A Creation Principle?

1. Mar 7, 2004

Mike2

This may be a naive question, but...

I know that quantum mechanics prescribes various possible paths given an initial and final state. But is there a principle that is responsible for predicting the necessity of an initial state to begin with? We have QM accounting for all the possible paths of a particle. But what creates the particle itself? Does String theory predict the strings themselves, or does it only predict how they propogate? As I understand it, M-theory predict the initial state of the strings themselves from higher dimensional object, membranes, etc. Does M-theory predict the creation of particles/strings from the expansion of space-time itself?

Thanks.

Last edited: Mar 25, 2004
2. Mar 8, 2004

Mike2

I'm thinking something along the lines of

$${\textstyle{d \over {dt}}}\int_{V(t)} {\alpha ^p } \,\,\,\, = \,\,\,\,\,\int_{V(t)} {i_X d\alpha ^p } \,\, + \,\,\,\,\oint_{\partial V(t)} {i_X \alpha ^p }$$

from The Geometry of Physics, by Frankel, page 139,
where $${i_X \alpha ^p }$$ is the interior product of the vector X and the p-form $${\alpha ^p }$$.

I'm not sure what the p-form should be, perhaps the curvature. But this would basically say that the expansion (change) of the overall space-time manifold is responsible for the existence of submanifolds, $${\partial V(t)}$$. These submanifolds would then serve as the p-branes of particles in M-theory.

This, of course, doesn't say where the particles/submanifolds exist or are created. And this gives rise to the concept of considering every possibility where it could exist, Feynman's path integrals.

Perhaps this belongs in Theory development. Or perhaps it is the essence of M-theory, the creation of p-branes.

Comments welcome. Thank you.

3. Mar 8, 2004

ranyart

Slight problem here,Quote:This, of course, doesn't say where the particles/submanifolds exist or are created. And this gives rise to the concept of considering every possibility where it could exist, Feynman's path integrals.

There would have to be an infinite number of String Theorists to work out all the Particle/String paths from a given moment of 'NOW!!' (which is the End/Final state) back to the initial state for every possible history of every possible String that is in existence(final) 'Now', and therefore had some connection with a History that leads to the Initial 'THEN!' state.

The task at hand is far beyond the scope of simplistic String Theorists, for every explination of 'String histories', the NOW is so complex that every path history gets more complex rather than the expectant value for the understanding of TOE.

The mathematics used to explain the Universe at any given moment, and a previous moment that goes backwards to the initial moment, should be getting more Simplistic, and not more complex.

The major stumbling block of any theory is to explain 'Now' and compare it with the explination of 'Then'. As every String theorist knows 'Now' is too complex to even start contemplating, and yet they define every equation as having a history from this end 'state'?

When String theory emerged some bright spark declared 'this will be the theory of everything, we are close to a single theory that will explain the Universe as it is?'..oops! let that one out of the bag?..back to the Maths, where is the single Equation?..buried somewhere in M-Theory?..Brane-Extensions-P-D?..truth is there will be an ever increasing of complex explinations.

Surely this is ringing alarm bells? if they cannot define a 'Now', then how can they derive all paths from this moment?

No detector can be located at two distinct and seperate locations at the same instant 'now/then'?, a particle cannot be registered at the same location as any other identical particle with the same energy-Volume?.

What detector/devise?.. are String theorists using to located a single string?

4. Mar 9, 2004

Mike2

I don't think our effort is to trace every particle back to Creation. We are only interested in explaining various types of interactions and how particles came into being in the first place.

Wouldn't the fact that at the very beginning, where the higher dimensional p-branes would exist, be created in an environment where all possible paths are restricted to a very small region? We would not be integrating paths throughout all infinity, but we would be integrating the paths only over a small region, right?

5. Mar 9, 2004

ranyart

To an extent Yes.

But a recent paper by Ed Witten 'swerved' around a fundemental problem, by working from not the 'top-down','Bottom-up', but from the 'down-further-down'. The estimation for the Proton Decay was thus extended (some would say this was in anticipation of obvious questions that automatically follow the said paper).. eliminating (prepwork!)certain questions before they can arise.

Ed Witten... moving the Goal-Posts before the match begins?

6. Mar 9, 2004

Mike2

I think the only relevant question in this thread is whether the left-hand-side of the above equation can indeed be applied to the manifold that is the early universe. If so, then how does the boundary term apply.

Another question might be does this equation apply if the early universe does not expand continuously but expands in quantum leaps.

7. Mar 9, 2004

Mike2

Even if the early universe did expand by quantum leaps, don't these leaps become smaller and smaller as the universe grows, so that at some point it begins to look like a continuous expansion?

8. Mar 10, 2004

Mike2

In the above equation, if V(t) were a 2-D surface and $${\partial V(t)}$$ is a closed curve, then that surface can be re-shaped into the form of a cylendrical tube with closed curves at each end. The boundary is now two closed curves, one on each end. This can be applied many times until the closed boundary is constructed in the form of many tiny close loops distributed about the surface. I suppose that the surface can be rearanged so that the tiny loops are distributed differently and this may appear as the motion of these loops the surface.

In a similar sense, cannot also the closed boundary of the universe be distributed into many tiny closed boundaries that are distributed throughout the volume of the universe? Might these also be interpreted as particles? And can't they also move throughout the volume of the universe? Could the farthest reaches at the boundary of the universe in fact be the subatomic particles? I wonder if the appearent movement of these tiny closed boundaries now be submanifolds of one less dimension sweeping out one higher dimension of a world-volume so that they in turn create an even lesser dimensional boundaries, etc?

Some questions I have is whether one can apply the above equation to the overall manifold. The book integrates the volume form of the full dimensionality of the overall manifold only over a region of the overall manifold, not over the entire manifold itself. Is there any reason why V cannot be or approach the entire manifold itself? Does V have to be a subregion of M so that it can grow with time and still remain inside M? Or can the overall manifold itself, M, grow with time so that the above equation applies?

The book talks about time as though it were completely seperate from the dimensionality of the overall manifold, M. So I'm not sure if the time derivative equation above applies when the manifold itself includes time as one of its dimensions.

9. Mar 10, 2004

ranyart

Sorry Mike2, but this quote:And can't they also move throughout the volume of the universe? Could the farthest reaches at the boundary of the universe in fact be the subatomic particles?

would be an inference that the Universe is in Contraction Phase?, and with a little further inquiry it would mean that our Galaxy is the centre of 'this' contracting Universe.

10. Mar 11, 2004

Mike2

No, only that the boundary can be split up into smaller boundaries that can be distributed throughout. I just thought that quote was an interesting way of looking at it.

And you can all me "Mike". The 2 is a carry over from a different forum where the USERID "Mike" had already been taken.

11. Mar 11, 2004

ranyart

Mike, Understood!

It may be that I have misread your post a little, as I expected you to maybe present an argument for the Universe as a Large Atom? I f just the boundery is made from smaller 'bits'..then I would expect that our Universe (or Galaxy at least), would have to be at the centre of all lesser bounderies?

But as you explain this is not the case.

12. Mar 16, 2004

Mike2

So in this view, matter would be the distributed boundary created by time slices of the expanding universe from one time to the next. I wonder, would movement of these distributed tiny boundary particles relative to each other be different from the changes in the boundary due time slices of the overall expansion? Or is movement ON the boundary actually perpendicular to movement OF the boundary?

Thanks.

13. Mar 16, 2004

Mike2

What confuses me is that the distribution of the boundary seems arbitrary for any particular boundary so that a change of this distribution doesn't realy change the nature of the boundary. For everything adds up the same no matter how you distribute it. So it would seem as though variations in the distribution do not change the character of a boundary created by a particular time slice of the expansion. This would give us the freedom to parameterize movement of a distribution by some other parameter we might call by a different time dimension. But then again, does it make sense to have 2 different time dimensions? If not, then changes in the distribution of the boundary are coupled to changes in the boundary due to different time slices. I suppose that the expansion is directly related to how particles are distributed, right?

Feel free to speculate/theorize along with me. That is the nature of brain storming.

14. Mar 23, 2004

Mike2

So suppose it is true that particles are the boundary of the universe. If space is 3D, the boundary is a closed 2D surface, or a bunch of tiny 2D surfaces. But what does that have to do with strings? Well, I wonder, a torus is also a closed surface. And I've heard it suggested that strings are an approximation of still higher dimensional objects like a torus. So are there any theorems that might suggest what genus these closed surface can have? More generally, when thinking of Stokes theorem relating a open volume to a closed surface that is its boundary, is there any regard to the genus of those closed surfaces? We can think of higher dimesional stuff later.

15. Mar 24, 2004

Mike2

It seems that the Gauss-Bonnet theorem relates the integration of the curvature to the genus of the closed surface. It seems possible to distribute one closed integral into many close surface integrals by imagining a thin tube between each smaller surface, where these tubes become vanishingly small, etc. Then as long as the addition of each tiny closed surface integral added up to the original, then the theorem still applies. This means that the tiny closed surfaces could have any genus as long as the total of all tiny particle surfaces add up to the genus of the original.

This means you could divide one closed surface of genus 0 into a bunch of tiny closed surfaces with twice as many with genus 2 as those with genus 0.

16. Mar 24, 2004

Mike2

And of course, you could have any number of genus 1 surfaces in relation to the others since they contribute 0 to the curvature integral.

The question is why the curvature integral. Is this some sort of conservation of curvature law?

One question I have is if the 6 or more compactified dimensions are always tightly curled up, then they are not expanding, right. It would be the expanding dimensional submanifold that would have a boundary associated with time slices, right? The conpactified dimensions would not contribute to the boundary since they do not change with time, right? Is there any question but that the 3 dimensions are expanding and therefore have a boundary associated with a certain time dimension?

Don't you just love the way a ramble on?

17. Mar 25, 2004

Mike2

These small genus 0, 1, and 2 surfaces that act as the boundary of the expanding universe are also boundaries of the space inside them. And so are equivalent to a volume intergral inside by reversing Stoke's Theorem.

OK. Then in this scenario, it may be that a genus 1 surface, a torus, is the 1 dimensional higher generalization of a string at one instance. A genus 0 surface would be a generalized D-brane. And a genus 2 surface would higher dimensional generalization of 2 genus one surfaces connected by a generalized string between them. Such a genus 2 surface might be recognized as two quarks held together by a string and thus cannot propagate independently of one another, but must be connected.

Have I gone beyond the boundary of physics yet?

18. Mar 25, 2004

Mike2

Or perhaps the space inside a particle is some sort of complimentary space and cannot be used the same way as normal space since it is "beyond the boundary of normal space".

I wonder, if particles are made up of the boundary of the universe, could it be that the particles cannot move any faster than the universe expands? Is that the reason for the spead of light? If a particle did move faster than the expansion, it would not be part of the universe, right?

Comments welcome, of course.

19. Mar 31, 2004

Mike2

Does the universe have a boundary? Is it a physical thing, would you bump into it and go no further?

I've been told that you could travel in one direction through the entire universe and end up back where you started. Is this right?

20. Mar 31, 2004