On the foundations of physics

Question

Scientific theories in physics have to be validated by experiments. But experiments are to be interpreted in the context of scientific theories. Isn'it like a snake biting its own tail?

For example, using a scanning tunneling microscope, one can see individual atoms. This sounds like the definitive proof of existence of atoms. But the image we see is in fact computed by a computer based on the concept of quantum tunneling.

I could also take the example of quarks that cannot be directly observed or Higgs bosons. Their discovery require complex experiments whose interpretations are far from common sense and require theoretical analysis.

I agree that scientific theories and realized experiments form a consistent whole. But might a different history of science have led to fundamentally different theories than quantum mechanics or relativity theory? Are currently accepted scientific theories only incidental historical constructions instead of the closest known approximations to the truth?

Answer 1

The point you are making wat notoriously emphasised by Kuhn in the structure of scientific revolutions. Here is a linguistic formulation: If the meaning of observations claims depends on the meaning of theoretical terms then theories are incommensurable. We cannot say we are approaching the truth because truth only makes sense inside a theory and theories cannot be compared with their alternatives on neutral grounds.

A possible answer is provided by Putnam: There might be a local incommensurability but there remain a continuity in meaning for theoretical terms between different theories. For example the meaning of "acid" does not change radically with modern atomic theories because acid was not referring to symptoms or sets of observations (taste...) but to the hypothetical cause of these symptoms, which is just made more precise with modern theories. The modern definition of acid arguably displays the kind of circularity you are referring to but there is continuity in meaning and neutral grounds for comparing distinct theories which is to be found for example in everyday language.

In conclusion it is true that theoretical statements are not strictly speaking verifiable because of this circularity but their global success in contrast with alternative theories gives us reasons to believe in their truth.

Answer 2

I think mathematics has taught us that 'foundations' are an inappropriate way to think of intellectual structures.

The 'foundation' of mathematics from a functional point of view is really more around the 'middle'. It is really based in geometry and number theory, things humans easily grasp. But those seem complicated in other ways, so there are deep attempts to construct everything from very basic concepts. A short way in, these attempts just flushed out Russell's Paradox, which pointed out that what we look at as very basic concepts are, in fact, quite complicated in other ways.

Physics, and all the other sciences have the same problem, but it is in some ways both more obvious and easier to hide. We agree that physics is constructed by agreement of those practicing it, in a way that mathematics does not seem, at least on the surface, to be. We can look at mass or gravitation as a more basic concept, we can prefer to consider either charge or nuclear composition a simpler way of seeing things. 'Down' in complexity is clearly more relative.

But at the same time, within the field if physics, the idea that 'down' really exists somehow persists better. As we see particles and integrating theories become more and more embedded in assumptions about the more complex processes that are used to detect them and prove their existence, it does not occur to us that we are getting deeply embedded in layers of assumptions. Each layer seems so obvious and clear. They are the same sets of assumptions we rely on to keep our day-to-day technology working, so why would we question them?

Only when something really deep goes 'wrong' do we question this kind of thing: when we cannot rush into a beam of light and see our relative velocities add up; when we need something continuous to act less like a continuum in order for there not to be infinitely much heat created by a finite quantity of entropy. Then we need extensions of theories that really seem to almost destroy the theories themselves.

Kuhn's model of paradigms captures this well. Faced with a theory that eats itself in this manner, we renegotiate what is more basic, and what is more derived, so that we can rearrange our view of the subject and get a sense of complete coverage back. In the process, we discover some of what we thought was reliable data is just wrong, or that we no longer have ways of explaining it.

In that sense, all of these theoretical constructs could be totally reframed in completely different terms if the discoveries that created them happened in different orders, and were rearranged on different terms. They very well may be rearranged extensively in the future.

This puts science in the same position where Set Theory put math: what is common experience is really what needs to be maintained as the 'foundation' of the science, the part that cannot be lost in a shift of paradigms. The things that scientists within the field see as 'more basic' are in fact almost infinitely renegotiable and likely to be seen differently in some future generation.

There is in that sense no 'downward' direction in complexity in any science.

Answer 3

A scientific theory is incomplete. Almost always it is backed by mathematics. Mathematics do not provide a physical foundation. I think mathematics has in some cases led us in the direction, in which it is believed that choosing to acquire a mental awareness of a 'foundation', is considered to be the wrong place to get off to a start.

Instead, we seem to be branching from one place to another via mathematics, even though mathematics is an external tool, external from the mind. How can we fully comprehend something, if much of the work being done remains external from the mind ? Thus we are left with a theory.

For instance, concerning Special Relativity, one most often encounters mathematics being used as a component(s) in the overall explanation of what Special Relativity actually is. In doing so, we usually end up using math that is related to Special Relativity to explain Special Relativity itself. In other words, we end up with circular reasoning. Thus we never expose the complete foundation or cause.

But this need not be the case.

As an example, due to not having any education in the field of physics, I was extremely curious about "motion". It seemed somewhat odd in the back of my mind and thus I in turn intended to fully understand it. I began analyzing it using nothing but the mind. The outcome was a full understanding of Special Relativity along with the exposure of the foundation of which it resides within. I also converted this understanding into equations.

The equations turned out to be the same as those known as the Lorentz-Fitzgerald Length Contraction equation, the Time Dilation equation, the Lorentz Transformation equations, and the Velocity Addition equation. Thus in this case, the equations were the outcome, and thus they were not the source. In turn, by starting at the foundation, Special Relativity became extremely simple and intuitive.

The method in which I had derived the equations is found nowhere else. My step by step analysis of motion, ( 9 short youtube videos, 1hr 39min long ), can be accessed via my profile if interested.