Multidimensional Time

In the article Is time a dimension? I tried to describe an understanding that time is not a dimension. And in that article I promised to describe opposite option. But first let's clarify the arguments against time as a dimension.

We looked at the situation with a car running over a cat. To survive, at least one coordinate of the cat had to mismatch with the corresponding coordinate of the car. And if time were a coordinate, then all the cat's spatial coordinates could coincide, except for one - the time coordinate, and this would help the cat to escape. And such speculation exists: it is claimed that the cat's coordinates could have been the same as those of a car passing by the cat's house, but the cat was here, at this same point in space, yesterday! That is, the time coordinates didn't match, and the cat is alive. This line of reasoning can be refuted as follows:

just ask, where is the cat now when a car passes this place on the road where it was yesterday? Indeed, if it was here yesterday, then today it's somewhere else, for example, sitting next to the road and looking at a car. And it's alive: because at least one of its coordinates - depth - doesn't match the car's. And yesterday it didn’t die not because its time coordinate was different, but because yesterday its spatial coordinates again didn’t coincide with the spatial coordinates of the car.

So, that was yesterday. And today the cat is somewhere again, sitting next to the road, and what makes you think its in a different time coordinate than the car's?!

Yesterday, when it was saved, being in a different place again, was cat's time coordinate different from the car's? Why?! Just because the cat was walking in this place on this road, and the car was parked on the side of the road, nearby?

Physics thinks differently, it had the same time coordinates (and from the point of view of the theory of relativity, too).

Whether time is "really" a dimension in the same ontological sense as space is still open to interpretation. To identify a point of an axis we need a coordinate - to find it, it is an "address" of a point. If somewhere something happened, to identify this event we need its "coordinates". They are (x, y, z, t). This forces us to interpret time as a coordinate.

Space dimensions allow you to move along some of them independently, without to change your other coordinates, the time is different: changing your "x", you change always your "t" coordinate, so phisicists came to Lorenz transformations and to the concept of Spacetime. So, 3 space dimensions and 1 non-spatial dimension form this, "new" object - "Spacetime continuum"...

The idea that time might have more than 1 dimension is a real idea in theoretical physics - not established fact, but something that has appeared in several serious frameworks. There are different ideas, theories of multidimensional "time" (I quoted it!), in general, some of them talk about additional time-dimensions, treating it as multiple yesterdays, tomorrows, and another theories just talk about non-spatial dimensions (they can be not exact time or something else)...

Let's start from esoteric view of the multidimensional time ideas.

First theory is the theory of Russian esoteric Piotr Ouspensky (1878) - a Russian philosopher and esotericist known for his expositions of the early work of the Greek-Armenian teacher of esoteric doctrine George Gurdjieff. He devoted quite a lot of attention to this issue and described in detail what he means by "multidimensial time". Next I will briefly describe his ideas.

                  now
past <---- -  - ---+--- -  - ----> future
        my                   my
      birth                 death

     _ _ _ _￪_ _ _ _
     _ _ _ _|_ _ _ _
     _ _ _ _|_ _ _ _ 
past -------+--------> future

     _ _ _ _￪_ _ _ _              who is living here?!
     _ _ _ _|_ _ _ _              and here too...?
     _ _ _ _|_ _ _ _
past -------+--------> future     you are living here!

birth event1 event2 ... event3 event4 death, then
birth event1 event2 ... event3 event4 death, then
birth event1 event2 ... event3 event4 death, then
...again and again

           eternity
              .
   +------+  .
  /      /| . 
 +------+ |.
 |      | +
 |      |/
 +------+ · · · · · timeline
        |
        :
        :
        :
  possibilities

         B
        /
A------o-------> C
        \
         D

Ordinary physics has 3 dimensions of space + 1 dimension of time: 3+1. Some theories explore 3+2, 4+2, or even more dimensions, where more than one coordinate behaves like a time dimension. nT notation is also used: 1T, 2T etc.

Wikipedia:

The additional dimensions may be similar to conventional time, compactified like the additional spatial dimensions in string theory, or components of a complex time (sometimes referred to as kime).

2T spacetime can have 2 equivalent time dimensions as well as 1 real time dimension and one imaginary time dimension - in this case we have complex time plane (similarly to usual, space complex plane).

Mathematically, imaginary time allows to avoid singularity:

...appears as a singularity in ordinary time but, when modelled with imaginary time, the singularity can be removed and the Big Bang functions like any other point in four-dimensional spacetime.

Turkish theoretical physicist Itzhak Bars popularized the idea of 2T:

[He] has proposed models of a two-time physics, noting in 2001 that "The 2T-physics approach in d + 2 dimensions offers a highly symmetric and unified version of the phenomena described by 1T-physics in d dimensions."

Another example is Vladilen S. Barashenkov.

Vladilen S. Barashenkov was a Soviet/Russian theoretical physicist at JINR in Dubna, working in nuclear and particle physics.

He explicitly developed a 6-dimensional Spacetime with a 3-dimensional vector of time: \(\hat{t} = (t1,t2,t3)\) and ordinary 3-space: \( x=(x,y,z) \).

His 1999 paper was literally called "Multitime generalization of Maxwell electrodynamics and gravity." he derived equations using a 6-dimensional space with a 3-dimensional time vector.

Then in 2004 he and collaborators published "Quantum Field Theory with Three-Dimensional Vector Time." The model treats particles as moving along arbitrary trajectories in the 6-dimensional spacetime.

Also he had a popular book called "The Universe in an Electron" where he discusses explosions, nuclear physics, cosmology, and even asks why space is 3-dimensional while time is 1-dimensional.

His 6-dimensional metric is:

\begin{aligned} d\hat{x}^2 = dx^2 - d\hat{t}^2 \quad \text{where} \\ d\hat{t}^2 = dt_1^2 + dt_2^2 + dt_3^2 \end{aligned}

Other Russian/Soviet literature on three-dimensional time, additionally to Barashenkov could be:

• V. S. Barashenkov
• R. L. Bartini
• A. P. Yefremov
• N. A. Zhuk
• I. A. Urusovsky
• D. G. Pavlov
• and others.

Another scientist is E.A.B. Cole. Cole proposed treating 3 temporal coordinates ti as independent, with proper time t acting as a parameter defining a trajectory through the 3-dimensional time space. This was already being discussed around 1980.

In the theory of relativity every moving "coordinate system" has its own local time and a British philosopher J.W. Dunne suggested that, in the context of a "block" spacetime as modelled by General Relativity, a second dimension of time was needed in order to measure the speed of one's progress along one's own timeline. This leaded to an infinite regress, but as we saw before, 2T systems exist.

The second real (not imaginary) time dimension could lead to:

• negative-norm states
• instabilities
• problems defining probabilities
• causality problems
• particles with unusual energy behavior
• difficulty defining a sensible initial-value problem

It is like "nature seems to strongly prefer one time direction" if to believe that time exists at all.

Example - "violation of causality":

 t₂
  ↑
  |   C     D
  |   :   ⋰
  |   : ⋰
  |   A·····B
  +-----------→ t₁

If there was an event A and 2 equivalent time dimensions then after A can happen even B, but also it can be something totally unexpected: C looking for t₁ as an event happening at the same time as A. Also there are possibilities of complex timelines - like the event D. But again: maybe the paradoxes of elementary particles and quantum mechanics explained by this? Another point defending multiple equivalent time dimensions could be the next reasoning: maybe we already live in such Mutlitime-Space but we treat (t1, t2, ...) cootdinates as one complex coordinate t? Sure, such fantasy requires strong definitions... I mean, 1T physics could emerge from 2T physics, because of special constraints, symmetries, an observer could effectively experience: 3+1 Spacetime.

This is somewhat analogous to how a 3D object could cast a 2D shadow.

Extra time dimensions, which are (apparently) not observed in the macrocosm, are considered compactified (folded up), similar to the extra spatial dimensions in string theory. They exist, and they could create problems, but they are too small. A dimension can't be small; it is infinite by definition, but given the possibility of space curvature, such a curling up, folding is permissible.

Also multiple time directions can introduce states with problematic signs - sometimes called ghost states. Ghost state is a state whose mathematical properties can cause the theory to have negative probabilities or catastrophic instabilities. But again, don't we observe them in quantum physics?

Additional time dimensions can make a lot of problems

• what determines motion in \(t_1\)?
• what determines motion in \(t_2\)?
• what is causality?
• what determines the observer's proper time?
• how does quantum mechanics work?
• how do particles propagate?
• how is energy defined?
• why don't we observe violations of causality?
• why do macroscopic systems appear to have one time direction?

Here I shared my thoughts on why time is not like a dimension. Let's try to look at it as a dimension. The problem was that kinematics equations look as:

\begin{aligned} x(t) = \ldots \\ y(t) = \ldots \\ z(t) = \ldots \end{aligned}

and t is a parameter (argument), not an individual dimension, just a parameter. Funny, but at the same time we describe some event (something happened somewhere and sometime) as \((x, y, z, t)\) and t here looks as usual coordinate... Actually, we don't need \(x, y, z\) if we know the equations of the motion, but usually we don't (and cannot) know them.

Well, to get out of this situation we can imagine:

\begin{aligned} x(t_2) = \ldots \\ y(t_2) = \ldots \\ z(t_2) = \ldots \\ t_1(t_2) = \ldots \end{aligned}

This primitive trick injects a time dimension \(t_1\) which looks like \(x, y, z\) and they all now depend on some another time which is again a parameter (\(t_2\)). Mysterious. But pay attention: now we have 2 time dimensions. What time would we measure in this case? Maybe \(t_1\). Or \(t_2\). Or \(\hat{t} = (t_1, t_2)\). Some physicists introduce 3 time dimensions, and the event's coordinates look then: \(E = (x, y, z, t_1, t_2, t_3)\). It means that you can have a lot of New Year's Eve parties at a club in New York! What would be the difference between them? Well... \(E1 = (x, y, z, t_1, t_2, t_3)\) and \(E2 = (x, y, z, t_1, t_4, t_5)\) - maybe they have difference in furnishings or lighting or... it is about probability, I am thinking about quantum world now... imagine that \(t_2\) can have any value in \([0, 1]\) range (let's talk about 2T) and if \(t_2 = 1\) - the event is happening now! If \(t_2\) is lesser, then... so, it can be about probability as well.

∵∴∵∴∵∴∵∴∵∴∵∴∵∴∵∴∵∴∵ shore
    <----           extra-"path" due time "current"  ^
    \   ↑           intended path                    |
your \  :                                            |
eff.  \◜:   ↜〜〜〜  "river current"              0x axis
"path" \:                                            |  
        ▲           you                              |

...the properties of spacetime near a singularity change even more radically and remain poorly understood. It is believed that their description is only possible with the development of a quantum theory of gravity, which describes gravitational interactions at distances on the order of the Planck length. For an external observer, the worldlines of particles falling into a black hole end at the gravitational radius, and all events for them lie above the event horizon. Anything that happens to the falling observer below the gravitational radius appears nonexistent to the external observer, since events below the horizon are unobservable. Thus, a falling observer experiences time that does not exist for an external observer, while time seems to stop at the event horizon.

This situation can be interpreted as follows. There are mutually perpendicular time axes, i.e., two times: one flows for the observer above the event horizon, and the other flows below it. The time coordinate below the event horizon is independent of and orthogonal to external time.

These two times have a single point of intersection on the event horizon. Thus, the absolute future in the spatiotemporal manifold (STM) of an external observer is a moment in time orthogonal to the original STM, and all events beyond the absolute future occur in a time orthogonal to the time of the external observer.

-- The multidimensional time hypothesis in the context of problems of modern physics, Artemenko, Spaskov, 2007

Singularities, quantum world are cases looking very promising in light of the theory of multidimensional time.

• Alien Code (multidimensional alien beings having non-linear time caught a human to contact with his "impossible" from their point of view consciousness)
• Arrival (multidimensional alien beings arrived to Eart and try to contact with humans)

Multidimensional time ("time cube") created by Otis Eugene "Gene" Ray diagnosed with schizophrenia: https://en.wikipedia.org/wiki/Time_Cube. He posits that each day actually consists of 4 days occurring simultaneously. Ray died in March 2015.

Here's a speculative picture - not established physics, but useful for thinking. Imagine that what we call: "the Universe evolving in time" is actually a lower-dimensional manifestation of a more complicated structure.

Perhaps fundamental reality looks more like: \((x, y, z, t_1,t_2, ...)\) and the particular physical conditions of our universe select one effective temporal direction.

Then "the passage of time" could be analogous to the way a lower-dimensional observer experiences a trajectory through a higher-dimensional structure. In that picture, time as we experience it wouldn't necessarily be fundamental. It would be an emergent feature of the way our physical world sits inside a deeper geometry.

It could be a script for a sci-fi movie.

Multiple-time theories are speculative theoretical possibilities. That's not the same thing as saying they're nonsense.

There are many ideas in theoretical physics that are mathematically sophisticated and worth investigating without having experimental confirmation...

---

See also:

• P. D. Ouspensky. A Biographical Outline
• A New Model of the Universe by P. D. Ouspensky
• Tertium Organum --- P.D. Ouspensky
• RECURRENCE - Dimensions, P.D. Ouspensky
• RECURRENCE - Time enfoldment
• Tertium Organum, Chapter V, P.D. Ouspensky
• Parallel Existences
• Tertium Organum by P. D. Ouspensky
• In Search of the Miraculous by P. D. Ouspensky
• Eternal return concept
• Eternalism
• Multiple time dimensions
• Two time physics
• Two-Time Physics, Itzhak Bars
• Youtube video: Two Time Physics
• Multitime generalization of Maxwell electrodynamics and gravity Authors: VLADILEN BARASHENKOV
• The International Society for the Study of Time
• New theory proposes time has three dimensions, with space as a secondary effect by Rod Boyce, University of Alaska Fairbanks
• Multidimensional arrow of time Sergey G. Rubin
• On multidimensional time J Strnad
• Research project: The 5D Universe of 3D Space & 2D Complex Time
• The 5D Space-Time-Matter Consortium
• Youtube video: Multidimensional Time
• The Privileged Character of 3+1 Spacetime