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Einstein’s General Theory of Relativity – The Revolutionary Idea That Changed Our Understanding of Reality

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I’ve chosen a biggie this week folks, Einstein’s General Theory of Relativity. And boy it really is a biggie! It would take volumes and volumes of books to take you through everything, and years and years of research and study for me to write it. So, I’m going to have a go and see if I can put together some kind of short comprehensive guide for you. Ready?

Imagine you’re standing on Earth, feeling gravity pull you toward the ground. For centuries, scientists believed gravity was an invisible force acting across space. Then, in 1915, Albert Einstein popped his two penneth in and proposed something that was truly astonishing. Einstein proposed that gravity isn’t really a force at all, and that instead, massive objects such as planets, stars, and galaxies actually bend the fabric of space and time itself, and what we experience as gravity is actually the result of moving through this curved spacetime.

In a flash, Einstein had overturned centuries of thinking and by doing so he gave humanity a completely new picture of reality.

Before General Relativity, Isaac Newton’s theory of gravity was king, and his equations successfully explained falling apples, planetary orbits, ocean tides, and the motion of the Moon.

However, for everything that Newton’s laws could explain, there were still some puzzles remaining. Newton’s explanation of gravity appeared to act instantly across vast distances, while Einstein’s Special Relativity showed that nothing can travel faster than light. There were also subtle discrepancies in Mercury’s orbit that Newton’s theory couldn’t fully explain, and Einstein believed there had to be a deeper explanation, and there was.

Einstein’s breakthrough began with a simple thought experiment.

Imagine you’re trapped inside a windowless lift (elevator to my American readers).

In one scenario, the lift (elevator) is sitting on Earth, and in another, it’s floating in deep space, but it is accelerating upward. In both cases, you feel pressed against the floor. But, without looking outside, you can’t tell which situation you’re in.

This observation became known as the Equivalence Principle, and that is gravity and acceleration are locally indistinguishable, and for Einstein, this was the clue that unlocked a completely new understanding of gravity.

This is where spacetime comes in, and it is so breathtaking in its simplicity it is mind blowing.

Einstein realised that space and time are not separate things, but instead, they form a single four-dimensional structure which he called spacetime.

Now then, you have to think of spacetime as the stage on which everything in the universe exists and moves. And, to do so, I’m going give you a classic analogy.

Imagine a giant trampoline stretched tight, and as it is stretched tight, it is flat. If you now place a bowling ball in the centre of the trampoline it creates a dip, and if you now roll a tennis ball nearby, its path curves as it rolls.

The tennis ball isn’t being directly pulled by the bowling ball, all it is doing is simply following the shape of the surface, and this is how planets move through spacetime that has been curved by stars and other massive objects.

I know it’s not perfect, but this analogy captures Einstein’s revolutionary insight that it is mass that changes the geometry of the universe.

So, to your first question, I know you have loads. How does gravity really work?

And the answer to this is when most people think about gravity, they imagine an invisible force pulling objects together, however, Einstein saw something completely different.

Here’s another simple analogy (there’s going to be a few of these, so stick with me).

Imagine it’s nighttime and you are driving along a mountain road. Although you keep the steering wheel pretty straight, the road curves left, looking from above, someone might reasonably think that an invisible force has pushed your car sideways when in reality, you’re simply following the shape of the road.

According to General Relativity, planets are doing exactly this, and the Earth isn’t being pulled around the Sun by a mysterious force, it is moving along the curved road of spacetime created by the Sun. The sun is the bowling ball on the trampoline, and the tennis ball is the Earth. Geddit? Of course you do!

Ok, let’s look how that applies to the whole of the cosmos.

At the heart of General Relativity is a set of mathematical relationships called the Einstein Field Equations, and physicists often summarise them this way, and again, it is incredibly brilliant in its simplicity.

Matter and energy tell spacetime how to curve, and curved spacetime tells matter how to move, and these equations connect the contents of the universe to the shape of the universe itself! Cool, huh!

These equations can describe everything from planetary motion to black holes and even the evolution of the cosmos.

And that neatly leads us on to the next question you are bursting to ask.

“If gravity isn’t a force, then why doesn’t the Earth fly away from the Sun?”

And for that answer we have another simple analogy.

Imagine you are throwing a ball. If you throw it gently it lands on the ground nearby to you, however, if you throw it harder, it travels further and if you were to throw it harder and fast enough, the Earth’s surface curves away beneath it as quickly as it falls. The ball keeps falling but never reaches the ground, and that is essentially what an orbit is.

Earth is constantly falling through curved spacetime around the Sun.

One of General Relativity’s strangest predictions is that time does not flow at the same rate everywhere, and near a massive object, time passes more slowly, and the further away, time passes more quickly.

OK, analogy number 3? 4? I’ve lost count already.

Imagine time as a river. Far from massive objects, the river flows quickly, and near a massive object, the current slows. Two people that have been travelling through different parts of the river can reunite and discover that different amounts of time have passed for them.

This isn’t science fiction; this is science fact, as GPS satellites must account for relativistic time effects to provide accurate navigation. To really delve into time, you should read The Order of Time by Carlo Rovelli. This book is a brilliantly understandable read, and you’ll have your head wrapped around time in no time. And it’s got Smurfs in it!

Something else General Relativity told us is that light can bend. Before Einstein, all the science nerds simply assumed that gravity only affected matter. General Relativity predicted that gravity affects light as well.

And to explain it, you guessed it, another analogy.

Imagine you are riding a bicycle along a painted line on the ground, you aren’t intentionally turning. You are simply following the path beneath you. Light behaves similarly. It travels along the straightest possible path through spacetime, and if spacetime itself is curved, the path of light appears bent. Observations of the famous solar eclipse of 1919 confirmed this prediction and also made Einstein world famous.

The bending of light creates one of astronomy’s most powerful tools, and that is gravitational lensing. This is where massive objects can bend light from distant galaxies and act like giant lenses.  If you hold a wine glass in front of a distant light, the image behind it appears stretched, distorted, or sometimes, even duplicated, and galaxies do the same thing to light, and astronomers use these natural lenses to study objects that would otherwise be too distant to see.

General Relativity also predicts objects so dense that spacetime becomes dramatically distorted, and, you’ve guessed it, as these are one of my favourites, it predicted black holes, and with them, their ever brilliantly baffling event horizons, which leads me to my next analogy, the river model of black holes.

Imagine a fish swimming upstream, and way ahead of it is a waterfall. While it is far away from the waterfall the little fishy can easily fight against the current, however, when it gets closer to the waterfall, the water moves faster, until eventually there is a point where the current exceeds the fish’s maximum swimming speed. Beyond that point, escape is impossible, and the little fishy is heading over. A black hole’s event horizon is similar. Beyond it, spacetime is being dragged inward so strongly that not even light can escape. But you know all this, I’ve written about it loads.

General Relativity also predicts that moving massive objects can create disturbances in spacetime itself and these are known as gravitational waves.

Drop a pebble into still water and waves spread outward in all directions. When massive objects such as black holes collide, they create ripples in spacetime that travel across the universe. And those clever scientists detected these waves directly in 2015, thus confirming another of Einstein’s remarkable predictions.

General Relativity has become the foundation of modern cosmology, and it helps explain the Big Bang, the expanding universe, the evolution of galaxies and the large-scale structure of the cosmos itself, and in many ways, modern astronomy is the story of applying Einstein’s theory to increasingly larger scales.

Unfortunately, Einstein’s theory, as brilliant as it is, isn’t perfect. Even though every major experimental test has supported General Relativity for more than a century, physicists know the theory is incomplete as it struggles to explain what happens at the centre of black holes, the earliest moments of the Big Bang, and how gravity works at quantum scales, that pesky teeny tiny stuff again, and finding a theory of quantum gravity remains one of the greatest challenges in science today.

If you remember only one thing about General Relativity, make sure it’s this

For more than 200 years, Isaac Newton’s theory of gravity successfully explained the motions of objects on Earth and the movements of the planets. In Newton’s view, gravity is a force that pulls objects toward one another. The Earth is pulled toward the Sun, the Moon is pulled toward the Earth, and an apple falls because the Earth exerts a gravitational force on it. This picture works remarkably well for most everyday situations and remains extremely useful today.

Einstein’s insight was way more radical.

According to General Relativity, gravity is not fundamentally a force at all. Instead, mass and energy change the geometry of the universe itself by curving spacetime. Planets, stars, galaxies, and even light move through this curved spacetime, following its natural paths. What we perceive as the force of gravity is actually the consequence of moving through a universe whose geometry has been distorted by matter and energy.

A useful way to picture the difference is to imagine a ball rolling across a landscape. Newton would describe the ball’s motion as being caused by forces acting upon it. Einstein would direct your attention to the shape of the landscape itself. If the ground is curved, sloped, or warped, the ball’s path changes naturally as it follows the terrain. In a similar way, planets orbit stars because they are moving through curved spacetime, not because an invisible force is reaching out and pulling them around.

This seemingly simple change in perspective transformed our understanding of the cosmos. From it emerged the prediction of black holes, the discovery of gravitational waves, the realisation that time can flow at different rates in different gravitational environments, and the modern picture of an expanding universe. More than a century after Einstein introduced his theory, it is still one of mankind’s greatest achievements, and it remains humanity’s best description of gravity and one of the most profound (I had to get that word in here somewhere) insights ever achieved in science.

And that my faithful readers, is Einstein’s Theory of General Relativity for you in a nutshell. For anyone who just wanted the 1905 Special Theory, it’s the short, sharp one about speed and simultaneity, no bendy trampolines required. You can pretend the last ten minutes didn’t happen, and, if you’re lucky, and you really want it, Special may get its own piece in a few weeks’ time.

E = mc² – The Tiny Equation That Changed the Universe

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Just a quick note before you start reading. This was supposed to be a quick hit for a midweek article, however, it actually took me bloody ages!! Surprisingly, it wasn’t just the maths that caused me issues, it was getting the damned equations into WordPress that made me swear profusely! In hindsight I should have rounded the speed of light to 300,000,000 m/s as most folk would do in an article of this nature. Me? No. I wanted to keep accuracy paramount and use the actual number which is 299,792,458 m/s. Anyway, it’s done now, so on with the article (I really hope you can make sense of it all despite the WordPress formatting).

For this week’s midweek article, just for you, my faithful few, I’m going to answer a question I’ve been sent. And that question is:

“Can you please explain E = mc²?”

And the answer to that question is:

Yes, I can. So, there we go. Question answered. Don’t forget to come back on Friday for this week’s full article on Einstein’s Theory of General Relativity.

Obviously, I’m joking. I wouldn’t leave you hanging like that. Here’s the actual answer, No, I can’t.

Sorry, still joking, I’m just trying to avoid doing the maths, you all know how much I hate doing maths, after all, I’ve only mentioned it a few times.

Ok, on to the real answer, what actually is E = mc² and what does it tell us?

Well, it may be the most famous equation ever written, yet its message is surprisingly simple, and that is, matter and energy are different forms of the same thing.

So, without further ado, let’s meet the world’s most famous equation. Ready? Of course you are!

In 1905, Albert Einstein published his Special Theory of Relativity, a paper that changed physics forever, and a few months later he published a follow up paper building on it, and in that paper was:

E=mc2E = mc^2

We’ve all heard it, the majority know it’s calculation, but not everybody actually knows what it really means, and that is, this beautiful little equation tells us that every object around us contains an enormous amount of stored energy.

Your phone. Your coffee mug. A sugar cube. The classic physics paperclip. Even you. Everything with mass contains energy.

Right then, let’s break it down.

E=mc2E = mc^2

E = Energy (joules). m = Mass (kilograms). c = Speed of Light

The speed of light is defined exactly as: c = 299,792,458 m/s

But, the equation doesn’t just use c, it uses c².

And that means:

c2=c×cc^2 = c \times c

So, if we substitute the exact value (it’s maths time) we get:

c2=299,792,458×299,792,458c^2 = 299{,}792{,}458 \times 299{,}792{,}458

=89,875,517,873,681,764= 89{,}875{,}517{,}873{,}681{,}764

Or

8.9875517873681764×10168.9875517873681764 \times 10^{16}

That massive number is nearly 90 quadrillion, folks, that is 90,000,000,000,000,000. A seriously big number. And it is this gigantic number that is the reason even a tiny amount of matter contains an astonishingly humungous amount of energy.

To work it out, just imagine a single sugar cube sitting beside a cup of tea, and let’s assume a typical sugar cube has a mass of 4 grams

First let’s convert grams to kilograms by dividing it by 1,000: 4 grams = 0.004kg

Next were going to use Einstein’s equation: E = mc²

Now we are going to substitute the variables with the actual values:

E=(0.004)(89,875,517,873,681,764)E = (0.004)(89{,}875{,}517{,}873{,}681{,}764)

And in joules that calculation gives us:

E=359,502,071,494,727.056E = 359{,}502{,}071{,}494{,}727.056

Or as a simple equation we have

E≈3.60×1014 JE \approx 3.60 \times 10^{14}\ \text{J}

So, the answer is, one ordinary sugar cube contains 359,502,071,494,727 joules of energy in its mass.

It may not look that remarkable, but Einstein’s equation reveals that our tiny 4-gram sugar cube contains an almost unimaginable amount of hidden energy.

Which leads us straight into your next question.  If a sugar cube really has that much energy stored in it, why doesn’t it explode?

And that is because, fortunately, ordinary matter doesn’t automatically convert itself into energy, and most of the energy remains locked inside the matter. Only special processes can release some of it and they are nuclear fusion inside stars, nuclear fission in reactors, and matter meeting antimatter. It is only in these situations that a tiny amount of mass is converted into energy, and you get a big bang.

A sugar cube does release energy when you eat it, and that energy is chemical energy, and it comes from rearranging atoms. Einstein’s equation is talking about something much deeper, and that is the energy contained in the mass itself. The energy your body gets from eating sugar is only a tiny fraction of the sugar cube’s total mass-energy.

Here’s a fun fact for you, if all the mass of a sugar cube could somehow be converted directly into energy, the result would be vastly greater than the energy released by burning or digesting it, and that is because chemical reactions use only a teeny tiny part of the energy hidden inside matter.

The Sun also runs on Einstein’s equation, as deep inside it, hydrogen nuclei fuse together to form helium, although the helium produced has slightly less mass than the hydrogen that went into making it, which leads to another question. Where did the missing mass go? And you’ve guessed it, Einstein’s equation gives us the answer. The missing mass became energy and this energy eventually leaves the Sun as heat and light.

That’s not all folks, there is an even bigger equation as the famous equation is actually a simplified version of a more complete relationship from Special Relativity, and that equation is:

E2=(mc2)2+(pc)2E^2 = (mc^2)^2 + (pc)^2

E = total energy, m = rest mass, p = momentum, and c = speed of light

This equation works for everything in the universe, whether moving or stationary. Imagine our sugar cube sitting motionless on a saucer, beside a cup of tea. OK, because it isn’t moving:

p=0p = 0

Next, we’ll substitute into the full equation:

E2=(mc2)2+(0)2E^2 = (mc^2)^2 + (0)^2

E2=(mc2)2E^2 = (mc^2)^2

And then we’ll take the square root of both sides which gives us…

E=mc2E=mc^2

And there it is, folks, the world’s most famous equation is simply a special case for an object that is not moving.

Ah, but what happen if you pick up the sugar cube and throw it across the room? Quite why you would do that, I don’t know, maybe it upset you or you have saccharophobia, an irrational fear of sugar cubes.

The sugar cube now has momentum, so:

p>0p > 0

Then the full equation becomes:

E2=(mc2)2+(pc)2E^2 = (mc^2)^2 + (pc)^2

Its total energy now includes energy from its mass and energy from its motion, and the faster it moves, the larger the momentum term becomes.

What about Light? I hear you say. Well, light is special because it has zero rest mass.

m=0m = 0

And substituting into the full equation gives us:

E2=(pc)2E^2 = (pc)^2

And taking the square root gives us:

E=pcE=pc

And remarkably, the result tells us that light carries energy even though it has no rest mass. And that means that every Wi-Fi signal, radio broadcast, mobile phone signal, microwave, X-ray, and ray of sunlight carries energy because of this relationship.

Before Einstein, mass and energy were thought to be completely different things, but, after Einstein, physicists realised they are simply different forms of the same physical reality. Matter can become energy. Energy can become matter. The universe constantly converts one into the other. And all of that profound insight can be demonstrated with something as ordinary as a sugar cube. How about that!

So to summarise:

We have the famous equation:

E=mc2E=mc^2

The full equation is:

E2=(mc2)2+(pc)2E^2 = (mc^2)^2 + (pc)^2

The exact speed of light is

c=299,792,458 m/sc = 299{,}792{,}458\ \text{m/s}

And the speed of light squared is:

c2=89,875,517,873,681,764c^2 = 89{,}875{,}517{,}873{,}681{,}764

Which means the mass and energy of our single sugar cube is:

m=0.004kgm=0.004 kg

E=359,502,071,494,727 JE = 359{,}502{,}071{,}494{,}727\ \text{J}

Which tells us that our ordinary cube of sugary sweetness contains an extraordinary amount of energy, and that’s because every kilogram of matter is multiplied by one of the largest important numbers in nature:

89,875,517,873,681,76489,875,517,873,681,764

And that astonishing connection between matter, energy, stars, light, and the universe is captured in just five symbols, which is perhaps the most famous and most powerful equation that has ever been written.

E=mc2E=mc^2

Entropy, Thermodynamics & Black Holes – The Article I Promised You!

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Hello again my faithful few, it is time, to discover the hidden rules that govern everything from your morning cup of tea to the edge of the universe. Are you ready? Of course you are!

Did you know, the universe has a favourite direction?

If you place a hot cup of tea on a table and it cools, if you drop an ice cube into a drink and it melts,  and if you spray air freshener into a room and it spreads out, none of these events require any effort, they just happen naturally.

Yet you’ve never seen the reverse occur on its own, have you? Cold tea becoming hot, melted ice spontaneously reforming, or air freshener spray gathering back in to the can.

There’s a reason for this, which lies in one of the deepest principles of nature, and that is, you’ve guessed it, the clue is in the title, it is entropy. A subject I love so much, it gets bolded.

Entropy is the central idea of thermodynamics, the branch of physics that governs energy, heat, and work, along with the direction of physical processes.

And what’s remarkable is, entropy doesn’t just influence everyday events, it plays a crucial role in understanding stars, galaxies, time itself, and even, as I’ve touched on in a previous article or three, black holes.

And now, my faithful readers, I am going to attempt to explain the science of energy without writing a full-blown scientific paper, or a book. Are you ready? Here goes!

Now then. Thermodynamics began during the Industrial Revolution as scientists attempted to build better steam engines, and as is usual when building these types of engineering feats, what they discovered was far more important.

The same laws governing steam engines also govern chemical reactions, batteries, human metabolism, planetary atmospheres, nuclear fusion in stars, black holes, and the evolution of the universe itself.

Thermodynamics became the universal rulebook of energy.

OK. There are four laws of thermodynamics. The first is the Zeroth Law. Now, this law was established by Robert H. Fowler in the 1930s quite some time after the other three laws were established, which is why it isn’t the first law. And it’s a simple one.

If object A is in thermal equilibrium with B, and B is in equilibrium with C, then A and C are in equilibrium with each other. Simples, right? Told you it was. And as simple as this sounds this law allows temperature to be measured. Without it thermometers couldn’t exist.

Then we get the First Law.

The First Law states that energy cannot be created or destroyed, energy only changes form, chemical energy becomes motion, motion becomes electricity, electricity becomes light. However, the total amount of energy remains unchanged.

After the first law, unsurprisingly we get the Second Law

The Second Law is the famous one, you often hear about in the movies, or albums by Muse, and is where entropy enters the story.

The Second Law states that the entropy of an isolated system never decreases. While entropy may remain constant in an ideal reversible process, it naturally tends to increase, and it is this law that explains why so many processes happen in one direction only.

Next? You’ve guessed it, we have the Third Law.

And that is, as temperature approaches absolute zero, entropy approaches its minimum possible value.

So, that takes us to the first question, what is entropy?

People often hear entropy described as a measure of disorder, and as useful as that description is, it’s incomplete.

There is a deeper meaning, and that is, entropy measures the number of possible microscopic arrangements of a system. Physicists call these arrangements microstates. Which, put simply, means the more possible ways something can exist while appearing the same overall, the higher it’s entropy.

Think of it like a jigsaw puzzle of an idyllic country cottage, surrounded by blue sky with fluffy clouds, a cute picket fence and dozens of flowers growing in the garden. One arrangement produces the completed image, whereas millions of arrangements produce a random mess. Nature overwhelmingly favours the states that are statistically more likely. And that tendency is entropy.

Still with me? Good. Let’s have a look at why ice melts. Ice contains water molecules arranged in an organised crystal structure and when ice melts, those molecules gain freedom. They can occupy vastly more possible arrangements which means the liquid state therefore possesses higher entropy than the solid state. Nature generally moves toward states with more possible configurations.

Next, we have one of physics’ greatest mysteries, the arrow of time, that is, why time only moves forward.

The fundamental equations of physics often work equally well forward or backward, yet reality doesn’t. Glass shatters, eggs break, and people age etc. We never witness these events naturally reversing themselves, and it’s entropy that provides us with the explanation.

As systems evolve, they overwhelmingly move from less probable states to more probable ones, and this increase in entropy creates the direction we perceive as the flow of time.

In the nineteenth century, Ludwig Boltzmann had an incredible insight. He had connected entropy to probability with one famous equation:

𝐒=𝐤ln⁡𝛀\mathbf{S = k \ln \Omega}

Where: S = Entropy, k = Boltzmann’s constant, and  Ω = the number of possible microstates. This equation links the visible world to the invisible world of atoms and molecules, and to many physicists (and amateurs like me), it is considered one of the most beautiful equations ever discovered.

Next, we’ll take a look at why perfect engines can’t exist

Suppose engineers build the ultimate engine, every bit of heat becomes useful work. There’s no waste, and no losses.

Thermodynamics says this is impossible. The Second Law requires that some energy inevitably becomes unavailable for useful work and is released as waste heat, so therefore, no heat engine can ever achieve 100% efficiency. Nature always demands an entropy bill.

Let’s have a look at one of my favourite examples, Black Holes, the very first article I wrote for this blog. Black holes changed everything as for much of the twentieth century, physicists believed black holes were simple objects. They appeared to have, no temperature, no entropy, and no internal complexity, and this, my friends, created an enormous problem.

Imagine throwing a book into a black hole. The book contains information and the information has entropy. If the black hole were to simply swallow everything and hide it forever, entropy would seem to disappear from the universe, and this would  violate the Second Law. That means, somewhere, something was wrong.

In the early 1970s, physicist Jacob Bekenstein had a revolutionary idea and  proposed, what at the time was, a shocking solution. He suggested that black holes themselves possess entropy.

At first, the idea seemed absurd.  How could an object that appears completely black have entropy?

Bekenstein, however, had a realisation, and that was entropy had to be related to the surface area of the black hole’s event horizon. In effect, the horizon was storing information about everything that had fallen inside. And this was one of the most important insights in modern theoretical physics.

Soon afterward, our favourite physicist, Stephen Hawking, made an even more astonishing discovery. Using quantum mechanics, Hawking showed us that black holes are not truly black. They emit tiny amounts of thermal radiation, now known as: Hawking Radiation. Regular readers will  know all about Hawking radiation, I wrote about it a couple of weeks ago, remember?

And this implied something absolutely astonishing. If black holes emit thermal radiation, they possess temperature, entropy, and thermodynamic behaviour. Black holes were no longer just gravitational objects. They were thermodynamic objects. And in some sense, they were giant cosmic heat engines.

Let’s move on to the entropy of a black hole. One of the strangest discoveries in physics is that a black hole’s entropy is proportional not to its volume, but to the area of its event horizon, and this was completely unexpected, as this meant that for ordinary objects, more volume means more storage capacity. Whereas for black holes, more surface area means more entropy. And this relationship became known as the Bekenstein-Hawking Entropy Formula, and it suggests that information about a three-dimensional region may somehow be encoded on a two-dimensional surface. This idea later inspired the famous Holographic Principle, one of the most profound concepts in modern theoretical physics, but sorry folks, once again that isn’t for now, that’ll have to be another article (which luckily for you I am working on, so it won’t be long).

What was discovered was black holes are entropy monsters. The entropy contained within a black hole is enormous. In fact, a black hole possesses vastly more entropy than an ordinary star made from the same amount of matter.

When a star collapses into a black hole, entropy increases dramatically, which means black hole formation actually satisfies the Second Law beautifully.

Far from violating entropy, black holes may represent some of the highest-entropy objects in the universe, which is why physicists sometimes describe them as the ultimate entropy engines.

And with that, it was time for another mystery to emerge from the shadows, The Information Paradox.

If Hawking Radiation causes black holes to slowly evaporate, what happens to the information that fell into them? There appears to be three possibilities to answer that question. Either information is destroyed, it escapes somehow, or, more likely, our understanding of physics is incomplete. This became known as the Black Hole Information Paradox, and it remains one of the greatest unsolved problems in physics. Entire fields of theoretical research have grown from attempts to solve it.

Today, many cosmologists believe the universe began in an extraordinarily low-entropy state and that this may govern the fate of the universe. Since then, entropy has steadily increased. Stars burn hydrogen, galaxies evolve, black holes grow, and entropy rises.

Far in the future, black holes may dominate the universe, and even they will eventually evaporate through Hawking Radiation. After unimaginable lengths of time, the cosmos may approach a state of maximum entropy known as Heat Death. This is standard cosmology, and in this state, all the stars are gone, temperature differences completely vanish, any useful work is impossible, and although energy remains, it is hopelessly spread out to be of any use to anything. The universe doesn’t run out of energy, but it does run out of opportunities to use that energy.

So, at the end of the day, thermodynamics began with steam engines, and it ended up explaining reality itself! Which again, as far as I’m concerned, absolutely boggles the mind!

To put it another way, entropy tells us why my favourite Assam tea cools, why stars shine, why time moves forwards, why engines have limits, why life can exist, and why black holes may hold the key to unifying gravity and quantum mechanics.

If the First Law says energy can never be destroyed, then the Second Law says energy becomes increasingly dispersed and increasingly difficult to use.

And nowhere is that truth more dramatic than in a black hole, where gravity, quantum physics, information, and entropy collide at the edge of the known universe.

Entropy is not merely a property of matter. It may be the accounting system for the whole of reality itself!

What Cost The Night Sky? How Three Unrelated News Stories Ruined My Sleep

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There’s a particular kind of headache that comes from reading three unrelated news stories in the same week and realising they’re not unrelated at all, and this has been one of those weeks. In truth, this article exists because I couldn’t quite let those stories go, and I’ve broken my own rule of not writing at the weekend because of it. The articles had been rattling around in my head for while, keeping me awake last night, and before I realised what I was doing, this morning, I was deep into research papers, budget tables, news archives and LinkedIn posts, trying to work out whether the numbers being quoted actually added up. The deeper I dug, the stranger the picture became. What follows is the result of several hours of increasingly obsessive fact-checking, prompted in equal measure by frustration at the money governments somehow always find for wars and by the determination of certain tech billionaires to spend vast fortunes attempting to turn themselves into the first Bond villain.

Let’s start with the sky itself, because that’s where this began, with 1.7 million satellites versus the whole of astronomy. The European Southern Observatory has just done something nobody had bothered to do properly before: modelled what happens to astronomy if everything currently proposed for orbit actually gets launched.

The number ESO astronomer Olivier Hainaut arrived at for “acceptable” damage, the point at which satellite interference stays roughly comparable to routine equipment failures is 100,000 faint, naked-eye-invisible satellites.

The number currently on the table, across every proposed constellation from every operator, is over 1.7 million.

That’s not a rounding error. That’s a different universe of consequence, and the specifics are grim: ESO’s Very Large Telescope could lose up to 28% of its field of view to Starlink alone. The Vera Rubin Observatory, arguably the most ambitious survey telescope ever built, stands to lose hours of observing time every single night. And then there’s Reflect Orbital, a company literally planning to put mirrors in orbit to beam sunlight onto Earth after dark, with up to 50,000 of them proposed by 2035. Hainaut’s modelling suggests they could make the night sky itself four times brighter, even from a light-polluted city like Munich.

We are, with a straight face, discussing whether to switch the night sky off. Not metaphorically, actually switch it off!

Here’s where it stops being an abstract problem for astronomers in Chile and starts being a very local one. Meanwhile at home, the same week this ESO analysis landed, the Royal Astronomical Society reported that the UK’s Science and Technology Facilities Council is withdrawing all funding for e-MERLIN, the network of radio telescopes that includes the Lovell Telescope at Jodrell Bank. Jodrell Bank. The place that tracked Sputnik. The place that’s been quietly doing world-class radio astronomy since before most of us were born. It’s now at genuine risk of closure.

That’s not the whole of it, either. The RAS reported the UK is withdrawing from the James Clerk Maxwell Telescope entirely, cutting 20% from the Square Kilometre Array Regional Centre, cutting 20% from the UK’s own contribution to Vera Rubin, yes, the same observatory the satellites threaten to steal hours from, and cutting 40% from the BISON solar monitoring network.

So: the instrument is being switched off from above, and the people who’d use it are being defunded from within, in the same month. If you set out deliberately to sabotage a field of science, it’s hard to imagine a more efficient one-two.

Now for the number that actually made me sit down and do the maths, and look at what we are proposing to spend it on instead, because I’d heard a vague comparison somewhere and wanted to check whether it held up. It doesn’t hold up quite the way I’d remembered. It’s a lot more startling than that.

The US-Israel war on Iran that began in February 2026, Operation Epic Fury, to give it its official name, has, according to the Pentagon’s own figures given to the Senate on 21 July 2026, cost $37.5 billion so far. That’s up from $29 billion in May and $25 billion in April; the number has been climbing by roughly a billion dollars a week. Defence Secretary Pete Hegseth is now asking Congress for up to $70 billion more in emergency funding, as part of an $87.6 billion supplemental request. If Congress approves that request, the total cost attributable to the conflict could exceed $100 billion.

Here’s the part that stopped me. NASA doesn’t actually cost all that much by federal-government standards. Its annual budget has been remarkably steady at around $24-25 billion a year. The $37.5bn already spent on the Iran war is therefore equivalent to roughly eighteen months of NASA: every mission, every telescope, every ongoing operation, every payroll. Already spent, already gone, no projections involved.

Add the funding now being requested and the comparison grows to roughly four years and four months of the entire US civilian space programme. Say it slowly: four-and-a-bit years of the entire United States space programme, potentially gone in five months of a war that hasn’t produced an observatory, a scientific instrument, or a single piece of usable knowledge about the universe we live in. But hey, that’s OK, it has put the cost of living through the roof.

The arithmetic is straightforward. Add together 2026 and roughly half of 2025 and you reach the equivalent of the $37.5bn already spent on the war. Continue through 2024, 2023 and part of 2022 and the total reaches roughly $107.5bn. Same source data, same calculation, just expressed in time rather than dollars.

I’m not usually one to get on my soapbox, and I do try not to be the “billionaires bad guy,” mostly because it’s boring and it’s usually not that specific a complaint. But specificity is exactly what we have here. We’re not talking about an abstract injustice, we’re talking about a precise, sourced, comparable set of numbers. A dark sky and a functioning radio telescope at Jodrell Bank, for the price of what a war spends in a matter of weeks. Actual, unglamorous, patient scientific research, the kind that doesn’t make anyone rich, doesn’t come with a rocket launch livestream, and doesn’t get you invited on a podcast, going begging for a fraction of a fraction of what gets found overnight for other purposes.

If there’s a genuine, defensible case for where the enormous fortunes of the “let’s conquer space” tech-billionaire set should go, it’s here: into keeping Jodrell Bank’s lights on, not into another few hundred thousand satellites and orbital mirrors marketed as innovation. And if there’s a case for where a nation’s money should go, the maths above makes it for me. NASA gave us the Moon landings, Hubble, and forty years of thinking a bit harder about our place in the universe, and it did all of that on this budget. The full Iran war bill, once the current request lands, could run past four years and four months of that budget. But you don’t even need the bigger number to make the point, eighteen months of NASA, gone in five months of a war that won’t produce a single new fact about a single distant galaxy.

We can afford to look at the stars. We just keep choosing not to.



A quick note on the sources: The comparisons made in this article are drawn from publicly available sources, including ESO’s satellite-impact study, the Royal Astronomical Society’s reporting on UK astronomy funding, Pentagon cost figures reported by Reuters, the BBC and The Guardian, and NASA budget data. The references are included so readers can verify the numbers for themselves and see exactly how the conclusions in this article were reached. Regular readers will know I don’t usually include a source list like this, but because this article grew out of several hours of fact-checking and number-crunching, I thought it was only fair to show my working.

Sources:
ESO, “Beyond the limit”: one million satellites and mirrors in space pose grave threat to the night sky — the original ESO/Olivier Hainaut study
New Atlas, “1.7 million planned satellites to have ‘devastating’ impact on astronomy” — corroborates the 28% VLT field-of-view figure
Royal Astronomical Society, “Mass cuts and potential Jodrell Bank closure ‘devastating’ for astronomy”
Reuters, “War in Iran has cost the US $37.5 billion so far, Pentagon says” (21 July 2026)
Reuters, “US war in Iran has cost $29 billion so far, Pentagon says” (12 May 2026)
The Guardian, “Hegseth tells Senate war on Iran has so far cost $37.5bn” (21 July 2026)
BBC, “Iran war has cost US $37.5bn so far, Hegseth says” (21 July 2026)
Wikipedia, “Budget of NASA” (figures sourced to The Planetary Society’s historical NASA budget dataset)

Five Things That Sound Completely Made Up (But Are Annoyingly Real)

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Following on from last Friday’s article, one of the side effects of learning about Hawking radiation is discovering that modern physics is less a collection of facts and more a collection of increasingly unsettling revelations. Every time you think you’ve found the weirdest thing in the universe, physics quietly says, “Hold my equations.”

Here are five examples.

1. Right now, you are hotter than a black hole.

Let’s begin with an insult to black holes. And that is that right now you are hotter than most, if not maybe all, the black holes in the universe

Despite their reputation as the ultimate cosmic monsters, most black holes are astonishingly cold. Hawking showed us that black holes possess a temperature, and the larger the black hole, the colder it becomes. Therefore, a black hole with roughly the mass of our Sun would have a Hawking temperature of only a tiny fraction of a degree above absolute zero.

Meanwhile, you are sitting there at around 310 Kelvin (37°C), radiating infrared energy into your surroundings like a particularly self-satisfied space heater. So, thermally speaking, you’re absolutely thrashing a stellar-mass black hole. That is the same object capable of swallowing stars is, from a temperature perspective, a pathetic overachiever. The universe’s most feared gravitational predator is colder than deep space and vastly colder than the cup of tea that is slowly cooling beside me.

Hawking radiation revealed that black holes aren’t just gravitational objects. They’re thermodynamic objects. And thermodynamics has a wonderful habit of humiliating our intuitions.

2. Space ain’t empty.

The phrase “empty space” is one of the most misleading expressions in science. You got it, empty space is most definitely not empty.

What looks like nothing is actually a restless sea of quantum fields. According to quantum field theory, even a perfect vacuum contains fluctuations, tiny disturbances that constantly appear and disappear throughout space. This isn’t a rare occurrence, it’s happening everywhere, right now, around you, and, amazingly, it’s happening inside you! Between every atom in your body! Creepy and weird or what!!

In fact, Hawking radiation exists because black holes interact with these quantum fluctuations near their event horizons, and without the vacuum’s constant activity, Hawking’s discovery wouldn’t work. Which brings us back to that unsettling conclusion that nature doesn’t seem particularly fond of “nothing.”

Give the universe an empty stage, it’s competing with the best improv stand-up comedians. It immediately starts improvising itself!

3. Black holes ain’t that heavy.

If black holes are gravity taken to the extreme, neutron stars are gravity’s terrifying warm-up act. A teaspoon of neutron star material would weigh around a billion tonnes

Now then. A neutron star forms when a massive star dies and its core collapses so completely that atoms themselves are crushed. Electrons and protons merge into neutrons and produce an object roughly the size of a city but containing more mass than our Sun.

The result of this is density on a scale that defies common sense. A single teaspoon of neutron star material would weigh roughly a billion tonnes. That’s not a billion kilograms. That’s a billion tonnes. The sort of weight that makes the phrase “pick it up carefully” somewhat academic.

If you somehow brought that teaspoon to Earth, it wouldn’t politely sit on a kitchen counter and reality would very quickly become an SEP (you know what that is, you’ve read the Hitchhikers Guide to the Galaxy, it’s when Ford and Arthur arrive at lords on a battered sofa at the beginning of Life, the Universe, and Everything, Ford, clocking Slartibartfast’s ship out of the corner of his eye has to explain to Arthur there’s an SEP over there, try and catch it unawares by glimpsing it from the corner of your eye). Somebody else’s problem.

And at this point, every Futurama fan is now thinking exactly the same thing. “Wait… isn’t this basically Nibbler?” To which science’s answer is both inconvenient and hilarious, and the answer is, “yeah, sort of.”

Nibbler’s species, the Nibblonians, are famously absurdly dense. In one episode, Nibbler casually produces poo that weighs thousands of pounds, despite  Nibbler himself being roughly the size of an enthusiastic housecat. For once, science fiction wasn’t completely making things up. A neutron star packs so much mass into such a tiny volume that a teaspoonful would weigh about a billion tonnes. Compared to that, Nibbler is practically watching his figure.

Somewhere in the universe, one suspects Nibbler is looking at a neutron star, nodding approvingly, and muttering, “Hmm… at last… a sensible-sized snack.”

Physics occasionally likes to remind us that density can be every bit as terrifying as size. And occasionally, it reminds us that Futurama was alarmingly well-informed.

4. Whatever is out there in the blackness, we can’t see it.

If Hawking radiation teaches humility, dark matter delivers the knockout punch. And that is most of the universe appears to be made up of something we can’t actually see.

For centuries we assumed that stars, planets, gas clouds and galaxies were the universe. Then astronomers started measuring how galaxies rotate, and the numbers didn’t add up.

Galaxies should have flown apart. But, instead, something invisible appeared to be providing extra gravity and holding everything together. Astronomers now call this missing ingredient dark matter.

And here’s one of those questions, you, my lovely readers, like to ask. What is dark matter?

The awkward answer is we still have absolutely no idea what it is. What we can infer is its existence from its gravitational effects. That is, we see the way it influences galaxies and bends light, but direct detection remains elusive. The evidence, however, says something is there. We just don’t know what.

Imagine discovering that most of your house consists of invisible rooms nobody can enter. That’s roughly where modern cosmology currently stands with dark matter.

5. What the hell is light doing?

And finally, quantum mechanics saves its strangest trick for last, and that is reality refuses to make up its mind until you look.

This is one of my favourites, and you can easily amaze your family and friends with it. This is the famous double-slit experiment, and it works like this.

If you fire particles through two narrow openings and don’t measure which slit they pass through, the resulting pattern suggests each particle behaves as if it travelled through both slits simultaneously.

Measure which slit it used and the pattern changes completely and the wave-like behaviour disappears and suddenly the particle acts as though it picked a side all along.

This doesn’t mean consciousness magically creates reality, despite what countless internet memes may suggest. What it does mean is observation and measurement play an extraordinarily deep role in quantum mechanics.

The universe, at its most fundamental level, appears less interested in giving definite answers than we would like, and it behaves more like a collection of probabilities than a collection of certainties.

Which is either fascinating or deeply irritating, depending on how much sleep you’ve had.

As I said, you can amaze your friends with this one, and I first saw this demonstrated in a physics class in high school many, many moons ago. All you need is a laser pointer and a couple of perfectly parallel holes in a piece of cardboard. Copy and paste this into google and it will show you how:

Can you do your own double slit experiment with cardboard and a laser pointer?

Let’s link these all together.

At first glance, these facts seem unrelated.  One is about black holes. One is about empty space. One is about neutron stars. One is about dark matter. One is about quantum mechanics.

But they all point toward the same uncomfortable conclusion. Reality is under no obligation whatsoever to resemble common sense.

Black holes glow. Nothingness isn’t empty. Matter can become unimaginably dense. Most of the universe appears invisible. And particles sometimes behave as if they’ve forgotten how choosing works.

Hawking radiation sits right in the middle of this collection of cosmic absurdities. It exists because gravity, quantum mechanics, thermodynamics, and information theory all collide at the edge of a black hole.

And every time physicists dig deeper into that collision, the universe responds with another fact that sounds fake, isn’t fake, and somehow makes everything even stranger.

I tell ya. You simply cannot win with Physics. Sort one thing out and it throws a spanner in the works.

Some of you asked: “How Do You Know So Much?” And honestly? Obsession, mostly. And I won’t shut up.

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Hi folks, quick interim post.

A few of you have been asking how I know so much about this stuff and how I write my articles. So, I thought I’d give you a little insight.

Truth is, I don’t know everything, obviously no one does, and although I’m not a professional physicist, I am a very well-read and well-studied amateur.

I got into it via my father, whose interest started with radio propagation when he was in the RAF. He was always fascinated with physics and space travel, planetary science, and in particular, anything to do with the possibilities of FTL communications.

In 1996 I bought my first tiny house in a small market town a few miles south of Norwich, and my dad lived around the corner. At the time I was working shifts in a factory, a week of days a week of nights, then I would get a week off.

During this time and for most of the rest of the nineties, my dad was always over and making use of my computer knowledge and internet and he introduced me to sites, such as Warp Drive When, and Breakthrough Propulsion Physics and other fun stuff. And it wasn’t long before I was hooked, and within a couple of years my knowledge had far surpassed my father’s.

I’m a serial learner, once I get my teeth into a subject I don’t stop. It’s an obsessive trait I’ve had all my life, and only in recent years have I discovered it’s due to OCD/ADHD/Autism. Every one of us is on the spectrum somewhere, for me and my particular place on it, it has turned me into a compulsive seeker of knowledge.

As for the articles themselves, I bang out a rough draft of what I know on the subject matter I have chosen, and then I do my research. I know quite a lot of useless stuff, how it works, when it was first performed etc.  Once my draft is complete, I then start the research to make sure I’ve got the science correct, haven’t missed anything, and check timelines and people etc. I have a ton of books on the subjects I write about, and I have also subscribed to several scientific journals over the years and have those, Nature, Science, JBIS and a few others. And of course, I have the internet.

With the Quantum Teleportation article, I remember the experiments and I remember the time, and as I said in my article, I was genuinely so excited at the time I wouldn’t shut up about it. As I said above, once the draft is written, I then google it to make sure I’ve got all the awesome dudes who participated, as readers can be ruthless if I make a mistake, miss someone out, or get something wrong.

I then do a second phase over the whole thing and rewrite it before I re-read it out loud to myself, as this is the best way to pick up errors in the narration, typos, dodgy grammar etc.

Once I’m satisfied with it, I send the final draft to some very old friends from school, get them to read it and to see if it makes sense to them. With their feedback, I tweak the final article and it’s ready to go. This is also why some typos and wrong words still get through occasionally.

And that’s it. Physics is a subject that I love, and I love it so much, I want to share it with everybody else, so they will love it too.

When I resurrected this WordPress site after a four-year hiatus, I wanted to write about general sciency stuff. A bit of physics here, a bit of astronomy there, and a bit of paleoanthropology (my first love, don’t get me started on it, honestly, I won’t shut up for days!) in between.

As physics has consumed most of my adult life though, that is the direction my writings have naturally taken, and going forward, apart from the odd article in the other sections from time to time, physics is where it looks like it’s staying.

One last thing before you go. I love receiving your messages, and I have to admit I was a bit overwhelmed at how engaged some of you guys are, flattered at how many new readers are joining, and I’m genuinely thrilled at the messages I have received. Mostly via social media, which is why I added the email address to the home page.

If you want to get in touch to suggest future articles, point out mistakes, or even have a go (I’ve had a couple of those), please do. At present I am able to reply to everyone who gets in touch, unless they’re a complete arsehole.

Thank you for your time. You are AWESOME!

Mal
hello@malandally.co.uk

The Black Hole Glow: A Journey into Hawking Radiation

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Howdy my loyal readers. I’d like to start my saying thank you for the messages I’ve received asking if there is anything else they should know about black holes, and as they are a common theme through most of my articles, I’m going to indulge you with this one, on how Stephen Hawking discovered that the darkest objects in the universe may slowly evaporate away

By any reasonable definition, black holes should be simple. They pull things in. Nothing gets out. End of story. Yet in 1974, Stephen Hawking discovered something astonishing, and that was, black holes are not completely black. Given enough time, they glow, lose mass, shrink, and may eventually disappear altogether. That prediction is now known as Hawking radiation and remains one of the most profound (you’ve heard my ear worm already) insights in the history of physics.

This was a problem nobody expected, although I’m pretty sure Stephen Hawking had an inkling. You see, Black holes emerge naturally from Einstein’s theory of General Relativity. According to the classical picture, they are regions of space where gravity becomes so powerful that nothing, not even light, can escape once it crosses the event horizon. I know, I know, this is old news to you guys, I’ve stated it several times in previous articles.

For decades, physicists assumed black holes could only grow. Matter falls in. Energy falls in. Nothing comes out. Yeah? Then along came Stephen Hawking, and he combined Einstein’s gravity with quantum mechanics and arrived at an answer nobody could have anticipated. Black holes should emit a faint thermal glow. And this implication was extraordinary. Simply put, it meant that Black Holes could die.

As humoungously massive as it is, the Universe is never truly empty, and to understand Hawking radiation, we need to start with a strange feature of quantum mechanics, and that is what appears to be empty space isn’t actually empty.

According to quantum field theory, the vacuum of space is filled with fluctuating quantum fields. That is, teeny tiny disturbances constantly occur throughout space, causing particle-like excitations to briefly appear and disappear. Something that physicists call vacuum fluctuations.

OK. This bizarre activity actually happens everywhere in the universe, and this includes some of the most extreme environments surrounding a black hole.

And this takes us to the famous story that everyone learns. And that is, the most common explanation of Hawking radiation goes something like this:

Near the event horizon, a particle and antiparticle appear as a pair. Now then, normally they would immediately annihilate each other, but if the pair forms close enough to the event horizon, gravity can separate them before they reunite. Which means, one particle escapes into space, while the other one falls back into the black hole. To a distant observer, the escaping particle looks like radiation emitted by the black hole itself.

And this is because, the particle that falls inward, effectively carries negative energy relative to faraway observers, thus reducing the black hole’s mass, so over immense stretches of time the black hole slowly evaporates.

It is an absolutely, beautiful explanation.

But, and there’s always a but, you know this by know, surely guys, there’s one problem.

This isn’t really how Hawking derived the result.

To look at the deeper truth, among physicists, this particle-pair story is considered a useful mental picture, but is not the actual mathematics (maths again, I know. Regular readers already know my issue with maths). Anyway, Hawking’s original calculation used quantum field theory in curved spacetime. And that is, the essential idea is subtle. Different observers can disagree about what counts as empty space. A vacuum for one observer may appear to contain particles to another observer. But, near a black hole’s event horizon, spacetime is distorted so severely that these differing perspectives become physically important

When Hawking compared the state of quantum fields before and after a black hole forms, he discovered that an observer far away would detect radiation emerging from the black hole. So, in other words, Hawking radiation is less about particles popping out of nowhere, and more about the deep relationship between quantum fields, spacetime, and observation itself.

One of Hawking’s greatest discoveries was that black holes possess temperature, and the temperature of a black hole is inversely proportional to its mass, so the heavier the black hole, the colder it becomes, and this leads to a surprising consequence.

A supermassive black hole containing millions or billions of solar masses is incredibly cold, and a tiny black hole is extraordinarily hot, and this relationship means, small black holes radiate far more efficiently than large ones.

Because Hawking radiation carries energy away, the black hole loses mass, and this results in the slow death of a black hole.

As it shrinks, something curious happens. The black hole gets smaller as its temperature rises, then radiation increases which causes the mass to decrease even faster, and therefore the process accelerates.

If the theory is correct, then the final phase could end up with an enormous burst of energy, however, what exactly happens during those final moments remains unknown.

If you got the time to watch one, don’t expect to watch one evaporate as the evaporation process is incredibly slow. A black hole with roughly the mass of our Sun would survive for approximately 10⁶⁷ years, and this is one hell of a lot of zeros, and an incredibly long time. Trillions upon trillions upon trillions of times longer than the current age of the universe. Told you it was a long time.

And what’s more, supermassive black holes live even longer! Fortunately for the universe, black hole death is not an urgent problem, and nothing to worry about. Not for a verrrrrry longtime, at least!

Before Hawking’s discovery, physicist Jacob Bekenstein, argued that black holes should possess entropy, a measure of information content (remember my last article? You did read it, didn’t you?), and Hawking’s calculations confirmed this. In fact, black holes possess staggering amounts of entropy. Even more surprisingly, that entropy scales with the surface area of the event horizon rather than the black hole’s volume!

This observation helped inspire one of the deepest concepts in modern theoretical physics, and that is the Holographic Principle (you know this, I mentioned it way back in my original Black Hole article). This principle suggests that information contained within a region of space may be fully encoded on its boundary surface. It may sound like science fiction, but it has become one of the central ideas in attempts to understand quantum gravity

There’s a problem though, and that is the Information Paradox, and that is the question that changed theoretical physics forever.

Let us suppose a black hole swallows, my laptop I’m writing this article on, books, planets, stars, people, and entire civilizations and the specific details seem to vanish behind the event horizon.

If the black hole later evaporates and only thermal Hawking radiation remains, where did the information go? And that, is what has become known as the Black Hole Information Paradox.

The paradox appears to pit two fundamental pillars of physics against one another. Again, you know this, I’ve mentioned it before. It pits General Relativity against Quantum Mechanics. And this is because quantum theory normally forbids information destruction. What’s surprising is, Hawking’s original result seemed to imply exactly that.  And that is why many physicists consider this one of the deepest unresolved problems in science.

Modern research increasingly views Hawking radiation as an entanglement phenomenon. The radiation escaping from a black hole appears linked to degrees of freedom hidden behind the event horizon, and these quantum correlations may play a crucial role in preserving information.

This current line of thinking has driven decades of research involving Quantum information theory, string theory, holography (my old, now dead, dad was a big fan of holography), and quantum gravity, as well as many other areas.

Moving on, there is another remarkable discovery that Hawking radiation appears closely related to the Unruh Effect.

The what, I hear you say? Another topic for later? Sorry, yes (picture me doing an emoji grimace in apology as I type this), the Unruh Effect predicts that an accelerating observer can perceive empty space as containing thermal radiation. And that is what one observer sees as a vacuum, another observer sees as heat. Many physicists suspect both effects arise from the same underlying physics linking horizons, acceleration, and quantum fields.

Which brings us to the puzzles of tine scales. And that is, there is another challenge lurking inside Hawking’s theory.

When researchers trace Hawking radiation backward in time, some calculations appear to involve wavelengths smaller than the Planck scale (you know what that is), where known physics may stop working completely, and this issue is called the Trans-Planckian Problem. Which suggests we may need a deeper theory of nature to fully understand what is happening near the event horizon of a black hole.

Ah, who was that at the back, another question do I hear? Have we ever seen Hawking Radiation?

Surprisingly, the answer is…

No. We haven’t.

Despite being one of the most famous predictions in science, Hawking radiation has never been directly observed from a real astronomical black hole, and that is because the effect is simply too faint. Remember how long it would take to observe it? That is how faint it is. Even paint dries at the speed of light in comparison. (It doesn’t, bit that sounded cool, didn’t it!).

However, researchers have built laboratory systems that mimic the behaviour of event horizons using optical fibre, fluid systems, and Bose-Einstein condensates, and these analogue systems have produced Hawking-like radiation and, yes there’s another and, in recent experiments, even evidence of the associated back-reaction effects predicted by theory! Cool huh?

While these are not actual black holes, they do provide valuable support for the underlying physics, which leaves us with the final mystery.

And that is perhaps that the most important thing about Hawking radiation is not the radiation itself. There is a deeper lesson, that black holes sit at the intersection of humanity’s three greatest theories, General Relativity. Quantum Field Theory, and Thermodynamics. Unfortunately, those theories do not fit together perfectly, but Hawking radiation exposes the cracks.

Hawking radiation tells us that spacetime has temperature, that gravity may be linked to information, and that entropy and geometry are somehow connected. Oh, and that our deepest theories are still incomplete.

More than fifty years after Hawking’s discovery, physicists are still trying to understand what the phenomenon is really telling us.

The black hole’s faint glow may ultimately reveal not just how black holes die, but how reality itself is built! I’ve said this before at the end of my articles, and I’m going to say it again. How amazingly awesome is that!!

Quantum Teleportation: Not Star Trek, But Still Pretty Wild

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Hello my lovely readers, you may be few, but I love you all the same.

Having had a read through my previous articles since I started this whole bringing physics to the masses journey, I noticed there’s a nice progression developing: Gravity > Relativity > Entanglement > Bell’s Proof, a quick side step into the footy  (let’s not talk about that), which leads naturally onto this week’s article:

Quantum teleportation.

Now then, there’s a misconception about teleportation, and I’ve touched on it with my Star Trek allegories in previous articles.

When most of us hear the word teleportation, we probably all think of Captain James T. Kirk demanding that Scotty gets the malfunctioning transporter fixed pronto and beams him up (or Benjamin Sisko making the same demand of Chief O’Brien, or Captain Janeway…. Sorry, got a bit carried away, on with the article). Quantum teleportation is both less dramatic and far more profound (every time I type the word profound, I can hear Prof Brian Cox saying it in my head).

Unfortunately, scientists have not discovered a way to transport humans, objects, genesis devices, or even particles from one place to another. What they have discovered is a way to transport the quantum state of a particle, that is a complete description of its quantum properties, from one particle to another, potentially over vast distances.

In other words, quantum teleportation does not move matter, it moves information.

And that distinction may reveal something fundamental about the nature of reality.

So, if it’s not Star Trek personnel being teleported, what is?

To understand quantum teleportation, we first need to understand a quantum state.

Again, as I mentioned previously, unlike a classical bit, which can be either 0 or 1, a quantum bit, or qubit to give it its correct term, can exist in a superposition of all states simultaneously: it can be zero, one, or both, at the same time. The state of a qubit contains all the information that can be known about it.

The remarkable achievement of quantum teleportation is that the exact state of one qubit can be recreated in another distant qubit without ever measuring and copying the original state. The original state disappears, and the new state appears elsewhere. There is nothing physical travelling between the two except for a teeny tiny amount of ordinary information.

Quantum teleportation relies on three extraordinary ingredients.

The first ingredient is quantum entanglement.

When two particles become entangled, they cease behaving as independent objects. Instead, they become part of a larger quantum system whose properties are linked regardless of the distance separating them. You know what’s coming, don’t you? Yep, you’ve got it, this is what our old mate Albert Einstein famously referred to as “Spooky action at a distance.”

You’ve read my previous article on Bell’s Inequalities, so you know this already, but I’m going to repeat myself again anyway.

Today, entanglement is one of the most experimentally verified phenomena in physics.

On to ingredient number two. The sender (traditionally called Alice, but who I have renamed Betty in honour of my dear old late Mum), performs what’s known as a Bell-state measurement on the particle she wants to teleport and her half of an entangled pair. This measurement destroys the original quantum state, this destruction is not a bug though, it’s a requirement.

Ingredient three is the classical communication.

Betty then sends Bob, the receiver, two ordinary classical bits describing the measurement result.

It is only after Bob receives those bits that he can perform the operation needed to reconstruct the original state on his entangled particle.

At that moment, the teleportation is complete.

Sound familiar? If you read my “Spooky Action at a Distance” series, it should. I’m about to reuse that same trick about entanglement and the speed limit on information. If you haven’t read it yet… well, what are you waiting for?

Now we have one of the biggest misconceptions concerning quantum teleportation. Why doesn’t it break the speed of light?

Because entanglement creates correlations that appear instantaneous, but usable information still cannot travel faster than light. Bob cannot reconstruct the teleported state until Betty’s classical message arrives. This keeps Einstein’s theory of relativity perfectly safe and intact. No matter how strange quantum teleportation appears, and I know I’m repeating myself here, it does not allow faster-than-light communication.

Let’s look at the rule that makes this all possible, which is a fundamental principle of quantum mechanics called the No-Cloning Theorem. This rule states that an unknown quantum state cannot be copied perfectly, essentially meaning teleportation doesn’t produce two versions of the same particle state, the original state is destroyed, and the distant state is created. Quantum teleportation is a transfer, not a duplication.

The theory of quantum teleportation was first proposed in 1993 by Charles Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William Wootters. Their groundbreaking paper showed how an unknown quantum state could be transferred using a combination of entanglement and classical communication. If you really want to have a deep dive into it, let me know and I’ll send you the paper. It took only four years for researchers to successfully demonstrate the effect experimentally using photons in 1997. I remember being really, REALLY, excited at the time, I still get goosebumps looking back to when I first heard the news.

What had once sounded like science fiction had become a laboratory reality.

To me, and I’m sure to many others, this has become one of the greatest ironies of modern physics. Poor Einstein, the phenomenon he disliked most of all, quantum entanglement, became the foundation of quantum teleportation. However, the universe turned out to be even stranger than Einstein imagined.

That’s where Bell came in with his theorem I tried to explain (and hopefully succeeded) in my previous article before the footy one.

For decades, some scientists hoped that hidden variables might explain away Einstein’s quantum weirdness. John Bell showed that certain predictions of quantum mechanics could be experimentally tested and the results repeatedly favoured quantum mechanics and ruled out large classes of local hidden-variable theories.

If it wasn’t for Bell, quantum teleportation might still be considered an interesting mathematical idea rather than a physical reality.

Ah, another question from you? How far have we been able to teleport?

Well, it’s actually a great deal further than you probably think. Quantum states have been teleported using photons, atoms, electrons, superconducting circuits, and solid-state quantum systems.

Researchers have demonstrated space-based teleportation using China’s Micius satellite over distances exceeding 1,000 kilometres. And more recent experiments have teleported quantum information between different physical systems and over telecom-compatible networks designed to support future quantum communications. Just this year, researchers reported teleporting a photon’s state between physically separate quantum dots connected across a 270-metre free-space link, another step toward practical quantum networking.

Looking to the future of this amazing technology, scientists believe quantum teleportation will one day become one of the foundational technologies of a future quantum internet.

Instead of simply sending data, future quantum networks may distribute entanglement between thousands or millions of devices. Quantum teleportation could be used to transfer qubits between quantum computers. It could also be used to construct ultra-secure communication links, enable distributed quantum computing, and build true global-scale quantum networks.

Can you imagine quantum processors in London, New York, and Tokyo acting like pieces of a single giant computer? Well folks, that’s the long-term vision.

Ok, ok, I know you’re desperate to ask the question everyone asks. Could we teleport a person?

Well, in principle, quantum mechanics doesn’t obviously forbid it, but in practice, it is almost unimaginably difficult.

A human body contains roughly 10²⁸ atoms, each participating in an immensely complex web of quantum interactions. Capturing every detail required to reconstruct a person would involve a truly humongously astronomical quantity of information. Oh, there’s also another problem.

Don’t forget the no-cloning theorem in the rules above. The original transported person would have to be destroyed during the process, which raises a somewhat disturbing philosophical question. If a perfect copy appears elsewhere while the original is destroyed, did the person actually travel? Or were they killed while an identical replacement appeared at the other end.

That is a question that science currently has no answer for.

And here we can link back to black holes and wormholes. Deep developments in modern theoretical physics suggest that quantum teleportation may connect to mysteries far beyond communication technology.

Researchers studying black holes discovered unexpected relationships between entanglement, information, spacetime, and wormholes.

There’s the famous proposal, known as ER = EPR, yep, that one from another of my previous articles, which suggests that entanglement and wormholes may be two descriptions of the same underlying phenomenon. Although this is still speculative, these ideas hint that teleportation may reveal something truly profound (there goes Prof B. Cox again. I didn’t know it was possible to have one person saying a single word as an earworm) about the structure of the universe itself.

And then we get to the biggest mystery of them all. Perhaps the most extraordinary aspect of quantum teleportation is that nobody fully understands why reality allows it.

The mathematics works flawlessly and the experiments work repeatedly. And the technology is rapidly advancing.

Yet the deeper philosophical question remains.

Why should information be able to move through the universe in this way?

Quantum teleportation sits at the crossroads of quantum mechanics, information theory, computing, cosmology, and philosophy. Beginning as a clever theoretical idea in 1993, today it is helping scientists build the foundations of the quantum internet.

Who knows, tomorrow, it may help explain nothing less than the nature of space, time, and reality itself! Wouldn’t that truly be profound!

The Magnus Effect: The Beautiful Games’s Most Beautiful Cheat Code

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I was in the pub Friday evening, having a sneaky pint after walking the pooch. As is inevitable at the moment, talk was on the World Cup. We were discussing England’s chances (I believe!), the Balogun/Infantino/Trump controversy, amongst other football related things. One of the guys, I shall call him Dave (because that is his name) said “what about that goal from Pavard for France in the 2018 final against Argentina.” We all nodded agreeing it is probably one of the finest goals ever scored in World Cup history (it really is). Before someone else (who probably doesn’t like the French, don’t worry France, we don’t like him!), piped up and said, “Pah, it was just a wonder goal, no skill in that, just luck. You never see defenders scoring goals like that. Even Beckham as good as he was in his day, wouldn’t have scored that.”

Now, this made me cross, for a number of reasons. Firstly, I don’t like the guy who said it very much anyway. He doesn’t know much about footy, just repeats other people’s opinions. And secondly, he was wrong. On many counts.

Number one:
Of course he intended to score, he took the shot for goodness’ sake!!
Number Two:
There was a lot of skill involved in that shot. As a professional footballer, he knew instinctively what he was doing     
Number Three:
Beckham so could have made that shot, even on whim, have you ever seen him hit a ball to switch play across field?
Number Four:
Yes, there was bit of luck in it, he hit it perfectly. That was the lucky bit.

The wonder bit came when physics took over.

Me being me, I then went on to try and explain how and why to all who would listen. That’s when everyone in the pub’s eyes started to glass over. So, I said, “I’ll tell you what, if you promise to read my blog, I’ll explain it in an article.”

And that is how I have found myself breaking one of my own rules and writing over the weekend.

Now then, after that massive intro are you ready?

Picture this:

A free kick is awarded 25 yards from goal. The defenders build a wall. The goalkeeper shuffles nervously across his line, pointing and shouting, the striker takes a few steps back, raises his hand (why do they do this?), runs up, and hits the ball.

For a split second the fans groan as it looks like the shot is heading straight into Row Z.

Then the ball changes its mind.

It bends around the wall, curls towards the top corner, and sends the goalkeeper flying through the air in pursuit of a ball that had already made its appointment with the net the second it was kicked. And the fans go wild!!!

Now then, this piece of football wizardry is the called the Magnus Effect after the dude who investigated this amazing phenomenon back in the 19th Century.

Most football fans often imagine a curling free kick as a battle between the player and the goalkeeper. Others are aware of the term Magnus Effect. And then you get people like me, who know far too much seemingly useless information that nobody wants to hear about in the pub when they’re discussing the footy.

It’s not a battle between the player and the keeper but against the air.

When a football is struck cleanly through the middle, it tends to travel fairly straight. But when it’s hit off-centre, it starts spinning, and as it spins, it drags air around with it, creating a pressure difference on either side of the ball. This results in one side of the ball ending up with lower pressure, and the other with higher pressure, which makes the ball get pushed sideways.

The result of which is you have a football that appears to have developed independent thought.

Players discovered this long before scientists explained that the spin is the power. If you add enough sidespin the ball curves left or right through the air.

This is why free-kick specialists are football’s equivalent of stage magicians. They know how to bend shots around walls, curl crosses into dangerous areas, shape passes around defenders, switch play so effectively as Beckham did and make highly skilled goalkeepers maybe question their career choices.

OK. There are three elements to this spin. There is sidespin, which is the classic freekick curve, hit the ball across its side and it swerves left or right through the air. It’s responsible for some of football’s most gorgeous goals. Think: David Beckham, Lionel Messi and pretty much every YouTube free-kick compilation that’s ever been made.

You have topspin, which makes the ball dive. The shot rises, clears the wall, and then suddenly plunges towards goal like it’s on its way to the World Cup and it remembers it’s left the oven on back home. This is the physics behind those infuriating shots that seem to drop out of the sky at the last possible moment.

And you have Backspin. It creates a lifting effect that helps the ball stay airborne longer, chip passes, floated crosses and delicate lobs often make use of it.

That was how Benjamin Pavard scored that amazing goal against Argentina back in 2018 when France beat them.

I don’t want to talk about that one though, I want to talk about another one, the one that Roberto Carlos hit against the French in 1997. This is the goal I asked you to imagine earlier, and no discussion of the Magnus Effect is complete without it.

In 1997, Roberto Carlos hit a free kick against France, in the Tournoi de France. A competition played in France with four international teams as a warm-up for the World Cup.

Now then, initially that free kick looked like it was going to go embarrassingly wide. It didn’t though, it turned out to be a 40 yard screamer into the back of the net, and is rightly considered one of the most famous and spectacular examples of the Magnus Effect in football.

For generations of football fans, this was the moment physics got a highlight reel, as it was all over the news with physicists explaining it. Just like I am now.

And this is why some players look like they have superpowers, as it gets stronger when players combine more spin, as this generally means more curve, more speed, as a faster moving ball experiences stronger aerodynamic forces, and technique.

And it is the technique that is the real secret here, and why elite players at the very top of their game don’t just hit the ball, they control exactly where, how, and what angle to strike it.

That’s why millions of Sunday-league footballers can understand the Magnus Effect, while the likes of Messi, can invoke it!

And there’s more! The Magnus Effect has a weird cousin, and that is the knuckleball which is where the fun really gets started.

Sometimes players try to do the opposite and hit the ball with almost no spin. So, instead of curving smoothly, the airflow becomes unstable and the ball wobbles unpredictably. The knuckleball is the famous free kick associated with players like Cristiano Ronaldo.

Where a Magnus free kick is a graceful ballerina, knuckleball is a shopping trolley with a faulty wheel. And that for me wins the ‘who’s better, Messi or Ronaldo’ debate.

The real magic involved with the Magnus Effect is that once you understand it, football somehow becomes even more impressive. Every curling free kick is a player manipulating air pressure, rotational velocity, aerodynamics, and fluid dynamics.

Where the crowd sees the magical, wizardly wondergoal, the physicist (and physics nerds like me) see pressure differentials, and the footballer sees a top corner that needs decorating with his mastery of the beautiful game.

And the ball? That’s the best bit, folks. The ball just follows the science.

The Magnus Effect is what turns football from a game of kicking a ball up and down the pitch into a game of mind-bending reality, just enough to make 60,000 people lose their minds!

Bell’s Inequalities: Spooky Action’s Reckoning

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Way, way back in 1935, Albert Einstein looked at the emerging theory of quantum mechanics and although he said a lot of things about it at the time, and a lot of things after that too, what it really boils down to is this. As I’ve mentioned in previous articles, Einstein had a teeny-tiny (did you see what I did there?) problem with quantum mechanics. To summarise, what he was basically declaring was…

“This cannot be the whole story.”

By the mid 1930’s quantum mechanics had already become hugely and enormously successful (LOL I did it again, didn’t I!). It correctly described atoms, light, and the microscopic world. Einstein, however, being Einstein, believed wholeheartedly that it contained a profound flaw. He couldn’t accept that physical properties might not exist until they had been measured.

As far as Einstein was concerned, the Moon was still there even when nobody looked at it. Which to him meant, a particle should possess a definite state before anyone measures it. If quantum mechanics suggested otherwise, then perhaps some deeper set of hidden facts and hidden variables remained awaiting discovery.

This argument seemed destined to remain philosophical for nearly thirty years, before a quiet physicist from Northern Ireland by the name of John Bell came along.

What Bell did was ask an astonishingly simple question. He didn’t ask whether Einstein or Bohr (brilliant Danish dude, one of many things he is most famous for is developing the Bohr model of the atom) were right. He asked a much more powerful question:

If Einstein’s intuition is correct, what measurable consequences would follow?

At the time this was revolutionary. In an instant, Bell had transformed a debate about the nature of reality into a scientific hypothesis that could be tested in a laboratory.

The result of which he published in 1964, which became universally known as Bell’s Theorem.

I hear one of those questions nagging at you again. You want to know what Bell’s Theorem is, don’t you?

Well, at its heart lies a family of mathematical relationships called Bell’s Inequalities.

Let’s assume for a moment, that the Universe trots along, as it does, according to good old-fashioned common-sense.

Let’s catch up with Bob and Betty again. Imagine that two particles, born together, have then been hurled in opposite directions.

One travels to Betty and the other one travels to Bob, so now two experiments are so far apart that even a light signal cannot travel between them quickly enough to coordinate their measurements.

Now you have to ask yourself, if that’s the case, how could the particles remain correlated?

And that is when the common-sense answer comes in and seems the most obvious. They must have left the source carrying matching instructions.

Like two naughty boys, who have already agreed on their response before getting told off severely for doing something stupid (middle school, my best mate Duncan and the green houses in the garden behind the Spar next door spring to mind, but that is 100% a different story and not for now). What if the particles already know how to respond to every possible measurement?

This view, however, rests on two assumptions:

Number one: Realism. That is the properties of the particles exist before measurement, and Number two: Locality. Nothing can influence something far away faster than light.

Put them together and these two ideas form what physicists call local realism (original, huh?).

Now then, to most people, like you and old me before I learnt all this stuff, local realism sounds less like a theory and more like plain old-fashioned common-sense.

And that was Bell’s perfectly set trap!

He wondered whether pre-arranged instructions could explain every possible pattern observed in entangled particles, and he imagined particles carrying complete answer sheets.

Here’s the clever bit though: Betty and Bob don’t just get asked one question each, they can each be asked one of two different questions. So each answer sheet needs a pre-written response ready for both, not just whichever one actually gets asked.

So, if Betty chooses measurement A, the particle will give a predetermined result.

And if Bob chooses measurement B, his particle will also give a predetermined result.

What’s so unreasonable about that? Sounds very reasonable to me. I hear you say.

The thing is, Bell had discovered something quite remarkable.

He discovered that no matter how cleverly those answer sheets are designed, they can only produce correlations up to a certain mathematical limit. And that limit, folks, is a Bell Inequality!

The most famous version of which is the CHSH inequality, which predicts that a quantity called S cannot exceed 2 if local realism is true.

Nature, however, had other plans. That’s right, you’ve hit the nail firmly on the head. It’s those pesky quantum mechanics breaking the rules again, isn’t it!

And you’re right! Quantum theory predicts that entangled particles can produce correlations stronger than Bell’s limit. Not infinitely stronger. Just strong enough. Instead of stopping at 2, quantum mechanics allows values as high as:

222\sqrt{2}

or approximately 2.828. This maximum quantum value is called the Tsirelson bound (you’ll have to take my word on this as it’s way to complicated for me to explain simply), and to Bell, this meant something extraordinary. (If you really wanna know about Tsirelson’s bound, have a look at Wikipedia here).

If experiments ever exceeded the classical limit of 2, then no theory based on local hidden variables could fully describe reality. That was when the argument ceased to be philosophical, as reality itself would have to choose a side.

And so the experiments began. In the 1970s, physicists John Clauser and Stuart Freedman conducted the first significant tests. The results of which agreed with quantum mechanics. Although a 1973 Harvard experiment by Francis Pipkin and Richard Holt initially produced opposite results before later experiments, such as Fry and Thompson in 1976, strongly violated Bell’s Inequalities, aligning perfectly with quantum mechanics.

There were still many sceptics who remained unconvinced though.

“Perhaps the experiments contained flaws!” they shouted

“Perhaps the particles somehow communicated!” they screamed

“Perhaps the detectors introduced biases?” the shyer ones whispered to each other.

Then, in the early 1980s, a French physicist called Alain Aspect and his collaborators performed more sophisticated experiments in which detector settings changed while the particles were already in flight. And, you’ve guessed it, once again, Bell inequalities were violated. And this time the evidence was growing harder to dismiss.

For decades, physicists searched for loopholes, but every escape route was closed.

Maybe detector inefficiencies could explain the results? Nope!

Or it could be experimental effects mimicking quantum correlations? Nope!

Ah, could the measurement choices somehow be known in advance? Nope!

Researchers attacked each loophole one by one, and every time the loopholes were firmly closed.

More recently in 2015, multiple groups began reporting “loophole-free” Bell tests. However, these experiments simultaneously addressed the major known objections and still found violations of Bell Inequalities exactly where quantum mechanics predicted them. The verdict was becoming increasingly unavoidable with everything they tried. Simply put, Nature does not obey local realism.

So, what did Bell actually prove?

We often hear popular science accounts say that “Particles communicate faster than light.”

Bell did not prove that. Nor did he prove that information travels instantaneously. Nor did he show that relativity is wrong. What he proved was way, way subtler.

Basically, Bell was saying that the world cannot be explained by a picture in which distant objects merely carry pre-existing local instructions, and that something about our classical understanding of reality must give way.

And so, the great mystery remains.

The awkward truth of the matter is that physicists still disagree about exactly what Bell’s theorem means, with some interpretations abandoning realism, and others abandoning locality.

Other physicists have attempted to rethink the measurement altogether.

But all serious interpretations must confront Bell’s result.  The experimental facts may no longer be in doubt, but the philosophical meaning remains fiercely debated.

And that leads us to why Bell matters. While many scientific discoveries tell us how the universe behaves, Bell’s theorem is fundamentally different. It tells us how the universe cannot behave.

It places a permanent limit on any explanation that can be built from everyday intuitions about objects carrying definite properties which are interacting only through local causes.

For centuries, philosophers wondered whether reality existed independently of observation. Bell found a way to ask the question experimentally.

The answer appears to be that the microscopic world is stranger than even Einstein imagined. And perhaps the most astonishing part of all is that a debate that began around blackboards and thought experiments ended with photons, detectors, laboratory equipment, and reality itself casting the deciding vote.

Hopefully, with my explanation of Bell’s Inequalities, my previous two articles will make a bit more sense now.

It’s mind-bogglingly amazing that with all the mind-bogglingly stuff all the clever physicists and quantum dudes have learned and discovered and now understand, that we have been going around in circles with this one for nearly a century. And that, my friends, is one of the many reasons I love physics!