Can black holes explode?

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I was not asking for a

Message 99428 in response to message 99427

I was not asking for a complete summary of the book. You claimed this book disagrees with my arguments in this thread. I expected reasonable counter arguments. I don't see how a personal account of a dream that might be or might not be metaphorically used in a book is a counter argument against anything, if that is what you are implying.

tullio
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My personal opinion is that

Message 99429 in response to message 99428

My personal opinion is that Dyson believes in God, but this in only an inference from the book. Other scientists that I have known and who believe in God, as they have told me, are astronomer Paolo Maffei, discoverer of two galaxies, theoretical physicist Luigi Radicati of Pisa University and Accademia Nazionale dei Lincei, Tito Arecchi, former director of the Istituto Nazionale di Ottica and builder of the first Italian laser, by which he demonstrated that photons follow the Maxwell-Boltzmann statistics. All people of the top scientific level. By this I am closing our discussion, since it is becoming useless. Cheers.
Tullio

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At least you closed the

At least you closed the circle by plainly restating your original argument. Claiming that some top scientists are religious is just as true as it is meaningless. Let me rephrase my critique to your argumentation by authority, for which you did not have an answer.

If you like the argumentation by authority you should take into consideration that the overwhelming majority of top scientists disbelief the God-hypothesis. The percentages are much greater than in the regular society.

Moreover, you also need to take into account other supernatural beliefs by even greater authorities, like Newton, that are currently generally dismissed , e.g. alchemy, magic, occultism, Zeus, Thor, etc. Why would you dismiss those if argumentation by authority is valid?

Also, you should consider that the scientist that have a personal belief systems are combining rational and irrational mindsets. And generally, the more intelligent of them do understand the irrationality of this stance.

Let me quote both Dyson and Pascal for you to close the discussion from my side as long as you do not bring new argumentation to the table:

Dyson:

Quote:
I am content to be one of the multitude of Christians who do not care much about the doctrine of the Trinity or the historical truth of the gospels.

Pascal:

Quote:
People almost invariably arrive at their beliefs not on the basis of proof but on the basis of what they find attractive.

Quote:
Make religion attractive, make good men wish it were true, and then show that it is.
tullio
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If Dyson says he is a

If Dyson says he is a Christian he admits a belief in God, as I said. Trinity is just a triplet representation insted of a singlet representation, as anybody with a basic knowledge of group theory knows.
Tullio

Mike Hewson
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Ahem .... I didn't mention

Ahem .... I didn't mention the other aspect of observation that inflation solves, not the 'horizon problem' mentioned below, that is : the 'flatness problem'. Ignoring stuff below the scale of clumps of matter, like black holes or galaxies, then the universe is as per Euclid. By that I mean, in large scale indeed, the interior angles of triangles add to 180 degrees. That sort of thing. Why should this be so?

I'll go back to some basic calculus. The main idea of taking a derivative ( thinking of one dependent variable of one independent variable now ) is to progressively approximate a tangent to a curve by a secant line. A tangent line is one which just 'touches' a curve, intersecting at one point only, in a way which yields the concept of slope. So we say the gradient of the tangent line ( rise divided by run ) is the slope of the curve at that point of tangency. Now a secant line runs b/w two points on the curve, so it cuts the corner so to speak. So imagine two points on a curve A and B, keep A fixed but slide B back and forth along the curve. As B gets nearer to A then the slope of the secant line becomes nearer to the slope of the tangent line at A. If you can find a single number that the secant slope can be as close as you like, provided you let B get close enough to A ( but not equal ), then you have performed a limit process - with that single number being given the name limit and thus said to be the slope of the tangent and hence the curve at the point where you performed the limit process nearby. Whew!

The moral of the story is : provided that you have a curve for which you can perform the above limit process upon, then any such curve will look straighter and straighter as you zoom in toward it. In algebraic terms one can write :

delta_y ~ f'(x) * delta_x

meaning a slight change in y is well approximated by a slight change in x times the slope of the tangent. Or in Leibniz notation ( with some background I'll leave out ) :

dy = f'(x) dx

In physics we nearly exclusively model reality with smooth functions, these are curves which are as differentiable as we please. One can create a beast called a Taylor's Series that gives the value of the curve at points nearby to a chosen point, based upon values of derivatives at that chosen point. The above formula is the first part of the Taylor's.

Back to inflation. Take any 'shape' of the universe in the early stages, pick a 'point' and then expand the shape by 10^(50) in size. It'll look locally flat for sure regardless of any wiggles and bumps it had beforehand. Mind you, what we see of the universe today isn't the whole universe. It's just the bit we can see, and so 'local' in this discussion means a bubble of some fourteen odd billion light years in radius. We just don't know what's beyond that.

Inflation also solved another issue as regards 'monopoles', which I don't understand but mention for completeness.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

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RE: Ahem .... I didn't

Message 99433 in response to message 99432

Quote:

Ahem .... I didn't mention...

...what we see of the universe today isn't the whole universe. It's just the bit we can see, and so 'local' in this discussion means a bubble of some fourteen odd billion light years in radius. We just don't know what's beyond that.


The speed-of-light thingy is a bit of a limit on our knowledge gathering! Is that going to be an ultimate limit to our horizon-of-ignorance?

Might we get over-the-horizon physics where distant objects act as a relay or proxy for yet more distant parts? (Nope... We get held back by the speed of information limit as always...)

Quote:
Inflation also solved another issue as regards 'monopoles', which I don't understand but mention for completeness.


Now that sounds rather like the sort of marginal comment made by Fermat about a certain theorem of his... Also involving triangles...

I still feel that there is a missing piece of understanding of 'how' we have forces acting at a (sub-atomic through to intergalactic) distance. We have greatly researched and finely described the 'what' of what happens, but what is the 'mechanism' by which the four forces operate beyond that they appear to 'exist'? Stuff certainly happens. Are our four observed forces multiple manifestations of a fundamental property of, or 'that is', what we call space-time?

Keep searchin',
Martin

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Mike Hewson
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RE: The speed-of-light

Message 99434 in response to message 99433

Quote:
The speed-of-light thingy is a bit of a limit on our knowledge ....... marginal comment made by Fermat about a certain theorem of his... Also involving triangles...


Yeah the margin was too small to contain the proof. Cheeky lad has kept us busy for centuries. He hinted at a method of 'infinite descent', a sort of Principle of Mathematical Induction in reverse, plus Proof by Contradiction. Roughly : assume some Proposition is true for some ( unspecified ) huge number(s), deduce that it must therefore be true for a case with lesser magnitudes - rinse, lather, repeat - arriving at some exact case with low numbers, but such that the Proposition is known to not apply. Therefore, flipping all the dominoes in reverse, it can't have been true in the original ( huge ) case. Trouble is he never specified the detail, so the truth ( via this method ) is unknown ie. how many trucks can you drive through this logic?

Quote:
I still feel that there is a missing piece of understanding of 'how' we have forces acting at a (sub-atomic through to intergalactic) distance. We have greatly researched and finely described the 'what' of what happens, but what is the 'mechanism' by which the four forces operate beyond that they appear to 'exist'? Stuff certainly happens. Are our four observed forces multiple manifestations of a fundamental property of, or 'that is', what we call space-time?


The easier answer is to avoid the depth inherent in the question and say 'that we just do models'. The current dominant paradigm for non-gravitational forces is that of particle interaction. So when I push my hand against your chest this is essentially electromagnetic. The other forces are there but they just are no where near the same magnitude for this situation. Hence we would posit a blizzard of ( virtual ) photons surrounding charges labelled as being in/on my hand interacting with a similiar photon fuzz around charges labelled as being in/on your chest. By simply speed limiting the photons then you get Special Relativity et al. You can run this logic across the distance between you and me, or trot all the way to the Great Attractor.

For the weak and strong nuclear forces one replaces photon by intermediate vector boson and gluon respectively. But .... you have to thrash the mathematics a tad to wrestle non-infinite answers out of the full quantum mechanical horror - see Feynman diagrams and sum over histories, normalisation, re-normalisation, effective theories etc.

However : these tricks ( for photon/intermediate-vector-boson/gluon ) assume a spacetime background, a structure within which they operate. Call this 'background dependence'. Not so with gravity. In addition to being a classical ( non quantum mechanical ) theory, we are talking about the behaviour of spacetime - the background itself. So if you want to speak of gravitons ( gravitational quanta ) then they don't operate within spacetime as they are spacetime! Call this 'background independence', meaning gravitons have no background. Up to a point you could call this semantics, wordplay and what not.

But a special implication here is that one graviton must affect another graviton, and it does so by using - guess what? - gravitons. Arrghh ! To say this is non-linear is an understatement. Two photons will pass by each other, and apart from the possibility of some other particle creation ( like an electron/positron pair ), they won't upset each other at all. The cloud of virtual photons alluded to above ( hand pressing to chest ) are really interacting with the charges from both of us. Our electrons and protons, regardless of labels. So photons aren't surrounded by 'their own' photon fuzz, so if one photon is choofing along undisturbed between here and the Andromeda Nebula then it can well be alone. But gravitons are surrounded by other gravitons ..... this gives rise to, at present, some unconquerable infinities in the mathematics.

There's some ancient cosmology that says the Earth is sitting on a tortoise ( not speaking of Terry Pratchett here ), but that is sitting on another tortoise, which is sitting on ....... well you get tortoises all the way down, but without a bottom. An infinite stack. With non-gravitational forces you can approximate quite well by ignoring the tortoises that are well down. Sums converge, so if you stop considering them below some level then any error ( because you did that ) is bounded. The gravity turtles don't do that, you can stop accounting for more complicated mathematical terms, but your error for that choice will not subside and you will have no idea how near or far you are from the 'true' result that would be obtained by summing over the lot.

QCD lattice theory ( strong nuclear force ) was difficult but tractable and eventually, with supercomputer level computing power, the sums converged to within a quotable range. So you didn't do infinite tortoises but you knew how far off you would be by stopping at some level. So they wound up with a terrifically accurate number ( with respect to measurement ) for the mass of a proton : two up quarks plus one down quark sitting in a blob of gluons. A significant fraction of the total proton mass is the energy of the gluons being exchanged, which is a manifestation of the degree of 'slowness' of convergence when extra levels of tortoise terms are added. In electromagnetism the 'anomalous' magnetic moment of the electron was calculable with fewer tortoise levels than QCD and gave even more decimal places of impressive agreement with measurement.

But there's a sense of incompleteness for sure, like dividing the circumferences of lots of circles by their respective radii, and coming up with an amazing constancy in that ratio. Why should a universe do that?

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

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RE: RE: The

Message 99435 in response to message 99434

Quote:
Quote:
The speed-of-light thingy is a bit of a limit on our knowledge ....... marginal comment made by Fermat about a certain theorem of his... Also involving triangles...

Yeah the margin was too small to contain the proof. Cheeky lad has kept us busy for centuries. He hinted at a method of 'infinite descent', a sort of Principle of Mathematical Induction in reverse, plus Proof by Contradiction. ... unknown ie. how many trucks can you drive through this logic?


Very cheeky yet very intriguing. I still wonder if that was the sort of idea that is wonderful late in the evening after a few beers but that is soon found to be too difficult in the cold light of the morning after...

For something significant, I would have expected him to follow it up.

Quote:
Quote:
I still feel that there is a missing piece of understanding of 'how' we have forces acting at a (sub-atomic through to intergalactic) distance. We have greatly researched and finely described the 'what' of what happens, but what is the 'mechanism' by which the four forces operate beyond that they appear to 'exist'? Stuff certainly happens. Are our four observed forces multiple manifestations of a fundamental property of, or 'that is', what we call space-time?

The easier answer is to avoid the depth inherent in the question and say 'that we just do models'.


Oooer... Doesn't that reduce science to that of just being an auditor?!

(Beware the Terry Pratchett "Auditors"... They get to be quite annoyed in the Science of Discworld #3)

Quote:
The current dominant paradigm for non-gravitational forces is that of particle interaction. ... these tricks ( for photon/intermediate-vector-boson/gluon ) assume a spacetime background, a structure within which they operate. Call this 'background dependence'. Not so with gravity. ... to speak of gravitons ( gravitational quanta ) then they don't operate within spacetime as they are spacetime! Call this 'background independence', meaning gravitons have no background [because they are the background/substrate/fabric and existence itself].


Is that behind all the excitement just now in that following the assumed properties for gravity, there need not be any assumption for a "god" to kick-start the Universe? Regardless, it adds a whole new dimension to Marketing :-)

Quote:

But a special implication here is that one graviton must affect another graviton, and it does so by using - guess what? - gravitons. Arrghh ! To say this is non-linear is an understatement.

... so if you stop considering them below some level then any error ( because you did that ) is bounded. The gravity turtles don't do that, you can stop accounting for more complicated mathematical terms, but your error for that choice will not subside and you will have no idea how near or far you are from the 'true' result that would be obtained by summing over the lot.


Rather curious.

So our entire Universe is itself the sum of all gravity that is (gives rise to the existence of) the Universe...

Ooooops! Those words don't convey the exact intended meaning... Further thought later...

Another aspect is that we have the very famous "E=mc^2". But, what of all the gravitational Potential Energy?... How does that get twisted by the assumed infinities of black holes? And all further mangled by time effects...

Or can we just cheat and average it all out?!

And gravity acts beyond the event horizon...

Is gravity timeless? (In that it is 'already there'.)

Quote:

QCD lattice theory ( strong nuclear force ) was difficult but tractable and eventually, ... In electromagnetism the 'anomalous' magnetic moment of the electron was calculable with fewer tortoise levels than QCD and gave even more decimal places of impressive agreement with measurement.

But there's a sense of incompleteness for sure, like dividing the circumferences of lots of circles by their respective radii, and coming up with an amazing constancy in that ratio. Why should a universe do that?


Is Pi and the other 'fundamental constants' a feature of the geometry inherent for our manifestation of gravity?

Are other geometries workable for other 'colours' or 'dimensional shades' of gravity where the circumference of a circle is exactly 3 for example?

The ratio Pi is an important key. Perhaps it is the answer rather than 42?

Another curiosity is that we have the theory that interactions/propagation cannot take place 'instantly'. Yet gravity locally still depends upon the gravity experienced throughout the entire Universe... (Because it 'already is and always has been there'?...)

Mmmm, more beer with not too high a specific gravity needed tonight!

Keep searchin',
Martin

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RE: But there's a sense of

Message 99436 in response to message 99434

Quote:
But there's a sense of incompleteness for sure, like dividing the circumferences of lots of circles by their respective radii, and coming up with an amazing constancy in that ratio. Why should a universe do that?

Funny that you chose to refer to pi, as I don't see how that number is related to our universe. Isn't pi transcended over the universe, because we talk about mathematical abstractions here? I thought that pi is a tautology that is a valid ratio between circle radius and circumference in every Euclidean geometry in or outside the universe.

In that sense I think that the speed of light is a very different beast, as that seems to be directly related to our universe and not necessarily others. As far as we know, of course.

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RE: RE: But there's a

Message 99437 in response to message 99436

Quote:
Quote:
But there's a sense of incompleteness for sure, like dividing the circumferences of lots of circles by their respective radii, and coming up with an amazing constancy in that ratio. Why should a universe do that?

Funny that you chose to refer to pi, as I don't see how that number is related to our universe. Isn't pi transcended over the universe, because we talk about mathematical abstractions here? I thought that pi is a tautology that is a valid ratio between circle radius and circumference in every Euclidean geometry in or outside the universe.


Allowing for 'alternate geometries', can not Pi take on other numerical values other than what we have for our own flat planes in our 3d physical space?

An easy example of 'something different' is for when you wrap a 2d plane around a sphere (using an additional dimension, our 3rd dimension). For that example, you can then have triangles that have all three corners with 90 degree angles. Also, Pi would then be a variable dependant on the radius of the circle!

Quote:
In that sense I think that the speed of light is a very different beast, as that seems to be directly related to our universe and not necessarily others. As far as we know, of course.

My big puzzles are how gravity and time make our universe what it is. Also, we observe quantisation effects but are those really due to some fundamental quantisation or merely the consequence of very strongly stable discrete states within what is really a non-quantised world?

And then there is Planck...

Keep searchin',
Martin

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