Why quantum gravity needs operationalism: Part 1

This is the first of a series of posts in which I will argue that physicists can gain insight into the puzzles of quantum gravity if we adopt a philosophy I call operationalism. The traditional interpretation of operationalism by philosophers was found to be lacking in several important ways, so the concept will have to be updated to a modern context if we are to make use of it, and its new strengths and limitations will need to be clarified. The goal of this first post is to introduce you to operationalism as it was originally conceived and as I understand it. Later posts will explain the areas in which it failed as a philosophical doctrine, and why it might nevertheless succeed as a tool in theoretical physics, particularly in regard to quantum gravity [1].

Operationalism started with Percy Williams Bridgman. Bridgman was a physicist working in the early 20th century, at the time when the world of physics was being shaken by the twin revolutions of relativity and quantum mechanics. Einstein’s hand was behind both revolutions: first through the publication of his theory of General Relativity in 1916, and second for explaining the photoelectric effect using things called quanta, which earned him the Nobel prize in 1921. This upheaval was a formative time for Bridgman, who was especially struck by Einstein’s clever use of thought experiments to derive special relativity.

Einstein had realized that there was a problem with the concept of `simultaneity’. Until then, everybody had taken it for granted that if two events are simultaneous, then they occur at the same time no matter who is observing them. But Einstein asked the crucial question: how does a person know that two events happened at the same time? To answer it, he had to adopt an operational definition of simultaneity: an observer traveling at constant velocity will consider two equidistant events to be simultaneous if beams of light emitted from each event reach the location of the observer at the same time, as measured by the observer’s clock (this definition can be further generalised to apply to any pair of events as seen by an observer in arbitrary motion).

From this, one can deduce that the relativity principle implies the relativity of simultaneity: two events that are simultaneous for one observer may not be simultaneous for another observer in relative motion. This is one of the key observations of special relativity. Bridgman noticed that Einstein’s deep insight relied upon taking an abstract concept, in this case simultaneity, and grounding it in the physical world by asking `what sort of operations must be carried out in order to measure this thing’?

For his own part, Bridgman was a brilliant experimentalist who won the Nobel prize in 1946 for his pioneering work on creating extremely high pressures in his laboratory. Using state-of-the-art technology, he created pressures up to 100,000 atmospheres, nearly 100 times greater than anybody before him, and then did what any good scientist would do: he put various things into his pressure chamber to record what happened to them. Mostly, as you might expect, they got squished. At pressures beyond 25,000 atmospheres, steel can be molded like play-dough; at 50,000 atmospheres all normal liquids have frozen solid. (Of course, Bridgman’s vessel had to be very small to withstand such pressure, which limited the things he could put in it). But Bridgman faced a unique problem: the pressures that he created were so high that he couldn’t use any standard pressure gauge to measure the pressures in his lab because the gauge would basically get squished like everything else. The situation is the same as trying to measure the temperature of the sun using a regular thermometer: it would explode and vaporize before you could even take a proper reading. Consequently, Bridgman had no scientific way to tell between `really high pressure’ and `really freaking high pressure’, so he was forced to design completely new ways of measuring pressure in his laboratory, such as looking at the phase transition of the element Bismuth and the resistivity of the alloy Manganin [2]. This led him to wonder: what does a concept like `pressureor `temperature’ really mean in the absence of a measuring technique?

Bridgman proposed that quantities measured by different operations should always be regarded as being fundamentally different, even though they may coincide in certain situations. This led to a minor problem in the definitions of quantities. The temperature of a cup of water is measured by sticking a thermometer in it. The temperature of the sun is measured by looking at the spectrum of radiation emitted from it. If these quantities are measured by such different methods in different regimes, why do we call them both `temperature’? In what sense are our operations measuring the same thing? The solution, according to Bridgman, is that there is a regime in between the two in which both methods of measuring temperature are valid – and in this regime the two measurements must agree. The temperature of molten gold could potentially be measured by the right kind of thermometer, as well as by looking at its radiation spectrum, and both of these methods will give the same temperature. This allows us to connect the concept of temperature on the sun to temperature in your kitchen and call them by the same name.

This method of `patching together’ different ways of measuring the same quantity is reminiscent of placing co-ordinate patches on manifolds in mathematical physics. In general, there is no way to cover an entire manifold (representing space-time for example) with a single set of co-ordinates that are valid everywhere. But we can cover different parts of the manifold in patches, provided that the co-ordinates agree in the areas where they overlap. The key insight is that there is no observer who can see all of space-time at once – any physical observer has to travel from one part of the manifold to another by a continuous route. Hence it does not matter if the observer cannot describe the entire manifold by a single map, so long as they have a series of maps that smoothly translate into one another as they travel along their chosen path – even if the maps used much later in the journey have no connection or overlap with the maps used early in the journey. Similarly, as we extend our measuring devices into new regimes, we must gradually replace them with new devices as we go. The eye is replaced with the microscope, the microscope with the electron microscope and the electron microscope with the particle accelerator, which now bears no resemblance to the eye, although they both gaze upon the same world.

Curiously, there was another man named Bridgman active around the same time, who is likely to be more familiar to artists: that is George Bridgman, author of Bridgman’s Complete Guide to Drawing From Life. Although they were two completely different Bridgmans, working in different disciplines, both of them were concerned with essentially the same problem: how to connect our internal conception of the world with the devices by which we measure the world. In the case of Percy Bridgman, it was a matter of connecting abstract physical quantities to their measurement devices, while George Bridgman aimed to connect the figure in the mind to the functions of the hands and eyes. We close with a quote from the artist:

“Indeed, it is very far from accurate to say that we see with our eyes. The eye is blind but for the idea behind the eye.”

[1] Everything I have written comes from Hasok Chang’s entry in the Stanford Encyclopedia of Philosophy on operationalism, which is both clearer and more thorough than my own ramblings.

[2] Readers interested in the finer points of Percy Bridgman’s work should see his Nobel prize lecture.

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