet), if they couldn't comply with the experimental method (which we currently don't have).