The Fine-Tuning Argument- Phase Space

Let's map out fundamental physical constants in phase space to get a better feel for the fine-tuning argument (anthropic principle)! In this post I am neither agreeing with or disagreeing with the fine-tuning argument. Rather, I am attempting to explain what the fine tuning argument is so that accurate debate can be made. Also, a shout-out to Roger Penrose who phrased the fine-tuning argument this way.

Physical Constants in Phase Space

We will start out with one constant, and one axis. Let's make the value of X be the gravitational constant, G.

The value of the gravitational constant could be one of many numbers, but in our universe it is about

6.67300 × 10-11 m^3 kg^-1 s^-2. Let's make a mark on our axis to represent this value.

According to the fine-tuning argument, if we moved the smiley face either slightly to the right or slightly to the left, our universe would not have developed in such a way as to allow for life.

But there is more than just one constant that needs to be set at a specific value for a universe to develop in which life can survive! And so, we shall add another axis to our figure. This time we will use the ratio of the electromagnetic force to the gravitational force between an electron and a proton, also known as "N". We will represent our specific value for N as a green smiley-face on the Y axis.

Once again, as the argument goes, if N were slightly larger or smaller, the universe would not develop in such a way as to be suitable for life.

Notice how the percentage of phase space which allows for a life-friendly universe is now represented by the place where G and N intersect:

For fun, lets add one more constant. But which one should we choose? Hhhhhmmmmye... Why not the fractional rate of expansion of the universe? This is also known as the Hubble parameter, or H. I'll go ahead and throw in all the additional info as well.

Once again, the turquoise region is the only region in phase space which allows for life, and once again, by adding an additional constant we have significantly reduced the proportion of phase space which will allow for life as we know it.



According to proponents of the fine-tuning argument, there can be as many as 36 of these constants. This would mean that our phase space would have 36 dimensions instead of the 3 we have displayed on this post.

Debate on the fine-tuning argument has to do with the following topics:

• How many (if any) constants are there?
• How 'finely-tuned' must the constants be?
• Is it even possible for the constants to vary?
• Are there multiple universes, each with differing values for the constants?
• If there are multiple universes, how many are there?
• If there are multiple universes, is there a way to tell whether or not the constants truly vary from one to the next?

And so there you go! A brief overview of the fine tuning argument!