a b s t r a c tOption traders use a heuristically derived pricing formula which they adapt by fudging and changing the tails and skewness by varying one parameter, the standard deviation of a Gaussian. Such formula is popularly called "Black-Scholes-Merton" owing to an attributed eponymous discovery (though changing the standard deviation parameter is in contradiction with it). However, we have historical evidence that: (1) the said Black, Scholes and Merton did not invent any formula, just found an argument to make a well known (and used) formula compatible with the economics establishment, by removing the "risk" parameter through "dynamic hedging", (2) option traders use (and evidently have used since 1902) sophisticated heuristics and tricks more compatible with the previous versions of the formula of Louis Bachelier and Edward O. Thorp (that allow a broad choice of probability distributions) and removed the risk parameter using put-call parity, (3) option traders did not use the Black-Scholes-Merton formula or similar formulas after 1973 but continued their bottom-up heuristics more robust to the high impact rare event. The paper draws on historical trading methods and 19th and early 20th century references ignored by the finance literature. It is time to stop using the wrong designation for option pricing.

For about hundred years, modern physics has not been able to build a bridge between quantum mechanics (QM) and gravity. However, a solution may be found here. We present our quantum gravity theory, which is rooted in indivisible particles where matter and gravity are related to collisions and can be described by collision-space-time. In this paper, we also show that we can formulate a quantum wave equation rooted in collision-space-time, which is equivalent to mass and energy. The beauty of our theory is that most of the main equations that currently exist in physics are, in general, not changed in terms of predictions and what we could call structural form, except at the Planck scale. The Planck scale is directly linked to gravity, which has obviously already been detected, and gravity is actually a Lorentz symmetry as well as a form of Heisenberg uncertainty break down at the Planck scale. Our theory gives a dramatic simplification of many physics formulas without altering the output predictions, except at the Planck scale, and this new formulation gives us a unified theory. The relativistic wave equation, the relativistic energy momentum relation, and Minkowski space can all be represented by simpler equations when we understand mass at a deeper level. This is not attained at a cost, but rather a reflection of the benefit in having gravity and QM unified under the same theory.

In this paper we show how it is possible to measure the Planck length through a series of different methods. One of these measurements is totally independent of big G, but moving from the theoretical realm to the empirical realm would require particle accelerators far more powerful than the ones that we have today. However, a Cavendish-style experiment can also be performed to find the Planck length with no knowledge of the value of big G. Furthermore, the Cavendish style set-up gives half of the relative measurement error in the Planck length compared to the measurement error in big G.

No abstract

In this paper, we will revisit the derivation of Heisenberg's uncertainty principle. We will see how the Heisenberg principle collapses at the Planck scale by introducing a minor modification. The beauty of our suggested modification is that it does not change the main equations in quantum mechanics; it only gives them a Planck scale limit where uncertainty collapses. We suspect that Einstein could have been right after all, when he stated, ``God does not throw dice." His now-famous saying was an expression of his skepticism towards the concept that quantum randomness could be the ruling force, even at the deepest levels of reality. Here we will explore the quantum realm with a fresh perspective, by re-deriving the Heisenberg principle in relation to the Planck scale. Our modified theory indicates that renormalization is no longer needed. Further, Bell's Inequality no longer holds, as the breakdown of Heisenberg's uncertainty principle at the Planck scale opens up the possibility for hidden variable theories. The theory also suggests that the superposition principle collapses at the Planck scale. Further, we show how this idea leads to an upper boundary on uncertainty, in addition to the lower boundary. These upper and lower boundaries are identical for the Planck mass particle; in fact, they are zero, and this highlights the truly unique nature of the Planck mass particle.