Why not two or more time dimensions?

In summary, the conversation discusses the concept of multiple dimensions of time in a given universe, with some arguing that it is necessary for mathematical consistency and others suggesting that it may be an inherent property of the universe. The idea of different signature metrics in Clifford algebras is also brought up, with the possibility that the universe may be "signature blind" and that a complete theory should be manifestly tilt covariant. The Leech lattice is mentioned as a possible explanation for the number of dimensions in string theory and the number of keys on a keyboard. The interconnectedness of time and space is also considered, with the concept of acceleration and the use of time squared in equations as evidence for multiple dimensions of time.
  • #1
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
 
Physics news on Phys.org
  • #2
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).
 
  • #3
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.
 
  • #4
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?
 
  • #7
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?
 
  • #8
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.
 
  • #9
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.
 
Last edited by a moderator:
  • #10
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.
 
  • #11
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.
 
  • #12
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.
 
  • #13
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.
 
  • #14
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.
 
Last edited:
  • #15
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.

R
 
  • #16
rtharbaugh1 said:
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.
 

1. Why do we only experience time in one dimension?

Our perception of time is based on the movement of objects and events in relation to one another. In order to measure the passage of time, we need to have a reference point and a way to track the changes in that reference point. This is typically done using the three dimensions of space (length, width, and height). The concept of time as a fourth dimension was introduced by Albert Einstein, but it is still considered to be a single dimension.

2. Could there be other dimensions of time that we are not aware of?

While it is possible that there are other dimensions of time that we are not aware of, there is currently no scientific evidence to support this idea. Our current understanding of time is based on the laws of physics and the theories of relativity, which do not account for multiple dimensions of time.

3. How would a second time dimension affect our daily lives?

It is difficult to say how a second time dimension would affect our daily lives as it is purely hypothetical. However, it is likely that it would drastically change our understanding of time and how we measure and perceive it. It could also have implications for the way we experience events and the concept of cause and effect.

4. Is it possible for humans to perceive multiple dimensions of time?

Our perception of time is limited by our biological and cognitive abilities. While it is possible for humans to understand and conceptualize the idea of multiple dimensions of time, it is unlikely that we would be able to perceive or experience them in the same way that we do with our current understanding of time.

5. Can we use mathematics to explain the concept of multiple time dimensions?

Mathematics is a powerful tool for understanding and explaining complex concepts, but it is limited by our current understanding of the universe. While there are theories that suggest the existence of multiple dimensions of time, there is currently no mathematical framework that can fully explain or support this idea. Much more research and evidence is needed before we can use mathematics to explain the concept of multiple time dimensions.

Similar threads

  • Beyond the Standard Models
Replies
5
Views
2K
  • Beyond the Standard Models
Replies
2
Views
2K
  • Beyond the Standard Models
Replies
4
Views
2K
  • Beyond the Standard Models
Replies
1
Views
1K
  • Beyond the Standard Models
Replies
1
Views
1K
  • Special and General Relativity
2
Replies
48
Views
1K
  • Beyond the Standard Models
Replies
25
Views
4K
  • Beyond the Standard Models
Replies
7
Views
1K
  • Beyond the Standard Models
Replies
0
Views
862
Back
Top