Is a theory of physics possible with no constants?

Question

The Standard Model of Physics has a number of constants. Obviously the fewer the better - simply in terms of there being less fundamentally inexplicable constants to explain.

It seems to me, in as far as this process is possible, it can reduce at best to a single constant.

But, am I correct in this? Is it philosophically possible to have a theory of physics that has no constants at all?

Whilst not a physical theory, one of the simplest productive axiomatic frameworks in mathematics is the Peano Axioms for the natural numbers. This, notably has a single constant.

Answer 1

When looking at a physical constant https://en.wikipedia.org/wiki/Physical_constant we find it consist of a number part and a unit of measure. The value of the number being the result of experimental observation, and the magnitude determined by the unit of measure. The unit used is arbitrary defined and it's function is to denote and categorize the constant. We see here that to relate quantities (not just constants) it is necessary to have a framework of measurement. https://en.wikipedia.org/wiki/System_of_measurement

But what if we could find the most basic constants, https://en.wikipedia.org/wiki/Dimensionless_physical_constant could we then define these in terms of each other? https://en.wikipedia.org/wiki/Natural_units This would give us a set of fundamental units with no dimension. Also known as Natural Units the most recognizable would be Planck units. https://en.wikipedia.org/wiki/Planck_units But here of note is even if the constants are interdependently defined a frame of reference is needed to do science with. Note for instance that the planck length is still expressed in m (meter), and the famous constant "0.08542455" is useless without more information.

Now lets consider what physics would look like if there where no constants at all. For instance if Time was not 'bound' by an underlying constant relation, then it would be possible to travel the same distance at the same velocity and record different durations; in such circumstance you couldn't form a theory of motion at all. Assuming the physical quantities still stood in some (variable) relation to each other, it could hardly be imagined that there would be any kind of stability in the universe.

TL;DR

If Physicists don't have physical constants that are somehow fundamental, they invent arbitrary 'constants' in the form of _units of measure _. The reason being that you can't do science without a particular framework. And if there is no fundamental constancy, there couldn't be any Science, or life presumably.

Answer 2

The physical constants are part of the observer's data- as events are usually first observed happening in nature or in a laboratory set up.

To build a relationship between observed numbers/properties and the varying environs or properties of materials or measured values a constant appears- which may be universal or restricted to the 'situation'.

Many times those constants get a physical definition when detail investigations become available. An example is 'mass' which plays a role of a constant in dynamics of bodies-or spring constant k, which plays a role in defining the energy of a spring { (1/2) .k.x^2 }, where x is the extension of spring. or Reynold number in the flow of liquids.

If the constants have dimensions it means that more info is required about the phenomena.

not only in physical sciences but in psychology or social sciences such properties may exist which may be related through some constants specific to the environs.

About the nature of physical constants-

Duff M.J. argued that the laws of physics should be independent of one’s choice of units or measuring apparatus.

This is the case if they are framed in terms of dimensionless numbers such as the fine structure constant, α.

For example, the Standard Model of particle physics has 19 such dimensionless parameters whose values all observers can agree on, irrespective of what clock, rulers, scales... they use to measure them.

Dimensional constants, on the other hand, such as ¯h, c, G, e, k. . . , are merely human constructs whose number and values differ from one choice of units to the next.

In this sense, only dimensionless constants are “fundamental”.

Similarly, the possible time variation of dimensionless fundamental “constants” of nature is operationally well-defined and a legitimate subject of physical inquiry.

By contrast, the time variation of dimensional constants such as c or G on which a good many (in my opinion, confusing) papers have been written, is a unit-dependent phenomenon on which different observers might disagree depending on their apparatus.

All these confusions disappear if one asks only unit-independent questions.

ref.https://arxiv.org/pdf/1412.2040.pdf