Understanding the Overlap of Calabi-Yau Manifolds in String Theory

[RingoKid]

Do calabi yau's overlap ?

Please correct me if i am making assumptions based on my limited knowledge of string theory.

If at each Planck size point particle in 4d spacetime there exists a manifold of 6 extra dimensions for a string to vibrate across.

Do the calabi yau's overlap and connect to open up into larger dimensions beyond the vibrational constant of our 4d universe ?...or are they all separate and self contained.

another question I was wondering is what type of personality or person makes for a good string theorist as opposed to a loop gravitist or classical relativist ?

Are theoretical physicists all cut from the same cloth ?

thanx in advance

 

[selfAdjoint]

If I understand your first question, the answer is no. Imagine our observed world was just a one dimensional line, and the Calabi-Yau manifolds were little circles. We need to go down to one dimension to be able to get the circles into our visualizable three dimensions.

Each point of the line has a circle touching it. Now the vision is, each circle touches the line, but doesn't extend into the line, so we represent it as crossing the line at right angles. Turned this way, all the circles at each point can lie next to each other without intersecting, and this is the way the Calabi-Yau manifolds are presumed to lie in string theory.

You may ask, couldn't it be different? Yes it could, but that would mess up the whole Calabi-Yau scenario, which is basic to string theory. String theory is not a field theory (there is a string field theory, but it is only able to handle simple questions). In field theory there is a famous problem that the vacuum at one point interferes with the vacuum next door and messes up the math. Field theorists have to approximate around this problem; it's one of the reasons they are stuck in perturbative (very weak interaction) physics.

Your second question is interesting. I can't tell you about the leaders, but I believe there are two kinds of followers, I call "pioneers" and "settlers". They come behind the leaders ("explorers") and occupy the new territory. Pioneers, like fermions, vant to be alone; they are proud of the brand new idea that no one else has got. Settlers, like bosons, like to group. They see discovery as a collective effort and their joy is completing somebody else's idea, and doing cultural things like comparing citations. Since QG has been a not very popular field for a long time, it has previously attracted mostly pioneers. Ever hot string theory is full of settlers. This may change, as QG is just on the cusp of becoming hot.

 

[RingoKid]

Thanks self adjoint and please correct my further assumptions

In using your analogy, the circles don't touch each other just the line and in taking it up to 4d again they only impact on spacetime fabric in one dimension.

Otherwise are you Implying that there is a gap between each circle and if the shortest length possible is a Planck unit then the gap between manifolds would have to be shorter still ?

Or do they operate like a 0 and 1 switch thing where a manifold blips out and another one blips in so there is an overlap space but they don't touch as one never occupies the same space at the same time?

In regards to the other question. Can you stereotype a "leader" in theoretical physics by comparing the personalities of Einstein, Bohr, Pauli, Hawking or Witten ?

 

[DivineNathicana]

Einstein was definitely a "pioneer" type, as he completely overturned everyone's perception of reality. Bohr was a "settler", as he worked mainly on further developing pre-existing ideas and was largely influenced by others such as Planck and Heisenberg. Pauli was also a "settler" because he was inspired by Einstein and Sommerfeld, and just generally was more social I guess. Hawking is tricky - he used to be more of a "pioneer"... He worked alone, locking himself in his room with vodka bottles. But nowadays he's a lot more relaxed with that sort of thing and shares ideas and bets with the likes of Thorne. Witten is also tricky... He is a "pioneer" with his ideas, but sort of drawn to groups... Of course, you can argue on any of what I just said because in essence, anyone of the is a "pioneer" as they all introduced new ideas, and anyone of them is a "settler", as they all had to build off of something - even Einstein used pre-existing mathematics in his theories, and I believe that we now regard him as one of the people who have changed our views on the world most drastically.

 

[RingoKid]

Thanks DivineNathicana

Those people i mentioned were examples and I was more wondering what if anything as children or adults they along with other great physical thinkers have in common eg... child trauma , religious upbringing, mental illness, prodigious mathematical ability, anything defining that steered them towards physics and the breakthroughs they made or will make.

Is it possible to identify those traits that make a pioneer physicist that can then be nurtutred in developing youth or is it all genetics ?

 

[DivineNathicana]

Creativity, mathematics, curiosity, and often mental illnesses, I guess - as with any true genius. Of course, it's often through parents. But with Einstein, it was pure curiosity... It all started out when he wondered around the age of 16 what would happen if he could reach the speed of light - would he be able to see light stand still? So basically physicists come in all colors... You just have to love what you're doing and be prepared for a challenging life: it can take many many years to search for the right theory (special relativity took 10 years to formulate) and it WILL affect your life (Einstein gave up his first love for physics, and later his first wife as well). But obviously, the outcome is extremely rewarding. So good luck!

 

[Gecko]

i have a question about the calabi yau's too. from what was said earlier, calabi yau's do not touch each other. does this mean that you could find points in spacetime where there isn't a calabi yau? i was under the impression that there are calabi yau's at every point in space time but i guess this couldn't be possible lol.

 

[selfAdjoint]

i have a question about the calabi yau's too. from what was said earlier, calabi yau's do not touch each other. does this mean that you could find points in spacetime where there isn't a calabi yau? i was under the impression that there are calabi yau's at every point in space time but i guess this couldn't be possible lol.

There is a Calabi-Yau manifold at every point of our spacetime. The points of our spacetime do not touch each other, though they (seem to) form a continuum. Take any two points; do they touch? Of course not, there is a distance between them. If there weren't, they wouldn't be two points, but just one. Likewise, the Calabi-Yau manifods extend only in the six compacted dimensions. Those dimensions are all perpendicular to our spacetime. Therefore the C-Y manifolds have no thickness in our four dimensional spacetime, and so they don't slop out from the point where they are defined.

 

[Gecko]

that didnt answer the question. you said that there was a C-Y manifold at everypoint in space time which would mean that the only way for them not to overlap would be for them to not have any dimensions. what I am saying is if you where to zoom way in, there would be space between each of the manifolds. therefore, you could pick a point in space time on one of these spaces in between the C-y manifolds and say that there is a point in space time that doesn't have a C-Y manifold at it.

 

[DivineNathicana]

that didnt answer the question. you said that there was a C-Y manifold at everypoint in space time which would mean that the only way for them not to overlap would be for them to not have any dimensions. what I am saying is if you where to zoom way in, there would be space between each of the manifolds. therefore, you could pick a point in space time on one of these spaces in between the C-y manifolds and say that there is a point in space time that doesn't have a C-Y manifold at it.

Gecko, what selfAdjoint is trying to explain to you is that the Calabi Yau spaces have no thickness in our four dimensions (only in the six or seven curled up dimensions they contain), and can therefore be thought of as single points, which you yourself said would allow them to not overlap each other.

- Alisa

 

[Gecko]

oh, i see. i thought that they did have shape in our 4 dimensional universe which, as you could see, would lead to confusion lol. but then how could we tell if they where 6 dimensions of they have no shape in our 4 dimensional universe? wouldn't it be impossible to see one?

 

[selfAdjoint]

oh, i see. i thought that they did have shape in our 4 dimensional universe which, as you could see, would lead to confusion lol. but then how could we tell if they where 6 dimensions of they have no shape in our 4 dimensional universe? wouldn't it be impossible to see one?

They are entirely theoretical at present. Superstring theory has to have 10 dimensions to be consistent. Four of them will be the dimensions of our spacetime, assumed to be a "flat" Minkowsi space. String theory doesn't do curved spacetime. This leaves six spatial dimensions to be accounted for. Since we don't see them they are assumed to be "compacted", rolled up as it were into tiny closed shapes.

Now Calabi-Yau manifolds already existed in mathematics, and the stringy theory suggested that they would fit right into the exra dimension picture. They are complex manifolds, and three complex dimensions equals six real dimensions, so we're off and running. String theory uses even more complex numbers than regular quantum theory does.

 

[CalabiYauSpace]

If you take a 2 dimesional sheet of paper and rolled it up so tightly that the diameter of the roll was next to nothing, then it would appear as though it were only a 1 dimensional line and would be hard to differentiat between an actual 1 dimensional line.

this theroretically is the same thing, the 6 dimesional shapes are rolled up/curlled up so tightly that they blend in or appear to be part of 4 dimensional universe.

correct me if I'm wrong PLEASE!

 

[Gecko]

i know they are small, but it seems from the posts above that because it is in a 4 dimensions universe, the 6 dimensional objects will not appear to unfold as we magnify deeper. that's what i thought until just earlier today and if this where true, then there cannot possibly be a calabi yau at every point in 4 dimensional space without them overlapping.

does anyone know a good way to visualize calabi yau's in 3 dimensional space? it hard to imagine one at everypoint in space without being able to see them. i mean, if they where at everypoint, wouldn't we be moving through billions and billions of them every second? yet they are invisible. i tried to imagine it as sand, when there is one piece of sand in a huge grass field, you would have a VERY hard time finding it, however, if the field was made of sand and had pieces of sand at every point on the field, you would clearly see it. but for some reason, the calabi yau's are invisible.

 

[selfAdjoint]

The C-Y manifolds are entirely orthogonal (perpendicular) to 4 dimensional spacetime, so they have NO DIAMETER in spacetime, and do not overlap there.

No, you can't visualize this in 3-D because the additional dimensions are not visualizable. CalabiYauSpace's 2-D example is the best we can do. In order to do the 'rolling' of the extra dimensions we need a minimum of two dimensions (to make a circle, the simplest surrogate for a C-Y manifold). So to have the whole thing contained in 3-D for visualization the base space (corresponding to spacetime) must be only 1-dimensional.

 

[CJames]

Think of a hose. From a distance it appears one dimensional. But there are two dimensions, one along the hose, the other around it. The circular dimension is much smaller than the straight dimension. A circle has no width, so it can't overlap with other circles. It's the same with C-Y manifolds, the way that I understand it. A C-Y manifold takes up no space in the 4 infinite dimensions. Keep in mind that the manifolds are mathematical in nature and may not exist at all, in the same way that strings may not exist at all. I'm not just saying String Theory could be wrong, I'm saying that even if it's "right" we're still dealing with models. A "string" is an entity that has mathematical properties very similar to a string, that's all.

 

[RingoKid]

so what is the simplest way to physically prove string theory ?

open up new dimensions, magnify a 3d point to visible size, jump in a black hole...

BTW Self Adjoint if strings don't do curved spacetime what shape is a brane if not a bubble/sphere ?

Isn't the flatness just an illusion like the straight back country road disappearing into the distance on a curved Earth appearing flat ?

 

[selfAdjoint]

Branes are things in spacetime, not spacetime itself. Just as the worldsheet is a thing in uncurved spacetime although it is itself curved and is analyzed by Einstein's methods reduce to two dimensions.

In spite of these and other flirtations with curvature, string physics remains wedded to Minkowski's flat spacetime.

 

[RingoKid]

I thought branes were what separate the inflating spherical universe from the next universe and as such were not so much in spacetime but border on it at the edges ?

 

[selfAdjoint]

I thought branes were what separate the inflating spherical universe from the next universe and as such were not so much in spacetime but border on it at the edges ?

That doesn't sound like any cosmological model I have heard of. In the ekpyrotic model there are two branes; one is our universe and the other one comes over and hits it every now and then. The last time this happened it caused the big bang.

 

[RingoKid]

you're right self adjoint...

It's probably not one you've heard of cos it's mine. My branes essentially act as a leading and trailing edge with the universe in between them. A spherical swirling bubble skin of a universe 13.7 billion light years thick with the speed difference between the branes accounting for expansion and permeated by black holes that lead to the edges...

...actually this isn't the place or the time but if you search thru my posts you'll get an idea of where I'm coming from

cheers