Dork Scratchings

When learning Quantum Mechanics the rules can seem very abstract, and also very arbitrary.  The starting point is often taken to be the Schroedinger Equation, a deterministic equation describing the rate of change of an isolated system's state, and the Born Rule, which describes how that state gives rise to probabilities for each outcome when you interact with the system by making a measurement.  These two form the axioms of quantum mechanics from which everything else flows. These axioms seem incredibly arbitrary, which makes accepting them harder.  In this post I will show that you can, in fact, start with much more basic axioms and then derive both the Schroedinger Equation and the Born Rule from them.  What's more, we'll be able to show how collapse of the wavefunction  emerges  from these simpler axioms as a  subjective  phenomenon.  This then deals with the measurement problem, which is that collapse appears  to require us to arbit...

  October 2023, I took an extended break from work to travel around Nepal and India, with my wife Anna.  For me it was a once in a lifetime trip; for her it was a return to the a place she spent a significant part of her childhood - so it was a big thing.  However, having initially suggested the trip I was suddenly hit by a wave of guilt: I'd completely forgotten about my no-flying commitment.  I was in a dilemma - either break with my commitment or pull out of a trip that meant a lot to both of us. I hit upon a solution: Climeworks.  This is a Swiss company selling carbon credits using Direct Air Capture (DAC) technology.  The plants are based in Iceland so they have access to abundant zero-carbon geothermal energy to power the fans which suck in the air, and the process that mineralizes and buries the carbon.  But it was eye-wateringly expensive.  We needed to offset 5 tons of CO2 - the emissions of two passengers travelling from London and back...

Great Larson cartoon But I can't make out the joke Oic 

I was watching Nate Hagens' Wide Boundary News, part of The Great Simplification project, and was struck by a reference to Sunset, a prize winning Holstein cow who produced 51,000 lb of milk in one year. This led me to start wondering exactly what kind of resources need to be fed into the machine that has a cow like that at the top of its pyramid. In the past I might have spent an hour or two making back-of-fag-packet estimates, but AI has made me lazy: now I just ask Claude. This is what he/it came up with:  

I just read this fascinating book by Jean-Baptiste Fressoz .  The premise is that there has never been a transition from one energy source to another (e.g. wood -> coal, or coal -> oil) and that, by contrast, novel sources of energy have simply piled up on top of each other.  Worse still, each new form of energy - and also each new material - has simply enabled increased consumption of each other form of energy and form of material. The conclusion is stark, supporting renewables will not be enough to avert a climate catastrophe.  As the book says: it may be a necessary condition but it is not a sufficient one.  For me, the most interesting part of the book was this diagram, taken from a 1983 Environmental Protection Agency report titled "Can We Delay a Greenhouse Warming?"  which used an energy model developed by Oak Ridge Laboratories:   The graphic shows how different scenarios and policies affect the date at which +2C warming is breached.  Not...

Nearly two weeks into the US-Israeli war on Iran many commentators have drawn attention to the climate cost of war.  But whether it's the BBC's Climate Question  on Radio 4, or Covering Climate Now's Press Briefing , they all ignore the elephant in the room: the blockade of the Straits of Hormuz.  So, what is the effect on the climate of this blockade? Saving Lives at Sea I made a meme, plz share... How many lives are saved by stopping a single tanker?  Estimates of the number of climate deaths this century vary enormously, with some sources saying around 10 million and others many billions.  There are plenty of serious climate scientists who believe most lives on Earth are at risk.  But let's follow this study  which says "The number of caused deaths will likely lie between a tenth of a person and 10 people per 1,000 tons." A typical tanker carries 1,000,000 barrels of oil, which when burned will create 430,000 tons CO2.  If we treat all anthropo...

  I've been thinking a lot about the limits to growth recently.  If you look up the non-renewable resources that our economy depends on it quickly becomes apparent that all of them, whether they be fossil fuels or metals like copper , are somewhere between 30% and 70% exhausted.  And the exhausted part is invariably the easiest to get to.  However, it has only recently occurred to me that land is also a non-renewable resource:  they're not making any more of it.... Checking out Our World in Data  one can see that nearly 5 billion hectares are currently in use by humans.  That compares with a total available of 13 billion hectares, if you discount the ice covered land.  So, in fact land falls into the same 30-70% exhausted range as everything else. I downloaded the data and produced a smoothed graph of growth (%) vs year and found something interesting: growth grew more or less exponentially until about 1956 at which point it fell sharply to zero....

Ever since the blackout that affected much of Spain , I've been wondering how it's going to work when renewable power starts to approach 100% of the power supplied by the grid.  That blackout may have been caused by a number of different factors, but the forces of evil were quick to point out that one thing that  may  have caused it was that there was too much renewable energy in the grid at the time. Renewable energy such as solar comes naturally in DC whereas the grid supplies AC at 50Hz (in Europe anyway).  This means that before it can be fed into the grid it has to be passed through an "inverter" to turn it into AC.  This is typically done by phase-locking to the grid signal, which is fine until the supply approaches 100% renewable at which point the question becomes: but who is setting the frequency?  I'm not sure whether or not this really was an issue in Spanish blackout, but it's a reasonable question to ask. A pretty good answer was provided by a...

Here's an image you're probably familiar with: it's the BBC News website banner.  The space between "InDepth" and "UK" is reserved for quick links to the most important issues of the day, and right now it reads "Israel-Gaza war | War in Ukraine | Climate".  It's fair to assume that the highest priority issues are closer to the left, based on how frequently these issues end up in the headline article. So, I wondered, how has the priority - according to the BBC - of the biggest issues changed over time?  I decided to sample the website using the wayback machine , once per year from September 2020 to September 2025, and here's the result:   Over these 6 years the BBC News banner has had between 1 and 4 quick links.  And it seems to be a consistent feature that whenever a new story comes along that threatens fewer lives, it takes a higher priority position in the banner.  "Climate" didn't turn up until 2022, and when it did it...

I did a little embedded project recently.  Years ago I bought a binary coded decimal clock which no longer works, and I thought I could replace it with one I built myself.  (In reality this was simply an excuse to play with programming a Raspberry Pi Pico.) Broken BCD clock (left) and home grown replacement (right).  The LEDs are in 6 columns and represent time in hh:mm:ss format, with each decimal digit represented in binary. During the project I realised I needed to create a little Finite State Machine to enable setting of the time using the bootsel button.  So I searched around on the internet and found tens of different libraries, but each with its own drawbacks. Some required a wizard executable to auto-generate code which you then edit, which has the drawback that if you change the input to the wizard you then need to manually merge new auto-generated code with your changes.  Other libraries, had this strange thing where each state had its own "enter" and...

In my previous post  Building a tensegrity structure I implied that when the thread was pulled taut an icosahedron would form.  I didn't directly use the word "icosahedron" but I did claim that you needed to allow enough thread for a stick length to triangle edge ratio of $(1+\sqrt 5)/2$, which amounts to the same thing.

 My latest project   This turned out to be a bit more fiddly than I expected.  This is partly because I set myself the goal of building it using a single piece of string and it wasn't entirely obvious how to do that without missing or repeating some edges.  Here are my tips:   1. Cut 6 pieces of bamboo Obviously these should all be the same length.  Hollow them out before going any further. 2. Measure out the thread The thread will pass through each bamboo 4 times, plus there are 24 edges between bamboo ends.  The bamboo sticks are $(1+\sqrt 5)/2$$^{[\text{see footnote}]}$ times the length of the edges (i.e. the golden ratio!)  You will need a bit more than this to make it easier to tie the ends.  Place two marks on the thread with a pen to identify where the knot should fall.   3. Blue tack the bamboo pieces in place This means creating a ball of blue tack and attaching 3 parallel pairs of bamboo to it in such a way that each pair is at...

This is perhaps the greatest epiphany of my life.  The moment I realized how to neatly summarize my understanding of the science I was learning: Time does not exist. Of course, this is just an interpretation, and a personal one.  It may not be true but in it's defence I assert it is consistent with many physicists' view of the world (though they may put it a different way).  It may not even make sense to ask whether it is true or not: what does it mean to say that a thing we don't understand, and haven't clearly defined, doesn't exist.  But like a lot of ways of thinking about reality, the real question is: Is this helpful? The things we know exist in the world can be divided into two categories: those for which we have direct evidence, and those for which we have indirect evidence.  In the former category we have light, sound, touch, smell; in the latter planets, atoms, and waves.  Time also belongs to the latter category.  We think about the future w...

 

  Time series showing the decline of growth in advanced (or "fully grown"?) economies since the 1960s suggesting an end to growth within one generation.  Growth in developing economies increased enormously between 1990 and 2005 but is now showing the same trend towards zero as advanced economies suggesting the entire world is hitting the same resource limits.  This graph took me 10 minutes to plot using publicly available data, but the obvious conclusions for the feasibility of long term growth are beyond the imaginations of almost all political leaders today.  Are we in the midst of a societal-scale shared delusion? Which do you want first...? Let's start with the bad news.  The bad news is that growth in industrialized, high income economies has been falling for the last six decades and looks like it will reach zero sometime within a generation.  (That's assuming it hasn't already reached zero with the positive growth figures that countries report...

I'm still a bit obsessed with the GHZ experiment.  This is the one where you prepare a GHZ state $\lvert 000 \rangle + \lvert 111 \rangle$ and send one qubit to each of 3 protagonists: Alice, Bob, and Charlie.  (I will be ignoring shared normalizer constants throughout this post, as I find they don't add anything to the understanding.) If you do the maths it turns out that when all three choose to measure in the $\lvert + \rangle$, $\lvert - \rangle$ basis (shorthand for $\lvert 0 \rangle + \lvert 1\rangle$ and $\lvert 0 \rangle - \lvert 1\rangle$) then they are guarranteed to get a parity zero result.  On the other hand if only one measures in this basis and the other two measure in the $\lvert +i\rangle$, $\lvert -i\rangle$ basis (shorthand for $\lvert 0 \rangle + i\lvert 1\rangle$ and $\lvert 0 \rangle - i\lvert 1\rangle$) they are guarranteed to get a parity one result.  As I showed in an earlier post this appears to be incompatible with the outcomes being prede...

It has occurred to me that the cartoon I drew two days ago will appear to most people as absurd: Alice measures one half of an entangled pair and instantly splits into two versions of herself!  Bob measures the other half and also splits, but each Alice is paired with one of the Bobs in such a way that, should they meet later to discuss their results, everything remains consistent. Yet if you replace Alice and Bob with two qubits - to get a quantum circuit like the one below - no quantum computing expert would find this outcome absurd. The Einstein Podolsky Rosen experiment in circuit form with non-classical Alice and Bob Alice is qubit q0 and Bob is q3 .  Qubits q1 and q2 are entangled into the Bell state $(\lvert 01 \rangle + \lvert 10 \rangle)/\sqrt 2$ and then q1 is shared with Alice, and q2 with Bob.  In the standard (collapse-based, non-multiversal) description Alice and Bob measure q1 and q2 , collapse the q1q2 wavefunction, and find that one gets 0 while the...

I just read this article on phys.org which claimed to "resolve the paradox" that entanglement appears to imply faster than light communication.  I don't think it actually resolves the paradox, it just side steps it.  Here's how the argument goes (and I paraphrase): Alice and Bob share a pair of entangled qubits in a Bell state $\left( \lvert 01 \rangle + \lvert 10 \rangle \right)/\sqrt{2}$. When Alice measures hers it "collapses" the pair's state immediately even if Bob is a great distance away.  However, this does not imply faster than light communication because, although Alice now knows what Bob will measure, Bob does not know until he makes a measurement himself, or receives a message from Alice which can only travel at the speed of light. This argument misses the point somewhat.  If the state of both qubits changes instantly when Alice measures her qubit (e.g from $\left( \lvert 01 \rangle + \lvert 10 \rangle \right)/\sqrt{2}$ to $\lvert 01 \rangl...