Category Archives: Physics

What exactly is temperature? Ever wondered?

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…

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.

Did you know…

…that… Magenta Ain’t A Colour?

A nice bit of odd science from Liz Elliot.

It turns out that the block below is not a regular colour (wavelength of light), but a clever thing your brain has done, especially for you. Nice.

Magenta!

Of course, that is true for all colours, they are projections from our brains onto the world. The world itself has no colour, only common EM signatures we recognise and label with what we call ‘colour’. Gotta admire the brain, really.

Energy Explained in One Page

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.

What exactly is ‘science’?

I used to think science was the practice of the scientific method; i.e. you propose a hypothesis, you develop a test of the hypothesis, execute it and prove the hypothesis.

That worked for me until the end of high school.

At university, I was a true nerd. I read all my textbooks cover to cover (mainly because as I was too shy for girls and too poor for booze). During this time, the definition above started to fail. So much of the science was maths, statistics, observation, pattern recognition, logic and quite a bit of rote learning. Not all of it fitted into my definition of science. I became a fan of a new definition: science is the study of the nature of reality .

But then I did post-grad, and I realised that not much in science is ‘proven’ (I guess this is the point of post grad study). Evolution, for example, is not proven. That the sun revolves around the earth is not ‘proven’. I discovered that the only things that could be proven were ‘ideas’ about ‘other ideas’. Bear with me on this one.

Let us say we define the number system – this is an ‘idea’ or conceptual construction. Within this construction we can ‘prove’ that one and one is two. Because we ‘made’ the system, with rules, then we can make factual and true statements about it. We can’t do this about the real world – we cannot say anything with absolute certainly because we rely on flaky inputs like our own highly fallible perception.

It’s like that old chestnut: how can you be sure you are not living in a giant simulation? Of course you can argue that it is pretty unlikely and I would agree, and right there we have a clue to a better definition of science.

It turns out that much of modern science deals in ‘likelihood’ and ‘probability’ rather than proof and certainty. For example, we can say that the theory of evolution is very likely to be more-or-less right, as there is a lot of corroborating evidence. Science cannot be run like a law court – where the prosecution only need to reach a threshold of reasonable doubt to ‘prove’ someone guilty.

Aside for nerds: Science says you can use logic to prove things absolutely, but logic only works with ideas, and there is a breakdown between ideas and reality, so one can never prove things in reality. So it is thoroughly wrong for a court to say that someone has been proven guilty. The courts use this language as a convenience, to “draw a line under” a case as they have not found a moral way to dole out punishments based on probabilities. Imagine a world in which a murder suspect gets a 5 year sentence because the was a 20% chance he was guilty! Sports referees often operate in this decisive way, perhaps because it saves a lot of arguing!

Anyway, good science cannot just give up and say once there is consensus something passes from theory to fact. This is sloppy. We have to keep our options open – forever.

Think for example of Newton’s Laws of Motion. They are called ‘Laws’ because the scientific community had so much faith in them they passed from theory (or a proposed model) to accepted fact. But they were then found wrong. Strange that we persist in calling them laws!

It took Einstein’s courage (and open mindedness) to try out theories that dispensed with a key plank of the laws – that time was utterly inflexible and completely constant and reliable.

So it is that the canon of scientific knowledge has become a complex web of evidence and theories that attempt to ‘best fit’ the evidence.

Alas, there are still many propositions that many so-called scientists would claim are fact or at least ‘above reproach’. Evolution is attacked (rather pathetically), but the defenders would do well to take care before they call it ‘fact’. It is not fact, it is a superbly good explanation for the evidence, which has yet to fail a test of its predictions. So it is very very likely to be right, but it cannot be said to be fact.

This is not just a point of pedantry (though I am a bit of a pedant) – it is critical to keep this in mind as it is the key to improving our model.

Two great examples of models people forget are still in flux…

1) The big bang theory

2) Quantum theory

I will not go into global warming here though it is tempting. That is one where it doesn’t even matter if it is fact, because game theory tells you that either way, we better stop making CO2 urgently.

Back to the big bang.

I heard on the Skeptic’s Guide podcast today about an NSF questionnaire that quizzed people about whether they believed the universe was started with a massive explosion, and they tried to paint the picture that if you didn’t believe that, then you were ignorant of science. This annoyed me, because the big bang theory is now too often spoken of as if it were fact. Yes, the theory contributes viable explanations for red-shifted pulsars, background radiation, etc, etc, but people are quick to forget that it is an extrapolation relying on a fairly tall pile of suppositions.

I am not saying it is wrong, all I am saying is that it would be crazy to stop exploring other possibilities at this point.

You get a feeling for the sort of doubts you should have from the following thought experiment:

Imagine you are a photon born in the big bang. You have no mass, so you cannot help but travel at ‘light speed’. But being an obedient photon, you obey the contractions in the Lorentz equations to the letter, and time thus cannot pass for you. However, you are minding your own business one day when suddenly you zoom down toward planet earth and head straight into a big radiotelescope. Scientists analyse you and declare that you are background radiation dating from the big bang and that you have been travelling for over 13 billion years (they know this because they can backtrack the expansion of the universe). Only trouble is, that for you, no time has passed, so for you, the universe is still new. Who is right? What about a particle that was travelling at 0.999 x the speed of light since the big bang? For it, the universe is some other intermediate age. So how old is the universe, really?

This reminds us of the fundamental proposition of relatively – time is like a gooey compressible stretchable mess, and so is space, so the distance across the universe may be 13.5 billion light years, or it might be a micron (how it felt to the photon). It all depends on your perspective. It is much like the statement that the sun does not revolve around the earth and that it is the other way around. No! The sun does revolve a round the earth. You can see it clearly does. From our perspective at least.

Now, quantum theory.

Where do I start? String theory? Entanglement? Please.

The study of forces, particles, EM radiation and the like is the most exciting part of science. But being so complex, so mysterious, so weird and counter intuitive, it is super vulnerable to abuse.

Most people have no idea how to judge the merits of quantum theories. Physicists are so deep in there, they have little time (or desire or capability) to explain themselves. They also love the mystique.

I do not want to ingratiate myself with physicists, so I will add that the vast majority have complete integrity. They do want to understand and then share. However, I have been working in the field for long enough to know that there are weaknesses, holes and downright contradictions in the modern theory that are often underplayed. In fact these weaknesses are what make the field so attractive to people like me, but is also a dirty little secret.

The fact is that the three forces (weak nuclear, strong nuclear and magnetic) have not been explained anything like as well as gravity has (by relativity). And don’t get me started on quantum gravity.

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Anyway, thinking about all these issues, I concluded that science was (definition #3) the grand (platonic) model we are building of reality, ever evolving to best fit our observations.

My man, Plato

That works well for me. However, I recently came across a totally different definition for science:

# 4) “Science is a tool to help make the subjective objective.”

OK I paraphrased it to make it more snappy. It was really a discussion about how science was developed to overcome the fallibility of the human mind. Examples of weaknesses it needs to overcome are:

  1. The way our perception is filtered by preconceptions
  2. How we see pattern where there is none
  3. How we select evidence to match our opinion (confirmation bias)
  4. How we  read too much into anecdotal evidence
  5. etc etc.

I could go on. So ‘science’ is the collection of tricks we use to overcome our weaknesses.

I like this definition. We are all going about, and in our heads we are building our model of the world… and its time for an audit!

Is the Earth like a fractal?

Have you ever spent any time looking at the Mandelbrot set? I don’t mean a cursory glance, I mean really contemplated it?

Mandelbrot set

The Mandelbrot set. The horizontal axis is the number line,

And I don’t even mean the fancy coloured versions, just the straight black-and-white one (see image on right)?

It is really far more interesting than it looks…

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At first glance it just looks like a prickly pear gone wrong, so what is so interesting?

Well, remember this graph shows a set, that is to say it divides numbers into two groups, those inside the set, and those outside.

You could easily create such a set with circle – you can define the co-ordinates inside the circle is ‘in’ the set and that which is outside the circle outside the set. Such a set can be defined in a sentence: it is all points c less than the distance r from the origin.

The Mandelbrot set is just the same – a shape that divides space into two regions – in the image, the black area shows the numbers in the set, and the white area show the numbers out of the set. The only difference from a circle is that the Mandelbrot shape is more wiggly.

It equation is not much longer to define:

It is all numbers c, where if you square the number, then add the number, then square the result and add the number again, then repeat, it does not tend to infinity.

So zero is in the set, if you square it, then add it, it is still zero.

How about 1? No, it will run off: 1,2,3, 4, …

-1, on the other hand, squared, is 1, then added, goes to zero, where it will get stuck: -1, 0,0,0…

Figuring out the contents of the set is however complicated. Bloody complicated. Infinitely complicated in fact, and one of the marvels of the mathematical world.

To get a feeling exactly how complex this set is, take a look at some animations in which you zoom in on the perimeter; you can google “fractal dive” for more…

Mandelbrot Zoom Animation

You can choose what part of the set to zoom into yourself, if you want, here: http://www.h-schmidt.net/MandelApplet/mandelapplet.html

It seems that one simple sentence has been able to define an infinitely complex boundary, and begs some interesting questions: have we created a sort of universe? What is the information content of this set?

It makes my head hurt.

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The area of specific interest to me, is the relationship between the platonic ‘world of maths’ and the real world; so are there parallels between such complexity in the world of numbers and the real world?

Clearly fractals sometimes have similarity to things in the real world – such as crystals, feathers and broccoli florets. We see many reminders of complex structure in the real world, and it brings me to think of the earth as a sort of giant 3-d fractal – where the solid matter is ‘in the set’ and the gas of the atmosphere and the vacuum of space is “out of the set”.

We can see that the interface, the earth’s surface, also has complex structure, including such things as crystal caves or the lining of your lungs – and like with the Mandelbrot, we also seem able to zoom in to many levels.

However, just as there are no perfect spheres in the real world, there are no perfect fractals, and it seems that the structure falls apart once we get to subatomic levels of zoom (or does it?)

Some part’s of the earth’s interface are fractal-like due to the iterative nature of their construction (tree growth, crystal growth, sea-shells, etc.), and you can see that a simple rule of “branching” in a plant can make a complex shape. However, some of the complexity, specifically organic and bio-chemistry, still seem different (to me anyway).

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Krzysztof Marczak Mandelbulb

Krzysztof Marczak's Mandelbulb rendering

Now it turns out that my idea of the earth as a fractal with its skin as a complex interface can be more closely matched to the newly invented (discovered?) “Mandelbulb”, the amazing 3-d set. The interesting story of their development is told by one of their key developers, Daniel White, here.

The Mandelbulb is amazing because, as with many other fractals, you can zoom in and see ever more fascinating detail, and with incredible variation, and if you zoom into it continuously it would not be unlike zooming in on planet earth using Google Earth.

This excellent video below shows the idea of zooming into the Earth off well  (it seems to be derived from a book I happen to have called “Powers of Ten“).

So of course, you can do a similar trick on the Mandelbulb:

Enough said!

Open question about relativity

A quick open question for physicists:

If you accelerate off in one direction, and keep accelerating until you are travelling fast (a relativistic speed), special relativity supposedly says the universe contracts in the direction of your travel. Fine, I can see how that makes some sense.

Now consider a massive body, such as the sun – it warps space time in its vicinity, presumably roughly equally in all directions, creating a symmetrical ‘dent’ in the fabric of space-time (if you like the trampoline analogy).

But if you fly past at a relativistic speed, and space is contracted in the direction of your travel, will the sun’s sphere of influence also be contracted, turning it from a “sphere of influence” into an ‘oblate spheroid of influence’?

Or will its shape be maintained for some beautiful reason (which is what I suspect)?

Thx.

The interesting implications of our theory of gravity…

The evidence is now pretty strong that Gravity is just a symptom of ‘curved’ space time.

While it’s cool to have gravity all figured out, like so many matters in science, the answer raises even more interesting questions.

Like what is the nature of the curvature? Well, people (including me) are still trying to figure this out. In the meantime it is a good pastime to pontificate about the implications of curved space time. Here are two of my most recent theories/perspectives…

Perspective 1: Trees and apples switch places…

Each mass has a ‘destined path’, a path it will follow if left to its own devices. Just as Newton suggested in his First Law of Motion, things only change velocity when experiencing a net force.

However, he thought that gravity was a ‘force’ that made apples drop, however, the new theory of gravity suggests the apple was stationary – it was the tree and the meadow that were accelerating (upwards), a result of being pushed by the ground.

It lets us think of falling objects as ‘free from force’, and obeying Newton’s First Law.

Now, switch gears. Think what would happen if you could walk through solid things like walls. You may think it useful, but it would certainly cause some inconvenience, as you would presumable fall through the floor and plunge into the Earth’s molten core. You would fall past the centre and then start slowing; you would then briefly surface on the other side of the Earth, only to fall again. You would thus oscillate on some sort of sine wave. This is your ‘destined path’, the straight line through space time that your mass and location intend for you, where you to follow Newton #1. It is simply all the floor tiles and rocks preventing you from going straight in space-time. You are thus constantly being pushed, and thus curving off that path, thanks to the force of the floor. Lucky thing really.

Perspective 2: Slow time really is a drag…

A gravitational field can also be thought of as a gradient in the speed of time. It is possible (to me at least) that rather than supposing space-time is curved, it may well be that it simply varies in ‘density’. How? Well if time passes at different speeds in different places, that can be thought of as a density difference.

Now, we know that even when standing still, we are still plunging ahead – through space-time – in the direction of time. However,  thanks to Earth’s gravity, time is going slower down at your feet, they are sluggish, stuck in the mud. Now if you have a pair of wheels on a fixed axle, what happens if your right wheel gets stuck in the mud? It slows and you turn to the right… and in the just the same way, your body is trying to ‘turn’ downwards toward your feet – the gravity you feel!

When I first thought of this model, I was smug and pleased with myself. Until I found someone else[1] had already used it to accurately model planetary orbits. Read about it here – they have shown that waves (and therefore particles) will curve for the above reason combined with Fermat’s Principle. Bastards! 😉

 

Refs:

[1] Landau, LD; Lifshitz, EM (1975). The Classical Theory of Fields (Course of Theoretical Physics, Vol. 2) (revised 4th English ed.). New York: Pergamon Press. pp. pp. 299–309. ISBN 978-0-08-018176-9

Gravity explained in 761 words

People seem to be harbouring the impression that there is no good theory of Gravity yet. I asked a few friends – most thought Newton had explained it, but couldn’t explain it themselves. This is rather sad, 80-odd years after a darn good theory was proposed.

Of course there is still some controvery and the odd contradiction with other beloved theories, but the heart of the General Theory of Relativity really does a great job of explaining gravity and it is really wonderfully beautiful, and can be roughly explained without recourse to jargon and equations.

This is a theory that’s just so darn elegant, it looks, smells and tastes right – once you get it. Of course, the ‘taste’ of a theory doesn’t hold much water; for a theory to survive it needs to make testable predictions (this one does) and needs to survive all manner of logical challenges (so-far-so-good for this one too).

This is not a theory that needs to remain the exclusive domain of physicists, so for my own personal development as a scientist and writer, I thought I might try an exercise in explaining what gravity is – according to the general theory of relativity.

For some reason, my wife thinks this is strange behaviour!

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The story really got started when Einstien realised that someone in an accelerating  spaceship would experience forces indistinguishable from the gravity felt back on Earth. 

He or she could drop things and they would fall to the floor (assuming the spaceship is accellerating upwards)  just as they would fall on earth.

So perhaps that’s all gravity is… some sort of accelleration? Let’s see.

In the spaceship, it’s clear to us that the objects would appear to fall to the floor, but in reality, it is the floor of the spaceship that is rushing up towards the objects – this explains why things fall at the same speed whether heavy or light, matching Galileo’s own test results when he dropped various things, supposedly from the leaning tower of Pisa. It further implies that things will ‘fall’ even if they have no mass at all… such as light beams.

The thought experiment goes thus: Consider if you had a laser-beam shining across the spaceship control room; it would curve slightly downwards, because the light hitting the opposite wall would have been emitted a little time ago, when the spaceship was a little way back, and going a bit slower (remember, its accellerating).

We know the light is not bending, it is just that the source is accellerating, resulting in a curved beam. Imagine a machine-gun spraying bullets across a field – as you swing the gun back and forth the bullets may form curved streams of bullets, but each individual bullet still goes straight.

So Einstein suggested that perhaps light beams will bend in this same way here on earth under a gravitational field. Now Newton’s theory of gravity says light beams may also bend if they have ‘mass’, but the mass of light is a dodgy concept at best (it has inertia but no rest mass, but that’s a whole different blog posting). Anyway, even it it does have mass, it would bend differently from what Einstien predicted. So the race was on to see how much gravity could bend light…

This bending of light prediction was proven by a fellow called Eddington who showed that during a solar eclipse, light from distant stars was indeed bent as it passed near the sun, and by exactly the predicted angle.

Einstein went further though, suggested that light beams on Earth are, just like on the spaceship, really travelling straight, and only appear to bend, and that this can be so if space-time itself is curved. They are going straight, but in curved space.

We know that the shortest distance between two points is a straight line, but if that line is on a curved surface, supposedly straight lines can do strange things – like looping back on themselves. Think of the equator. This model therefore allows things like planets to travel in straight lines around the sun (yes, you read right).

The model has been tested and shown to work, and gives good predictions for planetary motion.

So what can we take home from all this?

Well mainly, if this model is right, we need to let it sink in that gravity may not be a force at all, but an illusion, like the centrifugal ‘force’ you experience when you drive around a corner.

Secondly, it is an open invitation to think about curved space and its marvellous implications!

How to jump higher

Have you ever noticed that in order to jump your highest, you need a few preparatory steps and a preparatory hop? Have you ever wondered why?

Well, perhaps sadly, I have. I was wondering if this was mere mental preparation – because surely your ability to jump high is going to be dictated by a) the power in your legs on the one hand, and b) your weight on the other hand?

Turns out it’s not.

But why not? And what do the preparatory leg movements do?

If you think the steps are “warming you muscles up” in preparation for the jump you are, in some sense, right – right that you are preparing, but its not the muscles you are preparing but the tendons…

But what are tendons, and what do they do? Good question.

I used to think that tendons were there to help glue the muscles to the skeleton, like the ropes on sailboats glue the sail to the mast and boom. I later realised that they also help make the body more ergonomic by allowing the muscles to be positioned ‘out-of-the-way’ as is the case for your hands; if all the muscles used for your fingers were actually in your fingers they would be rather fat, and not particularly dexterous.

Likewise, if you had to carry your calf muscles in your feet, it would make your feet somewhat heavier and mean you would have to swing lots of weight back-and-forth, up-and-down when you walk and run. Although the calves and thighs still have to move a bit, tendons have allowed the movement to be reduced substantially by connecting these muscle groups to the feet from safer havens further up the leg. 

Interestingly (to me anyway), this also explains why some people can’t bend their little finger independently of the second (ring) finger – they are sharing tendons that go right up the forearm!

Ah, but none of that explains why we need to hop before we can jump.  True enough – there is another property or function of the tendon that had never occurred to me – until I read “The new science of strong materials” by J.E. Gordon (which I must recommend to scientists of all disciplines, it s a lovely book, I wish I had written it).

So what does a book on material science have to do with tendons? Well, it points out that tendon is unique among materials for its capacity to stretch and in doing so, to store energy. In other words, tendons make remarkably good springs (and explains why animal tendons have been used to make crossbows for thousands of years). 

Springs can be thought of as batteries, you put a bit of effort into stretching them now, and the effort is stored there for later use – to shoot an arrow for example.

So,  it’s simple really, your legs are like a pair of crossbows: if you pre-stretch the tendons before the jump, and then co-ordinate the energy release to coincide with the power stroke of your muscles, you will jump higher.

And finally, it turns out that a rather good way to pre-stretch the tendons is to hop before we jump. So there you are!

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You will probably have noticed that good basket-ballers and high jumpers have taken this further (whether understanding it or not). They run along horizontally at a fair speed (gaining kinetic energy), and then thump down their leg at an angle, transferring all that kinetic energy into their tendons, and then re-cooping it in a vertical jumping burst. I have not done the maths, but I am willing to bet the tendons do much more work than the muscles in the crucial powering phase of the jump.

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Something to try:

Have you ever noticed how much easier it is to do 20 jumps in a row rather than 10 jumps with pauses between each one? This is because the pauses between jumps force you to dissipate the energy in your tendons, and so every jump is pure muscle work.

It is also worth noting that even the task of dissipating the energy stored in tendons is tiring for your body – the muscles actually work against the tendons to turn the energy into heat, which is similar to the work your muscles have to do when you walk down stairs.

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Final word…

The really nerdy readers (those after my own heart) will have further noted that this all goes a long way to explain why PE teachers seem to be so obsessed with stretching. You thought it was just to prevent injury? Think again – while it is essential to warm up and down carefully and stretching once warm does reduce the risk of injury, this is largely because stretching improves the condition of your tendons.

So don’t rush through the stretching next time you go to the gym; stretching and flexing your tendons may well do more to improve your athletic performance than muscle work.  Tendons deserve a part in any workout, please don’t neglect them – they are, after all, the forgotten workhorse of the body.