MigL

Everything except the singularity ( and close vicinity ?? ) inside the event horizon is governed by estabilished physical laws of gravity, mechanics, thermodynamics and electromagnetism. If you know of any way these physical laws can be ignored to make anything travel faster than the speed of light, please let us know !!!

The double slit experiment has a mathematical explanation but certainly not a verbal explanation. When you guys say it is because a photon can act as a particle or a wave you are just confusing the OP. In some experimental situations it can be both and in some, neither. If you set up an experiment to detect wave-like behaviour, then you will find the photon to act wave-like. If you set up an experiment to detect particle-like behaviour, you will find the photon to act particle like. The math does not describe quantum particles as waves of anything, but as quasi-probability waves. It is these waves which interfere with each other, even for a single photon, and which make the situation so hard to verbalize and the emperor's clothes so hard to see.

I'm just going by memory here, so I could be wrong. T he observational evidence for spin ( other than in a Stern-Gerlach experiment ) is a splitting of spectral lines, called Lamb's shift. It was theorised by Pauli for the exclusion principle, and put on firm theoretical footing by P.A.M. Dirac with his version of SR compliant Quantum Mechanics, the precursor of Quantum Field Theory.

Actually spin is not represented by vectors as is classical angular momentum, but by spinors which behave differently under co-ordinate rotations. In effect, an electron of spin 1/2 needs 720 deg. to get back to its original orientation. See the Wiki page on electron spin. Gravitons are theorized to have spin 2 ( if they exist and are ever found ).

Sorry it took so long to get back, Sam, but a simple google search along the lines of " how do dimensions affect gravity" will bring up current ideas and research into compactified extra dimensions and the possible resultant increase in gravitational strength at small distances ( Planck scale ). Other ideas involve gravity 'leaking' between branes due to some possible peculiarities of gravitons compared to other bosons in various string theory 'versions'.

Agreed. My mistake Gen1GT,

Sorry I apologise for being pompous ( not the word I would have used but... ). I suppose the simplest way to see it is to imagine a sphere and extend angles from the origin to the surface so that an area on the surface of the sphere is defined. If we now extend the radius of the sphere to twice the original, we find the area subtended by the same angles is now four times larger. In effect any field density will now be spread over a four times larger area. It will be four times weaker than at the original ( half ) radius. This is the three dimensional case. We can repeat it in two dimensions with a circle, where we find the arc length subtended by a given angle increases linearly with radius of the circle. The field density in the 2d case falls off with the radius, ie ( n-1 ). This can also be shown in 4, 5, 6... dimensions, but is a lot harder to explain without math, or to visualise. This is accepted physics and can be easily looked up, that is what I meant by ignorance. I meant no disrespect. And the first line of my pompous post was just a 'play' on your dismissal of my previous post. You have earned my respect by asking for more detail and clarity, not just escalating the argument.

The fact that my post doesn't make sense to you has very little to do with actual physics and more to do with your lack of understanding. Do some research before putting your ignorance on display for all to see.

Elfmotat is absolutely correct with all his assertions about black holes, although I have to question his hint of causality violation ( if that is what he meant ), that the event horizon may expand even before mass-energy has actually crossed it. My thinking has been that as the mass-energy initiates crossing the event horizon, the horizon 'swells' outward to totally envelope it, at that point. This 'bulge' is then radiated away as a gravity wave to return the horizon to spherical ( for a simple Swartzchild black hole ) as per Wheeler's 'no hair' theorem.. Swartzchild co-ordinates can be used to describe simple, non-rotating, non-charged black holes as long as you keep in mind the limitations. The singularity at the horizon is mathematical, not physical

Frequency has units of cycles per unit time ( ie. t^-1 ). Negative frequency has no physical meaning.

Forces such as gravitational and electromagnetic fall off as the power (n-1), where n is the number of spatial dimensions. In effect in our 3 spatial dimensioned world, they fall off with the square of distance or radius. If there were any other 'large' spatial dimensions, they would fall off as a higher power. The fact that they don't pretty well excludes the possibility of more 'large', non-compacted dimensions.

The useable energy doesn' t peak when the core becomes iron. At that point there is no more energy left to liberate via the fusion process and the star is overcome by its gravity. The subsequent collapse and 'bounce' lead to the violent stellar explosions, but this energy is provided by the gravitational field. Not fusion. I'll repeat, unless we consider degrees of freedom, order and disorder are subjective and not quantifiable, so I hesitate to use that definition of entropy.

We don't observe objects ( whether macroscopic or quantum ) nor collapse their wavefunctions ( ? ). What we do is observe interactions, since any object that does not interact with anything else is unobservable. Look at all the trouble finding dark matter ( which still interacts gravitationaly ).. I would propose it is the interaction which renders probability too reality ( what some members call 'collapsing the wavefunction' ).

Electrons are very claustrophobic. If you try to localize one within a box ( made of atoms ), at some point the electron will experience degeneracy pressure from being too close to the state of another electron, and will as a result become extremely frantic and energetic. When this energy ( as momentum ) requires the speed of the electron to approach the speed of light, the electron cannot increase its momentum any further, no matter if the pressure sqeezing it is equivalent to a white dwarf star. However it can continue to increase its energy and momentum if it becomes more massive. It does this by merging with a proton to form a neutron. This is what happens in neutron stars where neutron degeneracy then rules. The Higgs mechanism was active during the electroweak dissociation era. An era too energetic for our current particles. It must therefore influence the whole universe. And no, there is no 'outside'.

But the set table example shows that symmetry is not related to order or disorder, as it is commonly defined. That is what I was attempting to show. Does the table become more disordered or less disordered when the right or left glass is chosen ? And yes, if you consider the true definition of symmetry ( and entropy ) liquid water is more symmetric than ice ( and has more useable, 'free' energy ). Only consider quantifiable properties, not subjective concepts like order/disorder and your definition of symmetry ( above ). There is a standard mathematical definition of symmetry where properties are classified into groups. You should look it up.

Entropy is related to the lack of USEABLE energy of a system. As an example, when a system converts all its energy to heat and comes to thermal equilibrium, no more energy is available to do work, and entropy is maximized. Thiis is commonly known as 'heat death'.

Damm, this mouse at work keeps double clicking and duplicating my posts, Is there a way to get rid of the second post ?

No. Lower symmetry means decreased energy of a system. Which means less energy to do work. Which means increased entropy of the system.

I would rather assume that as time>>0, all our notions and science must be abandoned, as there is a discontinuity at the boundary. At Planck lengths very close to t=0, we would run into Wheeler's quantum foam, where space and time are 'blended' and interchanged. Even a quantum gravity theory, while it may get us much closer to t=0, will probably still fail at t=0.

As an example of symmetry breaking consider a round table setting, with plate, silverware and a glass between each of the plates. The table and its setting is symmetric. Now when guests arrive, sit, and one of them chooses a glass, either to the right or the left of their plate ( manners be damned ), they are effectively breaking symmetry and everyone at the table is constrained to pick the same. As for the example you give from Zee's book. In a low energy state the magnetic domains align in a particular direction. Energy ( heat ) has to be added to the system to sufficiently randomize the domain directions and destroy the magnetic properties. In effect, the higher energy system is more symmetric. This is useable energy, and I would argue that a better measure of entropy is that it increases as useable energy decreases, and is maximised when no useable energy is left. Order and disorder are just labels we use and are not specific enough or quantifiable. Another example would be water, which is very randomized as a liquid, but as it loses energy, it freezes into a lowe symmetry state. Whereas as a liquid it was the same in all directions, as a solid it is only symmetric at 60 deg. intervals ( snowflake ). In effect, as it froze, symmetry was spontaneously broken, and it dropped to a lower energy state. The conclusion ? Symmetry breaking always leads to a lower energy state.

Apparently you misread quite a few people's posts Proximity1. Re-read mine again. My arguments are not flawed but show how an infinite space can expand, using no philosophy whatsoever ( imagine that ). Maybe next time read more and spout off less, as your misguided rebuttal to my post was four times longer and said the same thing.

All models of inflation that I've read about use an extremely aggressive rate for the inflationary period, but a finite one, as Airbrush explains above. Consider an infinitely long metre stick, with millimetre markings ( infinitely long I said ). Each point on this stick is one millimetre from the next, and there are an infinite number of points. Now consider every centimetre mark, they are now all ten times farther away from their neighbours than the millimetre marks, ie you have expanded the 'space' tenfold, yet there are still AN INFINITE NUMBER of points. Now consider the metre marks, they are now 1000 times farther away from each other as the millimetre marks were. So you've now expanded 'space' a thousandfold, yet you still have AN INFINITE NUMBER of points. Do you see now how an infinite universe can expand ? Its not the boundaries ( infinity has no boundary ) moving outward ( into what ??? ), but spaces in-between galaxies and clusters getting larger. This is a science ( with math ) forum, not for philosophycal discussion, I would add.

I've said this before, and AJB has alluded to it in his prvious post. Conservation of mass-energy is directly attributable to time symmetry, as per Noether. If we consider time=0, obviously there is no symmetry because there is no negative time, mass-energy then, need not be conserved. In effect at time=0, energy can be created or destroyed, according to our current understanding.

Sorry AJB, I should have said 'if it is a real classical spin, it would be very strange'.

Well if it is a real spin, its a very strange kind of spin. If you were to take the axis of spin and label the 'up' direction you would find that a rotation of 360 deg. would not bring the labelled axis to the 'up' direction again. You actually need to go 720 deg. to return to the original 'up' direction. Someone once described it to me 'as if the electron probability wave's peaks and troughs are out of sync at 360 deg. and interfere, while at 720 deg they are in sync again'.