Why not higher dimensions in string is timelike?

[ensabah6]

Strings live in 9+1 world, M, 10+1

one line of criticism is string theory is unable to account for the number of large and compactified dimensions, i.e 1 (line) large, 9 curled, 2 large (sheet), 7 curled, 3 large 6 curled (our world) all the way to 9 flat or 9 curled.

Is there an a priori reason that the degrees of freedom, dimensions, are spatial and not temporal? For example, why not 3 large dimensions and 6 time dimesions, or 3 large dimesions, 2 extended large brane worlds, 2 compactified dimensions, and 2 time dimensions?

Since the world we live in is fixed at 3 large dimensions, whose to say the higher dimensions aren't time dimensions? Are additional time dimensions part of the landscape? i.e 9 spatial and 2 time dimensions?

Is there an apriori reason string/m disallows multiple time dimensions?

 

[Naty1]

The only thing I've read along the lines of your question are the following excerpts from Leonard Susskinds THE BLACK HOLE WAR,2008: (339-342)

The subtle mathematics of string theory goes haywaire unless more dimensions of space are added. String theorists discovered many years ago that the mathematical consistency of their equations breaks down unless six more dimensions of space are added...String Theory's need for six extra dimensions has eluded a simple explanation for 35 years...string theorists make the six extra dimensions compact...wrapped up in very tiny knots...all modern theories of elementary particles make use of some form of extra dimensions to provide the missing machinery that makes particles complicated.

On the other hand, Schillers strand theory, under current discussion here, does not require the artifice of additional dimensions ...

 

[Naty1]

Here is some background from Brian Greene in FABRIC OF THE COSMOS where he discusses strings and spacetime around page 486 and offers similar insights:

When it comes to identifying spacetimes elemental ingredients, we have no ideas about which we are really confident...spacetime does not emerg from the theory, as physicsts imagine it would in a background independent framework, but is supplied tothe theory by the theorist.

He goes on to say in following pages we don't know if spacetime actually might result from the weaving together of strings or whether spacetime might be a brane...nor whether strings are fundamental or branes are fundamental or both are

Page 529,notes:

Researchers such as Itzhak Bars at Uinversity of of Southern California have investigated...extra time dimensions...has shown it is at least possible to formulate theories with a second time dimension that seems to be physically reasonable.

 

[ensabah6]

Here is some background from Brian Greene in FABRIC OF THE COSMOS where he discusses strings and spacetime around page 486 and offers similar insights:


He goes on to say in following pages we don't know if spacetime actually might result from the weaving together of strings or whether spacetime might be a brane...nor whether strings are fundamental or branes are fundamental or both are

Page 529,notes:

Why not 3 large spatial dimensions and 6 time dimensions?

If the multiverse includes 10^500 spatial compactifications, then would adding those universe with timelike dimensions increase the multiverse to 10^1500?

 

[arivero]

With generality, there are some things to look when using S+T dimensions. First, that the existence of fermions depends really of the signature mod 8, but also that we need some euclidean version of the theory. So it seems that that S-T mod 8 = 0 and S + T mod 8 = 2 are relevant to fix the number of dimensions.

Then, you want a mechanism to isolate a four dimensional manifold. This is pretty in 11 dimensions, where a tensor object with three indexes exists naturally, and it forces a particular role for a 4 dimensional submanifold.

Then you have also Witten's questions: which is the minimum number of dimensions for a space to admit the action of the standard model groups, in the same sense that, for instance, a 2-sphere admits the action of SO(3). It is seven.

Finally, you have Conway et al lattice and code theory, stressing the deep role in mathematics of signatures 8 and 24.

Nor to speak of octonions D

 

[Haelfix]

Some of the classical notions of spacelike and timelike are a little bit fuzzy in st. I believe there are some dualities where for instance Ftheory can be formulated with a 2 time signature.

But generically, no backgrounds have been found with more than that and presumably most signatures are disallowed in s.t. by consistency constraints.

As for why 3 large spatial dimensions and 6 compactified ones, well one way of looking at it, is that's just the way things work out that happen to fit the observed world. Otoh, there have been many proposals over the years where a mechanism exists that somehow forces the situation to be that way.

For instance, in string gas cosmology, you start off with a cosmology where all of the dimensions are essentially Planck sized, and wound up very tightly. Then as thermal processes take place in the early universe, 3 large spatial dimensions emerges very naturally b/c that number of dimensions just so happens to have the right finite crosssection for 2 strings to interact by intersecting, whereas all the other higher d choices leads to a vanishing probability. So they spontaneously emerge as the universe evolves, and we end up with the situation that we observe.

 

[ensabah6]

Some of the classical notions of spacelike and timelike are a little bit fuzzy in st. I believe there are some dualities where for instance Ftheory can be formulated with a 2 time signature.

But generically, no backgrounds have been found with more than that and presumably most signatures are disallowed in s.t. by consistency constraints.

As for why 3 large spatial dimensions and 6 compactified ones, well one way of looking at it, is that's just the way things work out that happen to fit the observed world. Otoh, there have been many proposals over the years where a mechanism exists that somehow forces the situation to be that way.

For instance, in string gas cosmology, you start off with a cosmology where all of the dimensions are essentially Planck sized, and wound up very tightly. Then as thermal processes take place in the early universe, 3 large spatial dimensions emerges very naturally b/c that number of dimensions just so happens to have the right finite crosssection for 2 strings to interact by intersecting, whereas all the other higher d choices leads to a vanishing probability. So they spontaneously emerge as the universe evolves, and we end up with the situation that we observe.

Has it been proven that 3 large spatial dimensions + 6 timelike dimensions would not also fit in the observed world? Or any combination of dimensions, large, braneworld, and timelike?

i.e 3 large spatial, 3 compactified, 4 timelike, one braneworld?

From the standpoint though of calculating the multiverse via string theory, does the current number of 10^500 include dimensions 1-9 large, 1-9 compactified, and 1-9 timelike?

If the multiverse includes complete different particle content and fundamental laws of physics with different cosmological constants, is there any reason why the non-string bosonic 26 dimensional world is not also included in the multiverse? I know that 10 dimensions were chosen due to consistency with massless photon, but shouldn't calculating the multiverse include those that have massive photons, or no photons at all?

So instead of 10^500, we get something like 10^40,000

 

[Haelfix]

You would have to ask a string theorist those questions, I am not qualified to answer them.

I seem to recall that generically having more than 1 timelike 'standard' metric direction is disallowed. Instead the 2 time physics that appears in things like Ftheory involves a little hocus pocus on supersymmetric dimensions that are essentially infinitesimal, where you can kind of mathematically show some sort of equality with a 2 time dimensionally reduced theory. They are working in highly abstract spaces, that aren't necessarily trivially related to low energy 'emergent' metric distances.

Generically string theory has a lot of constraints on allowed backgrounds. Most of those you could naively write down cannot be a part of the theory. So chances are if you pick a theory of 3 time physics out of a hat, then whatever that physics is, it cannot be string theory. I also believe that's easy to check, once you have specified the details. It might for instance display anomalies or break a unitarity bound or somesuch.

Whats harder to check is to disallow the possibility altogether, but I do not know of any consistent (never mind realistic) background with more than 1 'standard' timelike direction, maybe a theorist can elucidate the details.

 

[Thomas Larsson]

Yitzak Bars has worked on something he calls two-time physics http://physics1.usc.edu/~bars/research.html . Don't know if anyone else (except his students perhaps) ever cared about that.

Time is not only about the signature of the metric, but also about causality and unitarity. Event A happens before event B if t_A < t_B. It is hard to see how to causally relate A and B if there are several time dimensions.

 

[ensabah6]

Yitzak Bars has worked on something he calls two-time physics http://physics1.usc.edu/~bars/research.html . Don't know if anyone else (except his students perhaps) ever cared about that.

Time is not only about the signature of the metric, but also about causality and unitarity. Event A happens before event B if t_A < t_B. It is hard to see how to causally relate A and B if there are several time dimensions.

what about many worlds interpretation?

An electron or photon goes through a double slit experiment, in one time dimension it goes through one slit, and in the other time dimension, it goes through the other slit.

Other time dimensions could be curled up upon themselves so that a particle in that dimension ends where it starts, and other time dimensions traveling backwards are simply not observable.

 

[arivero]

Has it been proven that 3 large spatial dimensions + 6 timelike dimensions would not also fit in the observed world? Or any combination of dimensions, large, braneworld, and timelike?

Fermions, fermions. You need to build fermions. So you need to analyze Dirac, Weyl and Majorana equations in (n,m) space and time dimensions. A lot of combinations are rejected in this way.

Another bunch of combinations are rejected by looking to the relationship between lorentz invariance in the brane (string or whatever) and lorentz invariance in the total space.

So YES, it has been proven that 3+6 does not work. And a lot of them.

 

[Demystifier]

Fermions, fermions. You need to build fermions. So you need to analyze Dirac, Weyl and Majorana equations in (n,m) space and time dimensions. A lot of combinations are rejected in this way.

Another bunch of combinations are rejected by looking to the relationship between lorentz invariance in the brane (string or whatever) and lorentz invariance in the total space.

So YES, it has been proven that 3+6 does not work. And a lot of them.

Can you provide some references on that?

 

[ensabah6]

Fermions, fermions. You need to build fermions. So you need to analyze Dirac, Weyl and Majorana equations in (n,m) space and time dimensions. A lot of combinations are rejected in this way.

Another bunch of combinations are rejected by looking to the relationship between lorentz invariance in the brane (string or whatever) and lorentz invariance in the total space.

So YES, it has been proven that 3+6 does not work. And a lot of them.

Assuming arguendo that it has been "proven" that multiple time dimensions would not be compatible with our universe, from the standpoint of creating a multiverse where lorentz invariance is not kept, or has different properties for Dirac, Weyl, and Majorna equations, is there an apriori reason that these variances, including massive photons or no photons, are not also included in the calculations of the size of the multiverse?

Sean Carroll wrote "“You can turn an egg into an omelet, but not an omelet into an egg. This is good evidence that we live in a multiverse. Any questions?’"

Even if a universe that has 3 large dimensions and 6 time dimensions does not describe our universe, is there a reason they could not describe a universe in the multiverse?

Perhaps Dirac, Weyl, and Majorna equations and massless photons are accidents of our universe, as are 3 large spatial dimensions, as opposed to 2 with 8 dimensions of time, and 1 curled up.Isn't a universe with 10 flat large spatial dimensions and 1 time dimension and unbroken supersymmetry a valid solution?

Calculating the total possible multiverses would not be limited to 3 large spatial dimensions and 1 time, with 6 curled up, it would include any other possible combination.

 

[arivero]

the apriori way is not a way at all. If your only condition is "to have at the end some objects moving in 3 dimensional space" then most people should agree that even classical mechanics is a solution. Or any theory of differential equations. Or well, even discrete cellular automatas. What we usually do is to put some empirical input and see the output.

But we could try. We could perhaps argue for the existence of a lightspeed and a Planckconstant, but how to argue for them to be finite, ie a maximum speed and a minimum angular momentum? If we agree that they should be finite, we are forced hopefully into Dirac equation. But except for empirical measurement, I do not know any correct argument. Not that it could not exist, but I have never seen it; most arguments reduce to "the most sure value is not zero not infinite but between". And the same applies to mass, to symmetry breaking, to CKM mixing, Weinberg mixing, and even to 10 flat large spatial dimensions (probably the compactification size would relate at the end both with particle masses and with cosmological constant, and again we expect not zero nor infinity but "between").

 

[arivero]

Can you provide some references on that?

Not a low level. For postgraduates, I will suggest to revisit periodically the reviews of Duff, some collection of Kaluza Klein papers -including Witten's- and some material on fermions and bott periodicity, eg spinorial chessboard. Plus your usual material. As time goes by, the mixing can become illuminating.

 

[ensabah6]

the apriori way is not a way at all. If your only condition is "to have at the end some objects moving in 3 dimensional space" then most people should agree that even classical mechanics is a solution. Or any theory of differential equations. Or well, even discrete cellular automatas. What we usually do is to put some empirical input and see the output.

But we could try. We could perhaps argue for the existence of a lightspeed and a Planckconstant, but how to argue for them to be finite, ie a maximum speed and a minimum angular momentum? If we agree that they should be finite, we are forced hopefully into Dirac equation. But except for empirical measurement, I do not know any correct argument. Not that it could not exist, but I have never seen it; most arguments reduce to "the most sure value is not zero not infinite but between". And the same applies to mass, to symmetry breaking, to CKM mixing, Weinberg mixing, and even to 10 flat large spatial dimensions (probably the compactification size would relate at the end both with particle masses and with cosmological constant, and again we expect not zero nor infinity but "between").

Lee Smolin has claimed that naive SUSY is compatible with anti-DS and cc of exactly 0, but not dS or + cc. He cites Witten "I know no clear cut way to get a positive cc" with citation and reference in a footnote, although he mentions that KKLT offers a speculative mechanism.

Sean Carroll wrote "“You can turn an egg into an omelet, but not an omelet into an egg. This is good evidence that we live in a multiverse. Any questions?’"

per Sean Carroll and other landscapeologists, why should we even suppose a multiverse of 3d + 1t + 6yc 10^500 even exists and is the "explanation" for the observed small but nonzero cc per anthropic principle?

If the multiverse does exist, why should we restrict it to 3d + 1t + 6yc when other string theory solutions from 10 flat spatial dimensions + 1t, unbroken SUSY, to 1 spatial and 10 time like dimensions are also solutions to 26-dimensional bosonic string theory (granted they produce universes radically different from our own)

 

[Demystifier]

Not a low level. For postgraduates, I will suggest to revisit periodically the reviews of Duff, some collection of Kaluza Klein papers -including Witten's- and some material on fermions and bott periodicity, eg spinorial chessboard. Plus your usual material. As time goes by, the mixing can become illuminating.

Can you be more specific about the references? Like preprint number or journal reference?(And it does not need to be at the low level.)

 

[arivero]

Can you be more specific about the references? Like preprint number or journal reference?(And it does not need to be at the low level.)

Ok. I consider interesting "The world in 11 Dimensions", a recopilation by Duff focused on theory of membranes, so that it explains not only strings but other extender objects. https://www.amazon.com/dp/0750306726/?tag=pfamazon01-20
Then there is other collection called "Modern Kaluza Klein Theories" or something so. A must.

Both books intersection contains Witten's "Realistic Kaluza Klein Theory". Compulsory reading.

Colateral readings, to me, have been the appendix of vol III of Weinberg QFT (there the argument for 7+4 is briefly exposed) and scattered articles about division algebras. For instance, the argument of Evans showing that the existence of supersymmetry in some dimensions relate to the existence of a division algebra. But as I said, it is person-dependant. You read, keep reading, and revisiting the texts.

 

[Demystifier]

Thanks arivero!

 

[arivero]

Thanks arivero!

Let me stress that #extradim=7 is a bold, almost predictive, result. It is muddled in string theory because strings carry a Chan-Paton gauge group besides the Kaluza-Klein gauge group. If you postulate that all of the standard model gauge will come from KK (leaving Chan-Paton to flavours, for instance) then the choosing of groups is very very restricted.

The naivest group choosing, the rotations of the 7 dimensional sphere, fails instructively. It is SO(8); the sphere S7 decomposes as a fiber bundle of fiber S3 and basis S4, in the same way the group SO(8) decomposes to SO(4) times SO(5). The SO(4) group decomposes to SU(2)xU(1) in the same way that the fiber S3 decomposes as a fiber bundle of basis S2 and fiber S1 (remember that SU(2) has the same algebra that SO(3), and U(1) is the 1-dim rotation group, so relates to S1).

Thus the platonic "spherical world" in 7 dimensions predict the group SO(5)xSU(2)xU(1).

But Nature seems to prefer a small variant. To see it, look at the spheres as projective spaces. S1 is RP1, S2 is CP1, S4 is HP1. From them we get U(1)xSU(2)xSO(5). What happens is that instead of HP1, we have CP2, whose group of isometries is SU(3).

More over, it can be proved that the families got by combining S1, S2 and CP2 are the smallest (dimension-wise) spaces whose group of isometries contains the standard model group.

Why the hell Nature prefers the complex projective plane instead of the more elegant quaternionic line?

 

[arivero]

Why the hell Nature prefers the complex projective plane instead of the more elegant quaternionic line?

Well... this is interesting. The complex projective plane is in some sense "bigger" that the quaternion projective line, and the factor is O(1) (ie, complex conjugation).

There is an elementary but very striking result which asserts that the quotient of the complex projective plane $CP^2$ by complex conjugation is the 4-dimensional sphere

I would not be surprised if the need of involving this conplex conjugation were related to the problems to understand the mechanism of chiral fermions in Kaluza Klein theories.

On other hand, $CP^2$ is interesting per se because it jumps to seven dimensions with very little ambiguity; you can fiber it with S1 to produce S5, and then there is only a non trivial fibering of S5 with S2 to produce a seven dimensional manifold.