MigL

It seems everyone is trying to outdo each other with the math and losing any semblance of common sense/ As imatfaal has stated, when angular separation between the two test probes is zero, it is easy to see that swansont is right. However the situation does not change or become more complex when the angular separation is 180 deg ( or anywhere in between ). This is because although the large earth mass is accelerated towards the heavier test probe, the lighter probe has, in this case, a larger acceleration since it is drawn to the larger COMBINED mass of the earth and heavier test probe. I.E. they hit the ground simultaneously ! Is this not simple perturbation ? You cannot have different situations arising when the action ( as in Lagrangian ) is the same. This is dictated by conservation laws and symmetry.

Let me get this straight. If we have an object composed of two different parts of very different densities such that they have a coincident centre of mass, and we drop said object from great height, xyzt is claiming that there will be a measurable shearing force between the parts of differing density ???? This is absurd ! Keep in mind that mathematical models are just that, they can be applied wrong, and the ultimate test is weather they conform with experimental reality.

I think it was waaaay back in post #11 that xyzt stated that two test probes of different masses, if dropped simultaneously, would separate during their descent. He stated that swansont must be wrong in his assertions. It seems to be very easy to prove. Put two differing test weights in a bag and drop them from altitude. Does the bag rip and allow the heavier weight to land first ? If you go over a bridge in your car are you pinned to the roofliner during your descent because of the differing weight of you and your car ? Is that why we wear seatbelts, to hold us down ? Someone was definitely wrong, but I don't think it was swansont.

Actually he does have a point studiot, better atomization leads to more efficient combustion. Most efficient fuel injection systems are going away from throttle body into tuned runner injection to port injection or even direct chamber injection as on diesel engines. This is done to avoid the knock-out of fuel particles as the air accelerates through the runners. The point of combustion is not to have the fastest explosion possible, that leads to knocking unless initial timing is retarded severely. Higher octane gasoline actually slows the combustion allowing for timing to optimize power extraction. Maybe John C can provide some further insight into the combustion process, or do we have an automotive engineer in the house ?

Your edit was accurate md65536, Considering how vast the cosmos is arc.........gravity acts the same all over,

Thanks for pointing that out Janus. But at least Ringworld has the slight possibility of acheiving stability for a brief instant, like a pencil falling to the ground and landing on its tip. Torusplanet, on the other hand, cannot even form, like a pencil that's glued to your hand and can't drop.

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.