The nature of the physical world

by Sir Arthur Stanley Eddington

I am prepared to admit that frames of space in spite of their present resemblance may in the future turn out to be not entirely indistinguishable. (I deem it unlikely, but I do not exclude it.) The future physicist might find that the frame belonging to Arcturus, say, is unique as regards some property not yet known to science. Then no doubt our friend with the label will hasten to affix it. “I told you so. I knew I meant something when I talked about a right frame.” But it does not seem a profitable procedure to make odd noises on the off-chance that posterity will find a significance to attribute to them. To those who now harp on a right frame of space we may reply in the words of Bottom the weaver—

“Who would set his wit to so foolish a bird? Who would give a bird the lie, though he cry ‘cuckoo’ never so?”

And so the position of Einstein’s theory is that the question of a unique right frame of space does not arise. There is a frame of space relative to a terrestrial observer, another frame relative to the nebular observers, others relative to other stars. Frames of space are relative. Distances, lengths, volumes—all quantities of space-reckoning which belong to the frames—are likewise relative. A distance as reckoned by an observer on one star is as good as the distance reckoned by an observer on another star. We must not expect them to agree; the one is a distance relative to one frame, the other is a distance relative to another frame. Absolute distance, not relative to some special frame, is meaningless.

The next point to notice is that the other quantities of physics go along with the frame of space, so that they also are relative. You may have seen one of those tables of “dimensions” of physical quantities showing how they are all related to the reckoning of length, time and mass. If you alter the reckoning of length you alter the reckoning of other physical quantities.

Consider an electrically charged body at rest on the earth. Since it is at rest it gives an electric field but no magnetic field. But for the nebular physicist it is a charged body moving at 1000 miles a second. A moving charge constitutes an electric current which in accordance with the laws of electromagnetism gives rise to a magnetic field. How can the same body both give and not give a magnetic field? On the classical theory we should have had to explain one of these results as an illusion. (There is no difficulty in doing that; only there is nothing to indicate which of the two results is the one to be explained away.) On the relativity theory both results are accepted. Magnetic fields are relative. There is no magnetic field relative to the terrestrial frame of space; there is a magnetic field relative to the nebular frame of space. The nebular physicist will duly detect the magnetic field with his instruments although our instruments show no magnetic field. That is because he uses instruments at rest on his planet and we use instruments at rest on ours; or at least we correct our observations to accord with the indications of instruments at rest in our respective frames of space.

Is there really a magnetic field or not? This is like the previous problem of the square and the oblong. There is one specification of the field relative to one planet, another relative to another. There is no absolute specification.

It is not quite true to say that all the physical quantities are relative to frames of space. We can construct new physical quantities by multiplying, dividing, etc.; thus we multiply mass and velocity to give momentum, divide energy by time to give horse-power. We can set ourselves the mathematical problem of constructing in this way quantities which shall be invariant, that is to say, shall have the same measure whatever frame of space may be used. One or two of these invariants turn out to be quantities already recognised in pre-relativity physics; “action” and “entropy” are the best known. Relativity physics is especially interested in invariants, and it has discovered and named a few more. It is a common mistake to suppose that Einstein’s theory of relativity asserts that everything is relative. Actually it says, “There are absolute things in the world but you must look deeply for them. The things that first present themselves to your notice are for the most part relative.”

Relative and Absolute Quantities. I will try to make clear the distinction between absolute and relative quantities. Number (of discrete individuals) is absolute. It is the result of counting, and counting is an absolute operation. If two men count the number of people in this room and reach different results, one of them must be wrong.

The measurement of distance is not an absolute operation. It is possible for two men to measure the same distance and reach different results, and yet neither of them be wrong.

I mark two dots on the blackboard and ask two students to measure very accurately the distance between them. In order that there may be no possible doubt as to what I mean by distance I give them elaborate instructions as to the standard to be used and the precautions necessary to obtain an accurate measurement of distance. They bring me results which differ. I ask them to compare notes to find out which of them is wrong, and why? Presently they return and say: “It was your fault because in one respect your instructions were not explicit. You did not mention what motion the scale should have when it was being used.” One of them without thinking much about the matter had kept the scale at rest on the earth. The other had reflected that the earth was a very insignificant planet of which the Professor had a low opinion. He thought it would be only reasonable to choose some more important body to regulate the motion of the scale, and so he had given it a motion agreeing with that of the enormous star Betelgeuse. Naturally the FitzGerald contraction of the scale accounted for the difference of results.