On special relativity and matter waves.

I haven't really figured out why Einstein's E = mc^2 is probably the most well know physics equation. This equation, widely know as Mass–energy equivalence has been popularized so well that it can break down cultural and social barriers. Even if a person has no true interest on physics or sciences in general it is likely that he or she recognizes E = mc^2 formula and sees it as reference to something ingenious.

Despite of being as recognizable as Mona Lisa, mass-energy equivalence doesn't open up as a concept to most of the people even though the principle in it is pretty straightforward. Mass is a form energy. There you have it. According to Einstein, it is possible to transform energy into mass and annihilate mass into energy. So it's not like even physicists would need it in every calculation they make.

λ = h/p equation isn't considered common knowledge in a same manner that mass-energy equivalence is. Maybe it's because it has that strange letter λ- Lambda in it. Whatever the reason is, this second equation, know as The de Broglie Equation, could be arguably as momentous as Einsten's.

de Broglie's equantion main principle is that particles have wavelength λ. Greater the momentum, shorter the wave. This was quite revolutionary hypothesis when first proposed in 1924. Apparently there was not any proof of particles having wave properties at the time, but de Broglie had intuitive thought that if light has both wave and particle properties, electrons must have them both too. He came up with his equation which he published in his thesis and his hypothesis was later proven to be correct.

Why aren't there waves everywhere?

I don't know the rules of softball, but the ball never flew as a wave during
the time I observed game in Central Park, New York 

So de Broglie thought matter are waves and Einstein thought mass is a form energy. How this sum up together? Classical particles are far more difficult to model, as they aren't well located lumps anymore. Instead, particles with mass are spread out in space like waves in ocean since mass is form of energy. Really crazy part is that mass moves as a wave in a vacuum. So matter is like waves without ocean.

This of course conflicts with everyday life we all experience. We don't see billiard balls (or softballs) move like quantum waves. They are simply too complex to act that way. It was for long thought that quantum rules only apply when we measure very small particles, like singular electron. Researchers have eventually succeeded to perform the double slit experiment with rather massive molecules, like fullerene. It seems that quantum rules don't apply in matter of size but rather on how well particle is isolated from other particles or in the case of molecules, also from itself since molecules have multiple atoms.

How small can you go?

In the course of scientific advances man has gained ability to look ever deeper and further. Fundamental idea that there will eventually be one smallest piece of matter which cannot be divided into smaller ones is astonishingly old. In matter of fact that idea is quite ancient. It dates back to c. 400 BCE and it was, if not invented, at least promoted by Greek philosopher Democritus and his mentor Leusippus. Of course much has changed in the way to pursuit the tiniest particles. Still one cannot but wonder how come people 2500 years ago already come up with same hypothesis that scientist today claim with the help of their modern equipment.

Nowadays scientist have named and categorized at least 25 "fundamental" sub-atomic particles some which, like protons, are already believed being composed of even smaller pieces called quarks. Higgs boson is the latest entry in this group of sub-atomic crew. And there's not clearly a stop for detecting and adding yet more particles.

Smallest theoretical length, so called Planck length is 10^-35 m and size of a electron is less than 10^-15 m. So theoretically even smaller sub-sub-atomic or sub-sub-sub-atomic structures are possible. However it is getting harder and harder to research anything smaller than what has already been found out because of the uncertainty principle. More accurate measurement changes the reality of particle-on-measure further.

Would you reproach?

When we focus our mind on the tiniest scale in the quantum world along comes the concept of probability. Our everyday life can be relatively well predicted because we can measure our clumsy movement by dividing it into smaller pieces and different forces. But eventually there will be a limit (no matter if it has been already reached or not!) that you cannot divide movement or matter into smaller components. Then the only thing that is certain is the probability. Some people find this idea troubling. But they really can't do anything about it, they just have to live with it. This probability is the fundamental description of nature when we look at the double-slit experiment or in puzzling quantum entanglement phenomena.

I have already written few thoughts on double-slit experiment, but haven't mentioned the concept of probability in it even thought it seems to be quite fundamental part of it and whole quantum mechanics. Quantum mechanics state that a particle is in a "Probability distribution" and cannot be located in any precise location before it has been measured. Einstein for example never accepted this and once famously said "God doesn't play with dice." Considering the fact that probability waves give precise accurate prediction in numerous test settings and explains many concepts like quantum tunneling I have to agree with him. God doesn't play with dice, god IS a dice.

Clip art examples of different shaped and colored gods... I mean dices.