Tag: physics

This is a story about projection…

Do you want to predict the future? Would you like to be in the right place at the right time? Ever wonder how ice hockey star Wayne Gretzky gets to where the puck is going to be, not where it’s been? How does a torpedo fired from a submarine intersect with its target, while following a relatively straight trajectory? Welcome to the world of dead reckoning.

Imagine I have a single data point – a latitude and a longitude – which tells me the location of a target at one point in time. I don’t know how fast it’s going, and I don’t know what direction it’s going. Fairly useless information. In the parlance of physics, I know location, but I don’t know momentum. All we can say is that the probability of its next location spreads out from the point of origin: the thing being tracked is very unlikely to be a long way away, and it’s more likely to be somewhere near where it was last seen. This is a probability cloud.

Next, we’ve measured two data points. We’re sure it’s the same thing that we’re tracking, because we have identified some unique characteristic about it. In the submarine example, the sonar operator will be listening to the sound of the propeller, so they will know if it’s the same ship, because it’s got the same number of propellors generating the same kind of sound, underwater.

If we have two data points, we can draw a straight line between them, and assuming the same course and speed, we can predict where the object we are tracking is going to be next. We measure the distance between the two points, and divide by the time it took to travel between them, and we have the speed. Then, we simply extrapolate the line between the two points, and we can guess where the target will be on that line, at a future time.

But, the simple extrapolation model is flawed. Perhaps currents are pulling the ship in a different direction from the direction steered. Perhaps the captain of the ship is steering an arc-shaped course, to go around an obstacle, or to change direction.

With three data points, we can now fit an elliptic curve to fit those measurements. The elliptic curve shows us whether the captain is steering or drifting right or left. Additionally, we know whether the ship is speeding up or slowing down. If the ship is accelerating, but steering a constant course, it will be further along the line we plot than we think it will be. Equally, if the ship is decelerating, it won’t get as far along its course as we anticipate.

Finally, with four data points, we can come up with a mathematical function that fits the data. To give a very simplified example, if the captain of the ship is zig-zagging to avoid submarines, we could fit a sine wave to the data, and predict when the ship is going to make its next turn… assuming that the captain tacks with regular frequency, of course.

As we gather more and more data points, plotting the course history of the ship we’re tracking, we can come up with ever more sophisticated mathematical models to predict where we’re going to see the ship next.

The arc of a ball travelling through the air is fairly easy to model. We just need to model momentum, gravity and air resistance. Momentum would be constant in a vacuum, so if you whack a tennis ball with a racquet while floating in the outer reaches of the galaxy – where there is little gravity – then the tennis ball will continue on a straight trajectory, at the same speed, more or less forever. Back here on Earth, the tennis ball will be pulled down to the ground by gravity, and it will also slow down, due to air resistance.

Given that air density and gravity are more or less constant at ground level, where you expect to find tennis courts, we probably only need 3 data points, and we should be able to make an accurate guess as to where the tennis ball’s going to land. Even with gusts of wind, the flight of the tennis ball is relatively short, so the wind speed is unlikely to change dramatically during the flight of the ball. It should be a case of simply fitting an elliptic curve to the 3-dimensional co-ordinates of the 3 points of measurement, and then working out where that curve intersects with the plane of the ground, to predict where the ball’s going to land.

“But what about spin?” I hear you ask. Yes, good point.

Spin is angular momentum. For our tennis ball example: the fluffy exterior of the ball will exert a ‘grip’ – friction – on the air. Therefore, the spin of the ball makes a reasonable difference, as more air gets pushed towards one side of the ball, by the rotating face. Just like a wing, the ball will experience a small amount of lift: the ball is ‘pulled’ towards the side that is spinning in the same direction as the air flow. That’s the Magnus effect.

If we had hit our tennis ball with spin out in the vacuum of space, it would not create a curved trajectory, because the fluffy tennis ball has no air to grip on – a vacuum is frictionless. However, the centripetal force of the spinning ball will cause it to stretch to be slightly bigger than it would be if it wasn’t spinning, because the outside is being thrown away from the centre, like a centrifuge. The elasticity of the ball will be trying to pull it back inwards, and in so doing, energy will be released in the form of heat. Eventually, all the energy of the spin will be radiated away, and the ball will slowly stop spinning. This effect is far too minuscule to even bother calculating, for our tennis court example here on Earth.

Of course, all this maths is just to model a dumb tennis ball, which can’t make decisions and alter its own course, once it has left the racquet. To predict the behaviour of even a single individual is hard – this is the work of top poker players – and when we try to model complex systems made up of vast numbers of individuals – such as financial markets – the systems become chaotic and unpredictable. Thus, past performance is not a predictor of future results, unless you’re a tennis ball.

Tags: #physics

This is a story about ethics…

Let us suppose for a moment that the great scientists who gave us our quantum mechanical world, were also animal lovers. Instead of putting cats into boxes with radioactively decaying elements which trigger poison gas to be released, killing the poor innocent creatures, how’s about if we dress them up in clothes instead?

In this alternative quantum experiment, instead of Erwin Schroëdinger’s original design, we shall instead be putting socks on the poor cat that faced a 50% probability of death before.

In our new experiment, we shall be putting different coloured socks on the cat. The socks can be whatever colour we like, but they’re always different colours from each other.

As the cat walks into the room, we can see that the cat is wearing a pink sock. We can’t see the cat’s other foot yet, but we know that the other sock is not going to be pink.

It’s not like the second sock decided to choose its colour when we looked at the first. It’s not like the second sock needed to know the colour of the first, and have the information transmitted to it as soon as we made our first observation.

John Stewart Bell penned a tongue-in-cheek scientific paper explaining the simplicity of hidden variables, which seem to offer a much more objective reality than the Copenhagen Interpretation of quantum mechanics. For sure, the likes of Niels Bohr and Werner Heisenberg had elegantly described the subatomic world with mathematical precision, but the need to abandon a tangible objective reality seems unnecessary if we say that there are hidden variables.

However, from this simple thought experiment comes a theory that is very real and very testable. Bell’s theorem says that the experimental results will differ significantly in a quantum world versus one that behaves classically. Quantum mechanics makes predictions that no classical theory could. Therefore, if you want to know whether probabilistic behaviour indicates a failure to truly imagine what’s going on in the subatomic world, you just have to do the experiments.

If Bell’s theorem were proven correct, this could suggest that experimental observations are “known” in advance, and in fact we are living in the ‘clockwork’ universe as predicted, for example, by Newtonian mechanics. Were you to know the precise starting conditions of everything, you would be able to predict everything that would ever happen: no surprises!

In short, Bell’s theorem was tested, and the result was surprising: we may be living in a superdeterministic reality, where there is no free will and all outcomes are fixed in advance.

Tags: #physics

This is a story about spacetime…

We all know what Euclidian geometry is, right? Up & down, left & right, forwards & backwards. We know how to draw a triangle, a square. We know how to calculate the volume of a cube, a sphere, a cone. We even have methods of calculating where the points of 3-dimensional object will be, if we rotate it. We can use matrix transformations to do a rotational calculation, and work out where the corners of a spinning cube are going to be.

But what about when space gets all stretched and weird? What about non-Euclidian geometry?

If I draw two lines on a flat piece of paper, they will intersect at some point unless they are perfectly parallel. If I draw two ‘straight’ lines on a ‘flat’ hyperbolic plane, they will curve away from each other and not intersect. Even though both lines and both planes are 2-dimensional, the behaviour is very different, depending on the geometry.

Do you think you live in a 3-dimensional universe? Wrong.

So, you think you live in a 4-dimensional universe, where the 4th dimension is time? Also wrong.

You live in a 3 dimensional universe where the speed that you are travelling at relative to everything else affects the curvature of spacetime. Pretty obvious, huh?

So, if you’re not moving relative to the things that you can see, then you are moving in time. If you’re moving relative to something else, then you are moving in space, and ever so slightly less in time than the other object(s). Is that clear?

If I get in a rocket and fly away from the Earth at the speed of light, and fly back again at the speed of light. The whole time I was on the rocket, I was moving in space but not in time. The speed of light is the speed limit of the universe, so if I was travelling at the speed of light, then time stood still for me. However, the Earth was not moving anywhere, so it was moving at full speed through time, but not at all through space. Is this making sense?

Here’s an example: let’s say I travel to the moon and back. The moon is 384,400km away, so I travelled 768,800km. The speed of light is 299,792 km/s, so the round trip took me 2.6 seconds, according to your stopwatch. According to my stopwatch, my trip took me 0 seconds.

Why did it take me zero seconds to travel to the moon and back at the speed of light? It’s simple really: because I was travelling through space at the maximum possible speed, so therefore I was not travelling through time at all.

Why did the person on Earth with the stopwatch record a time of 2.6 seconds for me to travel to the moon and back at the speed of light? Again, it’s pretty simple: the person on Earth was not moving at all through space, so therefore they were travelling through time at the maximum possible speed.

This is the nature of spacetime: any movement through space means less movement through time, as measured by an independent observer. When you’re jetting through space in your rocket, your clock doesn’t seem to be ticking any slower, but the independent observer can verify that time had indeed slowed down for you when you get back to Earth and you compare your clocks.

We have just described special relativity and minkowski spacetime.

Albert Einstein is the headline act for special relativity, but it was Hendrik Lorentz who was the mathematical genius behind figuring out how objects move in minkowski space, and of course it was Hermann Minkowski who came up with the special geometry where the wonders of spacetime play out.

I got very excited a few years ago because neutrinos had been detected arriving on Earth from a distant supernova, before photons (particles of light) and this was reproduced in an experiment between CERN and Gran Sasso in Italy, 730km away. The experiment’s results seemed to suggest that neutrinos were travelling 8km/s faster than light.

We all learn at school that nothing can travel faster than the speed of light. So far, special relativity has proven to be a pretty robust piece of science. Discovering something travelling faster than light would have meant tearing up the physics textbooks and going back to the drawing board.

However, the beautiful theory and equations proved to be correct. The experiment was found to be flawed due to faulty timing equipment. Damn. No time travel for us, unless maybe you’re made of antimatter.

By the way, I made a little Lorentz/Lorentz joke at the start, because I was thinking of writing about chaos theory. Perhaps I’ll save that delight for another day. Let’s see how this one goes down before I delve into any more topics that I have a shaky understanding of.

Tags: #physics

This is a story about science fiction…

Do you know what the trouble with physics is? Are you aware how much the scientific community is dominated by dogma, doctrine and the status quo? The business world is full of powerful dinosaurs who have too much to lose if they were dethroned. So why would science be any different?

Let’s start with a madness that afflicts nearly every physicist.

Do you know what the difference between a model and a theory is? A theory is some equation, algorithm or logical thought experiment, that can empirically explain real-world observations and make testable predictions.

If I have a theory that explains the arc that a ball will trace when I throw it, it should be able to predict where it lands. I plug in the wind speed, the weight of the ball, the size of the ball, the strength of gravity on the planet, and the initial force and angle that will be imparted on the projectile, and the theory gives me the expected result. By testing various different balls and various different throws, the theory can be said to be proven insofar as the predictions are in agreement with the measurements, within a margin of error.

If I take various measurements from various experiments and gather them together in some great big database, and then attempt to infer a relationship between the measurements and the outcome, then I have a model. For example, it’s fairly obvious that a heavy ball will not travel very far versus a light ball, when thrown with the same force. From the data, there emerges this statistical correlation between the weight and the distance, but there is no underlying theory that predicts much beyond this simple association of variables.

This is what we understand as the most important distinction between theory and model: that theories can make useful predictions that are testable, and give us some elegant mathematically expressible equation about the true nature of the universe, but models can only give us clunky retro-fitted attempts to make sense of vast swathes of data.

To understand the theory of a thrown ball, we had to employ the laws of motion, the laws of drag coefficients (wind resistance) as well as gravity. Newtonian mechanics tells us about the movement of objects in a frictionless universe. Fluid dynamics tells us about an object travelling through something like air or water. General Relativity tells us about objects acted upon by the force of gravity. Through the combination of these three theories, we can accurately predict where a thrown ball is going to land.

However, a model can make a reasonably decent job of the numbers, within a margin of error. Big heavy balls didn’t travel very far, and small light balls flew further. No need for all that theory mumbo-jumbo. A model can easily be within the same order of magnitude as the theoretical predictions.

Have you heard of the Standard Model of particle physics?

The Standard Model tells us what goes on at a subatomic scale. Or rather, it attempts to, given vast quantities of experimental data.

Before I tell you any more about the Standard Model, let me let you in on a little secret. It doesn’t scale. Yes, that’s right. The Standard Model is very successful at the subatomic scale, but when we use it to model the entire universe, it doesn’t work. In order to use the Standard Model to explain what is observable in the universe, cosmologists have had to invent 3 massive cludges, for which there is no experimental evidence to confirm the existence of: inflation, dark matter and dark energy.

The Standard Model concerns itself with stuff that we can see, and how things interact with each other. However, cosmology has had to invent dark matter (27% of the universe, but you can’t see it), dark energy (68.3% of the universe, but you can’t measure or detect it) and inflation (which attempts to explain how we got into this mess in the first place).

Religion is often derided for asking the faithful flock to accept things at face value without evidence, but now the dominant science of physics and cosmology asks us to to believe that over 95% of the universe is made up from stuff that’s never been seen, never been measured, is not predicted by any fundamental theory and was basically dreamt up because our favoured model of the subatomic world doesn’t scale.

Now, please don’t get confused with quantum mechanics.

Quantum theory is quite empirically testable. The quantum behaviour of the universe is nearly impossible to visualise. Our day-to-day experience of the world is a deterministic one. When I put down the ball and look away, when I look back it’s still there. When I throw the ball, I can know both its momentum and its location. I can predict where balls are going to land, in the deterministic world of the macro scale. Things get mighty weird in the quantum world, but that doesn’t mean that things are not underpinned by good theoretical science.

The problem comes in when we model. The Standard Model has over 20 free constants, which are tweakable numbers fed in from experiments. The Standard Model is designed to be constantly improved, as new data become available. The often touted defence about how well tested and accurate the Standard Model is, is null-and-void, because many of those experiments actually feed back into the model itself. The Standard Model automatically adjusts itself to match experimental observation.

The problem with the Standard Model is that it doesn’t make any testable predictions. The tests that we have done have simply improved the model. The experimental measurements change the free constants that are plugged into the model. The model confirms itself, but it doesn’t tell us anything we hadn’t already experimentally measured.

The only true test of the Standard Model would be to scale it up to see if it matches observations from cosmology. It doesn’t scale.

Models don’t give us fundamental theories that underpin the universe, and allow us to make predictions about previously unobserved phenomena that we can then design experiments to investigate. Models cannot be proven or disproven, because they do not make predictions. Models are unassailable, because they can adapt themselves to include any new experimental data.

The whole era of shut up and calculate has been a hinderance to the progress of theoretical physics. When people talk about the staggering accuracy and number of experiments that confirm the Standard Model, they ignore the fact that the model is only as accurate as the measurements that were used to build it. The model has told us nothing about the fundamental nature of reality.

Now, when the Large Hadron Collider (LHC) detected a bump in experimental data at 75 GeV, we had over 300 papers published to explain such an anomaly. The bump turned out to be nothing more than noise, a glitch. Physicists are writing science fiction – fan fiction – to explain the workings of the universe, but none of it is backed by testable theory that makes useful predictions.

Show me the physics that predicts a discovery in advance as opposed to proton smashing and attempting to retrofit data to a model. The current design of experiments completely contradicts the scientific method.

Until we return to the era of coming up with hypotheses and fundamental theories that make testable predictions, and then building experiments to prove or disprove those theories, we will be stuck with our multi billion dollar particle smashers, that do nothing except to improve the accuracy of models by a few percentage points, and unearth no useful physics at all.

Tags: #physics

This is a story about preying on the weak…

I’m lucky enough to live in a secular society, so I’m not expecting a major backlash over what I’m about to say, but religion is still an emotive topic in some parts of the world, and amongst extremists.

As I thought about how this story should start, I considered word-play around the similarity between prey and pray. The friends I have who are overtly religious all seemed to find their God during periods of intense personal development, turmoil. The two things might be unconnected, but I somehow feel that they are not.

I myself reconsidered the existence of a deity, as death drew dangerously close. I don’t think I would exactly have found myself praying for my soul, pleading for forgiveness or any of that bullshit, as I drew my final breath, but certain events in my life brought theological questions into sharp focus in my mind.

One of the most profoundly unsettling questions I have, is not “what happens when we die?” but actually, is it possible to die at all? The conclusion I reached, when I really was at death’s door, was that it isn’t actually possible to die… at least in any way that you can usefully perceive.

That sounds pretty nuts, right? However, the conclusion is actually borne out of real scientific empirical evidence. I won’t go into the details, as I have already written at length about Quantum Eraser experiments and the problem of separating the scientists performing measurements from their experiments.

But what does it all mean in practice? Well, in actual fact, this line of thinking has brought me ever closer to Christian values than I would have ever thought possible. Do I mean Christian in the bible-bashing, ramming religion down people’s throat sense? No, what I mean is Christian… as in, the teachings of Jesus Christ, not the out-of-context bullshit peddled by dogmatic religious thought leaders.

Let me give you an example: heaven and hell. We are all familiar with the concept of eternal damnation in a fiery underworld full of sin and deviancy. Well, it was through a fairly sinful path that I arrived at my understanding of what heaven and hell might look like, in a world where we don’t actually die. But what the hell does that mean, we don’t die?

You’re going to die, but you won’t be aware of it. You’re going to see me die, but I won’t be aware of it. We’re going to see everybody die, except ourselves in fact… my interpretation of what I can see from the evidence, is that our own consciousness persists in some form or other, for eternity. This is the multiverse, and the many-minds theory.

If a consciousness lasts eternally, that means that you will be eternally haunted by your past actions. If you do ‘sinful‘ deeds, then you will have an ever-increasing amount of guilt, and your life will be increasingly awful, until destruction has wrought havoc over the entire surface of the Earth. Eventually, you will have exhausted every resource at your disposal, and you will be presiding in immortality over the scorched and blackened surface of the planet, wrecked by your increasingly ‘evil‘ behaviour. In essence, you will have created your own personal hell.

Equally, as an immortal living in a future shaped by your actions, you could preside over something that is the polar opposite of hell. With all eternity to refine and improve things, if you aspire to enhance the state of existence, then you will be able to create a kind of heaven.

What I’ve found, from personal experience, is that there is no heaven to be found at the bottom of a whiskey bottle or a crack pipe. The things that seem to offer heavenly euphoria or “floating on cloud 9” as some people say, are actually pathways that actually lead to misery and destruction. The short term quick-fixes eventually lead you to lie, cheat and steal.

Nobody preaches as loud as the converted former sinner, and so it is the case that if you examine the past of those who have found religion, you will very often find that there is very real repentance for a life of sin. We should remember this famous quote:

“The only difference between the saint and the sinner, is that every saint has a past and every sinner has a future” — Oscar Wilde

I believe it’s over-simplistic to talk about right & wrong, good & evil, dark & light and saints & sinners though. We are a product of circumstances, not free will. I strongly believe that it’s quite possible that time runs in both directions, and our memory is just a ‘trick‘ that makes us think we are actually making decisions.

Let’s examine what I just said in a little more detail. If time is running in the opposite direction, you know exactly what decisions you’re going to make and your final destiny, but you have no memory of any decision that you made in the ‘past‘ because your memory is being erased.

If you have no memory of things you did in the ‘past‘ then you have the opposite belief system. Instead of believing that the future is unknowable and that you’re in control of your destiny, you know that your destiny is fixed, but the past decisions that led you to your present existence are unknowable. The illusion of free will is shattered.

I don’t believe it’s actually possible to experience consciousness when the flow of time is reversed, so in theory, there is only one stream of consciousness that spans all time, and every conscious being, with time just zig-zagging its way backwards and forwards through all eternity. It seems, to me, probable that there is only ever one ‘active‘ consciousness at any one time in a Universe, and every other being that ever existed for all time in that Universe is actually part of the same chain of conscious periods, where time runs ‘forwards‘ as we perceive it.

Does your brain hurt yet? Look, it’s really simple: you feel conscious, and that you have free will, and that you have memories that go back to early childhood… however, you’re going to see everybody you know die, while you live for all eternity, and then bang! one day it seems to start all over again, but actually it’s the same Universe, but you just don’t remember the bit where time went into reverse, and you’re now living another person’s life in the same Universe as you’ll inhabit for all time. Simples?

If you think I’ve gone totally potty, don’t worry… I don’t believe in that hypnotherapy mumbo jumbo where we can remember past lives. There’s just no good scientific theory to support such a preposterous idea.

Also, by the way, there is no such thing as a space wizard who created the whole world in 6 days and then had a rest for a day. Sorry about that.

Go ahead and ask for whom the bell tolls… you’re immortal so it’s not going to be tolling for thee

Tags: #physics