Careful experimental investigations have revealed a stable, underlying order to the principles which govern the motion of matter and energy in our universe – at least on the length scales in which we go about our daily lives. The Law of Gravity, Coulombs Law, Maxwell’s equations, etc., are just three examples of stable physical principles which we have discovered, through experiment and observation, to govern the interactions between different bodies of matter and fields of energy.
In this article we take a step back and ask the question:
Why are The Laws of Physics the way they are?
If we believe in a random universe, perhaps the kneejerk response might be that there doesn’t need to be a reason. But, as I will demonstrate in this blog article, the anthropic principle can be deployed very effectively to explain why many physical laws are as they are.
The Anthropic Principle
The Anthropic principle is very simple:
The environment that any conscious entity finds itself existing in must be somewhere it is favourable – or at least possible – for it to exist in.
The environment where a conscious entity developed must be somewhere it is possible for conscious entities to develop in.
Although this may be a self-evident, obvious fact, when this self-evident statement is rigorously considered, it is possible to use it to arrive at far-reaching conclusions.
For the anthropic principle to make any sense with respect to the laws of physics governing our universe, we must either appeal to:
- An intelligent designer
- A multiverse where the laws of physics that govern the various universes within it vary wildy (Ultimate Ensemble)
While an intelligent designer – that deliberately creates our one universe in such a manner so as to harbour life – on the surface may seem to make sense, it has the problem of answering one question (Why has the universe come to be the way it is?) by opening up an even bigger question (How did the intelligent designer come into existence and how did the intelligent designer come to be the way He is?)
The multi-verse interpretation of the anthropic principle rests on the idea that there are many, many, many universes (where a “universe” is used to describe everything that emerges from a given big-bang) that are formed from many, many, different big bangs all with different laws of physics and that the overwhelming majority of them harbour no sentient life but that, being sentient, we live in one of the few universes that does harbour conscious, sentient living creatures.
These multiple universes don’t interact with each other, either due to physical separation over vast distances, physical separation through dimensions where the interactive forces of the particles that compose them do not penetrate, or perhaps because the particle sets from each multiverse have separate “charge” and “force” categories, and interact with particles from the same universe, but have no effect on the motion of particles from any other universe but their own and hence are, to all intents and purposes, invisible.
Could existence really be that vast? The observable universe is 46 billion light years in diameter and the total universe may go on forever – at least in the four dimensions of spacetime that we are familiar with. Is it really possible that, on top of this, our one universe is just one member of a vast number of multiverses?
If we are to meaningfully apply the anthropic principle to the laws of physics while rejecting the existence of an intelligent designer (which raises as many questions as it answers) then we must accept the existence of a multiverse. This is because the laws of physics are uniform throughout our universe. Not only does Noether’s theorem, combined with the observed conservation of linear momentum demand this (as will be discussed later) but the fact that the observed spectra of distant galaxies billions of light years away have line emission patterns of the same elements that can be observed in a laboratory implies that the laws of physics are uniform across our universe.
This implies we need a multiverse, if we are to pick and choose which subset of physical laws are conducive to the evolution of life…
Is there a strong case for saying the laws of physics can be explained with the anthropic principle?
Read on to find out…
Evolution And Energy Conservation
The Law of Conservation of Energy states that the total energy in an isolated system remains constant over time. In other words, that energy can neither be created nor destroyed but merely changed from one form into another.
Noether’s theorem shows that energy is conserved in physical systems whose laws do not vary with time.
Imagine we didn’t know that nuclear energy existed and we thought that the only forms of energy were potential energy, kinetic energy, heat energy and chemical energy. With only this knowledge, we then see the heat energy of a radioactive isotope spontaneously increasing.
We can either say:
1) This disproves the law of conservation of energy
or we can say
2) We have found a new source of energy
And then argue that the increase in heat energy coincides exactly with the reduction in nuclear energy and so energy is conserved.
What Noether’s theorem states is that, so long as the laws of physics remain constant with time, we can always state that energy is conserved through introducing new forms of energy to balance the books whenever energy appears to be created and that this approach is sound so long as we live in a repeatable universe where a given cause will always yield the same effect.
As an interesting aside, Noether’s theorem provides a bridge between physics and philosophy by reframing Hume’s problem of induction in terms of energy conservation.
At the heart of Hume’s induction problem was his conclusion that there was no a priori logical reason to conclude that just because any event occurred in a particular manner before, that things should occur in a similar manner in the future. In other words, Hume questioned the rational basis for assuming the repeatability of anything including the most fundamental physical processes.
…and in the absence of any presumption of any repeatability in anything at all, nothing can be predicted…
“For effect is totally different from cause, and consequently can never be discovered in it. Motion in the second billiard ball is a quite distinct event from motion in the first; nor is there anything in the one to suggest the smallest hint of the other. A stone or a piece of metal raised into the air and left without any support immediately falls; but to consider the matter a priori, is there anything we can discover in the situation which can beget the idea of a downward, rather than an upward, or any other motion in the stone or metal?” – David Hume (Limits of Metaphysical Speculation)
Framed in the terminology of physics, Hume’s problem of induction can be articulated as:
There is no fundamental a priori logical reason to believe that energy should be conserved.
Or is there?
Evolution is the process whereby complex structures, which are capable of performing complex functions, develop. In the absence of evolutionary processes, it is almost inconceivable that something as sophisticated as human consciousness could exist.
At its core, evolution is trial and error. You have a self-replicating information storage medium – DNA – that builds and modifies living creatures. These random modifications sometimes produce creatures that are better at surviving and reproducing and more often produces creatures that are worse. However, the creatures that are better at reproducing make more of themselves. This means their prevalence is far greater than their chance of emerging in the first place.
Evolution could be regarded as a gradual unconscious “learning process” where successful reproduction and death, gradually “teaches” the various evolving germlines how to produce phenotypes that are better at surviving and reproducing.
A key point is that each incremental change in structure, from generation to generation, is miniscule compared to the legacy information that each new generation inherits from the previous one. This legacy genome, that each new generation of living creatures inherits, represents information painstakingly gleaned from hundreds of millions of years of previous trial and error.
In order for evolution to advance and built more complex and capable creatures as time goes by, the “lessons” that germ lines previously “learned” through the process of natural selection must remain valid – to some extent – as time progresses, in order for the phenotypes to advance and further refine themselves.
If the basic laws of physics constantly changed, then all the information encoded in our DNA about how to build successful cells (let alone multi-cellular animals) would become obsolete at a rate which would be too fast for evolution to refine advanced multi-cellular organisms. That’s assuming life should sustain itself in any form – DNA itself might suddenly become impossible to chemically form. If the laws of physics constantly changed, the evolution of complex, advanced organisms would be like someone trying to build a skyscraper while someone else was routinely blowing up the foundations of that same skyscraper with dynamite.
The refinement and the advancement of phenotypes can only occur if previous functions “discovered” by evolution remain valid over evolutionary timescales.
Hence evolution and the corresponding development of advanced conscious structures with advanced cognitive functions can only occur in a universe where the laws of physics remain stable over evolutionary timescales and – hence – where energy is conserved over evolutionary timescales.
Einstein once said:
“The eternally incomprehensible thing about the world is its comprehensibility”
It should now be clear that the world is comprehensible because, at the most fundamental level, the process of learning (comprehension) and the process of evolution are basically the same – in that they both involve the accumulation of information. Thus, lifeforms could only evolve in a comprehensible universe where this is possible. The physicist James B. Hartle has also made this case.
Which, as has been previously mentioned, implies that energy is conserved as proved by Noether’s theorem.
Entropy
The second law of thermodynamics, that an isolated system left to itself will become more uniform and homogenous as time goes by ( which, if applied to energy, produces thermal equilibrium ) is pretty much logically unavoidable. Furthermore, the underlying principle of repeatability – which we discussed in the previous section as being necessary for evolution – implies an arrow of time. That cause A reliably, and repeatably, gives rise to effect B implies that, as time goes by there is a distinct preference for A to convert to B and not the reverse.
In the absence of irreversible processes, the world would be far less predictable (assuming it was predictable at all).
The ultimate purpose of all cognition (which is intimately linked to conscious experience) is to act on the world in order to realise certain preferred outcomes that would be unlikely to occur in the absence of such actions. All action, requires work and all work is ultimately generated by some kind of irreversible physical process.
An irreversible process can be regarded as a preference of our physical universe to the conversion of state A into state B over the conversion of state B into state A.
Perhaps the relationship between preference and entropy could even be regarded as the most fundamental way that conscious entities “negotiate” with the physical universe in which they exist to get what they want. (e.g. – “Hey Universe! I’ll let you convert diesel into water and CO2 if you let me build a skyscraper”)
The question is: In the absence of irreversible physical processes, could agents with distinct preferences exist, and – if so – what would be the underlying physical mechanism that would enable them to facilitate one preference over another?
Furthermore: In the absence of preferences and desires, could consciousness as we know it exist?
If not, then conscious creatures can only live in a universe where the second law of thermodynamics applies.
Conservation Of Linear And Angular Momentum
At the most fundamental level, structures are complex, somewhat ordered, arrangements of matter in space. We often talk about structures of language, structures of computer code, etc., etc., and while these structures seem highly abstract and detached from space, at the end of the day, if physical humans didn’t exist, language wouldn’t exist either. If physical computers didn’t exists in physical space, there would be nothing to execute the computer code.
In this sense:
All abstract, non-spatial structures, rely on the existence of spatial structures.
If consciousness as we know it ultimately relates to agency, in the sense that we think in order to do, then if all conscious entities are ultimately either spatial structures of some sort, or depend on spatial structures of some sort (as a simulation depends on the spatial existence of a computer), then it seems inconceivable that a conscious spatial entity could do anything in the world without moving. All action ultimately arises from spatial movement.
If we assume that both complex conscious agents:
- Must move information to act upon the world (even plants produce seeds that move)
- Their structural integrity and function depends on certain relationships of cause and effect remaining constant (i.e. to live, biochemical processes must occur predictably)
Then we arrive at the conclusion that, in any universe that harbours complex conscious agents, the laws of physics must remain constant in space as well as time.
And since Noether’s theorem proves that momentum must be conserved in any universe where the laws of physics are constant across space we must conclude that:
Momentum must be conserved in any universe inhabited by conscious agents capable of action.
In our case, if the laws of physics changed even slightly as we moved around the place then our finely-tuned, highly complex biochemistry would cease to function normally and we would die (or be reduced to a simpler, unconscious form of matter – as all the functional value gleaned from 100 millions of years of trial and error would be erased). However, this same statement would apply as equally to a computer as it would to a living organism, as the workings of computers are also finely tuned to the energy levels of semi-conductors and if the laws of physics changed – even slightly – computers would also be rendered functionless.
Extrapolating this principle to angular momentum is simple: any complex action, that does not ultimately destroy a complex structure, requires rotation.
Without rotation the complex structure can only go forward and backward, like a bullet. Furthermore, the entire structure would need to be frozen in place. The only alternative is that the structure itself effectively explodes. If the components of a structure move in divergent trajectories then unless they turn around at some point, the structure will become progressively more tenous until it becomes a cloud of fragments.
Hence:
If we assume that both complex conscious agents:
- Must rotate parts of their body to engage in complex activities
- Their structural integrity and function depends on certain relationships of cause and effect remaining constant (i.e. to live, biochemical processes must occur predictably)
Then we arrive at the conclusion that, in any universe that harbours complex conscious agents, the laws of physics must be rotationally invariant.
In other words, the fundamental physical laws that profoundly affect the biochemical processes in your body can’t change just because you’ve turned around.
Again:
Since Noether’s theorem proves that angular momentum must be conserved in any universe where the laws of physics are rotationally invariant we must conclude that:
Angular momentum must be conserved in any universe inhabited by conscious agents capable of action.
Anyone unconvinced by the argument that rotation is necessary for complex action should consider that rotation is also necessary for orbits, which in turn are necessary for complex stable structures – as I will explain later.
Gravity And Electromagnetism
Of the four fundamental forces, I will refrain from discussing the strong and weak forces as they are both complicated and short range and instead, I will limit myself to explaining why gravity and the electromagnetic forces have the form that they do as these are the only two forces whose spatial affects extent across the length scales over which living processes occur.
The mathematical form of Newton’s Universal Law of gravitation is:
Where:
F, is the force in Newtons
M, is the larger Mass in kilograms
m, is the smaller mass in kilograms
r, is the distance seperating the center of mass of both objects
G, is the gravitational constant
While the mathematical form of the law that governs the strength of force between two electromagnetic charges in a vacuum, known as Coloumb Law is:
Where:
F, is the force in Newtons
Q, is the larger Charge in Coulombs
q, is the smaller charge in Coulombs
r, is the distance seperating the center of charge of both objects
, is a constant of interaction composed of other constants including π and ε0 is the permitivity of free space.
We might now ask:
- Why does the equation governing these two Force have the form that it has?
- Why are two completely distinct forces described by very similar equations?
- Why is the force proportional to the product of both masses as opposed to some other relation such as, say, the sum?
- Why are both forces proportional to the inverse squared of the distance between the objects in question?
The fact that both gravitation and Coloumb’s Law, are both proportional to the product of the charges and masses of the objects exerting force on each other, respectively, follows from the repeatable nature of the universe. i.e. from the fact that identical charges or masses an identical distance away from each other will exert an identical force on each other.
This logically follows from the fact that we inhabit a repeatable universe where similar initial conditions give rise to similar outcomes.
To understand how this follows logically, imagine two very light bags, a distance, r, from each other where the size of the bag is negligably small compared to the distance between the bags. We fill these bags with identical balls, mass m, where m is much heavier than the mass of the bags. Because the balls are identical – and because the universe is repeatable – each ball is attracted to each identical ball in the other bag by exactly the same force. Now draw a line that links each ball in bag A to each ball in bag B. If each line represents the force that each ball is attracted to each other ball, the total number of lines will be the total gravitational force of attraction between bag A and bag B.
It is clear that the total number of lines linking the 2 bags is equal to the product of the number of balls in each of the bags.
Number of lines = (Balls in Bag A) X (Balls in Bag B)
This logic explains equally well why the electromagnetic force between two objects is equal to the product of their charges as it does as to why the gravitational force between two objects is equal to the product of their masses.
The fact that gravity and the electromagnetic force decrease with the square of the distance is less straightforward to explain. For a simple radiant body, the decrease in luminosity with the inverse square of the distance follows simply from the conservation of energy. If a point source radiates so much energy uniformly in all directions, then the flow of energy through a given surface area pointing normally in the direction of the flux, will vary inversely with the square of the distance simply because the area of the shell surrounding the light source increases with the square of the distance and, hence the fraction of the shell that a given surface area represents is the inverse square of the distance.
Gravitation and the electrostatic force do not radiate net energy. However, all force interactions are mediated through carrier particles, so if we imagine an object emitting virtual photons (the carrier particle for the electromagnetic force) or gravitons (the carrier particle for gravity) then, so long as they are emitted evenly in all directions, this would also produce an inverse squared law. And now we invoke rotational symmetry and the law of conservation of angular momentum, from further back in this article, to guarantee there is no angular dependence to either of these forces.
Why Space Has 3 Dimensions
I will finish this article with an explanation as to why space has 3-dimensions. When I say “space” I mean, the theatre in which life takes place. The anthropic principle can only be applied to the framework in which living, conscious entities develop and exist and, because of this, the existence of extra hidden dimensions postulated by some theories wrapped up tightly over plank length scales that are too small to impact anything we do or observe has no bearing on this matter.
The central importance of the orbit to the existence of life is a key fact to be aware of when considering the underlying reason why space is 3 dimensional.
- For a spatial structure to exist, there must be some stable relationship between the different spatial components from which it is composed. (And all information storage, ultimately depends in some way on the stability of a spatial structure which serves as a storage medium)
- For a spatial structure to be created, it must also be possible to adjust the relationship between the spatial components of adjacent structures (and replication/reproduction necessarily requires the ability to change the physical universe)
You may be interested to know that for a universe with a whole number of dimensions both conditions 1) and 2) only apply in a 3-Dimensional universe.
The importance of the orbit is that it imposes a stable relationship between the particles orbiting each other. It allows the stable formation of atoms, which can then have net dipoles and stick to each other with hydrogen bonds, ionic bonds or Van Der Waals forces. None of these higher order chemical effects could take place without atoms that are mostly neutral, but which “stick” to each other if they get close enough at a low enough temperature.
I will refrain from trying to derive things like the Pauli Exclusion principle, or quantized energy levels from the anthropic principle! I don’t know if this is possible, but, if it is, I’m personally not smart enough to do it!
Suffice to say that a balance between attraction and repulsion, on which solid spatial structures depend, requires a stable spatial relationship between two different particles – a stable relationship that can only be maintained by one particle orbiting the other.
From straighforward geometric considerations the acceleration, a, associated with circular motion is:
Where:
a, is the centripedal accelation
v, is the velocity
r, is the orbital radius
Given that the formula for angular momentum, L, is:
Where, m, is the smaller orbiting mass (where we assume a small mass orbits a much larger one).
Substituting L for v, gives:
And since:
Then we can express force in terms of angular momentum, mass and radius:
Lets substitute the force of gravity in for F, although the electromagnetic force would work just as well since the point of this exercise is to express the angular momentum of a stable orbit in terms of the orbital radius. Also the expression for gravity will be generalized for an N dimensional universe. Assuming conservation of flux yields:
Where, N, is the number of spacial dimensions.
Substituting F, on both sides yields:
If the dimensions of space are 3 or less, angular momentum increases with orbital radius, if space had 4 dimensions, angular momentum would be constant with orbital radius, if space had 5 or more dimensions, angular momentum would go down as the orbital radius increased.
Orbital energy, as a function of radius is the integral of force with respect to distance:
Again, N, is the number of spatial dimensions in the universe.
Note that for a 2 dimensional universe, the formula is:
We can see from this, that in a universe with 2 dimensions or less, as the orbital radius approaches infinity, the orbital energy also approaches infinity. In otherwords, in a universe with 2 dimensions or less, there is no such thing as escape velocity. One particle can never gain enough energy to escape the orbit of the particles it’s orbiting around!
Thus, in a universe with 2 or less dimensions, condition 2) the reconfiguration of matter and, hence, the ability of structures to reproduce themselves is not satified.
When space has three or more dimension, however, the orbital energy approaches a finite limit at infinite radius. Hence, in a universe with 3 dimensions or more each orbit has a well defined escape energy, or escape velocity which, if reached, allows the smaller orbiting particle to escape the orbit of the larger particle.
When we apply torque to a particle, we also add energy to that particle and if the universe has 3 or more dimensions, this extra energy results in the orbital radius increasing. In a universe with 3 dimensions, this is no problem, as both orbital angular momentum and orbital energy both increase with orbital radius. However, if the universe has 4 or more spatial dimensions then the orbital angular momentum reduces with increased radius. In practice, what this means is that the orbit is unstable. The slightest nudge or the addition of the tiniest amount of energy to an orbiting particle in a universe with 4 or more dimension would destabilize the orbit.
Paul Ehrenfest and Max Tegmark have proved that 3 spatial dimensions are necessary for stable orbits more rigorously.
In conclusion:
- Stable orbits cannot exist in a universe with 4 or more spatial dimensions (eliminating the possibility of information storage in a structure)
- Particles cannot escape their orbits in a universe with 2 or less spatial dimensions (eliminating the possibility of reproduction)
- Reproducing, evolving organisms can only exist in a 3 dimensional universe
Conclusion
Perhaps these aspects of our universe that appear to be especially favourable to the evolution of life may convince you that the universe we see around us is the result of the anthropic principle at work.
This would in turn imply, that the entire universe whose immense vastness we see around us is but a tiny spec in a mind-bogglingly infinite multiverse who’s sheer scale and diversity is completely impossible for our limited minds to comprehend.
However, our universe is comprehensible, because evolution can only occur in a comprehensible universe. Evolution also favours entities that can act effectively on their environment, and since comprehension increase the effectiveness with which an organism can act on its environment, it is, all else being equal, a trait favoured by evolution. So evolution can only occur in a comprehensible universe and it also has a tendency to (eventually) produce phenotypes that can comprehend it.
Are you convinced?
John McCone
