MigL

You are right the event horizon is defined in terms of mass and radius. However a non radiating collection of critical mass, has no counter to gravitational force, such as a 3-4 solar mass object compose of iron. It doesn't matter what its radius is, it will collapse to form a black hole if its mass is above the critical limit ( it'll just take a little longer to form a horizon ). The radius of its eventual event horizon will be given by the mentioned formula.

Unlike the mid-last cntury quest to find how and why civilizations rose and fell which failed miserably, quantum theories such as QED and QCD make unbelievably accurate real-world predictions even though the theory is probabilistic in nature. Most people accept the theory as' that's the way nature behaves' and use it for very accurate science. Some however see some results ( double slit as an example ) that cannot be adequately explained and argue that there are 'hidden variables' that haven't been accounted for ( see Bohm and Bell along with deBroglie and even Einstein ).

Sorry got a little confused there and posted too quickly. You are both right, it is white dwarfs that keep assimilating mass and upon reaching a specific limit ( Chandrachekar or about 1.4 sol mass ) collapse to become neutron stars. The gravitational collapse, subsequent heating and bounce leads to a 'standard' supernova.

Look up Kerr ( rotating ) black hole. They still form black holes but have many interesting proprties. The ambiguity as to the number of solar masses required for gravitational collapse to a black hole, is because stellar evolution is not completely understood. Before the collapse, to either neutron star or black hole, significant amounts of stellar material is blown off in the supernova explosion. If enough mass is blown off a 10 solar mass star it may only have enough remaining to form a neutron star. If not enough is blown off it may become a black hole. But the mass needed to form an event horizon is known exactly. Incidentally, neutron stars continue to assimilate mass due to their gravitational force, especially if they are located in a gas or dust cloud. Eventually they reach the critical mass at which an event horizon is formed, but on the way there, they go supernova, Type Ia supernova, because conditions are pretty well identical for all type Ia supernova and their luminosity is a fixed figure. These are used as standard candels to determine intergalactic distances. They were recently used in the determination ( at the end of the last century ) that universal expansion is accelerating.

In Newton's interpretation of gravity the force is dependant only on separation and mass. Einstein re-defined gravity as a curvature of space/time dependant on mass, energy and pressure. Now mass is easy to understand, and so is energy because it can be shown to be equivalent to mass, but actually increasing the temperature of a solid by about 10 degrees increases its mass by a miniscule amount ( don't want to do the calculation but probably about a trillionth of a gram ) and so the gravitational 'force' it exerts. Similarily pressure, a potential energy, increases the energy content of a mass, making it more 'massive' and generating a greater gravitatinal force. In effect compressing a spring, increases its mass and the gravitational force it exerts. Negative pressure would, by analogy, decreases potential energy, mass, and therefore gravitational force. I believe it was Alan Guth, when he came up with inflation, who postulated the energy of the universe to have hung at a false vacuum state. Picture a U shaped curve with a bump in the middle, or a sombrero shape or the mold for a bundt cake. If the energy is hung on the central bump of the curve, the hat part of the sombrero if you will, before rolling down into the brim part, it can be shown using GR that this is negative pressure condition. If this negative pressure is large enough it will overcome the gravitational attraction of the universe and lead to inflation. This is the Higgs mechanism since it involves a spontaneous break in symmetry ( the top of the hat is perectly symmetric, but once it rolls down into the brim, symmetry is lost ), and the Higgs particle in this case is called an inflaton to distinguish it from the electroweak Higgs particle or the GUT particle. Guth ( I believe, as its been a while since I read his stuff ) estimated that in the time it took for energy to roll down into the 'rim', about 10^-35 sec. the size of the universe increased by 10^30 to 10^100 in size ( depending on certain conditions ). This could still be happening on a much smaller scale, to account for the 'new cosmological constant', or the increase in expansion rate of the universe. Witten, I believe, has speculated on a vacuum fluctuation in a space ( say right beside you) which 'borrows' energy for a short period of time and on the way to re-paying the loan, gets hung up of this false vauum energy level, leading to new universes being created wherever the negative pressure is sufficient to overcome gravity. These new universes are causally disconnected because of the large expansion rate, and its called chaotic inflationary theory. I don't see a connection to syphoning waste, proton vibration or two cycle engines.

The theory predicts the Higgs particle to have a mass of 250 GeV, equivalent to Weak scale energy ( not 150 GeV where the blue peak is located ). It absolutely must have this mass to acccount for the masses of the electron and quarks. However, quantum contributions within the existing standard model, tend to raise this mass to Plank scale energies, roughly 16 orders of magnitude higher. Quantum contributions are comparable to an object moving through a viscous fluid where we cannot use just the object to calculate forces, but must take into account an appreciable amount of the surrounding fluid entrained in the object's motion, the boundary layer if you will. Faynman ( along with Wigner and Tomanaga, spelling ???) used this method to originally formulate the virtual particle contributions to QED, and it was later put into a rigorous framework by Wilson in re-normalization theory. This obviously leads to a problem for the Higgs particle. It turns out that if you invoke supersymmetry, ie every 1/2 spin fermion has a unit spin boson counterpart and vice-versa, then the quantum contributions will cancel ( or nearly cancel depending on the weights of the supersymmetric partners). The fact that no supersymmetric particles have ever been found indicates that their masses are rather high for our present colliders. In effect both the Higgs particle and the supersymmetry particles must have masses of several hundred GeV or even 1000 or more GeV. This then involves another spontaneous symmetry breaking to account for the differing masses of fermions and bosons compared to their supersymmetric partners, and I don't recall the details too well, but this leads to excessive flavour change in quarks. It just seems a little too convoluted for my liking ( as if the universe gives a damn what I think )

Re-read my post and the original question. I didn't say I could prove that time started at t=0. What I said was, given the original question ' if space/time is created at t=0 how is mass/energy conserved ', we can prove, using Noether's theorem, that the asymmetry in time at t=0 invalidates the law of conservation of mass/energy.

Thanks Swansont, my premise was that we can prove that at t=0 the law of conservation of mass/energy is not valid because of time asymmetry. And I'll go out on a limb and state that all our other physical laws are also invalid. As for your argument about the asymmetry, if we make the assumptin that space/time is 'created' at time t=0, since that was the original question ( if space/time is created then how is mass/energy conserved ??? ), then there is no time before t=0. I don't see how that wouldn't mean a time asymmetry of the physics.

Would the lier also not lie about being a lier and so give yet another inversin betwen right and wrong door ?

I don't have a clear understanding of Goldstone particles, other than they can manifest themselves as Higgs particles in some cases and combination particles in others. I always assumed these combination particles were bosonic in nature and not fermionic. I have a certain 'confort' with the Higgs field although its resistance to accelerating motion and not constant motion ( and as such giving rise to inertial mass ) is puzzling. Not so much with the Higgs particle. The fields that I've considered are QED and QCD which both give rise to force carrier bosons. Is it possible that the scalar Higgs field does not produce either force carrying bosons or fermions ??

At time t=0 we have an asymmetry in time, ie you can only go foreward not backwards ( into negative time ). This means the action is not invariant under a continuous transformation in time and Noether's theorem is violated. In effect, at t=0, the law of conservation of mass/energy is not valid. If certain physical laws are not valid at t=0 ( or approaches t=0 ), then they are all invalid. You cannot pick and choose.

Yeah, I did. But I stopped short of smart-ass.

Sorry, posted that wrong. The question to ask of the single guard should have been 'If you were a lier which door would you recommend I take'. A truth-telling guard will tell you what a lier would tell you, the wrong door, so you take the opposite A lie-telling guard, already being a lier, will also tell you the wrong door, so you take the opposite.

The Higgs mechanism supposes the energy state of the vacuum is not at the zero level such that there is a potential energy of the vacuum ( permeates all the causally connected universe ). This potential energy is equivalent to a directionless or scalar field. Any quantum description of a field, wether scalar or vector, predicts the existence of virtual force carrier bosons. I am of the opinion that the Higgs particle would therefore be a boson. Supersymmetry seems an un-needed complication of things.

The case of a single guard ( two doors ,one question ) is similar. Ask 'which door would a lier recommend I take', then take the opposite.

You are given 6 matches of equal length. You must make 4 equilateral triangles with side length equal to match length.

A towel. OOPS! didn't see you posted the answer.

If it doubles every second, the lake was half-full one second before 12pm. Don't overanalyze !!!

Maybe I'm misunderstanding the question as well. Can quarks be destroyed, ie annihilate with their anti-particles ? Well obviously we cannot isolate quarks to test this out ( yet ). But QCD is renormalizable, and, to me, that implies the creation of virtual pairs of quarks and their bosons ( gluons ) in their immediate vicinity to explain their interactions. Can we make the jump and assume that since virtual quarks and gluons are created and annihilated, then so are 'real' quarks ?

I don't want to go as deep as AJB ( doubt that I could ), but I believe you answered your own question. You state the speed of light is fixed at c , yet you ask how can light slow down as it tries to escape a black hole, and stop just inside the event horizon. Obviously it cannot. What it can do, however, is loose energy as it tries to climb out of a very steep gravitational well such that it is infinitely red-shifted and never leaves the event horizon. I hope this explanation makes the process easier to visualize.

Don't quite understand what you mean. A black hole will act just like any other massive gravitational source. It will have an escape velocity just like any other gravitational source, but, its escape velocity happens to be faster than C, such that light cannot escape its 'pull'. If an object falling towards the earth reaches its escape velocity ( about 18000 mi/hr ) and is not on a collision course, it will escape into interplanetary space. Similarily if an object reaches a velocity above C at the event horizon of a black hole ( fairly small with an escape velocity just above C ) then it would escape. This is clearly not the case. Objects with mass will not reach C at the event horizon.

What is your reason for thinking infalling mass approaches light speed at the event horizon ? The fact that a mass needs light speed to escape ( escape velocity = C ) doesn't mean infalling mass reaches that speed. If it did it would posses escape velocity and would pass right through the black hole.

Sure, you would bring up that specific quote since you are a mathematician. ( Just kidding )

Forget order and disorder as those are human ideas, look at it instead, in terms of an increase or decrease of degrees of freedom. Bound states obviously have less degrees of freedom and are therefore more ordered.

I could be wrong, but I seem to remember ( haven't done a search for info ) that when the supernova explosion was detected in the large Magellanic cloud, it was detected because of the increased incidence of neutrino detections in one of the experiments. The neutrinos arrived within hours of the magnitude increase of the star, ie the neutrinos travelled the distance as fast as the light did ( very large distance ). This would indicate massless neutrinos ( or extremely close to 0 ), although other experiments have put the mass at small but not inconsequential. Which is right ?