In the previous post (http://wp.me/p2IwTC-6m) I gave a simplified account of why time and position are considered relative, in which each observer has his own version of what “here” and “now” means. We need some means of describing what an observer sees. An absolute position would be like GPS coordinates. Everybody agrees where the equator is, and we have made Greenwich a reference point for longitude, but in the general Universe there are no obvious reference points. Without a reference point, “here” is meaningless unless expressed as a distance from something else, and this has been well established since Galileo’s time, if not earlier. There was thought to be “aether” through which everything travelled, but Michelson and Morley provided evidence there was no such thing. The formalism of Einstein’s relativity puts time in a similar position, and it dilates as velocities approach that of light. This is accounted for with what is called “space-time”, in which time is just another relative coordinate.

All observed evidence is in accord with this, and an example is the lifetime of muons. The muon is an elementary particle that decays to an electron with a half-life of about 1.5 microseconds. However, if the muons were travelling at about 98% the velocity of light, applying the Lorentz-Fitzgerald factor for time dilation, as required by special relativity, it has been shown that this half-life is about 5 times longer, and most importantly, muons behave as if they live five times longer when travelling at such velocities. From an observer considering the muon’s point of view, the reason it lasts longer is because the distance it thinks it has travelled is shorter. This suggests that time is relative, and the equations of relativity invariably give the correct prediction of a measurement.

Consider a space traveller. According to relativity, if the traveller heads off at near the speed of light and travels far enough, then comes back, time has essentially stopped for the traveller, but not for whoever is left behind. That was the basis of my scifi trilogy “Gaius Claudius Scaevola”. Within the trilogy, Scaevola starts in Roman times, gets abducted by aliens, and returns sometime like the 23rd century, and he has aged a few years only. The principle of relativity is that all clocks in a moving ship must slow down equally; as Feynman remarks in Six not so easy pieces, if this were not so, you could use something like the rate of development of a cancer to work out the absolute velocity of a space ship. To further quote Feynman, “if no way of measuring time gives anything but a slower rate, we shall have to say, in a certain sense, that time itself appears to be slower in the space ship”. The best-known application is the GPS system. Without the equations of General Relativity, this simply would not work.

Nevertheless, I believe there is a way of measuring an absolute time. Suppose a similar traveller headed off to a galaxy five hundred light years away at light speed, and, in accord with relative time, came back a billion years later without having aged. Now suppose he and another physicist from the future decided to measure the age of the Universe, that is the time from the big bang. The equipment is set up and gives a meter reading. Surely both must obtain the same reading since they see the same dial, yet according to the traveller, the Universe should be only13.8 billion years old, while the measurement gives it at 14.8 billion years old. There is only one possibility: the Universe is 14.8 billion years old, and all that has happened is that the traveller has simply not observed the passing of a billion years. The point is, when considering distance, there is no reference position. When considering time, there IS a reference time, and the expansion of the universe provides a fixed clock that is a reference visible to any observer. Worse, you could in principle work out the age of the Universe from within the ship, so in principle you could use this to work out the speed, apart from the fact that determining the age of the Universe is not exactly accurate. So why does muon decay slow?

Suppose we start with no muons, then at time t we shall have nt muons, given by (assuming the number of decays are proportional to the number there)

n_t=n_0 e^(-kt)

Now it is obvious that you get the same result if either k or t is dilated.

What is k? It is the “constant” that is characteristic of the decay, and it can be considered as the barrier to decay, or the tendency of the particle to hold together. Is there any way that could change? Does it have to be constant?

This gets a bit more difficult, but Einstein’s relativity can actually be represented in a slightly different way than usual. For those with a grasp of physics, I recommend Feynman’s “Six not so easy pieces”. When Feynman says they are not so easy, he is not joking. Nevertheless one point he makes is that Einstein’s special theory of relativity can be represented solely in terms of a mass enhancement due to velocities near the speed of light. What that means is that as the muon (or the space traveller) approaches the speed of light, it gets more massive. If that energy is concentrated on the muon, then the added mass might dilate k by increasing the barrier to decomposition. It is not necessarily time that is changing, but rather the physical relationships dependent on time. Does it matter? In my view, yes. I would like to think in science we are trying to determine what nature does, and not that which happens to be convenient at the time.

In many cases in science, like the equation above, there can be more than one reason why an equation works. Another point is that the essence of a scientific theory should be able to be conveyed without the use of difficult mathematics, although, of course, to make specific use of the concepts, difficult mathematics are needed. What the scientists should do is to ask questions of a theory, and then test the answers.

As an example of such a question, we might ask, did Michelson and Morley really prove there is no aether? My view is, no they did not, although that does not mean there is aether. The reason is this. If light always has the same velocity relative to the aether, it must interact with it. That means there is an interaction between aether and electromagnetism. Now molecules have local electromagnetic fields, and such molecules travel fast and randomly, and might very well “trap” aether. Think about a river flowing, with reeds along the bank. The water flows strongly, but if you try to measure the flow in a reed-bed, the water is virtually stationary. In the same way, the random motion of air might trap aether near the earth’s surface. What science suggests now is simple: repeat the Michelson Morley experiment outside the space station. Suppose the answer was still zero. Then Einstein’s theory is firm. Suppose the answer is not zero? Actually, the equations of Einstein’s relativity would not change all that much, and would actually become a little more complicated, but the differences would probably not be discernible in any current experiment. What do I think? That is actually irrelevant. The whole point of science is to ask questions, to try and uncover further aspects of nature. For it is what nature does that is relevant, not what we want it to do. What do you think?

# Monthly Archives: January 2015

# Simple relativity

During the summer break, I got involved in the issue of whether time was relative, but before I can discuss that, I need to be sure readers understand what relativity is. Most would consider relativity to be essentially mathematical. Not really. The principle of relativity is quite simple, and goes back a long way. In Il Dialogo, Galileo pointed out that if you were below decks in a boat, you have no idea how fast it was going, nor for that matter, in what direction. You could get up on deck and work out how fast you were going relative to the water, but there is no absolute velocity, for if you can see land, you may have a different velocity if there is a tidal flow or current. Then, of course, the earth is rotating, orbiting the sun, the sun is orbiting the galactic centre, and the galaxy is also moving relative to other galaxies. The point is, unless there is a fundamental reference there is no absolute velocity, but only a velocity relative to something else, and that depends on your perspective. As Einstein once remarked when on a train, “The Zurich Railway Station is approaching, and will shortly stop outside the train.” Bizarre though that may sound, that encompasses relativity.

The simplest way to look at this is to answer the question, “Where are you?” There are two probable answers. One is “Here!” Not very helpful when half the population answer the same way, in which case “here” is a different place for different people. The second answer is to give an address, or coordinates. The means you are defining your position as being at some distance from something else. Velocities represent the rate of change of position, and are vectors, which means they have magnitude and direction. Coming and going have quite different effects. Think of standing in the middle of a road and there is a car on it. However, when direction is properly taken into account, velocities are additive, at least in Galilean relativity. Suppose we have two fleets of ships heading to each other. Each is entitled to consider itself as motionless in its own frame of reference, with the other fleet approaching at a velocity that is the sum of the vectors in a third frame of reference.

James Clerk Maxwell gave physics a huge problem by writing his equations of electromagnetism in the form of a wave equation, when he found the velocity of his wave was more or less equal to the known speed of light. Accordingly, he stated that light was an electromagnetic wave that travelled at velocity c. The problem was, relative to what? His equation equated the velocity to constants that were properties of space itself. Still, if the waves moved through something, namely aether, they would have a velocity relative to the aether. When Michelson and Morley carried out an experiment to measure this, they found nothing. (Actually, they found a very small velocity, but that was put down to experimental error because it did not reflect the earth’s movement properly.) For Einstein, the velocity of light was constant to any observer, and there was no aether, nor any absolute motion. Making sense of this involves mathematics that are a little more complicated than those of Newtonian physics, and now we have a problem as to what it means. The interpretation most people accept was proposed by George Fitzgerald and Hendrik Lorentz, and involved space contraction in the direction of motion. The basis of this can be imagined by considering two space ships flying parallel to each other, and going in a fixed direction. Suppose one sends a signal to the other that is reflected. The principle of relativity is from the space-ships’ point of view, the other ship is stationary, but from an external observer, the signal does not go directly to the other ship, but rather travels along the hypotenuse of a right-angles triangle, which now requires Pythagoras’ theorem to untangle the maths. Complicated?

There are some seemingly absurd results obtained from relativity, but it should be noted that these arise from what different observers, each travelling at near light speed, interpret an event they see. The complication is each sees the light coming to them at the same velocity, and this leads to some more complicated maths. Strange though it may seem, the equations always give correct agreement with observation, and there is little doubt the equations are correct. The question then is, are the observations and equations being properly interpreted? Generally speaking, the maths have taken relativity quite some distance, using a concept called space-time, and in that, time is always relative as well. It would generally be thought to be near impossible to solve anything of significance in General Relativity without the use of space-time, so it must be right, surely? In my Gaius Claudius Scaevola trilogy I make use of the time dilation effect. To fix a problem in the 23rd century, a small party of Romans have to be abducted by aliens in the first century. They travel extremely close to the speed of light, and when they return, they arrive at the right time, having burned through 2,200 years, and have aged a few years. Obviously, I believe time is relative too, don’t I? More next week.

# Science, the nature of theory, and global warming.

My summery slumbers have passed, but while having them, I had web discussions, including one on the nature of time. (More on that in a later post.) I also got entangled in a discussion on global warming, and got one comment that really annoyed me: I was accused of being logical. It was suggested that how you feel is more important. Well, how you feel cannot influence nature. Unfortunately, it seems to influence politicians, who end up deciding. So what I thought I would do is post on the nature of theory. I have written an ebook on what theory is and how to form theories, and while the name I gave it was not one that would attract a lot of readers (Aristotelian methodology in the physical sciences) it was no worse than “How to form a theory”. Before some readers turn off, I started that ebook with this thought: everyone has theories. For most, they are not that important, e.g. a theory on who trashed the letterbox. Nevertheless, the principles of how to go about it should be the same.

In the above ebook, I gave global warming as an example of where science has failed, not because we do not understand it, but rather the public has not really been presented with the issue properly. One comment about global warming is that scientists have not resolved the issue. That depends on what you mean by “resolved”. Thus one person said scientists are still working on relativity. Yes, they are, but that does not mean that what we have is wrong. The scientific process is to continually check with nature. So, what I want to do in some of my posts this year is try to give an impression of what science is.

The first thing it is not is mathematics. Mathematics are required, and part of the problem is that only too often scientists do not state clearly what they are saying, preferring to leave a raft of maths for the few who are closely in the field. This is definitely not helpful. Nor are TV shows that imply that theories are only made by stunning mathematics. That is simply not true.

The essence of science is a sequence of simple statements, which are the premises. For me, the correct methodology was invented by Aristotle, and the tragedy is, Aristotle made some howling mistakes by overlooking his own methodology. Aristotle’s methodology is to examine nature and from it, draw the premises, then apply logic to the statements to draw some conclusions, check with observation, and if the hypothesis still stands up, try to determine whether there are any other hypotheses that could have given equivalent predictions. Proof of a concept is only possible if one can say, “if and only if X, then Y”, in which case observing Y is the proof. Part of the problem lies in the “only”; part lies in seeing the wood for the trees. One of the first steps in analyzing a problem is to try to reduce it to its essentials by avoiding complicating features. This does not mean that complicating features should be ignored; rather it means we try to find a means of avoiding them until we can sort out the basics. If we do not get the basics right, there is no point in worrying about complicating factors.

To consider global warming, the first thing to do is put aside the kilotonnes of published data. Instead, in order to focus on the critical points, try modeling something simpler. Consider a room in your house in winter, and consider you have an electric bar heater. Suppose you set it to 1 Kw and turn it on. That will deliver 1 kilojoule of heat per second. Now, suppose doors are open or not open. Obviously, if they are open, the heat can move elsewhere through the house, so the temperature will be slower to rise. Nevertheless you know it will, because you know there is 1 kilojoule per second of heat being liberated.

The condition for long term constant temperature (equilibrium) is

(P in) – (P o) = 0

where (P in) is the power in and (P o) is the power out, both at equilibrium. This works for a room, or a planet. Why power? Because we are looking to see whether the temperature will remain constant or change, and to do that we need to see whether the system is changing, i.e. gaining or losing heat. To detect change, we usually consider differentials, and power is the differential of energy with respect to time. Because we are looking at differentials, we can say, if and only if the power flow into a system equals the power flow out is it at an energy equilibrium. We can use this to prove equilibrium, or otherwise, but we may have to be careful because certain other energy flows, such as radioactive decay, may be generated internally. So, what can we say about Earth? What Lyman et al. found was there is a net power input of 0.64 watts per square meter of ocean surface. That means the system cannot be at equilibrium.

We now need a statement that could account for this. Because the net warming effect is recent, the cause must be recent. The “greenhouse” hypothesis is that humanity has put additional infrared absorbers into the air, and these absorb a small fraction of the infrared radiation that would otherwise go to space, then re-emit the radiation in random directions. Accordingly, a certain fraction is returned to earth. The physics are very clear that this happens; the question is, is it sufficient to account for the 0.64 W? If so, power into the ground increases by (P b) and the power out decreases by (P b). This has the effect of adding 2 (P b) to the left hand side of our previous equation, so we must add the same to the right hand side, and the equation is now

(P in + P b) – (P o – P b) = 2 (P b)

The system is now not in equilibrium, and there is a net power input.

The next question is, is there any other cause possible for (P b)? One obvious one is that the sun could have changed output. It has done this before, for example, the “Little Ice Age” was caused by the sun’s output dropping with a huge decrease in sunspot activity. However, NASA has also been monitoring stellar output, and this cannot account for (P b). There are few other changes possible other than atmospheric composition for radiation over the ocean, so the answer is reasonably clear: the planet is warming and these gases are the only plausible cause. Note what we have done. We are concerned about a change, so we have selected a variable that measures change. We want to keep the possible “red herrings” to a minimum, so the measurements have been carried out over the ocean, where buildings, land development, deforestation, etc are irrelevant. By isolating the key variable and minimizing possible confusing data, we have a clear answer.

So, what do we do about it? Well, that requires a further set of theories, each one giving an effect to a proposed cause, and we have to choose. And that is why I believe we need the general population to have some idea as to how to evaluate theories, because soon we will have no choice. Do nothing, and we lose our coastal cities, coastal roads and coastal agricultural land up to maybe forty meters, and face a totally different climate. Putting your head in the sand and feeling differently will not cool the planet.

* Lyman, J. M. and 7 others, 2010. Nature 465:334-337.