Determinism
By Areeba Abid
Determinism is the idea that if the physical state of a system is known, including the momentums, positions, and forces of each object in the system, the behavior of the system can be calculated using iterative prediction to determine its behavior at any given time. This idea is based on Newton's second Law: the Momentum Principle, developed by Isaac Newton.
Main Idea
Concepts of Physical and Philosophical Determinism
Newton's laws allow us to predict the motion of an object if we know the initial position, initial momentum, and forces acting on the object. If this idea is extrapolated to all objects in the universe, it would seem that we could predict the future of the entire universe if we only knew the initial conditions (the starting positions, momenta, and interaction forces) of each object. In philosophy and metaphysics, this principle has been used to argue that humans do not have free will, because the atoms that make up our bodies simply continue to move in the paths we would expect based on their initial conditions.
Deterministic Chaos
Based on an understanding of Newton's Laws, is may seem certain that determinism is correct. However, the story is more complicated, and in one manner or another those complications are the basis of most modern physics.
The first practical limitation is the fact that the initial conditions of a system may only be measured as accurately as our instruments allow. In most systems, uncertainties grow over time, which means the even small errors at the beginning may lead to drastic differences between predictions and reality after a given time period. This is why iterative prediction is generally only reliable for small time scales, although the exact nature of the system may cause the relevant time scales to vary drastically. In an idealized projectile motion problem, errors in the initial condition will generally have a linear effect upon the error of the prediction, which is manageable. If one introduces more complex forces, such as air resistance, these errors may be amplified much more substantially.
A related limitation is our use of phenomenology. We treat a billiard ball, for example, as a single object, when in fact it is a collection of atoms. Modelling the ball correctly would require modelling each of these atoms and their interactions, but this is well beyond our capabilities, and so we use approximate forces instead of considering the truly fundamental forces. Even if we did have a unified theory of everything, it would be functionally impossible for us to apply it to the universe, and so the dream of fully predicting a system is beyond our reach as humans.
The limitations described above give rise to what is known as deterministic chaos[1].
One may note, for example, that there is a million dollar prize for anyone who can prove that solutions exist for the Navier-Stokes equations, which govern the behavior of fluids[2]. As such, this section will focus n use computational modeling to observe the behavior of chaos, rather than trying to explain it. That being said, chaos theory is a specialty of the Georgia Tech physics department, and if you are interested in learning more there are a wealth of resources to explore.
Stochastic Systems
A stochastic system is one with an inherent amount of randomness. This may be introduced by the limitations above, but it may also have more fundamental roots. When one moves past Newton's theory, the idea of determinism is called into question. Relativity behaves nicely from this respect, being (to the best of our knowledge) a purely deterministic theory. Quantum mechanics, however, seems by its very nature to defy determinism: quantum states always have a degree of randomness, and so it is impossible to fully determine the future of a quantum system. None of this is certain, of course, since we still lack a unified field theory, and there is an argument to be made, such as is made by Gerard t'Hooft[3], that this theory will be deterministic, but we have no way to know at this time.
Mathematical Model
As per the above, in so far as we consider any modeling, we will focus on the interesting case of deterministic chaos, rather than on the stochastic (that is, non-deterministic) systems which occur as a result of quantum mechanics, or systems with noise in general.
Computational Modeling
Examples
All of these examples should be performed with the use of a numerical solution program, such as this
Simple
Use the chaotic spring system from Predicting Change in multiple dimensions, set [math]\displaystyle{ k = 4.9 }[/math], [math]\displaystyle{ \theta = \pi/6 }[/math], equilibrium length [math]\displaystyle{ L = 4 \; m }[/math], and initial extension [math]\displaystyle{ r_0 = 5 \; m }[/math].
Middling
Now, put the following system into a numerical solution program:
[math]\displaystyle{ F_x = (\frac{1}{10})(x^2-y^2-x) }[/math]
[math]\displaystyle{ F_y = (\frac{1}{19})(2xy + y) }[/math]
Difficult
Connectedness
Connection to Personal Interest: Philosophical Determinism
How is this topic connected to something that you are interested in?
Determinism has fascinating implications for the concept of free will. Even if it is impossible for us to calculate the future behavior of a system accurately, it is still without a doubt the direct result of the initial conditions, as directed by Newton's laws. Consider the human body as a physical system. If the body is simply a collection of particles and thoughts in the brain are just neurons firing, is every feeling experienced and every decision made by a person simply the result of whatever initial conditions they started with? Is it possible to differentiate between the laws that regulate matter and the laws that regulate our own bodies? What happens when we try to apply the laws of physics to the workings of our minds? It's difficult to think of your body as a collection of chemicals that behave like a very complicated deterministic system, but the implications are mind blowing and have been the subject of controversy since ancient times.
Connection to Major: Engineering Applications
How is it connected to your major (biomedical engineering)?
Predicting the behavior of physical systems is important for any engineer, and determinism makes this possible to some extent.
Connection to Industry: Ethernet Data Transfer
Is there an interesting industrial application?
Data transmission takes time, and knowing the time that it takes for information to travel from one location to another is important is some industrial applications, such as sending control variables to a high-speed CNC mill. Engineers need to be able to know how long it will take for a machine to receive data, and if a system is deterministic this can be calculated. However, Ethernet systems are not deterministic and the rate of data transfer is unpredictable, which poses problems for engineers.[4]
History
The concept of determinism has been around for centuries and was explored by thinkers around the world. Physical determinism was bolstered by Newton's Laws, and the first publication discussing it in a scientific context, "LaPlace's demon", was written by Pierre Laplace in 1814. He wrote that a hypothetical omniscient observer could potentially predict the entire future of the universe. Even though this is practically impossible for any human or computer to ever achieve, LaPlace argued that it was still hypothetically possible if physical determinism were true. However, this was before 1927. when the Heisenberg Uncertainty Principle asserted that initial conditions cannot be known with complete accuracy, even hypothetically.
See also
Background Physics
Fundamental Interactions
Khan Academy: Heisenberg Uncertainty Principle
General Information on Determinism
Determinism
Physical Determinism
More on Free Will
Khan Academy/MIT: The Problem of Free Will
Video Arguing Free Will Doesn't Exist
Video Arguing Free Will Does Exist (Sort Of)