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!

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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 probalme (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.

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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?

Because they do all the time! 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.

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Air Fresheners Exposed!

22 05 2011

Ok, so I know its not a conspiracy to take over the world, but my inner nerd has been provoked.

Have you ever wondered how air fresheners work?

Let’s take a sceptical look.

Nanobot

This cool pic is from hybridmedicalanimation.com

I’d love to think that AirWick / Glade / {insert preferred brand here} consist of an army of nano-bots that round up and deport any molecules without the right paperwork.

Although we aren’t there yet, it’s actually not too far from the truth!

Although many cheap deodorisers do simply mask the truth by overpowering our senses, I really like to give credit where credit is due, so I am happy to disclose that there are indeed certain substances that can detain odours – such as zeolites and silica gels, and there are also organic molecules that will react with a wide array or hydrocarbons rendering them odourless. These ideas are in fact used by several big brands today.

Hurrah!

But that’s not the whole story, is it?

No, because none of that really means the substance (or it’s source) is ‘gone’; all they have done is disabled our ability to detect all that foreign matter around us!

The last time I looked, our sense of smell, just like our sight and hearing, was there to help us survive – to detect when there is something unsavoury in the vicinity and force us to deal with it. If your bed or sofa stinks, you should probably take it outside and try to remove to 5 lbs of skins flakes and  other sundry bodily oozings rather than spray the bed with an extra long burst of febreze.

You wouldn’t season rotten meat in curry then serve it to your in-laws, would you?

Now, to be fair, the purveyors of these products do not intend for you to use their product to allow you to live in filth disguised with the scent of lavender, and their scientists are smart people – however, there marketing departments do need to be brought to book for giving a few misleading impressions.

The world ‘fresh’ for example is used universally. I don’t know about you, but to me this should mean clean, pure and new. It may certainly allow for some sweet floral aroma, but it certainly doesn’t include ‘complex organics we cannot smell’.

Some solutions – like Resolve carpet cleaner, where an absorbent powder is applied liberally then hoovered up, deserve a break – but, as far as I can see there are the exception - most odour control is still in the form of the old “cover up”.

What we have to remember is that in order to claim a product is ‘absorbing’ an odour, one only need prove it absorbs ‘some’ odour – not necessarily the majority and very rarely “all”. Thus it can be that it absorbs 2% of the odour and the other 98% of the odour is still there but overwhelmed by the scent of a pine forest. The same is true with biocidal deodorisers (like Lysol) which may kill bacteria – a common source of odour. These products can actually kill germs – however the impression that a quick spray will effectively sterilise is falsely reassuring.

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I sign off now by pointing out that the best way to avoid odours is by good hygiene, though not too good: remember that we humans co-evolved with this slimy little planet!





Hysteresis Explained

1 04 2011

Hysteresis (hiss-ter-ee-sis). Lovely word. But what on earth does it mean?

Hysteresis is one of those typically jargonny words used by scientists that instantly renders the entire sentence if not lecture lost on its audience. Sure, you can look it up on wikipedia, but you may die of boredom before you get to the point, so I am going to explain it here.

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Hysteresis on the way to school

Let’s go for a walk. Let’s say we are ten years old and we are walking to school. The route is simple. The school is a few hundred yards down the hill on the other side of the road. Now consider the question: at what stage do we cross the road? Immediately? Or do we walk all the way to opposite the school before crossing – or somewhere between?

Assuming there are no ‘official’ crossing points, I bet you cross immediately, then walk down the far side of the road.

How can I make this prediction? Well, I assume that crossing the road requires there to be no traffic, so if there is no traffic as you start the journey, it is a good time to cross. If there is traffic, you just start walking down the road until a gap appears, then you cross. This strategy allows you to cross without losing any time. If your strategy had been to cross at the school there is a real risk you will need to wait, thus losing time. So it turns out the best strategy to avoid any waiting is to cross as soon as you can.

So now picture your walk home. Again, it makes sense to cross early on. The result is that the best route to school is not the same as the best route from school. This is an example of hysteresis – or a ‘path dependent phenomena’.

Hysteresis  everywhere

The dictionary will drone on about magnetism and capacitance and imaginary numbers. A much nicer example is melting and freezing of materials – some substances actually melt and freeze at different temperatures. This shows that the answer to the question: “is X a solid at temperature Y?” actually depends – on the path taken to that temperature. Just like what side of the road you are halfway between home and school will depend on whether you are coming or going.

It seems to me that falling asleep and waking up also bear some of the hallmarks of hysteresis; although they could be considered a simple state change in opposite directions, they feel very different to me – I  seem to drift to sleep, but tend to wake to alertness rather suddenly.

Now think of a golf club in mid swing. As the golfer swings, the head of the club lags behind the shaft. If the golfer where to swing in reverse, the club head would lag in the other direction – thus, you can  tell the direction of movement from a still photograph. We can therefore say the shape of a golf club exhibits hysteresis – and again you see see why it is so-called “path dependent”.

This logic can be taken further still – wetting is not the opposite of drying and likewise heating is rarely the inverse of of cooling. Let’s imagine for example that you want to make a chicken pie warm on the inside and cool on the outside. This is best done by warming the whole pie and then letting it cool a little. The temperature ‘profile’ inside your pie thus depends not only on the recent temperature but has a complex relationship with its more distant temperature history. This particular point is somewhat salient at the moment as we ask the question: is the earth heating up? 

So what?

Good question. I’m not a fan of jargon, and hysteresis is not a word I hope to need to use in my smalltalk. However, you can see that it encapsulates a rather specific and increasingly important concept that is pretty hard to replace with two or three simpler words; thus it passes my test of “words a scientist should understand that most don’t”. Please let me know your own additions to such a list!

 

 





Educational way to spend four minutes…

2 01 2011




Stuff I Wish I Had Read When I Was Younger

6 11 2010

Over the years I have supervised and mentored several PhD students, and recently our firm started to award scholarships to undergrads, and I was asked to support one such scholar. These scholars are from the best and brightest and so I got to thinking…

Graduates today have it tough, competition is tough, people work longer and harder than ever and stress is hitting us earlier and earlier in life – or so it seems. I would argue that, to some real extent, things have always been getting worse, and therefore by induction, we can prove that they have haven’t really changed at all.

No, the graduates of today have unparalleled opportunity to learn, to travel and to experience. The brightest graduates have the world at their feet and will be its commanders when we are are all retired and done for.

So what could I do to support this scholar? In the end it was easy – I asked myself – what do I know now that I wish I had known sooner? Most of this is in attitudes and is deep in my psychology, and is the result of direct experience – but it turns out that a healthy chunk of my scientific learning experience can be re-lived – by reading some of the books I think steered my course.

So I made a point to summarize some of the best science related books I have read (and some of the most useful internet resources I have found), and dumped the list complete with hyper-links in an email to the scholar. I hope she goes on to be president!

Now having gone to the effort, it would be a crime to keep this email secret, so here it is, (almost) verbatim!

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As promised, here is a list of useful resources I wish I had known about when I was an undergrad. I am glad I got round to this, it should be useful for several other students I work with, and has also led to me revisiting a few things! I think I may brush it up and pop in on my blog if you don’t mind…obviously I won’t mention you!
Anyway, back to the business. To me, science is not all about chemistry, molecules, atoms, valence electrons and so on. To me, is is the process of trying to understand the world, and this set of materials I have hand picked, should you get through even a part of it, will not only educate but inspire.

This may not be the very best list, and I am sure there are many great books I have not read, but I have stuck with ones that I have, so you will have to rely on other people for further recommendations.

Jarrod’s reading list: science/psychology/economics & so on

  • I’ll start with something really easy, relevant and engaging – an excellent (if quirky) summary of material science: The New Science of Strong Materials – Prof Gordon  has written another on Structures that is also worth reading.
  • Ok, this next one is not a book, but a paper; I like it because it shows that many stuffy professors are wrong when they prescribe boring scientific prose for papers. This paper uses the criminal “us” and “we” and discusses subjects as if with a friend. Shocking form, especially for a junior scientist. This paper by an unknown, changed the world.
  • Guns, Germs and Steel” – this is large-scale scientific thinking at its best- the book looks at how we can explain why the world is the way it is (especially the inequality) by looking at how technology spreads through societies.
  • Mistakes were made…but not by me” – this is required reading if you want to work with other people, so its basically for everyone then…
  • Then to take it to the next level – “How the mind works…” – Stephen Pinker‘s other books are also good if you like this one.
  • “Flatland”, (full text here) was written in 1884, and is essential reading because it defines the cliche “thinking outside of the box”.
  • To make your upcoming economics courses more interesting, first read this easy-to-read popular book: “The Undercover Economist“.
  • Also, Freakonomics- it’s shameless self promotion by egotistical authors, but hell they are smart, so put up with it.
  • The Tipping Point –  Malcolm Gladwell is a current thinker I really like; he’s not satisfied to focus on one thing for very long – his other books are on totally different stuff, but are equally thought provoking.
  • The selfish gene” – Obviously I would firstly recommend “On the Origin of Species”, (full text here) but if you are short of time (which you should be as an undergrad), you can learn most of the basics, and also get updated (well up to the 1970′s at any rate) by reading Dawkins’ classic.
  • I couldn’t ignore statistics, so I will include two – one classic, “How to Lie with Statistics“  and a more modern one “Reckoning with Risk“, they are quite different, but either will get the important points across.

Alas, books are perhaps becoming obsolete, so I better include some other media:-

  • The first one is so good I can’t believe its free – try watch at least one a week, but the odd binge is essential too. http://www.ted.com/
  • Next, an excellent physics recap (or primer) – but  you need lots of time (or a long commute!) to get through this lot – look on the left menu for Podacts/Webcasts on this webpage: http://muller.lbl.gov/teaching/physics10/pffp.html – I cannot begin to praise the worthwhileness of this enough. It used to be called “Physics for future presidents” because it teaches you enough to understand the risks of nuclear energy, and the likelihood that we will all run our cars on water – and let you know when you are being duped or dazzled by big words.
  • When I was somewhat younger there was a TV show called Cosmos, hosted by Carl Sagan, you may know of it. You could watch in now here, though obviously it is dated, so perhaps you shouldn’t; the reason I mention it, is because it was key in creating a generation of scientists, people who were inspired by Carl to be inspired by the universe. The previous generation had the space race and the moon landings to inspire them, but since then science has been on a downhill, with 3-mile island, global warming, etc, etc, and we have had no more Carl Sagans to cheer for us; Cosmos was a rare bit of resistance in the decline of the importance of science in society. You may also know that there have been battles in society (well in the circles on intelligentsia at any rate) about science – on the one had the ‘two cultures debate‘ and more recently, the ‘anti-science’ movement (suggested in books like “The Republican War on Science“. I do not wish to indoctrinate you, but rather make you aware that being a scientist used to be cooler and used to be more respected and something is indeed rotten in the state of Denmark.
  • Getting back on track, here is an excellent guide to critical thinking (something else sadly lacking in the world) – don’t read it, listen to the podcast versions (also on itunes):
    “A Magical Journey through the Land of Logical Fallacies” – Part 1 and Part 2
    I think this should be taught in school. Brian Dunning’s other Skeptoid podcasts put these lessons into practice showing how a scientific approach can debunk an awful lot of the nonsense that is out there (alternative medicine, water dowsers, fortune tellers, ghost hunters, etc etc).
  • If you do happen to have any time left, which I doubt, there are several other podcasts on critical thinking – that use a scientific approach to look at the world and current affairs: -

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Postscipt – Dear readers, please feel free to append your own recommendations to my letter in the comments section below. If there is one thing I know well, and that’s how little I know. I feel I only started to read ‘the good stuff’ far too late in life, and so those with more years than me (or better mentors), please do share. But bear in mind, this is principally a science oriented list, and is meant to be accessible to undergraduates – I left out books like Principia Mathematica (Newton) because it is really rather unreadable – and the Princeton Science Library (though awesome) is probably a bit too intense. Also, in the 30 minutes since I sent the email, I have already thought of several others I sort of, well, forgot:

That’s it for now…





What exactly is temperature? Ever wondered?

3 11 2010

We take it for granted. We understand it. It is obvious what temperature is. Cold, warm, hot…obvious.

But how many of us have asked the next question: what is the real difference between a hot stone and a cold one? The answer is interesting and helps us to realise that measuring temperature is much trickier than we tend to suppose.

Over many hundreds of years, many clever people have devised lots of experiments to understand what temperature is, I hope in this article to round up the facts!

Temperature and Energy

For much of history, there were only a few sources of heat – the sun, fire, lava and of course the warmth of living creatures.

People were puzzled by what created it, but it was immediately obvious that it had one consistency – whenever it had the chance, it flowed – put something hot next to something cold, and the heat would flow.

Of course you could argue that it was the ‘cold’ that flowed (the other way), but there were no obvious sources of ‘cold’. While ice was clearly cold, it was not a sustainable ‘source’ of cold the way a fire was.

It was also noted that heat melted things – like fat or butter and that it make some liquids (like molasses) thinner. It could even boil water and make it ‘vanish’. The mechanisms for these were unknown and a source of fascination for early scientists.

Early experimenters noticed that gases would increase in volume upon heating, and that compressing gases would cause them to heat up. They also investigated other sources of heat, like friction, (rubbing your hands together).

It was the work with gas that led to the big breakthrough. Boyle and Hooke, as well as Edme Marriotte, working in the 17th century, realized that the temperature of a gas would increase consistently with pressure, and like-wise, decrease consistently with pressure. This sounds unremarkable, until you note that you can only decrease pressure so much…

Once you have a vacuum (no pressure), you should have ‘no temperature’. Thus their observations implied that there really was a limit to how cold things could get, and predicted it was around -275 Celsius. They were of course unable to cool anything that far simply by expanding it because heat always flows into cold things, so to achieve this you need much better insulation than they had available.

So they had a big clue in the search to understand what temperature is, but still no explanation.

It took until 1738 until another great scientist moved us forward. Daniel Bernoulli realised you could use Newton’s (relatively new) laws to derive Boyle’s temperature-pressure relationship. He basically asked: what if gas was made of a large number of very small billiard balls flying around crashing into everything? What if pressure was just the result of all these collisions? Using this theory he realised, for the first time I think, what temperature truly is.

Source: Wikimedia Commons

It turns out that his model equated temperature with the speed of the billiard balls. A hot gas only differs from a cold gas in the speed of the molecules flying around. Faster molecules crash with more momentum and thus impart more pressure. Squashing the gas into a smaller volume does not give them more speed, but means more collisions each second, so higher pressure.

This is a pretty serious finding. It basically says ‘there is no such thing as temperature’. There is only lots of little balls flying around, and their number and speed dictate the pressure they exert, and there is no ‘temperature’.

If we put a thermometer into the gas, what is it detecting then? Great question.

It turns out that solids are also made of lots of balls, except, instead of being free to fly around, they are trapped in a matrix. When a solid is exposed to a hot gas,  it is bombarded by fast flying atoms. When a solid atom is hit, instead of flying off, it starts to vibrate, like a ball constrained by a network of springs.

So the ‘temperature of a solid is also a measure of speed of motion, but rather than linear speed it’s a measure of the speed of vibration. This makes a lot of sense – as the solid gets hotter, the balls are going literally ‘ballistic’ and eventually have enough speed to break the shackles of the matrix (aka melting).

Source: Wikimedia Commons

So this model of heat as ‘movement’ not only explains how gases exert pressure, but also explains how heat flows (through molecular collisions) and why things melt or vaporise.

More importantly, it shows that temperature is really just a symptom of another, more familiar, sort of energy – movement (or kinetic) energy.

Energy is a whole story of its own, but we can see now how energy and temperature relate – and how we can use energy to make things hot and cold.

Making Things Hot

There are many easy ways to make things hot. Electricity is a very convenient tool for heating – it turns out that when electric current flows, the torrent of electrons cannot help but buffet the atoms in the wire, and as they are not free to fly away, they just vibrate ever faster, ‘heating’ up.

Another way to heat things is with fire. Fire is just a chemical reaction – many types of molecules (like methane, or alcohol) contain a lot of ‘tension’, that is to say, they are like loaded springs just waiting to go off. Other molecules (often oxygen)  hold the ‘key’ to unlocking the spring, and when the springs go off, as you can imagine, it is like a room full of mousetraps and ping-pong balls – and all that motion – means heat.

Making Things Cold

Manipulating energy flows to make things cold is much trickier.

One way it to just put the thing you want to cool in a cold environment – like the north pole. But what if you want to make something colder than its surroundings?

Well there is a way. We learned earlier that gases  get hot when compressed – it turns out they do the opposite when decompressed or ‘vented’. This is the principle that makes the spray from aerosol cans (deodorant, lighter fluid, etc) cold. So how can we use this? First we use a compressor to compress a gas (most any gas will do); in the process it will warm up, then you let it cool down by contacting it with ambient air (through a long thin copper tube, but keeping it compressed), then decompress it again – hey presto, it is cold! Pump this cold gas through another copper tube, inside a box, and it will cool the air in the box – and hey presto, you have a refrigerator.

Measuring Temperature

Before we had thermometers, temperature was generally estimated by touch.

However this is where temperature gets tricky. Because the temperature we feel, when we put our hand on the roof of a car is not really the temperature of the car, it’s really the measure of energy flow (into our hand), which relates to the temperature, but also relates to the conductivity of the car.

This is why hot metal feels hotter than hot wood, why cold metal feels colder than cold wood – the metal, if at a different temperature to your hand, is able to move more heat into you (or take more heat away) faster than wood can. Thus our sense of temperature is easily fooled.

The ‘wind-chill factor’ is another way we are fooled – we generally walk around with cloths on, and even without clothes we have some body hair – therefore, we usually carry a thin layer of air around with us that is nearly the same temperature as we are. This helps us when it is cold and when it is hot – however, when the wind blows it rips this layer up and supplies fresh air to our skin – making us feel the temperature more than usual. Also, because our skin can be damp, there can be evaporative effects which can actually cool you below the air temperature.

Scientists have long known that we cannot trust ourselves to measure temperature, so over the ages many tricks have been developed – can the object boil water? Can it freeze water? A long list of milestone temperatures was developed and essential knowledge for early scientists – until the development of the lowly thermometer.

It was noted that, like gases, solids and liquids also expand upon heating. This makes intuitive sense if you think of hot molecules as violently vibrating – they push one another away, or at least if the charge  (electric charge is what holds these things together) is spread just a little thinner, adjacent molecules will have slightly weaker bonds.

The expansion of liquids may only be very slight, and if you have a big volume of liquid in a cup, the height in the cup will change only very slightly, but if its in a bottle with a narrow neck, the small extra volume makes a bigger difference to the level. This principle is used in a thermometer – it’s just a bottle with a very narrow and long neck. The bigger the volume and the narrower the neck, the more sensitive the thermometer. Of course the glass also expands, so it is important to calibrate the thermometer – put it in ice water, mark the liquid level – then put it in boiling water and mark the new level. Then divide the distance between these marks into 100 divisions – and hey presto! you have a thermometer calibrated to the centi (hundred) grade (aka Celsius) scale. Now you know where that came from!

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So that is temperature explained in a nutshell.  If you enjoyed this article you may enjoy my related article on energy.





How to prove that space is curved…

26 10 2010

Question: if you lived in flatland (a 2-d world), how could you tell if the land was curved in the third dimension?

Answer: geometry!

It turns out many of the mathematical rules we learned at school ‘fall apart’ if the working surface is curved. For example, can you draw a square on the surface of a sphere? No!

So can we use this insight to tell if our 3-d world is curved in a mysterious fourth dimension? Yes!

If we set off from earth, went in straight line for, say 1 light-year, then turned 90º, went 1 light-year, turned 90º again, and then did this yet again, you should have traced a perfect square, and be back exactly where you started. If you aren’t, something is amiss!

 

Now it turns out that it we do this, we will indeed discover an error; but why? And how do we know this?

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Newton told us that a massive object in motion will continue to travel in a straight line, unless acted upon by external forces. Some people think that Einstein overturned this insight, but he didn’t; indeed he extended it: he said that the force of gravity is not actually a force, and thus objects falling under gravity are actually going in straight lines! Indeed this makes sense, as anyone ‘falling’ does indeed not sense any acceleration, but rather feels ‘weightless’. Thus they are not actually accelerating, they are going straight – in curved space.

Now anyone who has thrown a ball can see this is absurd on the face of it, but Einstein was serious, and he is right, from a certain perspective. The ball is not going in a straight line through ‘regular’ space, but is going on a straight path in a 4-d construct called ‘space-time’. Likewise, he would argue that the planets are tracing straight lines around the sun; and indeed the ‘parabola’ of a baseball is actually not a parabola, but a very small part of the enormous ellipse that would be traced in the baseball could fall though the earth and go into ‘orbit’ §.

Anyway, Einstein’s model says that light travels in straight lines, but we have seen that light bends when it passes near to the sun (this can most easily be tested during an eclipse) – so… if one of the sides of your ‘perfect square’ were to pass near the sun, it would also be bent and if you followed the above rule to draw the square, you would not end up where you started.

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Physicists have grown used to Einstein’s model, and better tests for the flatness of space have been developed. For example, if you drew a circle on the surface of a sphere, the area would not equal Πr2, but would be less. Likewise, in 3-D space, we could plot a sphere and then measure the volume and if it did not equal 4/3Πr3, we would know something was amiss.

So physicists have looked at how light bends, and how the planets move, and found out, amazingly (but predicted by Einstein) that the error in this spherical volume calculation is directly proportional to the mass of matter within the sphere – proving that the warpage in space is proportional to (and thus caused by) ‘mass’.  Thus mass warps space.

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MC Escher: 'Grid'

But is space really warped in some ‘extra’ dimension?

Well, this is a good question. Maybe it is some extra ‘spacial type’ dimension, but you could also look at time as a fourth dimension, and argue that this space is not ‘curved’ at all, but rather that space and time simply vary in density in different locations. I personally like this way of looking at it, it eliminates the need for some vague ‘extra dimension’, and therefore swiftly removes the possibility that space could be ‘closed’ or fold back on itself in this extra spacial dimension. Occam’s razor thus prefers the ‘density’ model!

Footnotes:

§. In Wikipedia, they state that balls bounce in perfect parabolas, but note they also mention a ‘uniform’ gravitation field, and it is well to remember that the earth gravitational field is not uniform, but radial. Thus I stand by my assertion that missiles follow elliptical paths just like planets and comets. Of course, an ellipse is a close relative of both the parabola and the hyperbola, so this is not really that dramatic.





Skeptics vs Deniers

31 08 2010

There is a growing movement, grassroots in nature, but starting to connect, called the skeptics community.

Who exactly are they? Are they people who are starting to uncover the truth – that most world governments are a sham and that secret societies control our every move? Do they deny the holocaust and suspect 9/11 was a complex plot?

No.

A skeptic is merely someone who needs to be convinced of things through reason, rather than one who accepts things on some-one’s say-so.

Simple!

So what is a global warming ‘skeptic’?

Climate science is complex, and consensus opinion is that man’s activity has led to increased greenhouse gas emissions which are likely to reduce outgoing radiation and thus lead to a net shift upward in the temperature of the Earth’s delicate surface. Yes, there are other possible causes, yes, the models contain assumptions, and yes, some fools have fabricated data to look cool. It is also true that many respected scientists will not say it is a cast iron ‘fact’.

So that is the scene – and there seem to be a few types of stakeholders:

  • the ‘global warming denier’
  • the  ’global warming skeptic’
  • the regular ‘skeptic’
  • and lastly, the gullible!

A ‘global warming denier’ has come to mean someone who does not think the evidence stacks up enough to warrant concern, or worse, thinks it is all a giant conspiracy.

A ‘global warming skeptic’ has come to be somewhat synonymous with a denier, but perhaps without the conspiracy angle. However, many are just people who are on the fence – they are often very smart, and don’t just believe what they are told, but on the other hand, they are easily misled, as there is just so much misinformation out there. They may be the ones who say “I heard the jury is out…” rather than actually looking at evidence.

Some legitimate scientists have foolishly allowed themselves to be given this label, just because they debate some small details (like the rate of heating, or the likely nature of socio-political impacts). These scientists are then lumped with deniers. Tough luck to them.

I found this is some random folder on the 'net. If it's yours, please let me know, I love it! Update: it looks like it may well be from thisisindexed.com - click it to link - nice one Jessica Hagy!

Now a true skeptic will weigh all evidence according to the following principles:

  • is it logical?
  • does it conflict with other strong theories? If so, is it strong enough warrant a change to your previous understanding?
  • is there independent corroboration?
  • do the proponents have a  proven track record (credibility)?
  • is there any incentive by stakeholders to twist the facts?

This describes most good scientists, so its not a bad thing.

In the case of global warming, most true skeptics who have looked closely at the evidence and weighed it appropriately, agree that there is real cause for concern.

But yes, we skeptics will always retain just a little doubt, because you just never know…





Energy Explained in One Page

24 08 2010

Ok, so we all want to be good to the environment. The first step to doing this, as is often the case – is to understand the main characters in the story – and possibly the biggest character in the story in Energy.

However, energy is such a very vague concept, so where do you go to learn more? Do you have to do a physics course?

I don’t think so, and to test my theory, I have tried to explain energy as briefly as I can in this post.

Energy 101

Energy is what makes the world go round. Literally. Every neuron that sparks in your brain, every electron that fires down a wire, every molecule burning in a fire, carries with it a sort of momentum that it passes on like a baton in a complex relay race. The batons are flooding in all directions all around us and across the universe – they are energy and we have learned how to harness them.

The actual word “Energy” is a much abused term nowadays – because energy is used to represent such a disparate range of phenomena from heat to light to speed to weight, and because it seems to be able to change forms so readily, it is cannon fodder for pseudo-scientific and spiritual interpretation. However, you will be pleased to hear that it actually has a very clear (and consistent) nature.

I like to think of energy being a bit like money – it is a sort of currency that can be traded. It takes on various forms (dollars/pounds/swiss francs) and can be eventually cashed in to achieve something. However, just like money, once spent, it does not vanish. It simply moves on a new chapter in its life and may be reused indefinitely.

§Energy currencies:{1}Matter is energy(see footnotes) {2} Radiation {3} Chemical energy {4} Thermal (heat) energy {5} Compression energy {6} Kinetic (movement) energy {7} Electrical energy

To illustrate the point, let’s follow a ‘unit of energy’ through a visit to planet Earth to see what I mean. The [number] shows every time it changes currency (see the key on the right).

The energy starts off tied up in hydrogen atoms in the sun [1]. Suddenly, due to the immense pressure and heat, the nuclei of several atoms react to form a brand new helium atom, and a burst of radiation[2] is released. The radiation smashes into other nearby atoms heating them up so hot [4] that they glow, sending light [2] off into space. Several minutes pass in silence before the light bursts through the atmosphere and plunges down to the rainforest hitting a leaf. In the leaf the burst of power smashes a molecule of carbon dioxide and helps free the carbon to make food for the plant [3]. The plant may be eaten (giving food ‘Calories’), or may fall to the ground and settle and age for millions of years turning perhaps to coal. That coal may be dug up and burned to give heat [4] in a power station, boiling water to supply compressed steam [5] that may drive a turbine [6] which may be used to generate electricity [7] which we may then use in our homes to heat/light/move/cook or perhaps to recharge our mobile phone [3]. That energy will then be used to transmit microwaves when you make a call [2] which will mostly dissipate into the environment heating it (very) slightly [4]. Eventually the warmed earth radiates [2] this excess of heat off into the void where perhaps it will have another life…

This short story is testament to an enormous quantity of learning by our species, but there are some clear exclusions to be read into the story:

  • Energy fields (auras) or the energy lines in the body that conduct the “chi” (or life force) of Asian medical tradition
  • Energy lines on the Earth (aka Ley lines)
  • Negative or positive energy (as in positive or negative “vibes”)

These energy currencies relate to theories and beliefs that science has been unable to verify and thus they have no known “exchange rate”. Asking how many light bulbs can you power with your Chi is thus a nonsensical question, whereas it would not be for any scientifically supported form of energy. And since energy flows account for all actions in the universe, not being exchangeable would be rather limiting.

Where exactly is Energy kept?

This may sound like s strange question, we know Energy is kept in batteries, petrol tanks and chocolate chip cookies. But the question is, where exactly is it stored in those things?

Energy is stored in several ways:

  • as movement – any mass moving has energy by virtue of the movement, which is called Kinetic Energy
  • as matter – Einstein figured out that matter is just a form of energy, and the exchange rate is amazing – 1g = 90,000,000,000,000,000 joules (from E=mc^2)
  • as tension in force fields

That last one sounds a bit cryptic, but actually most of the energy we use is in this form –  petrol, food, batteries and even a raised hammer all store energy in what are essentially compressed (or stretched springs).

What is a force field? Why on earth did I have to bring that up?

All of space (even the interstellar vacuum) is permeated by force fields. The one we all know best is gravity – we know that if we lift a weight, we have to exert effort and that effort is then stored in that weight and can be recovered later by dropping it on your foot.

Gravity is only one of several force fields known to science. Magnetic fields are very similar – it takes energy to pull a magnet off the fridge , and so it is actually an energy store when kept away from the fridge.

The next force field is that created by electric charge (the electric field). For many years this was though to be a field all on its own, but a chap called Maxwell realised that electric fields and magnetic fields are in some senses two sides of the same coin, so physicists now talk of ‘electromagnetic’ fields. It turns out that electric energy (such as that stored in a capacitor) consists of tensions in this field, much like a raised weight is a tension in a gravity field. Perhaps surprisingly, light (as well as radio waves, microwaves and x-rays) are also energy stored in fluctuations of an energy field.

Much chemical energy is also stored in electric fields – for example, most atoms consist of positively charged nuclei and negatively charged electrons, and the further apart they are kept, the more energy they hold, just liked raised weights. As an electron is allowed to get closer to the nucleus, energy is released (generally as radiation, such as light – thus hot things glow).

The least well known force field is the strong ‘nuclear’ force. This is the forces that holds the subatomic particles (protons) together in the nucleus of atoms. Since the protons are all positively charged, they should want to repel each other, but something is keeping them at bay, and so physicists have inferred this force field must exist. It turns out their theory holds water, because if you can drag these protons a little bit apart, they will suddenly fly off with gusto. The strong nuclear force turns out to be bloody strong, but only works over a tiny distance. It rarely affects us as we rarely store energy with this energy field.

Now we understand force fields we can look at how molecules (petrol, oxygen, chocolate) store energy. All molecules are made of atoms connected to one other via various ‘bonds’ and these bonds are like springs. Different types of molecules have different amount of tension in these bonds – it turns out coal molecules, created millions of years ago with energy from the sun, are crammed full of tense bonds that are dying to re-arrnage to more relaxed configurations, which is exactly what happens when we apply oxygen and the little heat to start the reaction.

The complexity of the tensions in molecules are perhaps the most amazing in nature, as it is their re-arrangements that fuel life as we know it.

What exactly is Heat then?

You may have noticed that I did not include heat as a form of energy store above. But surely hot things are an energy store?

Yes, they are, but heat is actually just a sort of illusion. We use heat as a catch all term to describe the kinetic energy of the molecules and atoms. If you have a bottle of air, the temperature of the air is a direct consequence of the average speed of the molecules of gas jetting around bashing into one another.

As you heat the air, you are actually just increasing the speed of particles. If you compress the air, you may not increase their speed, but you will have more particles in the same volume, which also ‘feels’ hotter.

Solids are a little different – the atoms and molecules in solids do not have the freedom to fly around, so instead, they vibrate. It is like each molecule is constrained by elastic bands pulling in all directions. If the molecule is still, it is cold, but if it is bouncing around like a pinball, then it has kinetic energy, and feels hotter.

You can see from this viewpoint, that to talk of the temperature of an atom, or of a vacuum, is meaningless, because temperature is a macroscopic property of matter. On the other hand, you could technically argue that a flying bullet is red hot because it has so much kinetic energy…

Is Energy Reusable?

We as a species, have learned how to tap into flows of energy to get them to do our bidding. So big question: Will we use it all up?

Scientists have found that energy is pretty much indestructable – it is never “used-up”, it merely flows from one form into another. The problem is thus not that we will run out, but that we might foolishly convert it all into some unusable form.

Electricity is an example of really useful energy – we have machines that convert electricity into almost anything, whereas heat is only useful if you are cold, and light is only useful if you are in the dark.

Engineers also talk about the quality (or grade) of energy. An engineer would always prefer 1 litre of water 70 degrees warmer than room temperature, than 70 litres of water 1 degree warmer, even though these contain roughly the same embodied energy. You can use the hot water to boil an egg, or make tea, or you could mix it with 69 litres of room temperature water to heat it all by 1 degree. It is more flexible.

Unfortunately, most of the machines we use, turn good energy (electricity, petrol, light) into bad energy (usually “low grade heat”).

Why is low grade heat so bad? It turns out we have no decent machine to convert low grade heat into other forms of energy. In fact we cannot technically convert any forms of heat into energy unless we have something cold to hand which we are also willing to warm up; our machines can thus only extract energy by using hot an cold things together. A steam engine relies just as much on the environment that cools and condenses water vapour as it does on the coal its belly. Power stations rely on their cooling towers as much as their furnaces. It turns out that all our heat machines are stuck in this trap.

So, in summary, heat itself is not useful – it is temperature differences that we know how to harness, and the bigger the better.

This picture of energy lets us think differently about how we interact with energy. We have learned a few key facts:

  1. Energy is not destroyed, and cannot be totally used up – this should give us hope
  2. Energy is harnessed to do our dirty work, but tends to end up stuck in some ‘hard to use’ form

So all we need to do to save ourselves is:

  1. Re-use the same energy over and over
  2. by finding some way to extract energy from low grade heat

Alas, this is a harder nut to crack than fission power, so I am not holding my breath. It turns out that there is another annoying universal law that says that every time energy flows, it will somehow become less useful, like water running downhill. This is because energy can only flow one way: from something hot to something cold – thus once something hot and something cold meet and the temperature evens out, you have forever lost the useful energy you had.

It is as if we had a mountain range and were using avalanches to drive our engines. Not only will our mountains get shorter over time but our valleys will fill up too, and soon we will live on a flat plane and our engines will be silent.

The Big Picture

So the useful energy in the universe is being used up. Should we worry?

Yes and no.

Yes, you should worry because locally we are running out of easy sources of energy and will now have to start using sustainable ones. If we do not ramp up fast enough we will have catastrophic shortages.

No, should should no worry that we will run out, because there are sustainable sources – the sun pumps out so much more than we use, it is virtually limitless.

Oh, and yes again – because burning everything is messing up the chemistry of the atmosphere, which is also likely to cause catastrophe. Good news is that the solution to this is the same – most renewable energy sources do not have this unhappy side effect.

Oh, and in the really long term, yes we should worry again. All the energy in the universe will eventually convert to heat, and the heat will probably spread evenly throughout the universe, and even though all the energy will still be present and accounted for, it would be impossible to use and the universe would basically stop. Pretty dismal, but this is what many physicists believe: we all exist in the eddy currents of heat flows as the universe gradually heads for a luke-warm, and dead, equilibrium.

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Ok, so it was longer than a page, so sue me. If you liked this article, my first in a series on energy conservation, you might like my series on efficient motoring.

Please leave a comment, I seem to have very clued-up readers and always love know what you think!

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§ Footnotes:

[1] Matter is energy according the Einstein and the quantity relates to mass according to E=mc^2 (c is a constant equal to the speed of light).

[2] Radiation (like sunlight) is a flow of energy, and energy content relates the frequency according to E=hf (h is the Planck constant).

[3] Chemical energy – the most complex energy, a mixture of different tensions in nuclear and electromagnetic force fields.

[4] Thermal (heat) energy- this is really just a sneaky form of kinetic energy [6 below] – small particles moving and vibrating fast are sensed by us as heat.

[5] Compression (or tension) energy – while compressed air is again a sneaky form of kinetic energy [6], a compressed spring is different - it’s energy is more like chemical energy and is stored by creating tension in the force fields present in nature (gravity, electromagnetism and nuclear forces).

[6] Kinetic (movement) energy

[7] Electrical energy – this energy, like a compressed spring, is stored as stress in force fields, in this case electromagnetic force-fields.








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