Common sense is the collection of prejudices acquired by the age of eighteen.
Albert Einstein
Introduction
My physics teacher at school once said: "Relativity isn't difficult to understand - it's difficult to believe". Certainly, one tends to be incredulous when told that the same object can be simultaneously observed to have different lengths by different observers. It defies common sense: surely an object can have only one length at a time? The problem is that the effect is too small to be readily perceived at the sort of relative velocities to which we are accustomed. If we were born and bred in a world where near-light-speed travel was commonplace, we would take the change in length with velocity as calmly as we now take the change in length of objects with temperature.
This sort of thing happens all the time in science. The idea that the Earth's mantle (which most of us would regard as being solid if we could handle a piece) can be in a state of natural convection takes a lot of getting used to; the problem is that we have no experience of, and therefore little intuitive comprehension of, the spatial and time scales involved. Another nice example is the sun, which, kilogram for kilogram, generates approximately 4 orders of magnitude less power than the human body. In view of the sun's obvious extreme hotness, this result seems preposterous; we make the mistake because we don't comprehend the sun's size, and hence fail to appreciate its huge relative shortage of surface area compared to our own bodies. Finally, the foundations of my own worldview were shaken recently when I realised that concrete (which I'd always considered as the epitome of rigidity) is about ten times less stiff than steel (which seems quite springy stuff). The misapprehension arises because concrete breaks at very low tensile strains, and therefore we never see a piece of concrete visibly deflecting elastically, whereas we see lots of pieces of steel behaving that way.
The general conclusion from these examples is that our everyday intuitions are apt to let us down when we try to apply them to situations where the magnitudes of the various quantities are unfamiliar. This failure is not because new laws of physics apply in these unfamiliar situations (or so we hope), but because their relative importance varies depending upon the absolute values of the physical quantities involved. This is a well-worn theme: an elephant's legs have to be much thicker in proportion to their length than do the legs of a spider, surface tension matters a great deal to an insect and hardly at all to an aircraft carrier, and so on. Cricket played with boundaries of 20 yards would be vastly different in character and strategy to a game played with exactly the same rules but 200-yard boundaries; laws that were effectively irrelevant in one game would be pivotal in the other.
Common sense and experience
So when can we justifiably apply common sense? I assume that what we call common sense is actually the result of our everyday observations of and interactions with the world around us. By this argument, a baby may be as startled the very first time they release something and see it fall to the ground as we grown-ups would be if we were to let go of something and see it accelerate sideways at 9.81 m s-2. Similarly, somebody born and bred in orbit, and visiting the Earth for the first time, would find gravity as surprising as we would find weightlessness. I am not going to attempt to justify this assumption (which may not be entirely true), other than by enlisting a distinguished supporter (see quotation at the head) and observing that my experience as a parent shows that "the sense you were born with" does not amount to very much.
Actually, we probably have to allow that common sense may result not just from our own observations of the world, but also from those of our ancient ancestors. It may well be an advantage to have some physics encoded genetically.
It doesn't matter at all how the commonsense rules come to lodge in the brain: the crucial point is that we can expect our common sense to apply only when the the values of the various physical variables are within the range that we encounter in daily life.
We now ask: as scientists explore the behaviour of things from atoms to planets to the whole universe, how likely is it that the resulting theories and experimental results will violate our commonsense intuitions? What we need to do is to establish how broad our human experience of the universe is in comparison to everything that can happen in the universe. But we have a problem: there is no practical way that we can catalogue every sort of thing that can happen in order to compare it to a similar catalogue of the things that we can experience directly. We have to step back a few paces and look at the issue in a different way.
Ranges of orders of magnitude
How can objects vary from one another? Well, they can vary in size and position. They can vary in mass. They can vary in speed, or in longevity, or in the order in which they exist, which we might summarise by saying that they vary in time. They can vary in temperature. You could generate scientific descriptions of an awful lot of objects and events using just these four quantities: mass, length, time, and temperature. To do a complete job, you'd need to throw in one or two others, like electrical charge and magnetic field strength, but we will stick to the four we have described because they are familiar and because they are quite adequate to make the point. The picture is of a 4-dimensional space of all possible combinations of values of our 4 chosen variables.
The argument continues like this. Suppose that we take the range of distances in the universe, from the size of the tiniest sub-atomic particle to the size of the whole universe. Of what fraction of that range of scales do we, as humans, have first-hand experience? By first-hand experience of a particular scale I mean that we can observe, with unaided senses, events happening on that scale. By this reckoning, we have first-hand experience of things happening on scales of centimetres, but not of micrometres and not of kiloparsecs. The fraction that we come up with will be reckoned on a logarithmic basis: over how many orders of magnitude of scale (powers of ten) does our everyday experience operate, and over how many orders of magnitude of scale do things happen in the universe? We can ask the same question for mass, time and temperature, too, and in each case we get a certain fraction. Multiplying these four fractions together, we get an estimate of the fraction of the total 4-dimensional space of circumstances of which we have immediate experience. It turns out that this final fraction is rather tiny.
The calculations
When reading the following, don't get too worked up about the exact numbers that I use. A lot of them are very approximate or uncertain. Not wishing to overstate the case, I have aimed to be flattering to the range of human experience, and even then the conclusion turns out to be so strong that it would survive quite radical adjustments of the numbers.
Length
What is the range of lengths of which the ordinary human being has direct everyday experience? At the small end, events occurring on scales smaller than about a tenth of a millimetre are probably beyond serious observation. The upper end is more difficult. We can certainly travel hundreds of kilometres, but do we have a real grasp of the size of those distances? I would suggest not; on the whole we just travel until we get there. A better choice would be the largest distance that we could encompass in a single glance on the earth - say about a hundred kilometres. This estimate is very uncertain, and probably rather generous, but you will soon see that it doesn't matter if we are out by even a large amount. The range of sizes of which we have some sort of direct comprehension therefore covers about 9 orders of magnitude.
Now we have to deal with the range of sizes that we know about in the universe. The nucleus of the smallest kind of atom, that of hydrogen, is about 10-15 metres across (I'm being conservative here and ignoring things smaller than protons), and the whole universe is about 1026 metres across, a range of about 41 orders of magnitude.
Therefore we could say that we have direct experience of about 9/41 of the spatial scales in the universe, or a bit less than a quarter.
Time
Although some parts of our bodies operate on faster timescales, the shortest times for which we have any sort of "feel" will be no less than about a tenth of a second, or 10-1 seconds. The longest timescale upon which we can see things unfold is a human lifetime, which is about 109 seconds, so we can experience times ranging over 10 powers of ten. I am being very generous to our powers of temporal comprehension here: like a long journey, we do not comprehend our lifespan as a piece, but instead take it day by day until it is over. However, I want to keep everyone on my side and would prefer to overestimate rather than underestimate our range of experience.
Physicists theorise about events happening as early as 10-43 seconds after the "big bang", and the universe is believed to be about 12,000 million years old already, which is roughly 1017 seconds. So the range of timescales in the universe is about 60 powers of ten.
Therefore, our experience of timescales represents about 10/60, or about a sixth, of the timescales upon which real events unfold.
Mass
The smallest things that we are able to observe unaided are things like specks of dust floating in the air. An extremely rough estimate might make the mass of a speck of dust to be 10-12 kilograms. We see lots of static heavy objects, like mountains, but we aren't seeing them "behave" in any way. Indeed, when geologists tell us how they do behave, we can be taken by surprise. The heaviest thing that we regularly see things actually happening to is probably something like a railway locomotive, say about 100 tonnes, or 105 kilograms. Therefore the range between the lightest and heaviest things that we deal with is 17 powers of ten.
Now for the universe. The smaller sub-atomic particles are believed to have masses of about 10-30 kg. The mass of the universe is a matter of great uncertainty, but we wouldn't be too far wrong if we said that it was about 1050 kg. Even if we are several powers of ten out, it wouldn't matter.
The range of masses in the universe is about 80 powers of ten, of which we have direct experience of about 17/80 or rather less than a quarter.
Temperature
To think about temperature, the Celsius or Fahrenheit scales are no use for our logarithmic estimation of ranges, because they are not ratio scales: their zero points are arbitrary and therefore multiplication is not a meaningful operation. Therefore we use the Kelvin scale.
The range of temperatures that we experience directly covers less than one power of ten: it goes from about 250 K (-23 °C ) to, say, 1500 K which we might see in a flame. To keep the numbers simple we shall be generous and say that the range of humanly experienced temperatures covers a whole power of ten.
The temperature shortly after the "Big Bang" that started our universe was round about 1011 K. It may have been hotter right at the very beginning, but this figure will do. At the chillier end of the scale, physicists have succeeded in producing temperatures within a very small fraction of a degree of zero Kelvin. A few years ago they had got within about one hundred-millionth of a degree (10-8 K) of absolute zero. The current record may be lower than this, but again, this figure is good enough. Thus the range of temperatures that are known to occur in nature is between about 10-8 K and 1011 K, or 19 powers of ten.
It follows from these estimates that we have first-hand experience of about one-twentieth of the range of temperatures that actually occur.
Length, mass, time and temperature
In the last few sections we have estimated that the fractions of the natural ranges of length, time, mass and temperature of which we have direct experience are about a quarter, a sixth, a quarter, and a twentieth respectively. Multiplying these fractions together, we find that of the 4-dimensional space in which we represent all possible combinations of the values of our chosen physical variables, our direct human experience is of approximately 1/1920, or about 0.05 %, of the whole.
Conclusion
The figure that we have just come up with is extremely small. It is also extremely approximate. The neglect of all but four physical variables suggests that it may be a gross overestimate. On the other hand, we have assumed statistical independence of our four variables, that is, that all values of one variable are equally likely to be associated with any given combination of the other three. In reality, this assumption will be false in some cases, which means that our 4-dimensional space is, in effect, not as big as we have assumed; in this case the value of 0.05% will be an underestimate. Nevertheless, even if adjustments of the arguments made the result as large as 1%, the point would still be made: our personal (or inherited) experience of the physical world is so woefully parochial that the resulting intuitions are likely to be an extremely unreliable guide to the way most things in the universe actually happen.