Gravity Debate: Unanswered Questions on String/Loop Theories

[Canute]

Wolram - I tend to agree with what you say about science but not with what you say about mysticism. Mystics do not read spells from a book, as you suggest, that's witches and alchemists. Admittedly, it is easy to muddle mysticism with supernatural mumbo-jumbo, and many fine scientists and philosophers make a habit of it, but I think you'll find that it's also easy to unmuddle them with a little research.

 

[wolram]

Wolram - I tend to agree with what you say about science but not with what you say about mysticism. Mystics do not read spells from a book, as you suggest, that's witches and alchemists. Admittedly, it is easy to muddle mysticism with supernatural mumbo-jumbo, and many fine scientists and philosophers make a habit of it, but I think you'll find that it's also easy to unmuddle them with a little research.

I agree, i used the wrong analogy, sorry.

 

[nightcleaner]

Hi Nightcleaner

Just want to strongly disagree on a few points.


It would be more correct to say that mystical practice, by which I mean certain forms of meditation/contemplation, is the search for experiences that are endlessly repeatable. But perhaps you meant not repeatable in public, in which case you're right.


I'm not sure how you reach these conclusions. Why do you say that mystical practice fails to produce results? What makes you say that the path to enlightement is difficult to distinguish from the path to madness? Why say mysticism is founded on belief when this is precisely what it is not? All these are the opposite of the truth. If any of these were true I wouldn't want anything to do with mysticism. Contrary to what is sometimes asserted in the non-mystical literature mysticism is not in any sense irrational. It just requires the transcendence of formal logic in certain respects, which even mathematics and physics requires from time to time.


This is nothing to do with mysticism, but just an instance of inspiration or subconscious mental processing. One or two authors tell this story as being relevant to mysticism, Paul Davies does I think, but I have no idea why.


Yes, there's no need to do this. They insist that there is only one truth so everyone will end up in the same place in the end. This is why all mystics of all epochs and all cultures end up sharing the same vision.


Well said. But in the mystical view there is no God, so mystics tend to get burnt as heretics by the religious authorities if they're not very careful. To the extent that it can be truthfully said that there is a God, and in this view there is a certain sense in which there is one, then we are each Him, an assertion which also doesn't go down too well with the authorities.


That must have been someone else I think. My view is that science is showing that the mystical explanation of reality is correct, not that science is no different to mysticism. Science is something like a religion perhaps, in certain ways, but is nothing like mysticism, albeit that there are one or two important similarities, the use made of rigorous logical reasoning for instance.

One fundamental difference is that science is built on hypotheses while the mystical view contains no hypotheses. This is why the masters do not use phrases like "let us assume ..." when writing about reality. Assumptions have no place in this view, other than that sometimes they may serve a temporary practical purpose as scaffolding, as when, inevitably, a person has to assume or take on faith that there is something to be learned from 'mystical practice' prior to verifying this for themselves. Mysticism is about knowledge, not the construction of theories.

By the way, thanks for your occasional writings on life in the woods. I've learned something important from them.

Cheers
Canute

Hi Canute

Thanks for the the critique, and I think your points are well-taken, given one or two small misunderstandings. By saying that mystical experiences are not repeatable, I meant to evoke the idea that one cannot at will produce the results for the benefit of casual on-lookers, not that the practitioner cannot achieve them again. A repeatable experiment can be done over and over again, and the experimenter need not be the same person. So a teacher can teach an entire class of students how to measure the acceleration of a falling body, for example, and it works in every class in the same way for every attentive student. I suppose I was guilty of enfolding the idea that scientific results are communicable along with the idea of reproducible, in the idea that they can be repeated. I've been a bit rushed lately. My internet access is rather restricted. I may have to drop this connection in a few moments.

I was not saying mystical practice does not produce results, only that the results are not always what was intended. Mystical experiences, in my finding, have an explorational quality. Perhaps this has to do with my lack of adequate teachers in this area.

I meant that mysticism has gotten a bad reputation, not on its own merits, but because some people have used the idea of mysticism as a cloak for their attempts to make fraudulent profit. And also that poorly guided or unguided mystical pursuits have led some would-be practitioners into madness, much as many alchemists fell to lead and mercury poisening. But your learning in this area is evidently more refined than my own. You make a distinction between alchemy and mysticism in your reply above to Wolram, which I might not have made.

I have to go now but again, thanks for the discussion. I should like to know more about how you came into your aquaintance with mysticism. I have copied your post to my word processor and will try to consider it more offline.

Thanks,

Richard

 

[nightcleaner]

Hi Canute

“What makes you say that the path to enlightenment is difficult to distinguish from the path to madness?”

I meant difficult, at times, for the practitioner. People have used all sorts of extremes for the sake of mystical experience. Certain Amanita mushrooms are sometimes ingested for the sake of a reputed mystical quality, but they are deadly poison. It is quite probable that some people who have died eating this or other substances were in hopes of a mystical experience. Some people use inoxia for similar reasons, or various anesthetic or narcotic drugs. Surely you would agree that these practices can lead to brain damage. I recall some years ago a practitioner in Canada who advertised a guaranteed method to enlightenment…it involved drilling a hole through the skull and into the medulla oblongata, IIRC. He reported that he had performed this operation on himself, become enlightened, and now had the ability to unfailingly enlighten any willing volunteers. I don’t doubt he would have found some willing volunteers if he had been allowed to continue to advertise his technique.

It is not difficult to tell the difference between madness and enlightenment, from the outside. Mad people and enlightened people are very different. The problem comes in when a person seeking enlightenment attempts to gain it through questionable means. The unfounded belief that one has attained enlightenment is not uncommon in schitzophrenia, and I myself have worked with individuals in hospital settings who announced their own godhead and expected to be worshipped.

Again, what I mean is that there is plenty of deception in the world, and no lack of people who would gladly lead you to your destruction in the name of mysticism. I am not saying that there is no genuine mystical experience, only that there are plenty of clever, and even not so clever, false paths.

“One or two authors tell this story as being relevant to mysticism, Paul Davies does I think, but I have no idea why.”

Kekule was not a mystic, he was a chemist. As I recall the story, he had worked himself into exhaustion trying to find a structure to account for the composition of benzene. In a fitful sleep, he had a vision of a snake eating its own tail. Well, I have seen that image before in mystical context. But Kekule realized, on dreaming of the self-consuming snake, that the structure of benzene could be a ring, and that has turned out to be the correct structure. The image in the vision, the exhaustion and exposure to various solvents, the leap from the image to the correct solution to the problem….all of these seem to me to be connected to mysticism. I am not sure what your objection is. Could you elaborate?



"Why say mysticism is founded on belief when this is precisely what it is not?"

Well, it seems to me that it is and has to be founded on belief. One has a direct experience, a vision or inspiration, often arriving from an unknown quarter. There is no proof available for the perception. The owner of the vision has to believe that it is genuine, not purely illusory. But you may have something to teach me. What then is the foundation, if not belief? In fact, ultimately, I suppose, what else is there?

Thank you for the articulate and interesting conversation.

 

[Canute]

“What makes you say that the path to enlightenment is difficult to distinguish from the path to madness?”

I meant difficult, at times, for the practitioner. People have used all sorts of extremes for the sake of mystical experience. Certain Amanita mushrooms are sometimes ingested for the sake of a reputed mystical quality, but they are deadly poison...snip

You're quite right. People look for such experiences in all sorts of ways, from ascetism to hallucinogenics. I didn't so much object to the idea that mysticism in its widest sense, as a practice, can be a path to madness. My objection was rather to the idea that it is difficult to distinguish the two paths.

However, on reflection, maybe you have a point, or perhaps we both do. If someone suggests drilling a hole in your skull then clearly they are nuts, although trepanning seems to have been quite common is some early societies. But when the Dalai Lama says "Everything that contradicts experience or logic should be abandoned" this does not sound at all like a path to madness. But I'll go for a draw on this one. It seems true to say that it may not be obvious which path is which from the outside, when starting out, but it soon becomes obvious. (Unless, that is, a person thinks that mystical practice means abandoning their reason, and some people do seem to take this approach).

It is not difficult to tell the difference between madness and enlightenment, from the outside. Mad people and enlightened people are very different. The problem comes in when a person seeking enlightenment attempts to gain it through questionable means. The unfounded belief that one has attained enlightenment is not uncommon in schitzophrenia, and I myself have worked with individuals in hospital settings who announced their own godhead and expected to be worshipped.

This is it really. If a person behaves insanely, or makes assertions which are incoherent or contrary to the facts, then obviously their path is the way to madness. This is one easy way to distinguish the genuine from the muddled or counterfeit.

The clincher is that in the end it is not possible to be deceived about mysticism for long. The practice is ones own, the experiences are ones own and the analysis is ones own. Nobody has any control over these things except oneself, and it is completely unnecessary to believe in any particular teaching or person except as scaffolding, in the sort of way I mentioned above. All the scaffolding can be removed in the end. As kids we learn our multiplication tables by rote on trust, but in the end we can dispense with the trust.

Kekule was not a mystic, he was a chemist...snip The image in the vision, the exhaustion and exposure to various solvents, the leap from the image to the correct solution to the problem….all of these seem to me to be connected to mysticism. I am not sure what your objection is. Could you elaborate?

Hmm. I'm not sure why you would consider this mysticism. Mystical practice is about directly contacting reality, about apperception, bypassing the theory-laden evidence of the senses and all conceptualisations and imaginings. I'm not saying that the vision of the snake, the worm Auroborus of metaphorical mythology, was not a mystical vision, in a sense. That's one way we use the word, and if Kekule had interpreted his dream as telling him something about reality rather about chemistry perhaps there would be some justification for calling it mystical. But there is no sense in which this vision brought Kekule knowledge, it just brought him a good idea. If you dreamt of a snake tonight I doubt you'd wake up thinking you'd had a mystical vision.

Well, it seems to me that it is and has to be founded on belief. One has a direct experience, a vision or inspiration, often arriving from an unknown quarter. There is no proof available for the perception. The owner of the vision has to believe that it is genuine, not purely illusory. But you may have something to teach me. What then is the foundation, if not belief? In fact, ultimately, I suppose, what else is there?

This is the core issue I think. The only form of certain knowledge is self-evident knowledge. All philosophers conclude this as far as I know, at least, all those who accept that certain knowledge is possible, and in mysticism it might be called an axiom. (cf. "Actual knowledge is identical with its object" - Aristotle). Knowledge of self is the only certain knowledge we can have. This is why solipsism is unfalsifiable.

Would you agree that Descarte's famous axiom is true? If so, then you are judging its truth on the basis of mystical knowledge, not on belief. It is self-evidently true, true because you have examined, to an extent, what you are. Now imagine that nothing exists that is not you! In this case you have access to all sorts of self-evident knowledge by examing what you are. Mystical practice can be defined as examing and accepting who or what one is, and in a way is no more and no less than this.

On the repeatability of experiences issue what you say seems correct. But by saying that the experiences of mystics are repeatable I didn't just mean repeatable by the person having them, with each person repeating different experiences, I meant that the same experiences can be repeated by anybody. This is the central claim or affirmation of all 'mainstream' mystics and mystical religions. If this were not true then the mystical religions would not exist. After all, there cannot be more than one truth in the final analysis.

Hope some of that makes sense - just came back from the dentist so not entirely with it at the moment.

Regards
Canute

 

[nightcleaner]

Hi Canute

You said:
"I didn't so much object to the idea that mysticism in its widest sense, as a practice, can be a path to madness. My objection was rather to the idea that it is difficult to distinguish the two paths."

We seem to be playing football with the idea of inside/outside. The definition of being.

The Dalai Lama is, in my opinion, quite sane, and I follow news of his doings with gratitude for his existence. However it is not difficult to find the counter-example. There are any number of sociopathic fanatics who have sought mystical vision as a source of truth, leading some entire nations into unjustified wars, even into self-destruction. The amount of ruin and misery they have inflicted on the planet is an abomination. They do this because they are absolutely certain that their vision, or that of their leader, is the correct version of reality.

I follow a path that is full of doubts, and if I have any followers tagging along behind me, they generally get shaken pretty quickly. I have no desire to be a leader, so it doesn't matter much, except I do like to chat, and I have already heard most of my own stories.

You said:
"If you dreamt of a snake tonight I doubt you'd wake up thinking you'd had a mystical vision."

That depends upon the snake. Actually, lucid dreaming is a part of mystical practice, I think you agree.

Descarte's famous quote has only one premise before its conclusion. Really he might as well have just said "I am," but that would not have drawn much attention. The unstated first premise would probably be something like, "All thinking is done by beings." Then, "I think, therefore I am (a being)." This is not a very poetic rendition, and if Descarte had written it this way, I am sure he would have justifiably been ignored. The argument is patently trivial.

You said:
"...by saying that the experiences of mystics are repeatable I didn't just mean repeatable by the person having them, with each person repeating different experiences, I meant that the same experiences can be repeated by anybody. This is the central claim or affirmation of all 'mainstream' mystics and mystical religions. If this were not true then the mystical religions would not exist. After all, there cannot be more than one truth in the final analysis."

Why not? In fact, I have been beaten down into the stance that "being" itself is a two-truth proposition. Being only exists because of an irresolvable conflict. Inside/outside. If there is only one thing, where is it? It has to be somewhere, and is that not another thing? Then there is not only one thing. Universe or multiverse? Instead of "I Am," perhaps the universal assertion should really be, "Huh?"

I hope you are recovering nicely from your trip to the dentist. I will tell you a dentist story. One time I was having some work done and decided I should practice a little meditative pain control. I picked a convenient spot on the wall across the way out the window, as the dentist wielded his drill, and willed my conscious self to be there, escaping thereby the locus of discomfort.

The poor dentist thought I was going into shock. He catapulted the chair into the upright position, upsetting his tray of needles and probes and drill points and what have you. He was very distressed and couldn't resume the operation for some time. In fact he was a very good dentist, and I was sorry to cause him any anxiety. I resolved after that not to withdraw my consciousness any further than my toes, at least not while in a doctor's care.

Thanks for being here,

Richard

 

[nightcleaner]

Hi again.

I think we should try to tie this discussion back to the strings branes and LQG topic, as we seem to have gotten rather far afield.

The definition of being applies to black holes. In fact, it applies to anything that can be defined at all, in a catagorical sense. And the black hole problem is of concern to S,B,+LQG because the conditions near black holes are an excellent laboratory for testing theories of spacetime.

Consider for example the location of a black hole. We might be able to "pinpoint" a BH location by triangulation from outside the event horizon. We take a bearing from two widely separated positions, then calculate the position using the usual Euclidian space and Pythagorean theorum. The problem is, spacetime changes near a BH. Space and time get compressed in some directions and stretched in others. This is what the textbooks try to show by means of pictures of a bowling ball on a stretched sheet, or, more usually, by an x,y graph distorted in the z direction, which looks something like a funnel with curved slopes.

Now if we try to calculate the position of the BH as above, by triangulation in Euclidian space, we are calculating the radial distance between our position and the BH, along with the measured angles. But the radial distance as calculated does not account for the z distortion. Or, really, since BH is in three dimensional space, not in two dimensions as shown in the diagrams, the distortion is in the time direction. THis is why BH is interesting as a potential time machine.

Now I hope you see the problem. We can calculate the position of the BH in 3d space, from the outside, but that tells us nothing about where the BH is, on the inside, where it is subject to temporal elongation. In the two dimensional analogy, it is as if we are trying to locate the bowling ball on the sheet using a straight edge ruler. If we lay the ruler across the sheet, and mark the center, that is where we calculate the BH location. However, the BH isn't there! It is depressed into the sheet, some distance below our ruler.

The question of being is also elusive, or even illusive, in a similar way. We can define our own being rather clearly in three dimensional space. If it were not so, we wouldn't be able to fit inside our clothes. The fact is we have a height, a width, a breadth, and various other 3d spatial measures, like hat size and so on. These measures, along with our center of gravity, completely define us in regard to our location in 3d space.

Now let us add time to the 3d picture of ourselves. First, it is clear that our definition has to be expanded. We were not the same size at 18 years as we are at 32, 54, 98 years. Even more clearly, we were small when we were children and have grown larger since. In fact we were very small when we were very small children, and in the womb we were just tiny. When does life begin? Let's say at fertilization. At that time, we were a single cell, not even of a size to be visable to the naked eye.

But fertilization is merely a convenient marker, not an absolute limit. The egg we came from was already there before it became fertilized. I am sure I have consensus on this from the stem cell research prohibitionists. The egg is a potential human being, given the right chance. Never mind that every fertile woman then becomes a serial killer, unless she gets pregnant at the first and every subsequent opportunity. And what about the wet dreams of juvenile males? Are all teenage boys mass murderers on a truly grand scale? It seems the Catholic catechism would have us think so. A terrible sin, if every sperm is not given a fair chance to compete in the race to the egg!

To be fair, we have to concede that the egg we came from and the sperm we came from are part of our definable self. We extend into our parents. And our parents extend into us. We extend into our eggs and sperm, and hence into our children. What kind of parents do not believe that the child is an extension of their own selves?

So where do we begin, where do we end? The definition of self, when it includes the extension of our selves into time, into our children and our parents, becomes a definition of our family tree, then our species, then a definition of life itself. In the full extension of being into time, every life on Earth is part of one superior being. Call her Gaia, if you like.

Now look into the origins of life on Earth and you will see the likelihood that Gaia is in fact related to life among the stars. All life, anywhere in the galaxy, anywhere in the universe, is one super-being, extended in time and space. We see that in the 4d multiverse there is only one being. And, as philosophy and mysticism tell us, there cannot be only one thing. There has to be another thing, the counter-example, or there is no definition. We are not alone, Gaia is not alone, the universal super being is not alone. There has to be another.

Or, by the same logic, taken in the reverse direction, the super being cannot be real, Gaia cannot be real, and we ourselves are totally imaginary. Actually I kind of prefer that interpretation. There is no self. All the 10,000 things spring up and fall down in an eternal, unending sea of illusion. Isn't that comforting?

You will notice that there are no fairy tales about heaven or hell in the above interpretation, no need for a bearded god to tell us how to behave. Morality is preserved, however, because all beings prefer pleasure to pain. Since all beings have been shown to be one being, it is immoral, on purely economic grounds, to take pleasure from causing unnecessary suffering. More exactly, if you act to increase the general store of suffering in the world, you will unavoidably increase your own share of suffering as well, just as the rising water lifts all boats. On the other hand, if you act to relieve unnecessary suffering, you will instantly be rewarded by having your own share of suffering reduced. So it is only simple economics that demands we act as far as is possible to ease the suffering of others, work toward the social good, and live in a way that promotes the most healthful environment for all.

So I say, for purely selfish reasons, my loves,

Be well...

Richard

 

[Canute]

There are any number of sociopathic fanatics who have sought mystical vision as a source of truth, leading some entire nations into unjustified wars, even into self-destruction. The amount of ruin and misery they have inflicted on the planet is an abomination. They do this because they are absolutely certain that their vision, or that of their leader, is the correct version of reality.

True. I suppose Joan d'Arc is an example. But my point is, and from what you say I imagine you'd agree, that one cannot follow someone else's mystical vision. If one does this it is the precise opposite of what mysticism is about. (Although, of course, one may decide to trust in some teacher temporarily). To believe what one is told rather than to find out whether what one is told is true is, as you say, horribly dangerous. But imho anyone who tries to persuade you to believe in their mystical vision rather than to have your own is not to be trusted. If they also try to persuade you to go to war on that basis then it's case closed, the person is not a mystic but an opinionated egotist.

[/quote]You said:
"If you dreamt of a snake tonight I doubt you'd wake up thinking you'd had a mystical vision."

That depends upon the snake. Actually, lucid dreaming is a part of mystical practice, I think you agree.[/quote]
Well, one might take a snake to be a mystical vision. But one would have to interpret its meaning, and so although such a vision might point towards a truth one could never be certain as to its real meaning, as to whether it did point towards a truth. It's meaning and truth/falsity would have to be confirmed by other means than a vision. (But this might depend on what we each mean by 'vision' here). Don't forget that mystics warn against mistaking visions for truth, for visions are conceptual creations. Yes, lucid dreaming is practiced, but it's still just dreaming.

Descarte's famous quote has only one premise before its conclusion. Really he might as well have just said "I am," but that would not have drawn much attention. The unstated first premise would probably be something like, "All thinking is done by beings." Then, "I think, therefore I am (a being)." This is not a very poetic rendition, and if Descarte had written it this way, I am sure he would have justifiably been ignored. The argument is patently trivial.

And its triviality is of course why Descartes chose it. I agree that 'I am,' would have done, except that Descartes never got around to explaining what he meant by 'I'. None of this matters though, my point was simply that when one affirms 'I am' this is mystical knowledge, knowledge by identity. We know we are because it is self-evident that we are, not because we can derive 'I am' from some axiom-set or other.

I think therefore I am
Therefore I think I am
Think I, therefore, I am!
Therefore I am, I think
...

Why not? In fact, I have been beaten down into the stance that "being" itself is a two-truth proposition. Being only exists because of an irresolvable conflict. Inside/outside. If there is only one thing, where is it? It has to be somewhere, and is that not another thing? Then there is not only one thing. Universe or multiverse? Instead of "I Am," perhaps the universal assertion should really be, "Huh?"

Yes, or 'Mu' perhaps. Can you explain this 'two-truth proposition' a bit? To me it seems unreasonable to suppose that there is more than one correct understanding of reality, but perhaps this is not what you mean. Are you arguing against monism here? If so I agree with you. Monism, as the basis of a cosmology, gives rise to paradoxes just as does dualism. My impression is that this is the problem that in the end Spinoza couldn't solve.

I enjoyed your dentist story. If you can transcend the dentists chair then you have my respect. I still feel the pain too much as if it were mine. It's good practice though, having someone drill ones teeth while trying to withdraw to a safe distance. Unfortunately, I fear, it will be many lifetimes yet before I can face the dentist without trepidation.

You're right I think to reroute the discussion back to physics before we get into trouble. What you say about determing the position of black holes seems true. Hawking takes the same approach to time, suggesting that we cannot say at what moment the universe began since close to the BB our measurements of time become untrustworthy. In fact he argues that time is imaginary close to the beginning and end of, um, time. This seems to imply that space, and therefore relative position, is also imaginary at the limit. So, perhaps, with a bit of luck, are dentists.

Regards
Canute

 

[Canute]

Ah, did you add some more to that post? Now perhaps I see more of what you mean by 'two truths'. You've pointed out the problem with monism. It just doesn't work. In the mystical view reality is not described by monism, dualism or pluralism, although it has these aspects. What it is, however, is 'nondual'. This is the only possibility not expored in Western metaphysics, which in my opinion completely explains why it never makes any progress.

 

[selfAdjoint]

Hawking meant imaginary as in complex numbers imaginary; a multiple of $$\sqrt{-1}$$.

 

[Canute]

Are you sure? If you're sure then thanks for putting me right. My source just says imaginary, which seems rather unrigorous. But what you say makes sense. I thought his idea was a bit out of character when I came across it. What does it mean to say that time is a complex number? Does he just mean that it has to be represented mathematically as a complex number? If so, does space have to represented the same way.

 

[Berislav]

What does it mean to say that time is a complex number? Does he just mean that it has to be represented mathematically as a complex number? If so, does space have to represented the same way.

This is the Euclidian path integral approach. It draws from Feynman's method of doing Quantum Field Theory and generalizes it to spacetime, which are topologically trivial (i.e, aren't full of holes :tongue2: ). In order to do this we need the metric to have a positive signature.* Physically interesting metrics have a negative one (beacause the factor next to time is negative). In order to change this we introduce imaginary time. Spacetime is then Euclidian as time becomes just another spatial dimension. We then simply calculate the S-matrix via a path integral over spacetimes (ala Feynman). After which we Wick rotate it into standard Lorentzian spacetime.

*Marcus, I think, wrote about Loll using path integrals without this.

 

[selfAdjoint]

What Berislav said. Just to add a little motivation, complex numbers can be identifies with points in the plane, just as real numbers can be with points on on the line. In fact iif you set up "X-Y" coordinates in the plane you can think of the real numbers lying on the "X-axis" and the multples of i lying on the "Y-axis". Multiples of i are called pure imaginaries. Then a general complex number a + bi (where a and b are any real numbers) is identified with the point (a,b). Algebraically it's obviously a sum of a real number and a pure imaginary.

Complex numbers have a lot more strong ways to make things simple and nice than real numbers do, because of the greater freedom to move around in the plane. One powerful theorem is that if you have a closed curve in the complex plane, and a function that is defined and smooth everywhere on the curve, then you can extend that function to all the points inside the curve, so that it will be smooth there too.

So if you have a smooth function of real variables, you can take it as defined on the "X-axis" of the complex plane, and you can complete a closed curve in various ways, maybe just a big half circle that goes from -big number to +big number throught the top half of the plane. Now your closed curve goes from -big number to + big number along the X-axis, then up along the semicircle and back down to -big number again. You have to argur the the function can be extended over the semicircle and be smooth, and you do that in physics by making big number big enough that all the interactions go to zero, or close to it.

Then you use the theorem to extend the function all over the inside of the semicircle, smoothly. In particular it is smooth on the Y-axis, where it is inside the semicircle. So you can take the special values of the function there and be sure that there is a smooth transition to the old values on the X-axis. That is you have a reliable smooth way to go back and forth between real values and imaginary values.

And that's what the Wick Rotation does with time. Defining $$t = i\tau$$, a pure imaginary, we have $$-t^2 = -(i\tau)^2 = - ((-1)\tau^2) = +\tau^2$$, so you go from $$-c^2t^2 + x^2 + y^2 + z^2$$ to $$+c^2\tau^2 + x^2 + y^2 + z^2$$ with all positive signs, which allows the path integrals to converge. Then after you get the result you know you can just plug in t in it wherever $$\tau$$ appears, because that smooth transition is guaranteed.

 

[nightcleaner]

This is the Euclidian path integral approach. It draws from Feynman's method of doing Quantum Field Theory and generalizes it to spacetime, which are topologically trivial (i.e, aren't full of holes :tongue2: ). In order to do this we need the metric to have a positive signature.* Physically interesting metrics have a negative one (beacause the factor next to time is negative). In order to change this we introduce imaginary time. Spacetime is then Euclidian as time becomes just another spatial dimension. We then simply calculate the S-matrix via a path integral over spacetimes (ala Feynman). After which we Wick rotate it into standard Lorentzian spacetime.

*Marcus, I think, wrote about Loll using path integrals without this.

Hi Berislav, and all...

Seems to me we are getting close to the nerve, here.

I have this book, and found it an interesting read.
An Imaginary Tale:
The Story of i [the square root of minus one]
Paul J. Nahin

Cloth | 1998 | $29.95 / £18.95 | ISBN: 0-691-02795-1
274 pp. | 6 x 9 | 47 line illus. 1 halftone

I actually thought I understood something after reading it, but I still get quite confused when encountering i in formulations. Not Nahin's fault, I am sure, but probably something to do with my own encylclopedic self-doubt. Or chaotic lifestyle. Or just plain bad memory. Anyway.

Actually I recall a pretty fair number of factoids about sqrt-1, but they seem to float about in my mind without clear edges, so I can't, yet, fit them together. Affine plane. AB=-BA. Complex number. To paraphrase Robbi the Robot, "Warning! Danger! That does not commute!" Perhaps i should write a new soap opera, "Lost in Spacetime."

About the Hawking comment, that, at least, seems to me to make perfect sense. Reality in spacetime is quite different from reality in ordinary space. Where did the big bang happen? Oh, well, pick any point. The whole idea of the BB is that if you go to the end of time, all points in our universe coincide into a single point. Trying to find the location of the BB in 3d space is very like trying to find the edge of a sphere. The sphere does have definition and limits, but it just doesn't have any edges.

It is the same thing when you try to find the edge of time, or "the end of time", in the more common but even less insightful phrase. It is like the fractal problem of trying to measure a curve with a straight edge. If you take the length of the straight edge to zero, then the length of the curve goes to infinity. We don't like that. It is just too wriggly, and it makes our nice clean Euclidian 3d space 1d time into a horrible can of worms.

What was there before the universe began? Not even nothing. (A tip of the hat to acknowledge Peter Woit's blog, Not Even Wrong, for its linguistic constuction.)

 

[marcus]

*Marcus, I think, wrote about Loll using path integrals without this.

If I gave the impression that Loll's method (CDT) doesn't use Wick rotation, I should correct that. It does use it: the Wick rotation is well-defined and an essential step. (when I try to describe the QG path integral approach I invariably omit details and gloss over points)

You mentioned "holes". As we discussed in another thread, Loll and students are just beginning to make progress with topologically nontrivial cases. Loll and Dittrich have some papers about CDT with black holes, Loll and Westra have some papers where microscopic wormholes are allowed in 2D. but still one can say that the usual or normal CDT path integral is only for simple spacetimes, no holes.

I wasnt sure when you said "without this" whether you meant without Wick rotation, or without holes/topology change. usual CDT is with Wick and without topology change

 

[marcus]

Hi selfAdjoint, I wonder if anyone else is having the same trouble that I do reading LaTex.
When LaTex is typed in line there is sometimes overwriting. So this from your last post should be perfectly legible but is not because part of the algebraic expression is typed overtop the other. And it doesn't happen with complete consistency every time I view the post! Now it is not doing it. This passage comes through perfectly:

...And that's what the Wick Rotation does with time. Defining $$t = i\tau$$, a pure imaginary, we have $$-t^2 = -(i\tau)^2 = - ((-1)\tau^2) = +\tau^2$$, so you go from $$-c^2t^2 + x^2 + y^2 + z^2$$ to $$+c^2\tau^2 + x^2 + y^2 + z^2$$ with all positive signs, which allows the path integrals to converge. Then after you get the result you know you can just plug in t in it wherever $$\tau$$ appears, because that smooth transition is guaranteed.

But earlier today, to make this readable I needed to insert carriage-returns after some of the LaTex to avoid having two Tex expressions on the same line. Like this:


<<...And that's what the Wick Rotation does with time. Defining $$t = i\tau$$, a pure imaginary, we have $$-t^2 = -(i\tau)^2 = - ((-1)\tau^2) = +\tau^2$$,
so you go from $$-c^2t^2 + x^2 + y^2 + z^2$$
to $$+c^2\tau^2 + x^2 + y^2 + z^2$$ with all positive signs, which allows the path integrals to converge. Then after you get the result you know you can just plug in t in it wherever $$\tau$$ appears, because that smooth transition is guaranteed>>

 

[nightcleaner]

Hi selfAdjoint, I wonder if anyone else is having the same trouble that I do reading LaTex.
When LaTex is typed in line there is sometimes overwriting. So this from your last post should be perfectly legible but is not because part of the algebraic expression is typed overtop the other. And it doesn't happen with complete consistency every time I view the post! Now it is not doing it. This passage comes through perfectly:



But earlier today, to make this readable I needed to insert carriage-returns after some of the LaTex to avoid having two Tex expressions on the same line. Like this:


<<...And that's what the Wick Rotation does with time. Defining $$t = i\tau$$, a pure imaginary, we have $$-t^2 = -(i\tau)^2 = - ((-1)\tau^2) = +\tau^2$$,
so you go from $$-c^2t^2 + x^2 + y^2 + z^2$$
to $$+c^2\tau^2 + x^2 + y^2 + z^2$$ with all positive signs, which allows the path integrals to converge. Then after you get the result you know you can just plug in t in it wherever $$\tau$$ appears, because that smooth transition is guaranteed>>

Marcus, I am not experiencing the difficulty you mention, but it sounds like a problem I had with my previous computer. I am afraid you may be having a hardware difficulty. I hope you can resolve this difficulty quickly and easily!

Richard

 

[marcus]

Marcus, I am not experiencing the difficulty you mention, ...

that's good. then hopefully it is not a general problem just something
my system does on occasion
not to worry about further

 

[Canute]

I'm going to stick my neck out a bit and try out some ideas.

Next to one of thread titles here, 'Relativity' I think, it is written that time and space are relative concepts, not absolute things. My impression is that there no agreement about this in current physics, but the statement has been there a long time and it seems true to me. If so then it follows that this spacetime universe reduces to, or emerges from, something that is unextended in spacetime, something that is absolute, for common sense says that there must be something that is absolute. This something would have to be like an infinitely curled up dimension (or number of them) perhaps, not so much at right angles to the usual four and innaccessible to us, but rather just unextended so unobservable and immaterial. If anything like this is the case then it's small wonder then that we are confused about where the BB happened and when it did, for it didn't.

I liked Hawking's idea when I thought he meant time was imaginary. It made sense, even if he didn't bite the bullet and considered only the beginning and end of the universe, leaving out the bit in between. However, to say that time (at the beginning and end) turns into an imaginary number seems meaningless to me, even if it is necessary to represent it by such a number in a mathematical formalism. Why not just say it's imaginary, as this seems to be generally accepted? (I'm still not quite convinced that Hawking didn't mean imaginary literally. If not then the writer I read on this was being very sloppy).

To use the sphere metaphor, which is misleading but helpful, this would mean that the spacetime universe could be represented as being on the surface of the sphere, and all points in spacetime would be directly and uniquely connected to the focus of the sphere, which would represent the unextended but paradoxically co-extensive-with-spacetime dimension curled up into an unextended singularity. If spacetime is not fundamental then the singularity is fundamental. If spacetime is conceptual/imaginary then the singularity remains fundamental and unchanged and there was no BB, or, rather, we are still experiencing the BB, a continuous creation or emergence of virtual particles and waves from another dimension into their conceptually-extended spacetime, causing the appearance of an expanding universe and a uniform background radiation. (Yes, I know this sounds crazy, perhaps it is).

So, conceptually, from one perspective the sphere can be thought of as a singularity, for if there is nothing outside of the sphere it doesn't make sense to assign it a size, although we have to give it a size to conceive of it. Or it can be thought of as infinitely extended, for the same reason, but only in the minds of its observers.

Is that lunacy? Perhaps. But if there is a fifth dimension or 'hyperspace' as suggested by some then I would have thought it'd have to be something like this, topologically-speaking. It's only a rough and metaphorical picture, however it seems to tie in with the paradoxical results we obtain from quantum cosmology and micro-physics. But I'll expect one or two objections.

Tying this in with the Higgs fied, which is where we started, is beyond me. It might suggest that the Higgs field is unextended in spacetime, which might bear on some of the properties of gravity and our inabilty to find the Higgs field (or is it just Higgs bosuns we can't find?) but this is where it all gets far too technical for me.

The key test of this idea is whether or not it is possible to explain the cosmic background radiation as generated uniformly over time and not just all at once at the "beginning" of time. I have no idea whether it is possible to do this, or possible to show that it cannot be done. I'm hoping someone here will know.

 

[galactus]

it's the return of the space cowboy just to say...

...imagine Canute, being not on the outside surface or the inside surface of a sphere/bubble but trapped in the membrane itself ?


Imagine, if you will bubbles...
expanding as they float around
bumping into other bubbles
and inside of these bubbles
is another bubble expanding
and so on...

...and if all these bubbles
made a musical note,
as they bumped and merged
and expanded,
they created chords and melodies
and so on...

if you look at the swirling effects on a bubble skin/membrane and took note of different points on the bubble you'll see patterns of points seemingly moving towards and away from each other while still maintaing surface tension...

...then it pops and you have to blow another one

equate that to gravity, redshifting and inflation then scale it up or down, throw in some black holes/wormholes to connect the bubbles and allow for energy exchange then VOILA...

bye for now...

 

[Canute]

Yes, this is more or less what I'm suggesting, but taking a broader view and going a little deeper.