Space and time

If time and space are similar and space is fractalled then time fractals are not far away.

Challenging Einstein might be blasphemy, but there are a host of papers and published scientific features asking the same question. Was Einstein wrong? Even if he was wrong, what’s that got to do with markets and economics? We already talked about self similarity of research in ‘The Time Fractal’. Physicists and economists have more in common than what is being published or talked about.

If the ongoing research proves that the thinker (Einstein) was wrong, it would bring old schools down and erect new institutions. Though this is not a very comfortable truth, there is nothing wrong in challenging an idea. Moreover, how much truth do we know anyway? And don't new ideas come from old ideas? Is this not what research is about, learning from the past and unearthing the future?

Why could Einstein be wrong?
In an article in Scientific American, David Z Albert and Rivka Galchen explore the idea. Einstein talks about certainty and locality which is intuitive i.e. A cannot affect B without touching it or being next to it. Quantum mechanics says that the idea of position does not exist. Physicists say that particles related in this fashion are quantum mechanically entangled with one another.  Entanglement may connect particles irrespective of where they are, what they are and what forces they may exert on one another. This kind of intimacy is counter intuitive.

This undermines Einstein's special theory of relativity. The idea that systems cannot be non-deterministic troubled him. Even today this crucial part of Einstein's legacy remains very much obscured. Physicist John S Bell proved in 1964 that the actual physical world is non-local and Einstein’s special relativity is back in the news again.

Tim Maudlin’s book (1994) on quantum non-locality and relativity says that the special theory of relativity claim about the geometric structure of space and time is incorrect. The author goes ahead and proves that quantum mechanical non-locality and special relativity cannot peacefully coexist.

Now this all might look like a scientific debate, but it is the same debate polarising economists, the idea of random and order, determinism and non-deterministic, the debate of efficiency and inefficiency and the fluctuating curves or proportionality challenging equality.

Euclidean triangle and fractalled space
The Euclidean triangles we have been speaking about regarding time fractals are taken as an intrinsic assumption of models representing curved spacetime geometries. In another research by Jerzy Jurkiewicz, Renate Loll and Jan Ambjorn, the authors highlight how triangle meshes can efficiently approximate curved surfaces, which is why triangles are frequently used in computer animations.

For spacetime, the elementary building blocks are four-dimensional generalisations of triangles, called four- simplices. It is only now that the ideas focusing on geometry are resurfacing. This is a new trend after the intellectual community including Stephen Hawking and others said that "time is imaginary," in both a mathematical and a colloquial sense.

Spacetime scientists have also witnessed how assembling microscopic building blocks in an essentially random manner ended up with symmetric shapes even on a large scale. Jerzy Jurkiewicz, Renate Loll and Jan Ambjorn performed a diffusion process by letting a suitable analogue of an ink drop fall into the superposition of universes and watch how it spreads and is tossed around by the quantum fluctuations.

Measuring the size of the ink cloud after a certain time allowed them to determine the number of dimensions in space. Evidently, a small object experiences spacetime in a profoundly different way than a large object does. To that object, the universe has something akin to a fractal structure. This implies there are no rulers and no other objects of a characteristic size that can serve as a yardstick. One possibility is that the universe becomes self-similar and looks the same on all scales below a certain threshold. If so, spacetime does not consist of strings or atoms of spacetime, but a region of infinite subdivision.

Visual conception is eternal to understanding nature, no wonder we keep remembering Euclid 2,500 years later. The very idea of fractals bring scientists back to the 80-20 rule, the Pareto principle, the idea of proportionality.

Is it time or space that is fractalled and quantized?
William G Tifft of the University of Arizona suggests that in order to unify general relativity (gravitation) with the theories of quantum physics that describe fundamental particles and forces, it may be necessary to quantize space and perhaps time as well. In this scenario, time is no longer one-dimensional! The professor observed that redshifts of galaxies seem to be quantized and registered discrete values. Redshifts of galaxies relate to the structure of time, indicating an underlying quantization.

The model implies that time, like space seems to be three dimensional. The professor thinks that three dimensional time may be the fundamental matrix of the universe. In the 3 D time model, space is a local entity. Galaxies are separated in 3D time, which we have misinterpreted as separation in space.

Conclusion
Einstein's theory of relativity introduced a new way of looking at the physical properties of the universe. The Newtonian constraints of absolute time and space were abandoned. Time and space were unified and made relative, it formed a continuum that curved and enfolded about itself. The ideas above suggest that Einstein did not see space as an extension of time and this might have lead him to an inappropriate geometric assumption.

Illusions are all around us and only time clarifies the real from the unreal. In his book ‘In Search of Time’, Dan Falk suggests that the idea of time is an illusion, Julius Caeser is still alive and everyday is a Wednesday. He also suggests that our mind plays games with us. There are a host of thinkers who are getting into understanding the connection of quantum mechanics and mind. It is not just the human mind that plays games but even minds of birds like Scrub Jay, which showcases a conception about tomorrow. How we will understand nature is also linked to tomorrow, even if we write books refuting the idea of time.

Nobody can doubt the genius of Einstein, but to assume that genius of a man could be eternal against time is too large an assumption. The solution out of the quantum relativity quagmire is linked with time fractals, whether we travel in it or through it. The best part of travelling back in time are the stock markets, at least you know what not to do.

The author is CEO, Orpheus CAPITALS, a global alternative research firm