M-Theory is a theory which 'combines' the five superstring theories

[drcrabs]

Waddup guys. To my understanding M-Theory is a theory which 'combines' the five superstring theories and supergravity.Also i understand that matematics is not yet advanced enough to make it work(or so I've been told) I am still not sure how this theory is meant to end up as a theory of everything. You thoughts?

 

[James Jackson]

When 'theory of everything' is banded about, it means a theory which unites all the four fundamental forces into one common framework. The forces are, of course, electromagnetic, strong, weak and gravitational.

 

[Mike2]

When 'theory of everything' is banded about, it means a theory which unites all the four fundamental forces into one common framework. The forces are, of course, electromagnetic, strong, weak and gravitational.

I believe a TOE would also explain where spacetime itself came from and how particles emerged from that.

 

[drcrabs]

Yea thanks i already know what a TOE is and the four fundamental forces are thanks ne way

 

[Mike2]

Waddup guys. To my understanding M-Theory is a theory which 'combines' the five superstring theories and supergravity.Also i understand that matematics is not yet advanced enough to make it work(or so I've been told) I am still not sure how this theory is meant to end up as a theory of everything. You thoughts?

Gravity is thought to be curvature of spacetime itself. But String Theory and M-theory are various dimensional submanifolds embedded in a background spacetime. Gravitons are thought to be some type of string or brane. So there seems to be a contradiction. Strings and branes are thought to be gravitons of gravity which is thought to be spacetime itself in other theories. So where did the background come from in the first place?

 

[Mike2]

Gravity is thought to be curvature of spacetime itself. But String Theory and M-theory are various dimensional submanifolds embedded in a background spacetime. Gravitons are thought to be some type of string or brane. So there seems to be a contradiction. Strings and branes are thought to be gravitons of gravity which is thought to be spacetime itself in other theories. So where did the background come from in the first place?

So what if they find a background independent formulation of string/M-theory? What would that mean? You would still have gravitons and all other particles explained in terms of this background, i.e. vibrations of something within a background space, right? The formulation would simply be background invariant, not depend on whatever spacetime is chosen in which to describe the theory, right? But that would still REQUIER a background, which the theory would not explain. Is that correct?

 

[selfAdjoint]

So what if they find a background independent formulation of string/M-theory? What would that mean? You would still have gravitons and all other particles explained in terms of this background, i.e. vibrations of something within a background space, right? The formulation would simply be background invariant, not depend on whatever spacetime is chosen in which to describe the theory, right? But that would still REQUIER a background, which the theory would not explain. Is that correct?

All the difference in the world between particles flying around in a curved, fixed, background space on the one hand, and particles causing the spacetime to bend, while it causes them to curve in their paths. Background independent means that the space is in the foreground, taking part in the physics, and dynamically altering and being altered.

 

[Mike2]

All the difference in the world between particles flying around in a curved, fixed, background space on the one hand, and particles causing the spacetime to bend, while it causes them to curve in their paths. Background independent means that the space is in the foreground, taking part in the physics, and dynamically altering and being altered.

How can gravity be both a curved spacetime and a particle moving through spacetime simultaneously? If gravitons are particles moving through a background spacetime, then where did the background come from? Even if it doesn't matter what the background is (it still results in the same physics), you still seem to need a background in order to calculate the particle properties. Where did that background come from? Is there a 5th force which does bend the background spacetime? If it doesn't matter what the background is in order to obtain the particle properties, then the particle properties cannot depend on the background, so the background, likewise, cannot be influenced by the particles, right?

 

[selfAdjoint]

How can gravity be both a curved spacetime and a particle moving through spacetime simultaneously? If gravitons are particles moving through a background spacetime, then where did the background come from? Even if it doesn't matter what the background is (it still results in the same physics), you still seem to need a background in order to calculate the particle properties. Where did that background come from? Is there a 5th force which does bend the background spacetime? If it doesn't matter what the background is in order to obtain the particle properties, then the particle properties cannot depend on the background, so the background, likewise, cannot be influenced by the particles, right?

All good questions. Nobody knows. If we quantize gravity by any method, there will be quanta of gravity. If our quantization is background independent - that is, it is a quantization of spacetime itself - then these quanta of gravity will also be quanta of spacetime. Einstein thought of "the field" as replacing spacetime, and there have been others who thought of spacetime as replacing the field! Quantize that!

 

[Mike2]

All good questions. Nobody knows. If we quantize gravity by any method, there will be quanta of gravity. If our quantization is background independent - that is, it is a quantization of spacetime itself - then these quanta of gravity will also be quanta of spacetime. Einstein thought of "the field" as replacing spacetime, and there have been others who thought of spacetime as replacing the field! Quantize that!

You understand the contradiction, don't you? You assume a continuous spacetime in order to calculate the quanta of spacetime. So which is it, right?

I'm trying to understand the meaning of background independence. Doesn't that mean an invariance of some sort, that the physics is the same no matter what the curvature of spacetime is. Is this right? I understand the term independence to be invariance, but you suggest it means quantization. Are you saying that invariance equal quantization. Maybe there is a principle to this effect that I forgot.

 

[nightcleaner]

If you start with nothing, and then make two somethings out of it, it should not surprise you if, when you add the two somethings together again, you get nothing. Does this mean that neither of the two somethings exists on its own? Of course not. This is the value of separation. A positron and an electron can be perfectly good somethings, until they happen together. Then they return to nothing again. The energy, or action potential, which results and propagates, wavelike, is not something, in itself, but only the reactions of the other somethings. Not?

Be well,

Richard

 

[Mike2]

If you start with nothing, and then make two somethings out of it, it should not surprise you if, when you add the two somethings together again, you get nothing. Does this mean that neither of the two somethings exists on its own? Of course not. This is the value of separation. A positron and an electron can be perfectly good somethings, until they happen together. Then they return to nothing again. The energy, or action potential, which results and propagates, wavelike, is not something, in itself, but only the reactions of the other somethings. Not?

Yes, I've often thought about this. I think it is expressed as a conservation of information law in the universe, though I don't have any proof of this. What I mean is that whatever structure exists is describable by some mathematical means. Its construction stands opposed to nothingness, obscurity, and chaos. There is information associated with its being, information necessary to describe it. However, there is also dissipative effects going on in the universe. For example, it might be that the expansion of the universe itself is a dissipative effect that increases the entropy in the universe. With expansion, more possible states exist for things to dissipate into. So there are dissipative effects that increase entropy which causes information loss, and there are constructive events which decrease entropy which increases information. It may be necessary for new, more complex structures to arise as the universe expands.

 

[Mike2]

You understand the contradiction, don't you? You assume a continuous spacetime in order to calculate the quanta of spacetime. So which is it, right?

String/M - theory does not explain where the background spacetime comes from to begin with, nor does it explain how the string/particles arise from the background. So of course their having problems with how spacetime is defined, which Calabi-Yau manifold is correct. And of course their having trouble deriving the mass of the particle. These problem seem inherent in how they approach the problem- that strings vibrate in the background, without defining the background or how mass emerges from it.

This inherent problematic approach may also affect Causal Dynamical Triangulation. For CDT also does not define where the background came from to begin with, nor does it say how mass arises from that background. So they too will probably not determine the correct ground state nor the masses of the particles.

 

[zelcon]

The M-theory does not state that it is the "T.O.E." or Unified Theory. Although it may be used to determine various possibilities and theories, but it is NOT a Unified Theory. There are countless properties of nature it cannot explain.
For more info on this subject, I recommend http://en.wikipedia.org/wiki/M-theory

 

[Mike2]

The M-theory does not state that it is the "T.O.E." or Unified Theory. Although it may be used to determine various possibilities and theories, but it is NOT a Unified Theory. There are countless properties of nature it cannot explain.
For more info on this subject, I recommend http://en.wikipedia.org/wiki/M-theory

The first sentence of your reference reads: M-theory is a solution proposed for the unknown theory of everything which...

Anyway, string theory isn't even able to calculate the thing it was originally investigated for, the masses of the particles. I wonder if this is not something problematic in the approach. Without first explaining how strings emerges from the underlying bulk, it may be that we are given a problem without initial conditions to calculate a unique solution. And this allows many different solutions from which we have no method of choosing the correct one. So we have the problem of the "Landscape".

And similarly, we cannot describe how strings or branes emerge from the background spacetime until we know what the background spacetime geometry is. So in order to get the masses, we need to know the background geometry which we cannot solve for until we have the initial conditions for that.

It seems at this point we may have no other option than to try to start from the very beginning of spacetime itself in order to make any progress at all.

Or is it the case that we are trying to find the initial conditions from the final solution, given the mass of particles can we find out how mass came into being in the first place. Is there an analogous situation from differential equations where we can derive the t=0 conditions from the t=something conditions? It seems problematic though to try to derive the given conditions from the given conditions. There is no way of knowing that your diff eq is correct to begin with, right?

 

[selfAdjoint]

The M-theory does not state that it is the "T.O.E." or Unified Theory. Although it may be used to determine various possibilities and theories, but it is NOT a Unified Theory. There are countless properties of nature it cannot explain.
For more info on this subject, I recommend http://en.wikipedia.org/wiki/M-theory

Whether or not M-theory will ever become a Theory of Everything, a theory that really did what the M-theorists would like to do - unify all four of the basic forces - would deserve the name. What are the "countless properties of nature it cannot explain"? emergent ones? They are still causally underpinned by particle physics. See self-organized criticality.

 

[Mike2]

Whether or not M-theory will ever become a Theory of Everything, a theory that really did what the M-theorists would like to do - unify all four of the basic forces - would deserve the name. What are the "countless properties of nature it cannot explain"? emergent ones? They are still causally underpinned by particle physics. See self-organized criticality.

Would String/M-theory explain where spacetime came from to begin with? Would it explain how particles emerged from the background to begin with?

 

[selfAdjoint]

Would String/M-theory explain where spacetime came from to begin with? Would it explain how particles emerged from the background to begin with?

Maybe it would. Consider the Ekpyric hypothesis as an example showing it could. And I believe present day physics has something to say about how the particles emerged.

 

[nightcleaner]

Hi Mike2

You ask "Would String/M-theory explain where spacetime came from to begin with?" This is not an uncommon question. It gets asked a lot in one form or another. To begin, let me make the assumption that String/M-theory certainly would answer the question if it could. Could String/M-Theory answer the question? I believe I know the answer to that, even though I am not able to function as a String/M-theorist. No.

Let me rephrase the question just a little, to generalize it to a more fundamental question. Where did spacetime come from to begin with? You see I have removed the part about String/M-Theory. I don't mean to avoid the intent of your quetion, as I hope to show in a moment.

Where did spacetime come from to begin with? I am sure you don't mean, "Who thought of the idea of spacetime?" I think you are asking about the physical origins of the physical observables.

Then consider the set that contains all of space and all of time and all of the relationships between space and time. This set contains the first time and all of the space present at the first time, as well as the last time and all of the space present at the last time, and all of the times and all of the spaces between the first time and the last time. Is there any space or any time or any spacetime that is not contained in the set of all spacetime? I think you will agree that there is not and in fact cannot be. Now let us return to the form of your question. You ask where spacetime came from to begin with. Where? Surely the place must be contained in the set of all spacetimes. And when, as you say, to begin with? Surely that time must also be contained in the set of all spacetime.

So the question, it seems to me, has no meaning as it is stated. You are asking, what part of spacetime is not part of spacetime!

Surely String/M-theory cannot answer a question that has no meaning. So the answer to your original question as originally stated can only be, No.

I don't want to seem harsh. You have shown great merit in attempting to think about these difficult things. But if you really want an answer, you have to go deeper. You have to think about what spacetime is. You have to transform your question, and your vision. You have to learn to think as a creature who inhabits more than our common three dimensions of space and one of time.

And there is so much more.

I wish you well. Have fun thinking.

Richard

 

[nightcleaner]

Maybe it would. Consider the Ekpyric hypothesis as an example showing it could. And I believe present day physics has something to say about how the particles emerged.

Hi selfAdjoint

I don't find anything on Google about Ekpyric hypothesis. It asks if I mean Ekpyrotic hypothesis, which seems to have something to do with theology. I don't have much interest in studying things that cannot be known so I did not go there.

Ekpyric. Out of the fire, as my memory of Greek serves me? Or maybe, just out of fire. That sounds right, since I find in the literature (Weinberg, The First Three Minutes, for example) that particles are thought to have condensed out of the cooling, expanding energy ('fire') sometime after the big bang.

Could you be more specific? I miss chatting with you here.

Richard

 

[Sempiternity]

nightcleaner, are you just saying that the question is meaningless simply because outside of the "set of all spacetime," space and time isn't defined? Which would be like asking what happened before the beginning? It's a meaningless question because if time was created at the beginning, there conceivably can't be a "before the beginning" if there's no conception or notion of time 'before' it was created.

(Spacetime, in The Elegant Universe, is defined as "A unsion of space and time originally emerging from special relativity. Can be viewed as the 'fabric' out of which the universe is fashioned; it constitutes the dynamical arena within which the events of the universe take place.")

Aside from this matter, M-Theory does explain where spacetime "came from," or it's origins. M-Theory makes usage of cosmic membranes that forms a multiverse, or a collection of many universes.

Michio Kaku explains in Parallel Worlds that the universal law that everything abides by is the quantum principle. He says that even when there is nothing at all, the quantum principle remains, and according to the quantum principle, even nothing is unstable. Before there was anything, there was nothing. This 'nothingness' bubbled with uncertainty due to the quantum laws and these bubbles spontaneously and arbitrarily expanded into a great multitude of baby universes. Michio Kaku conjectures that from this sea of bubble universes, our universe was formed, but of which is only one out of the myriad of universes formed in the beginning from the quantum laws.

 

[nightcleaner]

Hi Sempiternity

Well, yes, that is what I am saying, but beyond that, I believe what is required for better understanding of the origins of measurable phenomena, is a view which transcends our customary view of three dimensions of space and one of time. "Spacetime" is a concept which was advanced by Einstein and Minkowski to indicate the equality of space and time, in which questions about what came before the beginning or what lies outside the boundaries of our universe become meaningless. Better questions are required to explore the idea of what, if anything, lies outside the definition of spacetime.

I would like to try to encourage people who ask this kind of question to evolve beyond the 3 space 1 time mindset. I am sure you will agree that the branes and the bulk in which they are said to reside are not adequately described by three dimensions of space and one of time. Quantum theory requires us to study imaginary numbers, the complex plane, non-commutative algebras, higher dimensional geometries, and other mathematics which go beyond our ordinary visualizations of reality.

thanks,

Richard

 

[Sempiternity]

Thinking "outside of the box" is certainly something that must be done when dealing with such unusual ideas and concepts. It's a mind-bending journey attempting to grasp the conceptuality of multiple dimensions and fundamental origins, which makes your encouragement very well-founded :)

 

[Mike2]

Of course I meant "How did spacetime come into existence to begin with" and not where or when. The only answer is that it grew from a singularity. How it grew, by classical or quantum means I don't know.

Branes colliding to form our present spacetime only beg the question as to where the branes come from and how the spacetime in which the branes move came into existence.

I can't accept that spacetime arose from nothing through quantum effects. For quantum effects only effect things that exist, or at least can be calculated as if they exist. It seems quantum mechanics can only be done by using a background of space and time. Thus it assumes the existence of spacetime and so cannot be used to explain how spacetime emerged to begin with.

 

[Sempiternity]

On page 94 of Parallel Worlds, Michio Kaku further explains the concept of something from nothing:

The matter content of the universe, including all the stars, planets, and galaxies, is huge and positive. However, the energy stored within gravity may be negative. If you add the positive energy due to matter to the negative energy due to gravity, the sum may be close to zero! In some sense, such universes are free. They can spring out of the vacuum almost effortlessly...

This idea of creating a universe from nothing was first introduced by physicist Edward Tryon of Hunter College of the City University of New York, in a paper published in Nature magazine in 1973. He speculated that the universe is something "which happens from time to time" due to a quantum fluctuation in the vacuum.

 

[Spin_Network]

Of course I meant "How did spacetime come into existence to begin with" and not where or when. The only answer is that it grew from a singularity. How it grew, by classical or quantum means I don't know.

Branes colliding to form our present spacetime only beg the question as to where the branes come from and how the spacetime in which the branes move came into existence.

I can't accept that spacetime arose from nothing through quantum effects. For quantum effects only effect things that exist, or at least can be calculated as if they exist. It seems quantum mechanics can only be done by using a background of space and time. Thus it assumes the existence of spacetime and so cannot be used to explain how spacetime emerged to begin with.

Do you accept that at a singularity, everything exists?...I mean that everything you can think of is located at one point..the Singularity.

But then one has to consider the Vacuum?..Is this also within the Singularity? is there a Space Vacuum Of minimum content external to the Singularity?

The Singularity contains the Maximum Energy at the Minimum Location, is this similar(one the same), to the Minimum Energy contained at the Maximum Location that is Space Vacuum?..can the Bounce be reached from a Space Vacuum containing Singularity Location, and also from a Singularity, containing a Vacuum Point?

 

[Mike2]

Do you accept that at a singularity, everything exists?...I mean that everything you can think of is located at one point..the Singularity.

But then one has to consider the Vacuum?..Is this also within the Singularity? is there a Space Vacuum Of minimum content external to the Singularity?

The Singularity contains the Maximum Energy at the Minimum Location, is this similar(one the same), to the Minimum Energy contained at the Maximum Location that is Space Vacuum?..can the Bounce be reached from a Space Vacuum containing Singularity Location, and also from a Singularity, containing a Vacuum Point?

As I said in another post recently, a single point, which is what a "singularity" is cannot be described; it does not exist. there are no features that a single point has all by itself. Certain fields can have different values at different points. But if all that exists is a single point, singularity, then there is nothing else with which to compare it to, so it has no description. So it cannot exist... does not exist in the sense of describing it with respect to other points that do not yet exist.

Now that I think about it, does this argue for a continuous growth of spacetime from a singularity, or a quantum leap? At what point in its growth from nothing does it then exist?

 

[Sempiternity]

at a singularity, everything exists

Perhaps not everything, but at least everything known in our universe. If parallel universes do exist, then a singularity origin wouldn't have contained everything that exists, just everything in the known universe.

 

[Spin_Network]

Now that I think about it, does this argue for a continuous growth of spacetime from a singularity, or a quantum leap? At what point in its growth from nothing does it then exist?

Mike2, in my post I have try to convey a scenario whereby there are different singularities ,where one contains the other?..then if one emerges from a specific location, say at a point ofMaximum Energy at the Minimum Location ..then this location is/can..be contained within another Singularity!..the Background of which can evolve into a separate Singularity.

Let me specifically state again:One singularity that has a Maximum Energy at the Minimum Location is quite distinct and separate from another singularity that is Minimum Energy contained at the Maximum Location these two concepts are quite individual, whilst they can evolve from one to the other, the specific choice of one does mean important Leaps and Bounds for understanding.

Another poster 'Sempiternity' has convieniently highlighted this problem.

Einstein has I believe tackled these very notions above, but in a different context, let me relay this Einstein Quote How are we to proceed from this point in order to obtain a complete theory of Atomically constructed matter? In such a theory, singularities must certainly be excluded, since without such exclusion the differential equations do not completely determine the total field.

Now later Einstein gives a complete example of Quantum Wave "jumping", with respect of motion form one frame of reference to another. I believe it was with Dr Rosen?

 

[Mike2]

Let me specifically state again:One singularity that has a Maximum Energy at the Minimum Location is quite distinct and separate from another singularity that is Minimum Energy contained at the Maximum Location these two concepts are quite individual, whilst they can evolve from one to the other, the specific choice of one does mean important Leaps and Bounds for understanding.

Then what do you mean by singularity. My understanding is that a singularity is where you have infinite value only at one particular point. So if the whole universe consisted of only one particular point, then there is no comparing the value of a field with another point which does not exist yet.

I wonder how you would mark the differences between manifolds of slightly different differential sizes. It seems to me that if you don't have things like particles or strings yet, then there would be some sort of invariance with size, no means of distinguishing the quality or value of empty but growing universes. What's this called, conformal invariance? You'd have to know which point was the starting point and which points in the differential region were not the singualar point. But I think that the idea of a manifold growing from a singularity is that after it grows, you can no longer tell which point is the center. It seems then that you have some other invariant properties such that each point is just as likely to be the center as any other point. The laws of physics are the same at every point in space; there is then no preferential frame of reference for any measurable thing. And if that is so, then how do you even measure the size of the universe as it grows? Maybe that is why it may seem that space is broken into portions of the plank volumes. Below such scales there is no distinctions that can be made, no "measureable" observables.

 

[nightcleaner]

Perhaps it would be helpfull to refine some definitions. For example, the idea of a point. There seems to me to be nothing measurable about a point except its position in some extended matrix of points. We need to have a mathematical treatment to approach the idea of a point. Does mathematics describe reality? Yes, but not to the perfection of a point. No matter how subtly we build our mathematical systems, there is always a region of discontinuity between the mathematical description and the actual behavior of the observable. This seems to me to approach the status of a universal law.

For example, we may take a simple surface, perhaps one side of an envelope containing some object so that the paper is not flat. Now we may try to measure the surface area of some curved region of the surface. Perhaps we draw tiny triangles, made of short, straight lines of uniform length and known area, all over the surface. Then we may get an idea of the surface area by counting up the triangles and multiplying by the surface area of one triangle.

However small we make the triangles, there will alway be a region of discontinuity where the point of intersection of the triangle is not actually on the surface of the paper. So, the surface area we calculate using the tiny triangle method is not precisely the surface area we are trying to measure, but merely can be made close enough for our purposes by making the triangles smaller.

This can be reduced to the absurdity of trying to measure the surface area of the paper by counting up the number of mathematical points it contains. Clearly we get an infinity if we try to do so. By means of calculation and measurement, we can only hope to get a useful approximation of surface area. The same is true for all other calculations and measurements we undertake.

Mathematics is beautiful and perfect, but it is not reality.

A point is a mathematical concept, not a measurable reality.

As I recall, the idea of the big bang came from the observation that the universe we can see is expanding. It seems logical that if you could follow the paths of all the particles in the universe back in time, you would find that they had a common origin, a single point, at which space and time all the universe we know occupied a singularity. It isn't practical to actually follow all the particles back in time, but we can do calculations to show what might result.

There was some argument at first about whether the particles would actually come to a singularity. Maybe they just came into some close region of points, not actually a single point. But IIRC this argument was resolved in favor of the singularity. Gravitational forces would become immense, and no surface irregularities could endure. The universe, run backwards, would have to collapse into a perfect sphere, which would then have to collapse into a single point.

Now a single point has no possibility for differentiation. It can by definition only have a single quantum. This is what led Stephen Hawking to conclude that no information could possibly pass through. Of course, we all know that Dr. Hawking has reversed his opinion on this point. Perhaps he has come to believe that the universe is too imperfect to ever be resolved into a single perfect mathematical point. Saved by imperfection! This sounds like chaos theory.

I have to surrender this telephone line. But this conversation is interesting and I hope to resume it later.

Thanks,

Richard

 

[Mike2]

As I recall, the idea of the big bang came from the observation that the universe we can see is expanding. It seems logical that if you could follow the paths of all the particles in the universe back in time, you would find that they had a common origin, a single point, at which space and time all the universe we know occupied a singularity. It isn't practical to actually follow all the particles back in time, but we can do calculations to show what might result.

There was some argument at first about whether the particles would actually come to a singularity. Maybe they just came into some close region of points, not actually a single point. But IIRC this argument was resolved in favor of the singularity. Gravitational forces would become immense, and no surface irregularities could endure. The universe, run backwards, would have to collapse into a perfect sphere, which would then have to collapse into a single point.

Now a single point has no possibility for differentiation. It can by definition only have a single quantum. This is what led Stephen Hawking to conclude that no information could possibly pass through. Of course, we all know that Dr. Hawking has reversed his opinion on this point. Perhaps he has come to believe that the universe is too imperfect to ever be resolved into a single perfect mathematical point. Saved by imperfection! This sounds like chaos theory.

If the universe was ever smaller than the smallest particles, then it is clear that particles emerged out of the spacetime that existed before that.

My point is that before particles emerged, there was no way to gauge the size of the universe or how long it existed. Nothing existed with which to compare how long it was at that size or what size it was at that time. Somebody might suggest that you can gauge the curvature of space with its size, but that would be with respect to an arbitrary coordinate system. It becomes scale-invariant, gauge-invariant, where metrics of time and space have no meaning. This is probably the state of maximum symmetry.

Then for some reason this symmetry was broken. This probably gave rise to particles, perhaps not yet massive. And from then on time and space became measurable. But before particles, there existed no preferred metric with which to even measure time and space. So it was not even possible to talk about energy contained in the universe before then. The total energy of the universe, then is probably related to the process of this maximum symmetry breaking process. Perhaps this is calculable in principle, irrespective of what we observe. So again it looks as though we cannot know the true nature of spacetime until we know how particles emerged from it.

 

[Canute]

Hi folks

This discussion is amazing. IMHO it's more philosophically interesting and dispassionately intelligent than any of the discussions of reality that I've seen in the Philosophy threads, and I've always assumed it would be the other way around. I shall come here more often.

Nightcleaner - I'd like to comment on your last post just to see if I'm understanding you right, and perhaps to widen the discussion a little.

Perhaps it would be helpfull to refine some definitions. For example, the idea of a point. There seems to me to be nothing measurable about a point except its position in some extended matrix of points. We need to have a mathematical treatment to approach the idea of a point. Does mathematics describe reality? Yes, but not to the perfection of a point. No matter how subtly we build our mathematical systems, there is always a region of discontinuity between the mathematical description and the actual behavior of the observable. This seems to me to approach the status of a universal law.

I also feel that the discontinuity between reality and the mathematical description of reality is shown by this argument. Any argument for reifying fluxions or infinitessimals ends up as a reductio ad absurdam demonstration that the idea contradicts reason. Physicist Peter Lynds has reached this conclusion, and has recently published a couple of papers arguing that the idea of points in time or 'instants' is incoherent.

The discontinuity between the mathematical concept of reality and what is actually the case is also evident from the paradoxicality of motion when it is modeled mathematically but not when apparently real things are apparently moving. It can also be seen by the difference of opinion over whether the number line is a continuum or a series of points, and the same difference of opinion arises over whether spacetime is a continuum or a series of points.

When we think about the physics of the universe perhaps we carry over a mathematical concept that is not applicable to the actual fabric of reality, the notion that it must be one thing or the other. For example, we assume that spacetime is either a continuum or a series of points and that tertium non datur applies, But contradictions arise which suggest that it is neither, or both. In similar fashion we have the wave-particle duality in QM and the 'hypothesis of duality' in M-theory. The same paradox arises in discussion of whether a true theory of the universe should be background dependent or not. According to reason it cannot be either exclusively, as Mike2 points out. It seems rather like a metaphysical question, and I would argue that it is one. (Which is why I was suprised to come across this discussion here).

It is worth saying then, in the light of all these paradoxes, contradictions and antimonies, that in the 'nondual' or 'Middle Way' cosmological model (Buddhism, Taoism, Sufism, Christian mysticism, Advaita Vedanta etc - aka the 'mystical' view) spacetime is not fundamental, and what is fundamental cannot be properly characterised as being either a continuum or a series of points, as either a background or not-a-background, as spatially extended nor not-extended, as temporal or a-temporal, and so on. It is 'something' that is 'nondual' and which transcends all these distinctions. It is the Tao, Unicity, Allah and so on.

Don't panic, I'm not going to make an argument for this view here, it would get the thread closed down. But you have to admit that this is some coincidence. Perhaps it suggests that phsyicists and mystics need to talk to each other more, now that physicists have finally proved for themselves that naive realism is nonsense.

It is as yet still possible that it is a mistake to apply the tertium non datur rule to reality itself, and if so then in this sense one has to transcend reason in some way to resolve these antimonies and make sense of reality. (One benefit of assuming this to be the case is that it would immediately explain the existence of metaphysics, for if it were true then metaphysical questions would inevitably be undecidable, since both their answers would be false).

Suspending the usual laws of logic is, after all, what we do in quantum theory, and if spacetime is in some strange way both extended and unextended then nonlocality is immediately explicable rather than incomprehensible. The universe would simply exist in a superposition of states.

Mathematics is beautiful and perfect, but it is not reality.

Mostly I agree, but have you come across the mathematics of George Spencer Brown? He presents his 'calculus of indications' (Laws of Form, 1967) as a model of how forms arise from the void, or in other words a model of cosmogenesis. His calculus is 'nondual' in structure, thus quite unlike most mathematical schemes, and is thus able to model the 'mystical', 'Middle Way' or 'nondual' model of reality.

I would say his mathematics is as close to a conceptual model of the cosmos as can be, and it may be the one exception to your statement. (He asserts he is a 'Buddha' by the way, and was a good friend of Wu Wu Wei, the Irish Taoist philosopher and mystic, now dead. He was one of the Russell, Whitehead crowd, and Russell praised his book 'Laws of Form'. However it sank without much of a trace. Too mathematical for mystics and too mystical for mathematicians. He still has a small but loyal fan club. I recommend him whenever I can).

As I recall, the idea of the big bang came from the observation that the universe we can see is expanding. It seems logical that if you could follow the paths of all the particles in the universe back in time, you would find that they had a common origin, a single point, at which space and time all the universe we know occupied a singularity. It isn't practical to actually follow all the particles back in time, but we can do calculations to show what might result.

Yes. But there is something odd about all this. It is not right think of the BB as happening at a point within spacetime, so I'm told, since it happened at every point in spacetime at once. In this case, how can we retrace a particle back to the beginning, for all of them were everywhere at once in the beginning, and all points were the same point, which itself was not at any particular place or time. The scientific idea of the BB causes me what I think they call cognitive dissonance.

It seems more plausible to me to imagine that time is a mere appearance, and that at a deep level of the analysis of reality the BB is happening right now, and always will be. More scientifically, this could be stated in terms of frames of reference and the many different 'slices of spacetime' that different conscious observers can consider as their particular 'now'. Perhaps there is a fundamental frame of reference, an ultimate observer-actualised 'now', in which nothing ever really happens, as Buddist masters and their like argue.

Now a single point has no possibility for differentiation. It can by definition only have a single quantum. This is what led Stephen Hawking to conclude that no information could possibly pass through.

Yes. Leibnitz concluded that something undifferentiated could not exist in spacetime, and it seems to me he was correct. Likewise something beyond spacetime cannot be extended in time or space, so cannot exist in the usual sense. But it could be something like a curled-up dimension in string theory, and in this sense it could exist. One would have to say that it exists, but that in a sense it does not exist, since it does not exist in our normal sense of the word 'exist' but exists unextended in any of the four dimensions of spacetime. Perhaps one could say it is. In this view spacetime would be a mere appearance or epiphenomenon emerging from a deeper underling reality or dimension. Spencer Brown suggests that this happens by a process involving the making of distinctions or 'indications' in an underlying dimension or void, consistent with Lao-Tsu, Nargaruna and the rest.

Of course, we all know that Dr. Hawking has reversed his opinion on this point. Perhaps he has come to believe that the universe is too imperfect to ever be resolved into a single perfect mathematical point. Saved by imperfection! This sounds like chaos theory.

He doesn't really say this does he? It suggests desperation to me. I'm not sure I understand why Hawking is considered such an important thinker, but then I can't follow his mathematics so can't really comment. For sure he must be a better mathematician than he is a metaphysician.

I have to surrender this telephone line. But this conversation is interesting and I hope to resume it later.

I very much hope you can.

Cheers
Canute

 

[nightcleaner]

Hi Canute

Thanks for the thoughtful post.

Philosophy, like mathematics, seems to me to be free to think of space and time as infinitely divisible. Physics seems to find otherwise. Why is this?

Physics is tied to observables. We can and do speculate about all sorts of unmeasurables, but that isn't encouraged or respected, even when it is lots of fun. Instead, the ultimate test in physics is one of nuts and bolts. That may be why physics lags behind mathematics, and has often found mathematical formalisms already in place that describe newly discovered physical relationships.

So mathematics has proven itself a good guide to exploring unknown physics. Philosophy and mysticism, less so. But that does not rule out the possibility, so it seems to me, that philosophy and mysticism will ultimately play a role in our physical understanding of the universe.

Mysticism is not a pretty word in physical circles. Mystical statements, so it seems to me, reduce to the simple affirmation, "I saw it." That is fine and it is very satisfying to be able to see things for yourself, but it isn't physics. What we need in physics is tangible objects that behave consistently when placed in controlled situations. Mysticism and philosophy rarely provide anything like that.

That is not to say that mysticism and philosopy have nothing to offer. It is only that we cannot appeal to them as authorities. I personally have found much of value in the Tao Te Ching, and in other "religious" studies. And it is not uncommon, especially in the popular science genre, to give a knowing nod and wink to the role inspiration plays in the scientific process.

I am glad that Peter Lynd has found in favor of temporal quanta, but it is not a new idea. Discrete quanta of space have been a nuts and bolts fact since black body radiation and the ultraviolet catastrophe were investigated physically more than one hundred years ago. Spatial infinitessimals lead directly to infinite energies, which are not observed.

Instead, we observe that spatial and temporal measurements have a microscopic limit. This limit is calcuable and gives us the Planck length at about 10^-33 cm, or, if you are new to the formalism of very large numbers, one centimeter (half an inch) divided into 1,000,000,000,000,000,000,000,000,000,000,000 pieces. That is pretty small.

In fact the Heisenburg Uncertainty Principle begins to take effect at much larger scales, and the effective limit to our ability to directly measure things leaves us gasping at anything smaller than a proton, about 10^-9 cm, altho as I recall the Fermi limit on observation of particles goes further down to about 10^-12 cm.

Here on the Strings, Branes, and Loop Quantum Gravity board, we are trying to follow the progress of the really deep divers, who are currently discussing the structure of spacetime. The string theorists have for the past thirty years or so given us a start on a potentially physical approach to this topic, but there is dissatisfaction in the ranks, where testable results are demanded. It appears that string theory has given us no testable results, nor even any falsifiable predictions. Hence a certain consternation in physical circles.

Branes are a part of M-theory, an outgrowth of string theory. In my view, string theory takes the one dimensional case, and brane theory expands that to higher dimensionalities. Loop Quantum Gravity and Causal Dynamic Triangulation have had some success with other approaches, and Lee Smolin (LQG) has made what may be falsifiable predictions, so that is some progress. Essentially all these approaches are trying to fit geometry to what is known of spacetime, and the goal is to find the formalism which will pull the great white rabbit of the universe as we know it out of the black hole hat.

I am still studying the mathematics, and my poor attempts at visualization have been dismissed by some of the heavyweights around these boards. I persist, hoping to see for myself why my thoughts about densely packed expanding Planck Spheres are useless. I am not there yet. Actually, CDT seems to me to be an expensive and difficult way to generate Planck spheres, but I am glad someone working at the Planck scale has managed to attract some attention.

The stakes in this contest are rather high. One imagines teleportation, faster than light travel, plentiful energies accessible anywhere. New worlds upon which humans can conduct their petty squabbles and live out their archtypal histrionic dramas. Who finds the answers to these questions will be as the first bacteria in a freshly opened can of stew.

My goal is more modest. I merely wish to catch a glimpse of reality as it may be without the clouds of obstrefucation. I want to remove the scales from off mine eyes, lift the mystic veil from the face I had before the mother was born, take a clean inspiration, get a glance, with Paul Erdos, of the pages of The Book.

I did spend a few weeks with the George Spencer Brown book. It seems to address the root of all our mathematics and philosophy, and perhaps of mysticism as well. If I recall correctly it starts with an empty void and presumes one must make a mark upon it, and then goes on from there to generate addition and ratiocination and so on. I think I followed the first few chapters, but did not go through all of the derivations of mathematics, except to verify that it all looked reasonable. I should like to look at it again some day.

Anyway I am always glad of intelligent conversation to ease our passage.

Thanks for being here, and for my part, welcome.

Richard

 

[nightcleaner]

If the universe was ever smaller than the smallest particles, then it is clear that particles emerged out of the spacetime that existed before that.

My point is that before particles emerged, there was no way to gauge the size of the universe or how long it existed. Nothing existed with which to compare how long it was at that size or what size it was at that time. Somebody might suggest that you can gauge the curvature of space with its size, but that would be with respect to an arbitrary coordinate system. It becomes scale-invariant, gauge-invariant, where metrics of time and space have no meaning. This is probably the state of maximum symmetry.

Then for some reason this symmetry was broken. This probably gave rise to particles, perhaps not yet massive. And from then on time and space became measurable. But before particles, there existed no preferred metric with which to even measure time and space. So it was not even possible to talk about energy contained in the universe before then. The total energy of the universe, then is probably related to the process of this maximum symmetry breaking process. Perhaps this is calculable in principle, irrespective of what we observe. So again it looks as though we cannot know the true nature of spacetime until we know how particles emerged from it.

Hi Mike2

As selfAdjoint said, modern physics does have much to say about how particles came out of the original fire. Symmetry breaking does have something to do with it, but as I recall it usually speaks in terms of forces rather than particles. I think the evidence is strong that particles as we know them in the standard model are not fundamental. There must be, it seems to me, some underlying geometry of spacetime which leads to our observations.

Perhaps CDT or LQG or another such will lead us up to the Fermi limit. I am glad to have this forum to discuss the progress, and to test my understanding against that of other posters. Marcus has the right idea, I think, in working to increase our exposure to ideas like CDT. I try to read the maths, but still struggle with basic terms. Lately I have been trying to catch on to the idea of indices and brackets.

We need the most articulate and definite language possible, and that seems to be the intersection of mathematics and physics. Perhaps you would like to begin a discussion here of what is known, as revealed by popular authors such as Guth, Greene, Weinberg and others. I would be willing to go back to those sources. Review is good. Or we can use our timespace to explore what is going on right now as recorded in arXivs. I have been thinking of trying to recover the condensed matter work as it may apply to our geometries, but havn't done anything serious in that direction yet. Maybe you would like to find out what is known about the emergence of particles.

I will go look through my copies of Weinberg et al, and try to give you some thoughts on where to start with emergent particles. I guess if I were doing an internet search, I would start looking at virtual particles.

I hope to return to this next week, sooner if possible. Of course, there is much todo going on in the next few days. The gods are bowling and we will probably be interested in what the thunder says. Exciting times.

Be well and thanks,

Richard

 

[Canute]

Philosophy, like mathematics, seems to me to be free to think of space and time as infinitely divisible. Physics seems to find otherwise. Why is this?

Wow, some question. This is how I see it. The only thing that can be infinitely divisible is a continuum, since something that is quantised is not infinitely divisible. But, as I mentioned earlier, Leibnitz argues that a continuum, a thing with no parts, cannot have physical or temporal extension. This seems correct. So assuming that the fabric of reality is a continuum gives rise to a contradiction. On the other hand the assumption that it is quantised also gives rise to contradictions, as Zeno and more recently Lynds have argued, and as the continual um-ing and ah-ing on this matter among physicists and philosophers suggests. So I wonder if you're right to say that there is any difference between philosophy, mathematics and physics in this respect. It seems to me that they're all in the same boat, faced with a metaphysical question that has only two unreasonable answers. Since for mathematics (excepting GSB), philosophy (of the academic kind) and physics there can be no other option than that spacetime is quantised or not-quantised there is no way around this problem.

However, if, as I suggested above, we make use of the idea of nonduality, complementarity, superposition and other bits and pieces from modern physics then we can create a model of the universe that is consistent with the scientific evidence, with Schrodinger and Eddington's mystical views, with Spencer Brown's view, and with the cosmology of the 'mystical' religions.

Before physics advanced past Newton this view or model of the universe was totally inconsistent with physics. But we now know that classical physics is totally inconsistent with reality. The new physics is far more consistent with reality and far more consistent with the 'nondual' or 'mystical' description of the universe. To me it seems unreasonable to call this convergence a coincidence.

To be clear - in this other view the universe has two aspects, by one of which it appears to be quantised, one by the other of which it appears to be a continuum. I noticed that Stephen Ward in the Encyclopedia Britannica writes "In psychology a difference in aspects is a difference in things." This is very true. However it is not necessarily true outside of psychology, and may be as untrue for spacetime as it is for wavicles. Lee Smolin mentions this problem in his book, or a closely related one, and suggests that the 'hypothesis of duality' may be the solution, the hypothesis that a difference in aspects is not a difference in things. He is clearly unaware that this is what mystics have been asserting for the last five millenia.

You say that philosophy and mysticism have been less good as guides to exploring unknown physics than has mathematics. This is undoubtedly true. However this does not seem to imply anything for which is the best way of understanding reality, or the best way of resolving issues like the nature of spacetime, which is a metaphysical issue as far as anybody yet knows. But mathematics is also a good guide to exploring metaphysics and mysticism, so I'd agree that mathematics (and for similar reasons music) is a good way of exploring reality. Of course, to a mystic the idea that there is any better guide to reality than direct experience would seem mistaken.

But that does not rule out the possibility, so it seems to me, that philosophy and mysticism will ultimately play a role in our physical understanding of the universe.

When I read your earlier posts I gained the impression that you were a Buddhist, Taoist or similar. But in fact you take the scientific view. Perhaps this is an indication of how close the two views are becoming as physics develops. My mistake. But I'm impressed that you can consider mysticism capable of making any contribution to our understanding of the universe at all. It's a bigger concession than even most philosophers would make. The very mention of it enrages many people.

"Mystical statements, so it seems to me, reduce to the simple affirmation, "I saw it."

This is a slight misunderstanding. Mystics do not rely much on their physical senses for knowledge. They cannot, for solipsim is unfalsifiable so such knowledge cannot be certain and so cannot be knowledge. (Mystics take an absolutist view of knowldge - either one knows something or one doesn't). But if by 'seeing' you mean experiencing then in a way you're right.

What we need in physics is tangible objects that behave consistently when placed in controlled situations. Mysticism and philosophy rarely provide anything like that.

Quite so. Mysticism is about transcending the subject/object divide, and is the view that at a deep level of analysis there is no such thing as tangible objects. Many physicists now hold the same view, with events taking the place of objects. For example - "From this new point of view, the universe consists of a large number of events." (Lee Smolin, Three Roads to QG - his emphasis). Again we see physics becoming increasingly consistent with the nondual description of reality.

That is not to say that mysticism and philosopy have nothing to offer. It is only that we cannot appeal to them as authorities. I personally have found much of value in the Tao Te Ching, and in other "religious" studies. And it is not uncommon, especially in the popular science genre, to give a knowing nod and wink to the role inspiration plays in the scientific process.

Yes, it is common for physicists, or at least for popularisers of physics, to confuse mysticism with inspiration. Paul Davies's 'The Mind of God' is a classic. He heads a section 'Mysticism' and then drones on about inspiration and other irrelevances, not mentioning mysticism at all. I have great respect for Davies as a physicist and writer, but if he wrote about science with an equivalent lack of rigour he'd never have been published. Apparently in science it is acceptable to decide on the plausibility of Buddhist cosmology before finding out anything about it, or even instead of doing so.

I was disappointed to see recently that Lee Smolin takes the same aproach. For five thousand years, at least since the Upanishads, mystics and meditators have been arguing, ubiquitously and often in the face of ridicule, that naive realism is false and that spacetime is a conceptual construct. Then Smolin writes this -

"When we imagine we are seeing into an infinite three-dimensional space, we are falling for a fallacy in which we substitute what we actually see for an intellectual construct. This is not only a mystical vision, it is wrong."

This is pathetic scholarship in my opinion, and now that the mystical literature is so widely available it is unnacceptable from a professional. Mystics argue that to imagine that we are seeing into an infinite three-dimensional space is irrational, and about as wrong as it's possible to be.

I am glad that Peter Lynd has found in favor of temporal quanta

Is that a slip of the pen? Lynd comes down strongly against the idea of temporal quanta, and therefore also of spatial quanta. (I think his papers are on the Cern site by the way).

What you say about quantisation seems incorrect to me. Some theories require or assume quantisation, and some require or assume a continuous field, geometry or whatever. The question of which view is correct has not yet been resolved as far as I know. My prediction is that it never will be.

Essentially all these approaches are trying to fit geometry to what is known of spacetime, and the goal is to find the formalism which will pull the great white rabbit of the universe as we know it out of the black hole hat.

Many would argue that no formalism will ever manage this trick. Even Hawking accepts that Godel showed us that reason has its limits, and that physics as a formal mathematical scheme, and by implication any other such formal scheme, has inevitable limits.

My goal is more modest. I merely wish to catch a glimpse of reality as it may be without the clouds of obstrefucation. I want to remove the scales from off mine eyes, lift the mystic veil from the face I had before the mother was born, take a clean inspiration, get a glance, with Paul Erdos, of the pages of The Book.

More modest? I suppose that was tongue in cheek. But I agree with your approach. Aristotle concluded that true knowledge is identical with its object, in which case self-knowledge is the only knowledge we can have. All this string-theory stuff is just conjecture, and always will be. I recommend meditation, the empirical approach.

I'm glad to hear you already know Spencer Brown. Very few people seem to have heard of him. I can't follow his mathematics in detail, being very much into meta-mathematics but hardly able to count my change. However, I have spoken to him and confirmed that my view of his work is correct as far as the meta-physical or ontological interpretation of it is concerned.

Thanks for the welcome. Btw since last posting I spotted your discussion elsewhere of your life in the wilderness. I'm very envious. England's too small a country for any wilderness to have survived, and we made the mistake of starting the industrial revolution. My apologies if there's too much philosophy and not enough physics in my responses, I'm used to coming at all this from a different angle.

Canute

 

[Spin_Network]

Hi Mike2

As selfAdjoint said, modern physics does have much to say about how particles came out of the original fire. Symmetry breaking does have something to do with it, but as I recall it usually speaks in terms of forces rather than particles. I think the evidence is strong that particles as we know them in the standard model are not fundamental. There must be, it seems to me, some underlying geometry of spacetime which leads to our observations.
[QUOTE/END]

Richard, this recent paper will be very benificial to your inquisiteve line of thinking, a real gem to explore.

http://arxiv.org/abs/math-ph/0507016

 

[Mike2]

http://arxiv.org/abs/math-ph/0507016

In which he writes:
"It is necessary also to elucidate whether the total number of
microworld scales is principally limited or not, i. e., whether this
penetration to the depth of the microworld by the high-energy physics
cannot/can be continued up to its infinitesimally small scales."

If particles are extended objects such as strings, then no it does not extend to the infinitely small. If particles are point singularities, then maybe.

This would also suggest that the universe is infinite, always larger scales. This would deny its development from something more basic because a larger scale would have always existed before that.

 

[nightcleaner]

Hi Canute

You said: "I also feel that the discontinuity between reality and the mathematical description of reality is shown by this argument. Any argument for reifying fluxions or infinitessimals ends up as a reductio ad absurdam demonstration that the idea contradicts reason. Physicist Peter Lynds has reached this conclusion, and has recently published a couple of papers arguing that the idea of points in time or 'instants' is incoherent."


Quote:
I am glad that Peter Lynd has found in favor of temporal quanta


Is that a slip of the pen? Lynd comes down strongly against the idea of temporal quanta, and therefore also of spatial quanta. (I think his papers are on the Cern site by the way).

Ok, I should have looked before throwing down ink. I took the idea that there are no infinitesimals to mean that limits have to be set so that we do not go on dividing down to zero. In other words, there has to be a smallest length measure, and it has to be of some size, hence not infinitesimal.

Anyway, I think we are both saying that reality eludes either approach...that of continuity, in which there is no limit to how small a space can be, and quanta, in which the smallest space and time are set to be some amount greater than zero. The first approach leads to infinite energies, and the second approach leads to the absurdity of a material aether and hence a preferred reference frame. Neither approach is entirely satisfactory, but each approach may be useful in some particulars.

Can we accept a reality in which internally consistant logical systems conflict? Evidently so. In fact, when applied to the visual field, we use the conflicts between the evidence of our left eye and the evidence of our right eye to give us a sense of depth. Can we do something similar with the continuous/discrete conflict?



Wilderness notes: I had a productive day today at the cabin. The mosquitoes (I hear that you call them gnats in England) are in a huff about the weather, which has been alternately too hot and too cold for their likeing. I only saw one today and I swatted it before it could bite me, so you see I am not much of a Budhist after all.

I went down into the swamp to dig up some mud to cool person the walls of my cabin. I found arrowroot growing there, an edible plant, and I had not seen it there before so that was nice. The mud in the swamp is a mix of clay and humus and fine roots, and it compresses into a ball, dries hard. It is fun to push it into the chinks between the logs, squishy and smooth.

The cabin was chinked with moss when I built it thirty years ago, and I have had to push more moss in from time to time, but overall the moss has been a very good chinking material. Only it gets thin and the wind blows through. Mud is good but you don't want to put it on too soon after building, because the mud hardens, then the logs settle and push the mud out again. But after thirty years I think my cabin is done settling. I hope to be snug this winter.

Living in a cabin in the woods is idyllic in many ways, but it has some drawbacks. It can be a lonely life. I rarely see anyone in the woods. But on the other hand, neighbors still stop their vehicals when they meet on the road, turning off the engine for a chat. Last week I saw my neighbor to the west this way, and he wanted to talk about string theory!

It isn't really wilderness you know, but there are plenty of trees, rocks, animals. Lakes and streams, swamps and hills. There are maybe not more than a handful of roads between my cabin and Hudson Bay, which is hundreds of miles to the north. Last night a black bear raided my kitchen again. I think he was surprised by the cornstarch, and he didn't have much use for the popcorn kernals either, and he retreated before finding the cooking oil. Bears love cooking oil. If it is old and rancid, so much better.

But the really productive part was that I dug in my boxes and found my copy of Mandlebrot on fractals. Didn't find Weinberg, but Guth was there and also Smolin. Smolin has a chapter titled something para "The universe is process, not things." I have the book in my truck and will try to get into it more tomorrow. CDT predicts that spacetime is fractal at small scales. Makes perfect sense, actually. Mandlebrot talks about how dimensionality changes with scale in his introduction. Also finished chinking the east wall on the outside.

Well tomorrow the townfolk are having their summer festival, known here as "Heritage Days." There will be a parade and booths downtown. The parade is a big event. They have to go around twice, so everyone gets a chance to watch it once and be in it once. (Stole that from Garrison Keilor, but it is too true to be interrupted by facts.)
I plan to make another day in the woods.

Thanks Canute. Come to Minnesota some day and I will show you what is good and what is bad about living rough.

Richard.

 

[nightcleaner]

Richard, this recent paper will be very benificial to your inquisiteve line of thinking, a real gem to explore.

http://arxiv.org/abs/math-ph/0507016

Thanks, Spin Network. I'll take a look. R.

 

[Canute]

Hi Canute

Ok, I should have looked before throwing down ink. I took the idea that there are no infinitesimals to mean that limits have to be set so that we do not go on dividing down to zero. In other words, there has to be a smallest length measure, and it has to be of some size, hence not infinitesimal.

Hmm. I hadn't thought of looking at it that way. But I think this is not what he's arguing. Rather, he's arguing that time is continuous. If it is then there are infinitessimal 'instants' of time, but only as conceptual constructs, useful for mathematical purposes but not real things.

Anyway, I think we are both saying that reality eludes either approach...

It seems so. I don't know why physicists don't just accept this antimony as a fact of reality and start from there.

Can we accept a reality in which internally consistant logical systems conflict? Evidently so.

Quite. We couldn't do QM without accepting this. On the other hand we do it very reluctantly. Metaphysics is caused by the non-acceptance of such conflicts, and look at the progress philosophers have made as a result.

Thanks Canute. Come to Minnesota some day and I will show you what is good and what is bad about living rough.

I have a friend who lives in a garden shed in the woods near me. No services at all and not even a mobile phone. Hard work in a way, but the most sensible lifestyle of anyone I know.

Do you know the Zen master and poet Ryokan. Japan's most revered poet. From your own writing I'd say you'd really enjoy him.

Cheers
Canute

 

[selfAdjoint]

Hmm. I hadn't thought of looking at it that way. But I think this is not what he's arguing. Rather, he's arguing that time is continuous. If it is then there are infinitessimal 'instants' of time, but only as conceptual constructs, useful for mathematical purposes but not real things.

Philosophers don't seem to be able to let go of this old idea of infinitesimals, which mathematicians abandoned two hundred years ago. Please do read up on basic measure theory. I have no problem in amgining a temporal continuum, or a spacetime on, for that matter. Then how you look at it is another problem; if you really need to look at an instant you can do a Dedekind cut.

Others, please don't post on nonstandard analysis and its definition of inifinitesimals; that contributes nothing to this intuitive issue.

 

[nightcleaner]

Hi Canute

I am reading Mandelbrot again, "The Fractal Geometry of Nature." He has a chapter, 5, "How Long Is the Coast of Britain," in which he discusses the idea of length. I have shamelessly repeated his discussion in other places on this board, having forgotten where I first found it. But one must work within one's own limits.

Mandelbrot explains that the measured length of a coastline depends upon the length of the stick used to measure it. This idea is easily accessible. A stick a kilometer long will cut across many bays and inlets, while a centimeter stick will have to trace the curve of every point and boulder. The same coastline, measured with a centimeter stick and a kilometer stick, will have wildly different "lengths."

In fact, it is easy to see that the measured length quickly goes to infinity as the stick gets small.

No one, in England anyway, is likely to doubt that the coast of Britain is a real object. It may please some nationalists that the coastline of their country is infinitely long, but it is a nuisance to geometers. Mandlebrot goes on to show that a similar problem affects measurements of area, volume, density, pressure, and temperature. Suddenly our notions of science are on shakey ground.

I said:
"Can we accept a reality in which internally consistant logical systems conflict? Evidently so."

You replied:
"Quite. We couldn't do QM without accepting this. On the other hand we do it very reluctantly. Metaphysics is caused by the non-acceptance of such conflicts, and look at the progress philosophers have made as a result. "

When I read the Tao Te Ching, a very old book, I have to wonder if philosophers have made any progress at all. And when I compare my swamp to the streets of any major city, I can lump the scientists and mathematicians in with the philosophers and still have cause to wonder. Of course, the manicured and pampered hostess of a garden party will feel perfectly justified in thinking her lifestyle superior to that of a druid living, literally, under a tree, but the druid can consistantly think that blue skin and witchetty grubs have the advantage. Somewhere in the middle, I wonder which way to go, or if it might be better to go have a nice nap.

Thank you for mentioning Ryokan. I remember that name, and I am sure I would remember the poetry, if I saw any of it. Somewhere in my boxes in my cabin there are books which would surely have his work. But it is a hot, humid day in the woods today, and my plans do not include digging in the attic for books.

Lets see if I can remember anything at all. Umm, well there is the one hand clapping Koan. And, am I a poet dreaming of being a butterfly, or a butterfly dreaming of being a poet? I can't seem to remember any haiku. Then there was something about some drunken poets on the deck of a boat which carries us away from the shores of this life. One one side, the boat was labelled "heaven", on the other side, it was labelled "hell". Was it Wu Wei and Bashan? Something like that.

Do you know the contemporary American poet, Gary Snyder? The real work: chop wood, carry water. He studied for a while in a monestary in Japan. He tells a story about an interview with his Zen master in which Gary suggested that the monks should run a hose from the well to the gardens, so as to make it easier to water. "Mr. Snyder," the monk said. "Who told you we want to make life easier?" Chop wood carry water, the real work.

Actually, I suspect that existence is contradiction. There is only one thing, and all our little being, all our definitions, all our words and diagrams and fine machines, are false representations. I don't have an exact quote, but a friend attributes to Einstein the idea that being, separate from the whole, is a delusion of consciousness.

Well the locals are gathering for their Heritage Days Parade and celebration. I rather admire the simple energy of the thing. Old men in straw hats carry lawn chairs to claim their strategic positions along the boulevard. Matrons with covered casseroles stream from kitchens to decks. Youngsters ride horses up and down the street, which has been blocked off to traffic so the floats can assemble. Atheletic girls jog past my window, shiney convertibles with the tops down line up, dogs bark.

I am sitting here at my friend's table, using her telephone line. She has already fled the commotion, gone to Duluth to look for paint and linens for her new house. She is moving away from here in a month or two, as soon as the gods of property transfer are legally satiated. I don't know yet what I will do after that for internet access. Maybe have to steal Wi-Fi from the parking lot outside of a local business traveler's motel, or take a job as a night auditor. There is no telephone, electricity, plumbing or emergency services at my cabin. Nor, to be true, do I want any.

I will find some way to continue. Or not.

Be well,

Richard.

 

[arivero]

When I read the Tao Te Ching, a very old book, I have to wonder if philosophers have made any progress at all.

I am not sure how do you read the TTC, so I can not tell you. Strings, and M-theory, are slightly our from the line of research of TTC, that favours the use of a duality between matter and nonmatter. Such duality is orthodoxy in mathematics (vectors and covectors for integral calculus) and quantum field theory (point particles separated by spatial plaquettes), and the simple fact of being able to formulate with precision such theories is already an huge advancement on the TTC line.

 

[nightcleaner]

Hi arivero

I read the TTC in translation by Gia Fu Feng and Jane English, with lovely full page pictures and caligraphy. But I don't know how to read the Chinese ideographs.

I am working on reading the mathematical formulations for quantum theory. It is a very beautiful and elaborate structure, obveously crafted with skill and pride of workmanship, but remains mysterious, to me, in operation. For example, there is indicial notation. Penrose informs me that the upper indices represent vectors, and the lower indices represent covectors, but I have less notion of what that means than I have of form and emptyness. I don't have the Tao or the Penrose book in front of me, so I can't go into more detail now, especially since fire engines and ambulances decorated in tinsel and flags are lining up on the street in front of this house. A golf cart overflowing with clowns just drove by. I am afraid I cannot bear any more of this happiness. I am of a mind to go look for a quiet corner in a dark cafe.

But I am thankful for this great fellowship here and will return as often and as soon as possible.

Oooops. They are starting to throw candy to the epsilons. I really have to go.

Richard.

 

[selfAdjoint]

For example, there is indicial notation. Penrose informs me that the upper indices represent vectors, and the lower indices represent covectors, but I have less notion of what that means than I have of form and emptyness.

You comfortable with the idea of a vector? Something you can add, subtract and multiply by a constant? You can set up a basis and write every vector as a sum of basis vectors times constants. The individual products, constant times a basis vector are the components of that vector in that basis. All square?

Now imagine a linear function that maps vectors into the constants (which are nearly always either the real numbers or else the complex numbers). Take the set of all such functions. You can add them, subtract them and multiply then by constant (c*f(v) = f(c*v) ). So they act like vectors! They are called covectors. If your vector space has basis vectors e^1, e^2, etc. then the functions e_1,e_2, defined by e_i(e^i) =1 and e_i(e^j) = 0 for i \ne j form a dual basis of the dual vector space containing the covectors. As I have indicated the covectors (linear functions from the vector space to the constants) have lower indexes and the ordinary vectors have upper indexes.

An important case of dual vectors is the derivatives. The partial derivative \partial / \partial x acts on a vector and produces a number: \partial v/ \partial x =c. And it is linear, so the derivatives form a dual vector space to the vectors.

 

[Canute]

Nightcleaner

Nothing to add but chat really. I also like the Jane English version of the TTC. There are a number of dire translations about, but this one gets the meaning and the music. Some translations seem to have been done by people who don't realize what Lao-Tsu was saying.

The wonderful thing about the Tao, taken as fundamental, is that it is neither a background nor not-a-background, a useful concept for science given the current stalemate on this issue.

Hope you mange to sort your connection.

Philosophers don't seem to be able to let go of this old idea of infinitesimals, which mathematicians abandoned two hundred years ago.

Could you expand a little? I fear I may be misunderstanding the current mathematical notion of infinitessimals. Are they considered real or conceptual these days?

You say you can imagine an extended temporal or spatial continuum. Perhaps so, but you must admit this doesn't show the idea actually makes sense. I would argue that it doesn't, but don't have a knock-down argument yet.

Regards
Canute

 

[rain.w]

The wonderful thing about the Tao, taken as fundamental, is that it is neither a background nor not-a-background, a useful concept for science given the current stalemate on this issue.

I have a strong feeling that the current pure mathematics/theoritical physics is
representing/constructing the thoughts of ancient philosophy such as Tao and YiJing,
and this seems be a "philosophy-science" duality also?

 

[Canute]

Hello Rain.w- welcome to the forum. I also hold this view.

 

[arivero]

OK I was refraining for it, but given the ambiance it seems I should sell here my own references:
http://arxiv.org/abs/physics/0309104 Democritus as Taoist (see also http://dftuz.unizar.es/~rivero/research/0309104fn.html )
http://arxiv.org/abs/math/9904021 On the section of a cone
http://arxiv.org/abs/physics/0006065 Rhythmos, Diathige, Trope

the last one is in Spanish, but you can get a smaller English version selecting v1 of the same article.

Mathematicians can understand duality in the sense of De Rham, expanding on the explanation of selfAdjoint. One needs a cycle and a cocycle in order to get an integral.