Fundamental Constants in String Theory

How many constants are needed to define the universe? This statement gets to the very heart of a profound goal in theoretical physics.

When string theorists like Michele Duff (who is likely the developer you're thinking of) or others state that the universe could be defined by 3, 2, or even 0 fundamental constants, they are implying something radical about the nature of reality and the ultimate goal of a "Theory of Everything."

The implication is that what we currently call "fundamental constants of nature" are not truly fundamental. Instead, they are emergent properties derived from a deeper, more fundamental theory with fewer or even no arbitrary parameters.

Think of it like this: The number π (pi) isn't a "fundamental constant" of a circle that we have to measure; it emerges inevitably from the definition of a circle itself. String theorists are proposing that the laws of our universe might work in a similar way.

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The "Three Constants" View

This is the most conservative of the three claims. The idea is that only three truly fundamental, dimensionful constants are needed. From these three, all other constants can be derived. The three constants are typically:

c: The speed of light in a vacuum.
ℏ (h-bar): The reduced Planck's constant.
G: Newton's gravitational constant.

These three constants define the scales for Relativity (c), Quantum Mechanics (ℏ), and Gravity (G). From these, you can create the "Planck Units," which are thought to be the natural units of a quantum theory of gravity like string theory. In this view, all other "constants" are actually dimensionless numbers that, in principle, string theory should be able to calculate from first principles.

The "Two Constants" View

This view argues that we can be even more reductionist. Since c and ℏ are essentially conversion factors, they are more about the language we use to describe physics than physical constants themselves.

In this picture, the only two physical constants that set a scale for the universe are:

G (Newton's Constant): This sets the scale for gravity and the curvature of spacetime.
α (The Fine-Structure Constant): This dimensionless number sets the strength of the electromagnetic interaction.

Proponents of this view argue that if you have a theory that can predict the value of α, and you have G to set the scale of gravity, you can derive everything else. c and ℏ can be set to 1 by a choice of units, meaning they don't represent physical degrees of freedom.

The "Zero Constants" View (The Most Ambitious)

This is the ultimate endpoint of the reductionist program. Here, the implication is that the fundamental theory of the universe has no adjustable parameters whatsoever.

In this scenario, c and ℏ are set to 1 by our unit system. The value of G is not a free parameter but is determined by the dynamics of the theory. All other constants are uniquely determined by the mathematical self-consistency of the theory.

The universe described by such a theory would be inevitable. If the theory is correct, it could only describe one possible universe with one specific set of laws and constants. The "cosmic lottery" of why our constants have the values they do would be answered: "There is no other option."

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Summary: What They Are Implying

Radical Reductionism: The seemingly complex set of ~26 fundamental constants in the Standard Model and cosmology is an illusion. They are not all independent.

The Primacy of Theory: The true fundamental laws are mathematical and abstract. The concrete world we measure in experiments emerges from this deeper structure.

A Uniqueness of the Universe: The ultimate goal is a theory with no free parameters. This would mean our universe is the only logically consistent possibility described by the final theory.

A Test of String Theory's Validity: For string theory to be correct, it must eventually make a definitive prediction for these constants. The fact that it currently has a "landscape" of possible solutions is seen by many as a weakness that the "zero constant" view aims to overcome.

In short, they are implying that the universe is, at its most fundamental level, a pure and inevitable mathematical structure.