Something from nothing

Recently reading the book Why Does The World Exist by Jim Holt I came across the idea of an arithmetic nothingness. Holt explores the mystery of existence including taking a philosophical tour and quantum based spontaneous creation of something from nothing and so on…

So back to the arithmetic – and in particular Zero and One (0 and 1). To the Greeks and Romans the very idea of zero was inconceivable how could a nothing be a something.

If we let 0 stand for nothing and 1 for something then we get a sort of toy version of the mystery of existence. How can you get from 0 to 1. In advanced mathematics there is a simple sense in which the transition from 0 to 1 is impossible.

A number is regular if it can be reached via the numerical resources lying below it. More precisely, the number n is regular if it cannot be reached by adding up fewer than n numbers that are themselves smaller than n.

We can see 1 is regular because it can’t be reached from below. The sum of 0s is 0.So the big question is whether there is a way of bridging the gap between 0 and 1 – between nothing and something.

Leibniz thought he had found an answer and this is fascinating. One infinite series is 1/(1.x) = 1 + x + x(2) + x(3) + x(4) + ……

By plugging in -1 into this series

½ = 1-1 + 1-1 + 1-1 + 1-1  + …..

½ = (1-1) + (1-1) + (1-1) + (1-1) + ……

and so

½ = 0 + 0 + 0 + 0 ….

The equation seems to suggest that something can appear from nothing. Had Leibniz stumbled on something?

This is of course invalid. The infinite series isn’t convergent and so therefore a series jumping between 0 and 1 makes no sense.

God and the Delayed Choice Quantum Eraser – he may never be able to see the wave-like nature of reality.

In the last few months pretty much all the available time I have – I’ve been thinking about the implications of the Delayed Choice Quantum Eraser. All my life I understood the double-slit experiment to need ran observer in order to collapse the wave-like nature of reality. I have, as perhaps others, never grasped the deeper, the more subtle implication – the idea that:-

If we can know the path the entangled photon takes, that in itself is enough to bring about a collapse.

In quantum mechanics, the quantum eraser experiment is a double-slit experiment that demonstrates several fundamental aspects of the quantum theory, including quantum entanglement and complementarity. Brian Greene describes the experiment in his recent book The Fabric of the Universe. Consider

“A simple version of the quantum eraser experiment makes use of the double-slit set up, modified in the following way. A tagging device is placed in front of each slit; it marks any passing photon so that when the photon is examined later, you can tell through which slit it passed…when this double-slit-tagging experiment is run, the photons do not build up an interference pattern.

What if just before the photon hits the detection screen, you eliminate the possibility of determining through which slit it passed by erasing the mark imprinted by the tagging device?

As we know, it turns out, that the interference pattern shows up again. Which, is unexpected, counter initiative and strange to say the least.  But again it gets even stranger with the delayed-choice quantum eraser. Greene describes it thus,

It begins with [the set-up of the quantum eraser], modified by inserting two so-called down-converters, one on each pathway. Down-converters are devices that take one photon as input and produce two photons as output, each with half the energy (“down converted”) of the signal. One of the photons (called the signal photon) is directed along the path that the original would have followed toward the detector screen. The other photon produced by the down-converter (called the idler photon) is sent in a different direction altogether. On each run of the experiment we can determine which oath a signal photon takes to the screen by observing which down-converter spits out the idler photon partner. And once again, the ability to gleen which-path information about the signal photons– even though it is totally indirect, since we are not interacting with any signal photons at all– has the effect of preventing an interference pattern from forming.

So all we know about the signal photon we learn by observing the idler photon. But even so, we get the photons acting like particles. Greene again

What if we manipulate the experiment so as to make it impossible to determine from which down-converter a given idler photon emerged? What if, that is, we erase the which-path information embodied by the idler photon? Well, something amazing happens: even though we’ve done nothing directly to the signal photons, by erasing which-path information carried by their idler partners we can recover an interference pattern from the signal photons.

The implication here is the fact that we can know which slit the photon exits is exactly what causes the interference pattern to collapse. In the double slit experiment it isn’t the detector (the measurement) that collapsing the waveform. It is that fact that we can know that collapses the wave.

Now if a God can always knows which-path information a photon is to pass, he/she can therefore never see the interference pattern, the wave like nature of reality will be hidden from such a God.

13 most important numbers and our perception of reality

Ever science I can remember I was fascinated by the idea that if an ant was to crawl around the inside of a clock – if it or its ancestors would ever understand the passage of time as we interrupt the it. Time tightly coupled with space and affected by relativistic factors. I guess I have overtime refined my thinking to consider whether man can ever really comprehend the complexity of the universe - everything.

1^st Movement

We don't after all expect dogs or cats, to be able to figure out everything about the universe. And in the sweep of evolution, I doubt that we are the last word in intelligence. There might well be higher levels of intelligence later, which again, are unable to understand everything. Complexity may be logarithmic and approach infinity rendering it just un-understandable.

A proof for the 1637 theorem (Fermat’s last theorem) was finally published in 1995 despite the efforts of countless mathematicians during the 358 intervening years. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20^th. And yet, Fermat's Last Theorem would fade in comparison to the infinitely complex and wondrous universe.

2^nd Movement

Having said that it is amazing just how much we have gleaned about the universe from a tiny distant and largely insignificant vantage point. Which brings me to my next and related fascination.

That is - does the universe even exist if mankind isn’t there to perceive it? I know this type of a question has been asked in many forms over the centuries, including for example; If a tree falls in a forest and no one is around to hear it, does it make a sound – a philosophical thought experiment that raises questions regarding observation and knowledge of reality.

So without a conscious observer  [us] does the universe exist?
 Quantum physics has taught us that reality is not what it seems. Sub atomic particles for example are believed not to hold a position in space until they are observed.  Their location otherwise is governed by a probability wave. The more we discover about the location of an electron (say) the less we can know about its mass and speed. QED goes much much further.

Now this has some interesting implications that inspire all sorts of theories. One such theory is that everything that is possible does happen in one dimension or another simultaneously (parallel universe) which places "responsibility" on the observer to interpret which "reality" or "universe" is manifesting. A consistent theory of everything that ignores consciousness is probably (philosophically) impossible. You need an observer who looks at the universe. This includes of course universal constants or important numbers.

3^rd Movement

Physics, in particular cosmology is full of physical constants or physical quantities that is generally believed to be both universal in nature and constant in time. Some of the most widely recognized being the speed of light in vacuum c, the gravitational constant G, Planck's constant h, the electric constant ε₀, and the elementary charge.

So, once again, are these empirical truths that have been discovered or if it is simply invented by us to co-construct reality. The Classical Greek philosopher Plato was of the view that math was discoverable, and that it is what underlies the very structure of our universe. He believed that by following the intransient inbuilt logic of math, a person would discover the truths independent of human observation and free of the transient nature of physical reality.

So the question remains; if a mathematical theory goes undiscovered, does it truly exist? Maybe this will be the next “does a tree falling in the forest make any sound if no one is there to hear it?”

4^th Movement

What follows is the 13 most important numbers in the Universe based on James D. Stein's Cosmic Numbers - Popular Mechanics. But the numbers on this list are of cosmic importance— they are the fundamental concepts that define our universe, that make the existence of life possible and that will decide the ultimate fate of the universe

1.    The Universal Gravitational Constant

2.    The Speed of Light

3.    The Ideal Gas Constant

4.    Absolute Zero

5.    Avogadro's Number

6.    The Relative Strength of Electricity and Gravity

7.    Boltzmann's Constant

8.    Planck's Constant

9.    The Schwarzschild Radius

10. The Efficiency of Hydrogen Fusion

11. The Chandrasekhar Limit

12. The Hubble Constant

13. Omega

http://www.popularmechanics.com/science/space/13-most-important-numbers-in-the-universe#slide-7