Archimedes Would Have Known Better If He Could Count To A Million

Today is March 14th, or Pi Day because 3.14 is March 14th rendered in month.day date format. A very slightly better way to celebrate the ratio of a circle’s circumference to its diameter is July 22nd, or 22/7 written in day/month order, a fractional approximation of pi that’s been used for thousands of years and is a better fit than 3.14. Celebrating Pi Day on July 22nd also has the advantage of eschewing middle-endian date formatting.

But Pi Day is completely wrong. We should be celebrating Tau Day, to celebrate the ratio of the circumference to the radius instead of the diameter. That’s June 28th, or 6.283185…. Nonetheless, today is Pi Day and in the absence of something truly new and insightful — we’re still waiting for someone to implement a spigot algorithm in 6502 assembly, by the way — this is a fantastic opportunity to discuss something tangentially related to pi, the history of mathematics, and the idea that human knowledge builds upon itself in an immense genealogy stretching back to the beginning of history.

This is our Pi Day article, but instead of complaining about date formats, or Tau, we’re going to do something different. This is how you approximate pi with the Monte Carlo method, and how anyone who can count to a million can get a better approximation of one the fundamental constants of the Universe than Archimedes.

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Will the Real Schrodinger’s Cat Please Stand Up

The story of Schrodinger’s cat is well known, and one of quantum theory’s most popular phrases on the world stage. You can find his cat on t-shirts, bumper stickers, internet memes and the like. However, few know the origins of the cat, and how it came into being. I suspect many do not understand it beyond the “dead and alive at the same time” catchphrase as well. Not surprisingly, it was Einstein who was at the center of the idea behind Schrodinger’s cat. In a vibrant discussion between the two via letters across the Atlantic, Schrodinger echoed Einstein’s concerns with the following:

Contained in a steel chamber is a Geiger counter prepared with a tiny amount of uranium, so small that in the next hour it is just as probable to expect one atomic decay as none. An amplified relay provides that the first atomic decay shatters a small bottle of prussic acid. This and -cruelly- a cat is also trapped in the steel chamber. According to the wave function for the total system, after an hour, sit venia verbo [pardon my language], the living and dead cat are smeared out in equal measure.

This was the first mention of Schrodinger’s cat, and one would not be incorrect in stating that this paragraph from a letter was where the cat was born. However, the original idea behind the thought experiment was from Einstein and his loathing of the wording of the Einstein-Podolsky-Rosen (EPR) paper. He expressed his frustrations with Schrodinger with a few simple examples, who then catapulted it into his famous paradox . In this article we’re going to explore not so much the cat, but the meaning behind the thought experiment and what it is meant to convey, while keeping it simple enough for anyone to understand. So next time you see it on a t-shirt, you will be able to articulate the true meaning and know the real Schrodinger’s cat.

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The Quantum Eraser

Richard Feynmann noted more than once that complementarity is the central mystery that lies at the heart of quantum theory. Complementarity rules the world of the very small… the quantum world, and surmises that particles and waves are indistinguishable from one other. That they are one and the same. That it is nonsensical to think of something, or even try to visualize that something as an individual “particle” or a “wave.” That the particle/wave/whatever-you-want-to-call-it is in this sort of superposition, where it is neither particle nor wave. It is only the act of trying to measure what it is that disengages the cloaking device and the particle or wave nature is revealed. Look for a particle, and you’ll find a particle. Look for a wave instead, and instead you’ll find a wave.

Complementarity arises from the limits placed on measuring things in the quantum world with classical measuring devices. It turns out that when you try to measure things that are really really really small, some issues come up… some fundamental issues.  For instance, you can’t really know exactly where a sub-atomic particle is located in space. You can only know where it is within a certain probability, and this probability is distributed through space in the form of a wave. Understanding uncertainty in measurement is key to avoiding the disbelief that hits you when thinking about complementarity.

This article is a continuation of the one linked above. I shall pick up where I left off, in that everyone agrees that measurement on the quantum scale presents some big problems. However, not everyone agrees what these problems mean. Some, such as Albert Einstein, say that just because something cannot be measured doesn’t mean it’s not there. Others, including most mainstream physicists, say the opposite — that if something cannot be measured, it for all practical purposes is not there. We shall continue on our journey by using modern technology to peer into the murky world of complementarity. But first, a quick review.

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Fixing the Ampere: Redefining the SI Unit

We all know that it’s not the volts that kill you, it’s the amps. But exactly how many electrons per second are there in an amp? It turns out that nobody really knows. But according to a press release from the US National Institute of Standards and Technology (NIST), that’s all going to change in 2018.

The amp is a “metrological embarrassment” because it’s not defined in terms of any physical constants. Worse, it’s not even potentially measurable, being the “constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10–7 newton per meter of length.” You can’t just order a spool of infinite length and negligible cross-section wire and have it express shipped.

So to quantify the exact number of electrons per second in an amp, the folks at NIST need an electron counter. This device turns out to be a super-cooled, quantum mechanical gate that closes itself once an electron has passed through. Repeatedly re-opening one of these at gigahertz still provides around a picoamp. Current (tee-hee) research is focused on making practical devices that push a bit more juice. Even then, it’s likely that they’ll need to gang 100 of these gates to get even a single microamp. But when they do, they’ll know how many electrons per second have passed through to a few tens of parts per billion. Not too shabby.

We had no idea that the amp was indirectly defined, but now that we do, we’re looking forward to a better standard. Thanks, NIST!

Thanks [CBGB123B] for the tip!

Uncertainty – The Key to Quantum Weirdness

All these fifty years of conscious brooding have brought me no nearer to the answer to the question, ‘What are light quanta?’ Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken.

                       Albert Einstein, 1954

As 1926 was coming to a close, the physics world lauded Erwin Schrodinger and his wave mechanics. Schrodinger’s purely mathematical tool was being used to probe the internal structure of the atom and to provide predictable experimental outcomes. However, some deep questions still remained – primarily with the idea of discontinuous movements of the electron within a hydrogen atom. Niels Bohr, champion of and chief spokesperson for quantum theory, had developed a model of the atom that explained spectral lines. This model required an electron to move to a higher energy level when absorbing a photon, and releasing a photon when it moved to a lower energy level. The point of contention is how the electron was moving. This quantum jumping, as Bohr called it was said to be instantaneous. And this did not sit well with classical minded physicists, including Schrodinger.

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The Ultraviolet Catastrophe

As the light of the 20th century was peeking over the horizon, a young physicist by the name of Max Planck was taking to heart some career advice he had received while he attended Munich University in Germany. With the recent discovery of thermodynamics, there wasn’t much left in physics to know, or so his adviser thought. Hindsight is indeed 20/20.

It turns out that Planck was an expert at thermodynamics. Having mastered the subject gave him some leverage to use against a growing group of physicists known as atomists who were using statistical models along with so called ‘atoms’ to predict experimental outcomes. Atomists believed that matter was composed of discrete units. Planck believed the world was continuous and could not be divided into any type of discrete component. And he would draw the second law of thermodynamics from his holster and put this atom idea in the clay.

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Uses for Quantum Entanglement with Shanni Prutchi

For those of you that weren’t at the Hackaday SuperConference, it started off with a pretty intense talk that could have been tough for anyone to follow. However, [Shanni Prutchi] presented her talk on quantum entanglement of photons in a way that is both approachable, and leaves you with plenty of hints for further study. Check it out in the video below, and join us after the break for a rundown of what she covered in her presentation.

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