Exceeding the Speed-Of-Light Explained Simply (and the Quantum riddle solved at no extra cost)

27 09 2011

It has recently been in the news that some particle may have exceeded the legal speed limit for all things : 299,792,458 metres per second.

Of course, this will probably turn out to be a bad sum somewhere or perhaps waves ganging up, but the whole hubbub has raised my hackles, and here’s why.

Because Albert Einstein at no time said what they say he said (see here for example). They misunderstand relativity! Things can move at any speed we want, and I will try to explain the fuss now.

So let’s get to it!


First, we have to consider the way space warps when we move.

The problems started when people realised that light always seems to have the same speed, regardless of the speed you were moving when you saw it. This seems to be a contradiction, because surely if you fly into the light ever faster, it will pass you ever faster?

Well the tests were pretty clear, this does not happen. The speed is always c.

For several years, people were unsure why – until they were told by Einstein in 1905. In the meantime, another ponderer of the problem (Lorentz) decided to write down the maths that are required to square the circle.

The so-called Lorentz equations show, unequivocally, that space and/or time need to warp in order for relative speeds of c not to be exceeded, even when two items are going very close to c in opposite directions to one another.

So something needed to give, and it was space and time!

So, newsflash! it was not Einstein that first published on space and time warping. His contribution (along with Henri Poincaré and a few others) was to explain how and why. His special theory showed that because there is no ‘preferred’ frame of reference, a speed limit on light was inevitable. The term ‘relativity’ come from this – basically he said, if everything is relative, nothing can be fixed.


Ok, so we have some nice observations that nothing seems to go faster than the speed of light  – and we have a nice maths model that allows it. So why do I persist in saying things can go faster than the speed of light?

Let me show you…

There is a critical difference between ‘going’ faster than light and being ‘seen to be going’ faster than the speed of light, and that is where I am going with this.

So lets take this apart by asking how we actually define speed.

If a particle leaves point a and then gets to point b, we can divide the distance by the time taken and get the mean speed (or velocity to be pedantic).

The issue with relativistic speeds are that the clock cannot be in both point a and point b. So we need to do some fancy footwork with the maths to use one or other of the clocks. So far so good. This method will indeed never get a result > c.

The nature of space forbids it – if the Lorentz transformations that work so well are to be taken at face value, then for something to exceed c by this method of measurement, is much the same as a number exceeding infinity.

So all is still well. Until you ask, what about if the clock is the thing that travelled from a to b?

In this case, the transformations cancel! The faster the movement, the slower time goes for the clock, and you will see its ticks slow down, thus allowing its speed to exceed c.

The clock will cover the distance and appear to have tavelled at c on your own (stationary) clock, but the travelling clock will have ticked fewer times!

If you divide the distance by the time on the travelling clock, you see a speed that perfectly matches what you would expect should no limit apply. Indeed, the energy required to create the movement matches that expected from simple Newtonian mechanics.

The key point here is that while the clock travelled, the reader of the clock did not. If you do choose to travel with the clock, you will see it tick at normal speed, and see the limit apply – but see the rest of the universe magically shrink to make it so.

Some have argued that I am not comparing apples with apples, and that by using an observer in a different frame to the clock I am invalidating the logic.

To those who say that, I have to admit this is not done lightly. I have grown more confident that this inference is valid by considering questions such as the twin paradox over and over.

The twin paradox describes how one twin who travels somewhere at high speed and then returns will age less than his (or her) stationary twin.

Now if we consider a  trip to Proxima Centauri (our nearest neighbour) the transformations clearly show that if humans could bear the acceleration required (we can’t) and if we had the means to get to, say, 0.99c for most of the trip, that yes, the round-trip would take over 8 years and no laws would be broken. However the travellers themselves will experience time 7 times slower (7.089 to be precise). Thus they will have aged less than 8 years. So, once they get home and back-calculate their actual personal speed, it will exceed all the live measurements.

This has bothered me endlessly. Although taken for granted in some sci-fi books (the Enders Game saga for example) this clear ‘breakage of the c-limit’ is not discussed openly anywhere.

Still uncertain why people were ignoring this, I read a lot (fun tomes like this one) learned more maths (Riemann rules!) and also started to look at the wider implications of the assertion.

On the one hand, the implications are not dramatic, because instant interstellar communication is still clearly excluded, but that whole issue of needing a 4 years flight to get to Proxima Centauri is just wrong. If we can get closer to c we can indeed go very far into the universe, although our life stories will be strangely punctuated, just as in the Ender books.

But what about the implications for the other big festering boil on the body of theories that is physics today – quantum theory?

Well, if one is bold enough to assert that it is only measurement that is kept below c and not ‘local reality’, then one can allow for infinite speed.

In this scenario, we are saying measurement is simply mapping reality through a sort of hyperbolic lense such that infinity resembles a limit. Modelling space with hyperbolic geometry is really not as unreasonable as all that, I don’t know why we are so hung up on Euclid.

With infinite speed at our disposal, things get really interesting.

We get things like photons arriving at their destination the same tme they leave their source. Crazy of course… but is it?

Have we not heard physicists ask – how is it the photon ‘knows’ which slit is blocked in the famous double slit experiment? It knows because it was  spread out in space all the way from it’s source to it’s final point of absorption.

If you hate infinities and want to stick with Lorentz, you can equally argue that, for the photon, going exactly at c, time would stand still. Either way, the photon feels like it is everywhere en route at once.

If the photon is indeed smeared out, it probably can interfere with itself. Furthermore, it is fitting that what we see is a ‘wave’ when we try to ‘measure’ this thing.

A wave pattern is the sort of thing I would expect to see when cross sectioning something spread in time and space.

Please tell me I’m wrong so I can get back to worrying about something useful. No, don’t tell me – show me – please! 😉

Confirmation bias: confirmed as bias.

13 08 2011

I have this theory that ‘confirmation bias’ is a load of BS, so I looked on the net and found, after careful search, some people who clearly agree with me. Most don’t, but they must be idiots.


Does natural really = good?

8 05 2011

Don’t you hate being taken advantage of?

You don’t have to look far in supermarkets to see scientifically dubious claims on product packaging. We already know about dubious health effects of certain foods and the arms race by advertisers to come up with fancy ways to pretend their products are good for us. Now the latest trend is to crow about how ‘natural’ a product is – the world natural, is however now officially anointed a weasel word.

What exactly does it mean? We all know what they want us to think: wholesome, pure, robust, healthy; but what does natural really mean?

As the provincial scientist, I will take a scientific view: natural originally meant ‘of nature’, that is to say, real, or not-supernatural. So technically humans are natural as is all we do. Of course, the term has now been somewhat perverted, and is commonly taken to mean: not man-made.

Any decent scientist is going to have trouble with this definition because it is far too open to interpretation and begs the question: how much human involvement is required to make something non-natural?

This is the vagueness has has been unconsciously used to create a definition that helps sell products: this definition suggests somewhat arbitrarily that ‘some’ degree of purification, or ‘some’ types of blend constitute something unnatural. In addition, if the substance is not found in nature at all it is considered even worse. Sometimes the product is cast as unnatural just for having a chemical sounding name, or because it’s produced by a drug company. On the other hand, some products are branded natural despite containing preservatives, colourants and so on. We simply cannot trust food marketing.

Modern diet sodas would meet most people’s definition of synthetic: but what about bread? Milk? Where do we draw the line?

One argument says if all the ingredients are natural, then the product is natural – so, for example, beer made without recourse to ‘chemicals’ may be considered natural.

Unfortunately, this argument simply displaces the vagueness: now the question is: what constitutes a ‘chemical’? We are all chemical, after all. So yet again, chemicals are arbitrarily divided into good and bad depending whether they occur in nature. Fruit flavoured sodas rarely contain actual fruit: we learned which chemicals were responsible for apple, strawberry and banana flavours and can now synthesize them perfectly – this is done in large quantities that make it far cheaper than actually farming the fruits themselves. It is fair to say that the supply chain for these flavours is often complex, so a little skepticism is warranted, but upon inspection, it turns out that most synthetic flavours are very well understood and are often far purer than the ‘natural’ alternatives. The idea that we eat barbecued meat, smoke tobacco and drink coffee, but are afraid of Acesulfame K is somewhat irrational.

So it leads us to ask – why? Why is the devil’s brew OK, and Acesulfame K not? Why is something man-made inferior to something natural? Why have we got it in for synthetic stuff?

In the study of ethics, there is an argument called the appeal to nature used to justify actions as moral: this is an argument that basically says natural=good.

However, there is no good reason to suppose this. I propose that this fallacy is behind our fears of the synthetic and is the driving force behind major societal trends such as the organic movement, and is a mainstay in the ongoing survival of many useless alternative medicines… so I thought it deserves to be unpacked a little.

The Moral Maze

Get this shirt, click the image!

It is worth reading up on the thought experiments done to try and understand morals. See for example the trolley problem: would you push someone in front of a train to save five lives? Or consider the scene in the last episode of M*A*S*H were a mother is given the choice to smother her own child to avoid a group of villagers from being detected by enemy soldiers.

By thinking through these scenarios, and unpicking our reactions, scientists have learned that different parts of us have different reactions – there are the more emotional reactions and the more logical, reasoned reactions. The logical reactions can seem immoral, and we would struggle with guilt if we made them, but why?

Emotions like fear, revulsion, guilt and love often seem illogical – and so they often are. They we not designed, but emerged as evolutionary advantageous, thus they often seem without purpose. Thus we can have emotions that do not make logical sense; on average they help, but they do malfunction, as in the trolley problem.

Will knowing this failure of the mind help us make these hard choices by reducing the guilt? I don’t think so – we cannot escape our emotions. However, the logical approach should still be used – for example by leaders who need to create policies for the greater good. This makes me think of the famous line in A Few Good Men “You want the truth? You can’t handle the truth!”. I am suggesting that there are situations when the most moral act for a leader is immoral on the face of it and would be condemned if made public.

Thus, we see that the study of what is moral is a tricky field and we see that the systems used in society, while designed to be ethical, may often not be moral (such as a lawyer defending a suspect they know to be guilty).

So how does this tricky world apply to the question of naturalness? Well I would assert that our reaction to substances, like our reaction to the trolley car problem, is again a battle between deep evolutionary instincts and our power to reason.

Firstly, we have a natural (and wise) aversion to new things, especially foods: eating anything new increases the risk of poisoning, and so, eating things eaten for generations is safer. Synthetic foods are clearly ‘new’; they do not have grandma’s stamp of approval – we do not know if generations of people have thrived on this stuff. While this rule of thumb is a good starting point, it is obviously an emotional generalization that fails simple examination. What’s more, as our understanding of both nutrition and hygiene have massively improved health and lifespan in the last hundred years, we should actually favour the new – and fear the old!

The next argument goes something like this. We have a vague feeling that as our bodies evolved in a natural world, and the highly purified chemicals will somehow put our wonderfully complex systems out of whack. It is true that when we eat natural foods, our bodies are very adept at ‘processing’ them; and many natural foods do contain a wide array of essential and complementary nutrients, but it is unsupported speculation to suggest that our bodies needs cannot be met by more processed ingredients. Modern nutrition science understands very well what the body needs in terms of fuel, salts, roughage and so on, and we also understand how diet effects the risks of disease. While modern nutritional science does conclude that natural foods have many benefits – it does not conclude that synthetic is bad. There is room for both!

Lastly, there is an argument straight from moral philosophy: does it makes sense, for example, so say that killing someone is morally worse than failing to save someone, even though a choice is made in both cases and the outcome is effectively the same? If so, then this reveals a built-in preference for ‘non-interference’. So perhaps in a similar way, nature may be considered a ‘default’ – it’s what happens when humans are absent, ‘it’s what would happen anyway’ – like animals hunting for food – and so has a moral free pass. Following this through, nature has no immorality, morality is something tied to us humans and our choices – and so everything we do as humans is therefore potentially immoral.

This argument is also a little weak – as humans have the power to do tremendous good – and the evidence that animals do things we find immoral is there – after all, we are animals. Animals, like us have complex societies, trade favours, shun freeloaders and much more. If you want to learn more, the writings of Marc Beckoff shine a spotlight onto this.

So is there a take home?

OK, now we know – the ‘nature card’ will take advantage of our irrationality, it will stoke our fears and play with our conscience. It will manipulate how we spend our money, and it will sometimes do us more harm than good.

But what makes it worse, is that most people who draw the nature card are good people.

This is one of the many small tragedies that make up our modern times.

Reality: a hard sell

2 04 2011

I can’t help but wonder if doggedly debunking all spewings from the purveyors of woo is somewhat a fool’s errand.

There are a number of pseudo-scientific disciplines whose concepts are inherently highly attractive and contagious to the average Joe, saying things that make him feel good and making him want to pass on the good news. Think of how easy to sell these messages are:

  • organic food – frolicking chickens, steaming compost, happy farmers, healthy food – a return to basics, back to a purer time when humans actually had roots in the earth and cared for it; you too can go organic!
  • complimentary medicine – age-old wisdom, so long suppressed by big pharma is unlocked just for those open-minded enough to look. Are you open-minded! Yes? Here are your keys to healthy prosperity!
  • astrology – our fates, entwined with the universe, form a beautiful unity; enigmatic scholars have acted custodian to its cipher through the ages. Are you a spiritual soul? You too can share time’s secrets!
  • parapsychology – our minds are more powerful than science knows, and we all have potential beyond our wildest dreams! But hold on! Only those willing to break free from the trappings of conventional science will ever see the light…
  • and of course the big kahuna, religion – imagine for a minute the greatest most wonderful thing in all the world, and that is but nothing compared with the joys that await the believer, and for all eternity too!

It is little wonder the bible I had as a kid said “Good News” on the cover.

The issue is that the logical shredding of these pieces is often a sobering dose of reality that fills most people with instant sleepiness:

  • organic food is not always kinder to the planet and claimed health benefits are of the ‘hard to verify’ sort
  • alternative medicine actually does work, but only the level one would expect from getting time, care, attention and the placebo effect
  • the laws of physics do allow marvellous things (x-rays, computers, holograms) but it takes serious study to understand why they don’t allow for the positions of stars and planets to have predictable effects of the day-to-day ongoings in suburbia.
  • the mind is indeed fabulously clever and poorly understood, but those tedious laws of physics, and indeed dry, cold logic, are annoyingly sticky when it comes to clairvoyance, ESP, psychokinesis and precognition.

So YAWN! Boring!! Logic and analysis mean effort, work, thinking things through, totting up totals, cross-checking claims, testing, questioning and doubting. Pretty much the opposite of nice & easy. Accepting we are not all-powerful, we are not immortal and that we will all be forgotten someday is just no fun. These are not messages that will go viral, that will breed missionaries, that would generate a manic fervour. More like manic depression.


So the deck is stacked. Pseudo-scientific ideas persist because they are tenacious memes, and they are almost impossible to kill. They are contagious and sticky, and lovely and easy, and fighting them off requires not just the will, but also the ammunition.

And that is why it worthwhile to continue to fight the good fight – to keep trying to debunk poor thinking – to provide the ammunition to that small number, those that may be on their own, surrounded by superstition, but with that gift in their heart that is that first inkling of doubt.

I will do it for those that think they are alone as I once did.

We live in a time of unprecedented opportunity – people have better access than ever to the tools to arm themselves to achieve a new sort of ideal: to make life choices with full access to all the facts. We are after all free to choose to believe anything, the problem only comes when we are not given the choice. No information, no balance, no choice.

Confessions of Scientific Atheist

31 05 2010

The Evolutionary theory of Natural Selection makes extraordinary claims. It explains the ability of creatures to convert sunlight to useful energy, to spin silk, to metabolise sulfurous rock – and much more besides.

Such amazing feats in nature require an amazing explanation. The existence of a God is very helpful in this regard; after all, humans have designed diesel cars and digital computers, so why couldn’t an entity with God’s power and talent create all the nature we see?

The trouble many people have with Natural Selection, is that while it can clearly explain some biology, using it to explain away practically all biology (and psychology, language, culture, etc.)  is an extrapolation – and a big one at that.

Why do scientists allow such an extrapolation? Surely this is arrogance?


Thinking about this, I have an proposition…

If you come from the premise that there is nothing outside of nature (see my recent post), then it comes easily. If the God option is written off a priori, we have no other logical option than to expect that the gaps in our knowledge of evolution will be filled in eventually. This allows us to sleep at night with the extraordinary.

If you start from the premise that there is a God, then this will strike you are arrogant.


The constant supply of greater details, filling in the gaps, gives encouragement to those who feel the theory is right (see God of the Gaps). It’s a bit like looking for Nessy – we can’t do a Star-Trek style ‘scan for lifeforms’ to be sure she does not exist, but the more we search the less likely she is to exist.

Of course, while evolution explaining away the wondrous variety in life does not prove there is no God, it sure makes God less necessary, and less necessarily capable.

Overlapping Magisteria

30 05 2010

Those who say science and religion are mutually exclusive are working from the philosophical premise that there can be something outside of nature.

Those who claim that religion can be scientifically investigated, come from the philosophical premise that there is nothing outside of nature.

As neither position is superior one cannot use logic to assign greater truth.

However, the claim that there is anything beyond nature (i.e. supernatural) is the more extraordinary claim, and thus carries with it the onus to justify and explain how to reach this conclusion.

The futility of being outside of nature:

If religion is truly outside of nature it can have no measurable effect on it. If it has no measurable effect then, even if existant, it would be fair to say it couldn’t be detected by science – but then neither could it be detected by the clergy.

Thus in a non-overlapping model, the benefits of a benevolent God, such as good crops, good weather, good luck, healing or charity are impossible, as they are generally detectable.

I guess you could argue that God goes to the trouble to disguise the causes for His blessings, but why is he so afraid to show it was the result of your good faith? This argument gets a little stretched once the solutions to that are proposed. It is similar to the argument that God planted the fossils in the order of their evolutionary development to fool us into thinking that life evolved…

The Apple Mac: It’s a religion…

6 02 2010

It has been explained by writers better than I how our minds are wired in a way that makes them vulnerable to religion.

Whether it is our desire to feel secure or have simple and complete explanations for natural phenomena or simply because we enjoy the social scene at church, there is no doubting the power of the effect. Even in modern times, entire lives, indeed entire civilizations are devoted to the superstitious concept of supernatural Gods.

Although L. Ron Hubbard may have started a religion while knowing it was all a sham, most religions did not need such deliberate action. Our innate need to have faith in things has allowed religious concepts to emerge and evolve freely in our communities as far back as records go.

So why do I bring that up?

It occurred to me today while pondering why people are so defensive about Apple Mac computers – I realised that their behaviour had much in common with religious ‘zeal’.

Then it occurred to me how much the success of Apple relies on perception and conception. If it was just about getting the fastest computer, you would not buy a Mac. If it was about buying something that has wide compatibility, you would not buy a Mac. If it was about cost, you certainly would not buy a Mac.

Some might argue that Macs are more intuitive and ‘easy to use’. These are people whose idea of computing is buying a shiny box, plugging it in and doing exactly what they are expected to do. They are people who just accept it when they are told they need to buy a new printer. Or worse, they blame the printer – what a crappy printer, not compatible! These are people who do not need to set up a complex network, or run a database server.

Anyone who has a Powerbook G4 that cost several grand and is not actually compatible with the latest OSX release, yet needs that OSX release in order to actually work, and still hugs and caresses the machine as it it were a newborn baby while defending its honour and wanting to spend another several grand on a newer shinier one, is, in my opinion, dabbling in a cult.

OK, before you write me off as some sort of anti-mac fanatic, I will admit they are beautiful.

Moving swiftly on, I think it is worth analysing Apple’s success.

How does a company that controls the details of their products so completely compete with a product (the PC) that is made by hundreds of companies all constantly competing, innovating, coming and going, rising and falling? The modular design of the PC allows almost anyone to buy all the bits and assemble the machine themselves; with so many companies making monitors and keyboards and hard drives, some will make bad (fatal) decisions and die, some will make good decisions and thrive and if there are enough upstarts to keep up the supply, the consumer will only ever see the winners, even if their victory was a flook, it was a victory none the less.

You could say that PC is the computer you get from natural selection (survival of the fittest), the Mac is the the computer you get when you try to control the evolution (unnatural selection).

Now a company that tries to make everything itself can capture the value chain, sure, but as it is only one company, it cannot make even one fatal decision, and thus needs to be a little more cautious. This means it is doomed to always lag slightly on the performance vs value curve – so what does it do?

Easy, get the consumer to accept poor value. Make up for performance by buying in high quality technologies (lcd screens, hard disks, etc), and make the customer pay the premium. Then focus on marketing.

Marketing is the art of making people want something. It is unnecessary for products people need.

So what happened at Apple?

Apple, perhaps by good luck, became perceived as a David vs the Goliaths of IBM and Microsoft. For some reason (was it deliberate?) Apple computers gained traction in music recording and graphic design, and gained a sort of bohemian chic that is rather impressive considering that it is essentially “Big Business” and, like most companies, designed to make money.

Clever partnerships, and particularly the inspired partnership with Adobe (think Acrobat PDF’s, think PhotoShop) strengthened their position with journalists, publishers and illustrators establishing the Mac as the creative profession’s computer of choice.

This turned out to be a good thing, as the naughties have been the most art friendly decade yet, as popular culture has come to resent things like ‘work’ and ‘industry’, and a certain sections of society have come to view activities like sport as trivial and meaningless when compared to the value and depth in culture, poetry, good food, yoga, spiritualism and so on.

In other words, the artists have moved up in the world.

Some of the more switched on folk will realise that brands like Gucci/Armani/Christian Dior or Ferrari/Porche/Aston Martin  or Rolex/Michel Herbelin/Patek Philippe are based entirely on massaging the egos of their customers, and in the last case, they probably don’t even keep better time than a black plastic Casio.

But not many of the arty crowd have realised that Apple is using their independent nature against them. The Mac user seems to be infected with the idea that in using a Mac they are somehow being beneficent to the world, will somehow be more creative, they they are part of some loving brotherhood that has exclusive access to the truth and the light.

This is because, by accident or design, the Apple brand has been developed to find that part of our mind that wants to believe and wants to belong, and is easily dazzled; the brand is acting like a religion.


Apple’s alliance with artists continues with U2 and the Black Eyes Peas, both highly credible symbols of free-thinking modernism. But I want you to ask yourself: what is free thinking about this computer company? I’m not sure, but I suspect the only free-thinking thing about Apple is its association with icons of the free-thinking world. It is just an electronics company for Pete’s sake. Like Sony, like Samsung, like Nokia.

If you believe there is any more to it than that, then you are welcome to pay for it.


PS: Besides the defunct G4 in the drawer, there is also an iPod classic in my home. I like it. I like to hold it. Mmm.