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“Now, I (being very thin) think differently; and that so much of motion, is so much of life, and so much of joy–––and that to stand still, or get on but slowly, is death and the devil–––”

Laurence Sterne, Tristram Shandy, Vol. VII, Chp. XIII.


This post has nothing to do with politics or economics. Surprisingly, this discussion on time does fold back onto human dignity, however briefly, but even this is somewhat tangential. At its core, to be honest, it is simply a brain-fart conjecture that has been swimming around in my thoughts for some years. It is time to let this go public so I can get it out of my head.

So here is the brain-fart conjecture, posed as a question:

Is time best modeled as a helix?

A helix, as graphed by OS-X Grapher.

A helix can be plotted in one of two ways. First, there’s the parametric equation:

Next, there is the use of Euler’s Formula:

And in graphic form appears as:

Credit: By Qniemiec – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=10308744

(Note: The gray lines are simply 2D projections of the wave functions, displaying how they manipulate the helix.)

There’s no attempt here to harmonize this brain-fart conjecture with General or Special Relativity, Minkowski spacetime, or Quantum Mechanics, although the helix does lend itself to the concept of wave-particle duality, and thus connects to light itself.

The helix also allows for changes in its radius, frequency and amplitude, adaptable to varying conditions over the evolution of the universe, and changes in inertial frames of reference.

It also leads to the inevitable discussion on time travel since, as recognized in physics, time holds no direction (we only witness dispersion, a.k.a., the Second Law of Thermodynamics, as a direction in time). The helix is symmetrical, so there is no contradiction encountered here, and time holding a frequency and amplitude brings us one step closer to a technology for time travel.

However, it is my conjecture that time travel will only be achievable – if it is achievable at all – on unique timelines. We have always assumed, both in physics and in popular culture (e.g., the Back to the Future series of movies), that if time travel is possible, we will travel backwards on the same timeline and thus be able to insert ourselves into history.

But such a notion brings us to a paradox: Could a time traveler return to the past and prevent, for example, his/her parents meeting, thus stopping the conception of the time traveler? Then we have to pull out the Novikov self-consistency conjecture.

Yet, if we eliminate the possibility of time travel on the same timeline as our present existence, we eliminate the need for the Novikov self-consistency conjecture. Like energy, timelines disperse and transform, and cannot be re-used in their original form.

Thus, we preserve the idea of free will, as an energy-like timeline would not allow the time traveler to inject him/herself into past choices that have already been made, and the consequences that have already played out. [1]

Rather, if we could envision a technology that would create a new timeline, but using a helix slightly shifted not unlike sidebands in radio frequencies, would time travel then become possible? By this means, we would simply become traveling observers of the past, but unable to act upon history.

The idea of time as a helix started when I discovered a few years ago how Incas, Mayans, the Lakota and other cultures such as Babylonians, Hindus and Buddhists modeled time in a circular fashion. [2] But operating in two-dimensional space, a circle has nowhere to move, either forwards or backwards.

Linear concepts of time, the straight-line arrows we’re familiar with in the west, allows for movement. Yet these concepts force us to associate time with change, with decay, which is also inaccurate (see comments above on the Second Law of Thermodynamics). [3]

But the helix is circular, in that it has a radius, and the “circles” are linked via the sine and cosine functions, and thus hold both a frequency and amplitude, allowing movement both forwards and backwards “between circles”.

Is the helix, however, compatible with the idea of the geometric constructions of a worldline passing through a point of origin from a past to a future cone (for a diagram, see the section “Causal Structure” on this Wikipedia page)? Is the concept compatible with the models of spacetime? Or with the Hole Argument? Or???

Better minds than I possess will sort this out… assuming the effort is worth anyone’s helical time.

End notes

[1] For my take on free will v determinism – seemingly unrelated to discussions of the physical universe but entirely applicable to human dignity, see the white paper Humans as Commodities (formerly The Dignity of Humanity) on my Google Drive page, in particular, see end note Nos. 14 and 21.

[2] My deeply felt thanks to Mary Ahenakew at the Resource Center of the Native Information Network, Smithsonian Institute, for a thorough bibliographic listing of books on Native American time concepts. If anyone is interested in seeing this list, I’ll be glad to trot it out here. Contact me at thesmallr(at)gmail(dot)com. With enough interest logged, I’ll do just that.

[3] All that dispersal in the cosmos leads me to ponder this question: In order for something to be dispersed, it had to have first enjoyed the property of being assembled. So how did we get to the assembly before the dispersal? And doesn’t dispersal simply lead to another, but different, assembly? Isn’t the universe on a circular cycle of assembly and dispersal, rather than just a linear dispersal? To believe in asymmetrical, linear dispersal probably says more about our nihilism than it does about the cosmos. Some physicists seem unable to separate what they investigate from their worldviews.