MigL

My point was, that unless you have other parameters to define the curvature of the spiral, you cannot locate a position on a curved line. You still need more than one dimension, if the spiral is in a plane you need two, if in a volume you still need three.

Spontaneous symmetry breaking and the Higg's mechanism ( field ) give mass to not only the weak gauge bosons, but also quarks and leptons. As a matter of fact, it is the only theory which explains the short separation/hi energy and large separation/lo energy behaviour of the standard model that doesn't run into short separation/ hi energy nonsense ( like infinities, probabilities higher than 1 or things happening more often than always ). It acheives this by not having a longitudinal polarization to massless particles ( lo sep/ hi energy ), only the two perpendicular polarizations. Upon symmetry breaking, all three polarizations are allowed and mass is induced ( lrg sep/ lo energy ). I guess it wins by default.

Don't really understand what you're asking, but if you derive Coulomb's interaction in spherical, polar co-ordinates, you find that it depends solely on the separation R and not on the two angles. This implies that the interaction is spherically ( or is the proper term, rotationally ) symmetric. But if you were familiar with Noether's theorem, or global symmetries/conservation laws you would already expect that.

Niven's 'Ringworld' is stable because it encircles its sun, i.e. it is a ring occupying the total orbit of its terraformed former planet. What we are discussing here is a toroidal planet orbiting its sun. Definitely not stable.

Aside from the physical misconceptions, how would you define a specific point on the spiral ?

Don't see how this configuration could be stable. As Imatfaal points out gravity is always towards the centre, and zero at the centre, in effect the exact same as for a sperical configuration, along with the same forces trying to collapse it spherically. There is no reason why a 'donut hole' would form, rather if the spin was excessive, after flattening it would start coming apart at the outer edges where the forces are highest. You also still have all those old yellowed paperback sci-fi books from the 50s and up, Moontanman ? The first book of the type I ever read was 'Galactic Derelict' by Andre Norton ( actually a crazy cat woman ) and I was hooked. Read all of her stuff and moved on to other writers. My favourite R.L. Foreward is still 'Dragon's Egg', but I've read some of his others.

Niven's 'Ringworld' ?

The LHC has found an energrtic particle which fits the description of the Higg's boson very well, but is this actual proof ot the spontaneous symmetry break/Higg's mechanism/electroweak separation ? Let's grab an electron ( we obviously cannot grab a single quark ), put it in a briefcase, take it to Switzerland and drop it in the LHC. We now accelerate this electron to approx. 250GeV ( I don't know if its even possible using the LHC ). What do we expect to happen ? At this energy, any and all non-zero valued Higg's fields ( depending on the model ) should appear to the electron as all zero valued and completely symmetric and the weak vacuum charge should cease weakly interacting with the electron. In effect, the electron will become a massless particle whose energy is solely dependant on its momentum. We would expect an immediate jump to lightspeed as all massless particles move at c. And if we were to use one of the shorter lived, but heavier ( again, don't know if possible with LHC ) electron families, we expect to see its lifetime extended indefinitely. Any idea if any experiment like this is planned ?

Extracting and using energy from a black hole is discussed in several books. The most readily available are Hawking's "A Brief History of Time" ( IIRC ) and Thorne's " Black Holes and Curved SpaceTime: Einstein's outrageous legacy".

The spaceship that's bringing him arbitrarily close to the event horizon is, by necessity, moving at very close to the speed of light. And so is he. Does that help clarify the situation, Ender ?

While I accept that inflation 'dilutes' the universe enough so that the cosmological constant becomes the driver rather than gravity, Mordred, I believe we're avoiding the issue. What keeps the universe from collapsing prior to inflation ( 10^-36 sec ) ? The energy density is there as expansion and inflation only affect separation or volume of space, and you can't invoke the HUP since even though we are dealing with a very short time, we have an immeasurable amount of energy which goes on to become our whole universe. We are never answering the question, just pushing the goalposts back to avoid having to. There has to be a fundamental reason and I'm not sure its a quantum gravity effect.

My understanding is the same as md65536 has posted. The measurable quantities are conserved by the event horizon, as GR predicts there is nothing inside the event horizon other than a possible singularity at the center. And as Delta1212 has stated a static gravitational field doesn't consume energy, however it is possible to extract energy from a BH's gravitational field by taking advantage of its conservative nature, or by manipulating the frame drag effect of a rotating BH ( the only kind which can exist ). This energy extraction will manifest itself as an areal reduction of the event horizon.

Your thought experiment is wrong. You are using this 'bending' of light as a way to measure and detect absolute speed or velocity and from that, implying that there must be an absolute frame. There is no preferred or absolute frame. There is no absolute speed or velocity, only relative speed or velocity. And light within an inertial frame doen't 'bend' as it does within an accelerating or gravitational frame.

Both the big bang singularity and a black hole singularity have enough energy density to collapse in on themselves to create either a black hole or a still-born universe, and we currently lack a model to describe this state as it involves a quantum gravity theory. There is a subtle difference however. A black hole is a timelike singularity, existing in a small, limited space for an indefinite period of time. The big bang singularity, on the other hand, is spacelike, existing through all space but only at the beginning of space-time. One is a boundary or edge to space, the other is a boundary or edge to time.

I liked the explanation given by a member who hasn't been here for a while ( elfmotat where have you gone ? ). Consider two planes that take off at the equator and fly straight north on a parallel course. As they fly they notice their separation is decreasing and they keep getting closer together. Finally as they reach the north pole they crash into each other. They assume, since they weren't moving towards each other, that a force must have drawn them together. They call this force gravity. This is how GR explains gravity. As a frame ( curved ) dependant geometric effect. All other frame dependant forces that I know of are termed fictitious forces, because while they are manifest in one frame, they are not in others. If gravity is a fictitious force, however, I've never been able to figure out which would be the other frames where it is NOT manifested.

Not very well versed in group theory I'm sorry to say, Mordred. Other than the basic symmetry groups of GUT, my knowledge is very limited, and I ( and many others on this forum ) look to AJB for help and direction, I would be very interested in anything your research leads you to as you're always providing links to interesting papers and books.

You're right AJB, this would be the same mechanism which gives us the excuse to use the ( terrible ) mathematical tool known as re-normalization ( although it does seem to work just fine ). It seems that a particle's field strength is then temperature ( energy ) dependant, as a more energetic test particle will penetrate further into the surrounding virtual particle cloud. What I find interesting is that without supersymmetric virtual particles the field strength converges to two distinct points, not at the GUT field strength. The calculation for the mass of the Higg's boson also uses this mechanism and without supersymmetric virtual particles, the calculated mass is huge. With supersymmetric virtual particles the mass turns out to be approx. the experimentally found ( LHC ) mass. So where are these supersymmetric particles ???

I do remember reading about this years ago but I can't give a source after all this time. Basically at low energies particles are not energetic enough to get close to other particles such that they 'see' each other's true field strength. This happens because particles surround themselves with a multitude of virtual particles which pop in and out of existence.. An electron for instance, would be surrounded by positive and negative charged virtual particles, and for a brief instant, the positive charges would move closer to the real electron before vanishing. This migration of positive virtual particles towards the electron would 'screen', or mediate, some of its true charge, and we would detect it to be less than it actually is. At higher energies such as the GUT scale ( about 10^15 GeV IIRC ), particles are energetic enough to reach inside the virtual particle screen and see the true strength of that particle's field. At this temp the particle's field strength are all equal ( if you include supersymmetric virtual particle contributions of course ).

According to GR black holes conserve the properties of mass, charge and angular momentum. QM considerations also lead to the conservation of other properties such as entropy. For the OP we can disregard all but mass and charge since the others aren't affected by whether they are matter or anti-matter. Since mass is always positive and negative mass is a theoretical construct, it is always additive irrespective of matter or anti-matter or even if a particle is its own anti-particle.. Charge on the other hand, can be positive or negative for matter or anti-matter, so it is additive or subtractive like positive and negative numbers.

But if individual universes in the 'multiverse' are related through the time dimension, then they are also causally related. In effect they are not separate universes, but parts of the same single universe. I've always had a problem with the multiverse model. If something is not causally related and can never affect us or be detected in any way, does it make any difference if it exists or not ?

Well if the slow roll inflationary model is still the benchmark ( didn't know there was an encyclopaedia inflationaris ), why doesn't anyone speak of multiple inflationary periods. I would think there would be one after each symmetry break. The latest would be the electroweak break where EM decouples from the weak nuclear. The previous would be where the grand unified breaks and the strong ( colour ) nuclear decouples from the electroweak at approx. 15 GeV ( IIRC ). and there may even be one where gravity decouples ( this one is still undecided depending on the nature of gravity ). And if each inflationary period leads to a causal break from the previous epoch, how can we possibly proceed backwards along the timeline to get closer and closer to t=0

As I said I agree with your earlier post and thank you for the additional references. I just wanted to make it clearer for everyone that heavier particles, being higher energy, start being created earlier in the timeline, at higher temperature. And I still would not have included photons and neutrons in the model due to the reasons given previously. Haven't really given much thought to the eras before the symmetry breaks, but don't some models predict inflationary periods following a symmetry break due 'rolling' down from the false vacuum zero energy level. I believe Guth's original inflation made use of this mechanism.

Thanks John and Mordred, a quantum particle has a definite definition , but it's not a classical particle or a wave. A lot of the wave/particle duality results depend on the experiment set-up. If you set-up detects wavelike behaviour you will 'see' waves, and if it detcts particle like behaviour, you will 'see' particles. Just like looking at pictures of your extinct animal from different directions John.

Are you sure you want to include neutrons in that Mordred ? All primordeal neutrons would have undergone decay as thy were not stabilized in nucleii at this time. All present day neutrons are the product of recombination in later ( lower temp ) eras. If that wasn't the case we'd still see massive particles around, maybe even magnetic monopoles. Are you sure you want to include photons in that Mordred ? The photons, or radiation, are what the massive particles are in thermal equilibrium with. They would be present throughout the particle creation/destruction era in various ( decreasing ) energies. One point I'd clarify is that production of massive particles actually starts earlier, but thermal equilibrium quickly ensures that just as many are destroyed as are created. It is only after they drop out of equilibrium due to cooling that that the reverse order of lighter to heavier takes over. Not implying you're wrong by any means, just thought it needed some clarification and re-consideration.

If I may elaborate... The satellite is, in effect, falling. A fall with no horizontal component, such that it falls through the centre of the earth, is in orbit, If it has enough horizontal component, it goes right around the earth, still in an orbit. This is simple Newtonian gravity. What GR adds is that an object in free fall, such as an orbit, has and feels no forces on itself. If it has no forces acting on it, it experiences no acceleration ! And Orodruin is absolutely right, your weight, i.e. the force you feel, is not due to gravity pulling you down, but from the ground pushing you up.