# Why not two or more time dimensions?

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#### echolocator

Is there a reason why a given universe should include only a single dimension attributed to time? Why not two? Or ten? Is there any particular law that prevents this?

Cheers

echolocator

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#### Mentat

Originally posted by echolocator
Is there a reason why a given universe should include only a single dimension attributed to time? Why not two? Or ten? Is there any particular law that prevents this?

Cheers

echolocator
Well, you have to remember that dimensions of time (and space, for that matter) are not added for fun or because it might look neat, they are added out of mathematical necessity (or mathematical convenience).

Anyway, if there is more than one Universe (as you indicate by saying "a given universe"), then there must be space between it and the next Universe, meaning that there is an ultimate Multiverse, and spacetime would be a property of the Multiverse, not of the individual Universes (or so it seems to me).

#### Demystifier

2018 Award
With number of times different from 1, the field equations of motion would not be hyperbolic. Then the corresponding dynamics would be typically unstable. A similar argument excludes tachyons.

#### Kalimaa23

Demystifier said:
With number of times different from 1, the field equations of motion would not be hyperbolic. Then the corresponding dynamics would be typically unstable. A similar argument excludes tachyons.
Interesting. Any references on that?

2018 Award

#### Dcase

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#### yanniru

I recall that the original 26-d closed string theory had two time dimensions as well as tachyons and was considered undesirable for both reasons. Does anyone have a similar recollection?

However, in reading Lisa Randall's book "Warped Passages", the claim is made that 26-d theory has but one time dimension. Is she correct and/or are both possibilities?

#### coalquay404

yanniru said:
I recall that the original 26-d closed string theory had two time dimensions as well as tachyons and was considered undesirable for both reasons. Does anyone have a similar recollection?

However, in reading Lisa Randall's book "Warped Passages", the claim is made that 26-d theory has but one time dimension. Is she correct and/or are both possibilities?
By "original" string theory, I presume that you mean bosonic string theory. Bosonic string theory was proposed as a string theory in a D-dimensional Minkowski background and was found to be even semi-consistent only if D=26. While it does indeed predict negative mass states (tachyons), there was only ever one time direction.

J

#### josh1

Demystifier said:
With number of times different from 1, the field equations of motion would not be hyperbolic. Then the corresponding dynamics would be typically unstable. A similar argument excludes tachyons.
You can change the signature of the spacetime metric without losing hyperbolicity. But what you can`t have are equations of motion with more than two derivatives of time.

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#### CarlB

Homework Helper
From the point of view of Clifford algebra, a classic article on the signature of space time is this:

Should Metric Signature Matter in Clifford Algebra Formulations of Physical Theories?
William M. Pezzaglia Jr., John J. Adams
Standard formulation is unable to distinguish between the (+++-) and (---+) spacetime metric signatures. However, the Clifford algebras associated with each are inequivalent, R(4) in the first case (real 4 by 4 matrices), H(2) in the latter (quaternionic 2 by 2). Multivector reformulations of Dirac theory by various authors look quite inequivalent pending the algebra assumed. It is not clear if this is mere artifact, or if there is a right/wrong choice as to which one describes reality. However, recently it has been shown that one can map from one signature to the other using a "tilt transformation" [see P. Lounesto, "Clifford Algebras and Hestenes Spinors", Found. Phys. 23, 1203-1237 (1993)]. The broader question is that if the universe is signature blind, then perhaps a complete theory should be manifestly tilt covariant. A generalized multivector wave equation is proposed which is fully signature invariant in form, because it includes all the components of the algebra in the wavefunction (instead of restricting it to half) as well as all the possibilities for interaction terms.
http://arxiv.org/abs/gr-qc/9704048

My work is (-+++) or (-++++) signature, or, when I let my real feelings out, (++++) newtonian.

#### arivero

Gold Member
Clifford Algebras are classified by signature (number of spatial - number of temporal dimensions). It serves to string theoretists (and to Conway) to explain that 26 Minkowski is really a 24 dim thing.

#### yanniru

arivero said:
Clifford Algebras are classified by signature (number of spatial - number of temporal dimensions). It serves to string theoretists (and to Conway) to explain that 26 Minkowski is really a 24 dim thing.
It seems that arivero is contradicting coalquay404 who in answer to my question said that 26-d string theory has only had one time dimension.

#### CarlB

Homework Helper
yanniru said:
It seems that arivero is contradicting coalquay404 who in answer to my question said that 26-d string theory has only had one time dimension.
26 = 25+1

25-1 = 24.

No contradiction, only one time dimension in 26-d string theory.

Doesn't mean string theory makes sense.

#### arivero

Gold Member
CarlB is right. It is a nice trick in Clifford algebras and also of selfdual lattices.

I have a far fetched conjecture related to this: count the alphabet keys in your keyboard. There are also around 24. It could be that the neural recognisers in the brain are optimum for Leech lattices, thus 24 dimensions. In English sound recognision seems to pivot aroun 24 + 24 for vowels and consonants either. In other languages is more as 8 + 24.

So it is not a coincidence that the numbers of keys in your keyboard is about the same as the bosonic string: both facts would came from the same mathematical object, the Leech lattice. As you may know from theoretical computation lectures, this lattice is also reponsible for the format of self-correcting codes.

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#### rtharbaugh1

Time and space are inseparable, maybe even the same thing. So if there are spatial dimensions, and most agree that there are at least two or three, then there are also that many time dimensions.

Consider acceleration. We use time square in the denominator. So it is quite evident that the idea of time having more than one dimension is not only acceptable, it is necessary to explain ordinary phenomena.

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#### paw

Consider acceleration. We use time square in the denominator. So it is quite evident that the idea of time having more than one dimension is not only acceptable, it is necessary to explain ordinary phenomena.

R
Time squared arises because acceleration is the second derivative of position wrt time not because of multiple temporal dimensions.

"Why not two or more time dimensions?"

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