MigL

I'm sure DrR is just trying to get you going by being very picky with the definition of solution. I'm sure he's more familiar than most with perturbation and approximate methods. There may be no exact solution to many body problems, but given enough computer time, you can get as close ( decimal places ) as you wish. I, myself have not done any >2 body gravitational approximations. But I'm sure anyone who'se studied physics will have solved the Helium atom using these methods. At the time I was in school we used Hollerith punch cards and programmed in Fortran IV. Several hours later you'd have your stack of fanfold results which then needed debugging. Ah, the convenience of modern computers.

Appreciate your imput Janus. I guess if you are also of the opinion that none of the disintgrating moon's pieces will impact the Earth, then my thinking must be at fault and I obviously need to re-examine the situation.

I know that a lower orbital speed will usually just drop you down into a lower orbit. But did you miss the part in the OP where the moon has moved a LOT closer to the earth and is torn apart by tidal forces ( wouldn;t be a day in the park for the earth either ) ? Do you know at what distance this would happen ? I don't. But I base my reasoning on observation of similar situations. Have you seen pictures of Saturn's rings ? Have you ever wondered why there are no 'stragglers' below or above some very clearly defined orbits ? Does your book on orbital mechanics explain that ? Maybe my choice of words was wrong and I shouldn't have used unstable. But pick up a rock and throw it. It is now in an orbit. Unfortunately its orbit passes through the earth, ie IT HITS THE GROUND !

At no time did I mention circular orbits. But if you know your Kepler as you say, then you know that for any orbit there is a well defined orbital speed associated with the distance, whether we are talking circular elliptic or even parabolic orbits. Deviations from this relationship makes for unstable, ie not sustainable, orbits. Or was Newton wrong ?

Uncertainty is an inherent property of quantum reality. The measurement problem is used to explain the situation because most people find it very hard to believe reality is so strange. Go back and re-read some of the excellent guidance you've been given in previous posts. Oh, and a very good authority says 'The Grand Design' is a sell-out and not up to the standard of his previous books ( I haven't read it yet myself ), and you'd be better served by the Feynman lecture series ( which I have read and are excellent ).

Last time I checked, a decaying orbit is a spiral. The moon's centre of gravity is in a somewhat stable orbit at a given orbital speed. If you break apart the moon such that there is little cohesion between the pieces, then the close face fragments are closer by a moon radius than the centre of mass, but are not orbiting any faster than the centre of mass, By Newton's law then, those pieces are in a less stable orbit will experience a decaying orbit.

I would say that the 'change in geometry of spacetime' is not 'the source of gravitational force', rather the geometry of spacetime IS gravity, which then influences the 'motion of objects'. I believe that's the question you asked. The rubber sheet analogy does work, as long as you remember that its basically a 2d representation. Most shopping malls have funnel like devices ( intended to collect money for charities ) where a child can pitch in a coin, and it will slowly spiral down into the collector. If there was no friction between coin and funnel/air, I'm sure you could set up a stable orbit for that coin. Just like in the universe at large. It seems, AJB, that most effort is put into making GR comply with QM to acheive unification. Meanwhile Loop Quantum Gravity seeks to constrain QM with GR ( like the abolition of an absolute spacetime frame ), yet its not discussed as much as say, Sstring theory, even though it has no need for supersymmetry and additional dimensions. Trying to gain even a basic understanding of the theory is a bear because of the formidable math involved. I don't want to hijack this thred and incur Swansot's wrath, but maybe if you or another member is familiar with the subject, you could start a separate thread/tutorial.

I would have to disagree Swansont. Since the moon is quite large compared to earth, it would experience tidal forces, ie greater on the close face compared to the far face, while all of its fragments would be moving at the same orbital speed. So a lot of the closer fragmenys would sppiral to earth and a lot of the farther fragments would spiral out or even escape (?). But maybe the portion closer to the moon's centre of mass would form some nice rings.

Doc, you DO have a sense of humour. Oh wait, you were being serious.

Well I was going to say that massless particles such as a photon are their own anti-particles, and, if they could possess a charge, couldn't possibly be their own anti-particles anymore. But then i remembered gluons...

Sorry its taken so long to get back Guenter. I realise that the source of Hawking radiation is virtual particles of the vacuum surrounding the event horizon, but they do affect the event horizon. For sufficiently small black holes such that their lifetimes coincide with the lifetime of the universe, ie. they can evaporate, the 'incorporated' virtual particles making up Hawking radiation shrink the surface area of the small black hole until the event horizon disappears and the 'contents spill back out in a gamma ray explosion. So if the information is greatly randomized by entropy into the surface area of the event horizon like a giant book where all the pages are ripped out and tossed in the air ( example by Brian Green ), it is no longer available ( just like entropy 'renders' energy unuseable or unable to do work ) and, so I think, not preserved. It then disappears altogether when the black hole evaporates. So even if you want to say it is 'somehow preserved on the horizon's surface, according to Hawking's own ideas, eventually this surface disappears. I know very little about string theory myself, other than the basics and am not familiar with Susskind's work. But Hawking's resoning for information conservation seems to be based on Quantum mechanical considerations. Maybe its too early to start mixing the apples and oranges of the classical and quantum. Sometimes it works as in Hawking's entropy/temperature/radiation picture, but maybe it doesn't hold up for information since one of his ideas implies the other is wrong.

Sorry guenter, maybe I oversimplified so that everyone can understand, and I wasn't specific enough for you. However I believe both points you addressed were trivial and due to mis-understandings. I believe I did state that the 'frozen star' concept applies to external observers only and that an infalling observer notices no abnormalities in the passing of time. And no I do not believe this to be caused by choice of co-ordinate system. It is an abnormality of space/time itself, and not of the mathematical model used to describe it. And yes your time coordinate is spacelike since the infalling observer's future is a spatial direction ( to the centre of the black hole ) and no deviation is possible. But like I said, I used simple english. But all that was secondary to the point I was trying to make, in response to G. Anthony that intact information could ever be re-radiated via Hawking radiation from a black hole. The black hole part was merely to 'introduce' the main point.

Well I guess its time to add my two cents... When a relatively massive star reaches the end of its sustainable fusion process, it eventually undergoes gravitational collapse. The remaining material which cannot be ejected by a massive stellar explosion, is more or less in free fall towards the geometric centre of the former star, now a black hole. Einstein's equations have the peculiar consequence that the stellar material can continue to exist forever in a state of free fall without ever reaching the bottom. This can be nearly visualised with a Penrose diagram. The space/time in the region of the black hole is so strongly curved that space and time become interchanged. If you are an outside observer, you see the stellar collapse slow down and come to a stop because the direction of time inside the black hole is 'perpendicular' to the direction of time as seen externally, i.e.the only thing in your future once inside the black hole, is a direction ( the geometric centre ).The experiences and observations of the infalling and outside observers are vastly different ( to say the least ). This is due to the purely classical nature of GR. Stephen Hawking came along and introduced a bit of QM and Thermodynamics into this classical picture of black holes, much the same as Max Planck did with his quantization of black body radiation in 1900.. Planck's equation E=hv was a long way from QM which took at least another 25-30 yrs and 50-60 for QED. Similarily Hawking has given us S=kA, where S=entropy, A=area and k is a constant, but like Planck's itt is only a modest beginning. Entropy is very similar to heat capacity and is measured in cal/deg while area is in cm^2. Hawking's constant k, then has a value of about 10^41 cal/deg/cm^2. This is a very large proportionality constant, and since entropy is a measure of randomization, this shows the degree to which any infalling material / energy / information is randomized. So yes, I will agree black holes have a temperature and therefore radiate, and so, if small enough will evaporate and eventually finish with a gamma ray explosion, during our universe's lifetime. But no, I don't agree that information could possibly be conserved after that degree of randomization.

I believe one of the best explanations was given by Richard Feynman in his lecture series ( They are very easy to find online and may even be here as a sticky ). It arises from the fact that the amplitude of the 'wave' is related to probability. Only an infinitely long wave has a clearly defined wavelength, wave number and amplitude. This amplitude is related to a probability in QM, such that in this case the probability of finding a particle at a certain place is the absolute value of the square of the amplitude. And so, in this case, since the wave is infinitely long, it can be found anywhere; position is uncertain. A wave packet on the other hand, has an increasing/decreasing amplitude BUT the wave number cannot be easily defined. so although the particle is more localised in this case, its energy and also momentum are more undefined. It is basically a trade-off, shortening the wave packet locates the particle with more accuracy, but makes the momentum more indeterminate; conversely lengthening the wave packet introduces more uncertainty in the particle position, but makes the determination of momentum more accurate.

Did not know that about Mitchell, DrR. Then again, when I was in my teens I read all of Andre Norton's work ( some about time travel including my first science ficrion story 'Galactic Derelict' ), without realising that he was actually a she. An older woman with a thing for cats ( she had many ), not your typical science fiction writer.

No, no, no... I meant who came up with the idea for the time machine in my example of a paradox ( see previous post and response to Morgsboi ). By the way, I certainly know who H.G. Wells is Airbrush, but you got me stumped Doc, who is E. P. Mitchell ?

Really ? Alternate timeline or not, who came up with the original idea of the time machine ? Causality violations cannot always be explaned away by 'alternate timelines'.

Say you lived in the year 2112 and you found, in your attic, the schematics for building a time machine drawn up by your great grand-father. So you build it and go back in time to our present, 2012, and discuss the idea of the time machine and its function with your great grand-father, who after you leave and return to 2112, draws up the schematics. Who actually came up with the idea, or was the information just created ( I love these paradoxes ) ?? But seriously... Say you and Kip Thorne have two wormhole generators and use thrm to estabilish a wormhole with the one opening at your end and the other in Kip Thorne's office. You then take your wormhole generator, hop aboard your spaceship and blast off to Proxima Centauri at an appreciable fraction of the speed of light, all the while conversing with Kip Thorne through your end of the wormhole. You descibe the sights to him and turn around and come back to Earth, still talking to Kip Thorne through the wormhole. Upon landing on Earth you find that although only acouple of years have passed for you, the Earth you have returned to has advanced thousands of years into the future and everyone you knew is long dead. 'No problem' says Kip thorne through the wormhole, 'Just step through the wormhole and return to the present'. So you do and have just travelled thousands of years into the past. This is an example of a macroscopic closed time-like loop, and it involves way too many unproveable assumptions and unacheivable effects ( macroscopic wormholes ??? ) for my liking. But it hasn't stopped Kip Thorne ( physicist ) from exploring the possibility. Look him up, he has done some very interesting work with so called 'time travel'.

Yet negative pressure could drive expansion, and at the very least is postulated by Guth to have driven inflation. If the universal vacuum energy 'hung up' at a false ( higher than ) zero level just after the big bang, it would have experienced violent inflation while it slowly fell to the actual zero point vacuum energy. If it never actually reached the zero point, but just drastically slowed down its descent ( much lower slope ), then it could still be driving expansion at a much reduced rate, ie. accounts for the cosmological constant. But I guess that unless we can get a handle on a realistic value for the vacuum energy, all this is just speculation,

Yes, chapter 7 of Hawking's 'A Brief History Of Time' has a reasonable if simplistic explanation of Black hole entropy>temperature>radiation. The book is available everywhere, even used or as a download.

I don't remember since its been a long time since I read it, but does Hawking's A Brief History Of Time include a simple explanation of Hawking radiation and its relationship to energy conservation and virtual particle behaviour near the event horizon of a black hole ? It may be enlightening reading, questionposer.

Virtual particles don't carry motion, whatever that means. All force carrier bosons in quantum field theory are virtual particles, not all virtual particles are force carrier bosons. Think of virtual particles as surrounding real particles such that they must be included in any calculation of mass, charge, etc. A real world analog would be a baseball moving through a viscous fluid like air, to calculate forces on the baseball you have to include contributions from the boundary layer or entrained air. Black holes, at least outside the event horizon, are no different than any other gravitating body. They 'attract' other mass/energy.

Some advice questionposer... I'm sure Dr Rocket doesn't need me to toot his horn, but he's not 95% classical mechanics ( maybe you mean General Relativity ). As a matter of fact his understanding of Quantum Mechanics is probably better than 95% of us on this forum. I have dealt with him for a couple of yrs and have nothing but respect for him. He can be abrasive at times, but is always insightful and steers you in the right direction. I have learned a lot from him. There is no clear demarcation between classical and quantum physics. Some classical concepts apply to the very small and some quantum concepts apply to the very large ( you yourself alluded to the evaporation of black holes via hawking radiation, but there was considerable confusion in your argument). Some understanding of the basics is required to know which can be applied and which cannot. Do not catagorically state that since a concept is classical in nature, it is osolete and no longer viable. "Reading a book" might give you a deeper understanding of the basics.

But we don't measure to a dimensionless point... There is a limit to accuracy we can acheive, and it is fairly 'smeared out'. Also as Widdekind has explaned, put an EM wave through a double slit. Do you measure a point ??? Wish I had more time, gotta run.

Re-read the whole discussion. It seems you are confused about what happens when a measurement is made on a Quantum Mechanical system. By your misunderstanding, the collapse of the wavefunction when an observation is made, implies that the wave nature of the system becomes an actual point particle. That is NOT the way it works. Wave function collapse is an 'interpretation' to allow for the multitudes of possibilities represented by the wavefunction and the single observed result. The wavefunction does not collapse to a particle, and time certainly does not stop.