Einstein’s approach to physics may be compared to Kant’s approach to philosophy. Where Kant derived things about the world we perceive from the possibility of human knowledge, Einstein derived things about the world we perceive from the possibility of human physics. At the basis of Kant’s philosophy lies the thought that the world must be such that our knowledge of that world is possible. Kant said that if knowledge is possible, then the world we perceive must have certain features*. In a way that appears similar, Einstein said that if physics is possible then the world we perceive must have certain features. At the basis of Einstein’s physics lies the thought that the world must be such that physical knowledge of that world is possible.
Kant’s Synthetic A Priori
Let’s start with Kant. To understand Kant’s view it is important to understand that he made a distinction between propositions that are analytic and propositions that are synthetic. A proposition is analytic if its its truth-status can be judged by analysing the definitions of the terms used in the proposition (a standard example of an analytic proposition is “a square has four sides”). A proposition is synthetic if more than mere terminological analysis is required: we must make an observation. A standard example of a synthetic proposition is “the apple is red”.
Kant called analytic propositions a priori, which means that he believed that the truth-status of such propositions can be judged prior to any observation. It won’t surprise anyone that Kant believed that most synthetic statements are a posteriori. Wait a minute… most? why not all? Kant believed that besides the analytic a priori and synthetic a posteriori there is yet a third category of propositions: the synthetic a priori. Synthetic a priori propositions tell us something about the world around us, yet can be known to be true independent of observation.
How is Einstein’s approach to physics comparable to this? Einstein analysed physics and came up with the idea of relativity: to be able to do physics, it must be possible for different observers to agree on what the physical laws are. In other words: physical laws must be the same in all reference frames. The thought of relativity was not new. Galileo already observed that if you do an experiment in a uniformly moving lab (say, the cargo hold of a steadily moving ship) or in a lab at rest (on the shore) you will find the same physical laws. However, for Galileo that was a result of how we do physics. The innovative thing about Einstein’s approach is that the thought that physical laws must be the same in all reference frames is no longer a result, but lies at the basis of physics – it has become a postulate.
Is Einstein’s Relativity Postulate Synthetic A Priori?
A debated question about the relation between the approaches of Einstein and Kant is whether Einstein’s postulates are synthetic a priori. Einstein regarded relativity as a postulate – doesn’t that mean that he believed that relativity is a priori?
Being the empiricist that he was, Einstein did not think of his postulates as synthetic without observations telling us so. Only experiment can tell us whether the postulates we choose as the basis of our theories “latch on to the blueprint of reality”. Period. Case closed.
But suppose, for the sake of the argument, that someone with sound common sense but a scientifically untrained mind (a tabula rasa, if you will) were given the following task: try to find a system of laws or rules that can be used by a group of people to make accurate predictions about the things that surround them. What will she find?
One might argue that our scientifically untrained friend comes up with a principle of relativity, as laws and rules are most useful if they hold for everyone in the group**. But after that our untrained friend would have to say for who (which reference frames) relativity holds. It might seem as if she should assume relativity for all reference frames, as Einstein did. But Einstein never did that. Einstein only assumed relativity for all reference frames that move either uniformly or acceleratedly relative to each other. He assumed nothing about reference frames that differ from each other in other respects. Here one could think of different movements (eg. irregular, or even discontinuous) or other parameters (such as size, colour or mass).
In other words, our friend doesn’t have any idea what relativity is (what it means that all laws are the same), because for that it is necessary to say what parameters are relevant in describing physical laws. For Einstein it was Newton’s definition of force in terms of acceleration that singled out different states of motion as relevant for reference frames. Only with a definition of force in hand our friend would know which parameters should be the invariants.
*) Where Kant seems to have gone wrong is in thinking that the knowledge of his time (featuring absolute simultaneity and euclidean geometry) was the only possible knowledge.
**) Or she could come up with some kind of subjective relativity: Physical laws are not necessarily the same in all reference frames, but physical laws which can be associated with more reference frames are considered to be better.
Read about Hans Reichenbach’s take on Kant & Modern Physics here.
Thanks for your new article Fedde, food for thought!
There are two papers still on my reading list that are a bit similar to your thought experiment:
A Derivation of Special Relativity from Causal Sets
Kevin H. Knuth, Newshaw Bahrenyi
On simplified axiomatic foundations of special relativity
Sergey S. Stepanov
My expectation about this exercise is that we will repeat the fallacy described in your first asterisk. Over and over again we will realize that we made assumptions that we thought were true a priori but that turn out to be wrong a posteriori, not only for synthetic propositions, but also for propositions thought to be analytic. E.g. the law of the excluded middle. Each time this realization will lead to a better, more general theory.