Multidimensional time simulation

[DyerMaker]

TL;DR

Can multidimensional time be simulated with a computer?

If there are computer simulations of four-dimensional space are there any possibilities to digitally simulate a space -time with time having more than one dimension?
Please, leave some related links, if possible.

 

[Ibix]

It's easy enough to add a second minus to the metric signature. However, a lot of important features of time (like the one-way nature) stem from there being only one minus sign in the metric, so it probably won't behave like a spacetime, just a rather odd space. And linking it to any physics would be difficult because that isn't the way the world works.

What do you want to do? To just muck around with the tensors Maxima can do the job, and probably SymPy if you're more into python.

 

[Vanadium 50]

You can implement anything on a computer you can write down on a pad of paper. I think the tricky bit here is to decide what goes on that pad of paper.

 

[jedishrfu]

I found this article on Relativistic Mechanics and Multiple Time Dimensions

https://www.researchgate.net/public...ivistic_mechanics_in_multiple_time_dimensions

one question I have is what does it mean to have multiple time dimensions? What do you envision?

One possible scheme would be each object would have its own time based on its speed relative to other objects. Viewing a collection of objects then one could assign a clock to each one that represents the time that object is traversing due to its relative speed from a particular vantage point.

As an example, particles traveling from deep space to the Earth would have differing speeds and hence differing lifetimes like muons. You could model that.

Another place where multi time dimensions come into play is in faster than light frames of reference where you have three time-like dimensions and one space-like dimension. One could perhaps model that to understand what we might see. If we were observing a faster than light particle.

Programming languages that could be used would be python, Java, C/C++, Fortran or Julia/ Matlab. All of these languages have third party libraries and frameworks to do modeling and simulations of systems described by differential equations.

As an example in the past, Ive used Open Source Physics and Java to do modeling of orbital systems.

Www.compadre.org/osp

 

[PeterDonis]

I found this article on Relativistic Mechanics and Multiple Time Dimensions

https://www.researchgate.net/public...ivistic_mechanics_in_multiple_time_dimensions

I don't think that's a good reference (and researchgate is known for questionable papers).

one question I have is what does it mean to have multiple time dimensions?

The definition of that in the paper you referenced is that the "fifth dimension" is the Minkowski interval $ds^2$, so if $ds^2$ is timelike, the paper says there are "two time dimensions". Which is nonsense.

One possible scheme would be each object would have its own time based on its speed relative to other objects. Viewing a collection of objects then one could assign a clock to each one that represents the time that object is traversing due to its relative speed from a particular vantage point.

As an example, particles traveling from deep space to the Earth would have differing speeds and hence differing lifetimes like muons. You could model that.

This isn't adding another time dimension. It's just picking a particular coordinate chart and assigning a special meaning to its coordinate time--in other words, LET. (Which is off limits for discussion at PF.)

Another place where multi time dimensions come into play is in faster than light frames of reference where you have three time-like dimensions and one space-like dimension.

No, you don't. You can't change the metric signature of spacetime by choosing coordinates. You can have a coordinate chart that has three timelike and one spacelike basis vector (in fact you can have one that has four timelike basis vectors), but that doesn't change the nature of the dimensions of spacetime. It just means you've picked a coordinate chart that will be very difficult to work with (since the metric will look very complicated in it--none of the basis vectors are orthogonal, there will be cross terms all over the place, and you won't be able to read off anything useful from the line element).

 

[PeterDonis]

A sci-fi example of a universe with two time dimensions is Greg Egan's Dichronauts:

https://www.gregegan.net/DICHRONAUTS/DICHRONAUTS.html

Egan does quite a bit of math for the basis of this universe, but it's still sci-fi, not an actual physics proposal. AFAIK nobody has ever tried to actually do a detailed analysis of the physical implications outside of Egan's novels.