MigL

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 ?

Yeah, I see what you mean. A flat torus preserves angles and distances. That was my mistake , thinking it had to curve to join one end to the other, which is , in effect, embedding it in higher dimensional space. All it means is one end continues into the other end. So I guess my attempt at using conservation laws to determine the shape of the universe fails. However I still believe that a simply connected space makes more sense, and wasn't it Poincaire 's conjecture which Pearleman won the Field's prize for proving ( and refused the million dollars ) that a 3-sphere is the only simply connected finite ( compact ) manifold ? But as to size, ie finite but unbounded or infinite, let's try a variation of my previous argument. If the universe is infinite, does that imply an infinite amount of energy. And, if so, does the law of energy conservation make sense ? The law basically tries to 'balance the books', but any finite amount taken from infinity still leaves an infinite amount. It would seem that only afinite amount of energy allows the conservation law to work, implying a finite but unboundes universe. Or am I again missing something ?

Maybe so, but The theories that predict gravitons are incomplete and certainly GR doesn't. And even if predicted at the Planck scale energy at which gravitons would be observed, we might need a collider about 10 light years in diameter to supply the required energies, making the likelyhood of actually seeing one about as likely as a unicorn. As for monopoles, doesn't Guth's inflation do away with the solitons ( monopoles ) created at domain boundaries ?

If I understood you correctly, yes, fields of infinite range like an EM field, are propagated by massless carriers like photons. Short, limited range fields like the Weak force are propagated by massive particles, the +/-W and Z. At Weak scale energies, before the scalar field ( Higgs??) breaks symmetry, the combined electroweak force is propagated by photons and massless +/-W and Z particles ( see Weinberg, Salam and Glashow ). The Strong force is a different beast as it is asymptotic. The force is effectively zero up to a certain distance at which point it starts increasing with distance. But maybe someone else can give you the particulars as gluons and quarks have too many properties ( up, down, charm, strange, colour etc. ) for me to remember. Gravity is also an infinite range field, but our best theory of gravity, GR, makes no predictions of carrier particles. Quantum gravity theories would make a prediction one way or another,but we don't have one yet. Massive gravitons have been postulated, but so have monopoles and unicorns. I believe that accounts for the four fundamental forces, but I also don't understand the relevance of expansion.

Marqq and pantheory, you guys do realise that a theory is developed as a model of reality such that things can be explaned and predicted. In the case of string theory, I realise the math is horrendous, but its there for a reason. String theory attempts to unite the fundamental forces of the universe. GR and the 4 dimensions of space/time are sufficient for gravity. Five dimensions sre sufficient for gravity and electomagnetism ( see Kaluza-Klein and Planck size rolled up dimensions ). To explain the weak and strong nuclear forces, another five, six or possibly up to 21 more dimensions are needed, all rolled up at Planck lengths. It would seem to me that to explain the chirality or handedness of the weak force we need an odd number of spatial dimensions so 10 and 26 total ( including time ) seem to work but eleven doesn't. However, current strng theory is pushing towards 11 dimensions, so I'm probably wrong. So... just saying your theory is simpler doesn't cut it. What is your theory trying to accomplish ? It certainly doesn't seem to be trying to unite forces. As to making valid predictions please tell us what predictions, if any, your 'theory' might make so that it may be tested. If it doesn't make any, its on even more precarious footing than string theory which also doesn't make any predictions , but it at least manages fundamental force unification.

Sure DrR, I understand your point, but there has been a lot of talk about a donut shaped universe and that's what I have a problem with. But using your same example of the rectangle rolled over into a tube and identifying the two ends together, would motion along the 'tube' length ( ie from one end to the other ) be the same as motion along the circumference of the tube ( Its very hard to describe directions on a donut shape, sorry if I'm not very clear )? I can easily 'see' that motion in any direction on a spherical surface ( and by extension on a 3-sphere ) is equivalent with no preferred direction. Even rotation of a given angle is equivalent. But I cannot 'see' the same for a donut shape, or a flat torus. That is why I say ( rather believe ) that there is preferential direction and inequivalent rotations, implying violation of momentum and angular momentum conservation laws.

Sorry I was in a rush when I wrote the previous post. What I meant to say was that since motion along the bigger circumference of a torus or donut is different from motion along the smaller circumference, then translational symmetry invariance is violated and so is the law of conservation of momentum ( there is also a difference in curvature which may mean a different gravitational constant in different directions as well as posiibly differing vacuum energy states in said directions ). For that matter, if you draw triangles on the inside curve of a torus the added angles will be less than 180Deg while on the outer curve the triangles added angles will be greater than 180Deg. since curvature is positive on the outside and negative on the inside, saddle shaped, curve. This means rotational symmetry invariance is also violated and the basis for conservation of angular momentum is invalidated. The only one of the 'simple' symmetries that is conserved is time symmetry invariance so conservation of energy would still be valid. Base on this and, assuming my logic is correct ( I'm no expert on differential geometry ), I don't see a torus as a valid model for our universe.

When most people talk of an expanding universe they imagine the whole and think of the edges moving apart. They should instead consider the expansion as the constituents of the universe moving apart from each other. Whether it is infinite or finite is not important, the galaxies are still moving apart, so it is expanding. But to get back to a previous point, My understanding of Airbrush's 'coconut shell model ' may have been incorrect, but I still think simple connectivity is essential to a model of the universe. I assumed the 'coconut shell model' had a hole in the middle. A torus certainly does and is not simply connected. Other than the loop test failiure, a torus, or any other manifold which is not simply connected, also has preferred directions. In effect movement along the 'orbit' of the donut id different from radial movement. Now of course I cannot provide rigorous proof ( I'll leave the heavy lifting to DrR who has an understanding of differential geometry ). Now, I may be wrong, but preferred directions imply a violation of longitudinal symmetry, which would then imply a violation of the momentum conservation law. This would then mean quantum theory as well as Newtonian laws of motion ( and gravity ) become obsolete ( not sue abour GR ). I don't think we're ready to, or can, take that step.

Haven't you been following? There is no moving edge. Your premise of an edge implies an outside. There is and, cannot be, either ( and even if there was, it could never affect us or be detected, so it's inconsequential ). The universe ( means everything ) is all that we know and can ever know, and it is expanding by the average distance between objects of galactic scale getting larger.

Airbrush, assume we lived in a version of your thick-skinned balloon universe, or 'coconut shell mode'. We now take a string and make a giant loop. We then grab the ends of the loop and pull it tight. In an isotropic universe where all things happen the same throughout the universe, we should be able to pull the loop right down to zero dimension. In your model, however, if the loop goes around the innermost shell ( or inner sphere ) we can only pull the loop down to the dimension of the inner shell. Incidentally this also holds true for a torus and higher order topologies such that the 3-sphere is the only topology which seems to work. And unfortunately I forget what this property, exibited by the loop contraction, is called. Help me out here DrR, is it called simple connectedness, or am I thinking of something else ( math and especially topology aren't my strong suits )