Determinism: Difference between revisions

Revision as of 14:53, 16 July 2019

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

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.

Practical Limitations

While the idea of determinism seems intuitively true based on our everyday experience, the true story is more complicated, though it remains unresolved.

One practical limitation is the fact that initial conditions can only be measured as accurately as our instruments allow, and after a few time steps, small inaccuracies build on each other. This means that over time, our model of the system and our predictions of its future state stray farther and farther away from the actual future state of the system. 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.

For an example of a chaotic system, consider a game of pool. The blue and yellow paths are the result of very similar forces on the cue ball, but the outcomes are not similar. Slight changes in the force applied to the ball result in a wildly different outcome seconds later.

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.

These limitations prevent us from ever exactly determining the evolution of a system, but they don't necessarily say anything about the nature of the universe itself. When one moves past Newton's theory, however, the entire 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^[1], that this theory will be deterministic, but we have no way to know at this time.

Chaos

Mathematical Model

Position updating using Newton's laws. (from Iterative Prediction)

For an understanding of the mathematical equations relevant to determinism, see Iterative Prediction.

Computational Modeling

Example: Weather Systems

The atmosphere can be considered a physical system, and rough predictions can be made about its future state.

For a practical example of a system that should theoretically be deterministic, consider the weather. Meteorologists use the movement of weather fronts to predict the weather in the near future, and if the temperatures and velocities of masses of air were known with precision, they should be able to determine what the weather will look like in the next few days. However, we all know how inaccurate weather predictions can be just a couple days in advance. This is because of the difficulty of measuring atmospheric conditions with the level of precision required for iterative prediction.

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. Source

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.

References

Understanding Ethernet Speed and Determinism

↑ https://arxiv.org/pdf/quant-ph/0212095.pdf

[1] ttps://arxiv.org/pdf/quant-ph/0212095.pdf

[1]

@@ Line 6: / Line 6: @@
 ===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. Using iterative prediction, we should be able to calculate where the object will be at any given time in the future. 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 and momentums, and forces being applied) of each object. From a scientific standpoint, this means that the future state of the universe should theoretically be able to be determined by scientists using simple physics. This idea has been taken even further in a philosophical context 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.
+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.
 ===Practical Limitations===
-While the idea of determinism seems straightforward at first, there are actually complicated reasons that we cannot precisely predict the future of small, simple systems, much less the entire universe.
+While the idea of determinism seems intuitively true based on our everyday experience, the true story is more complicated, though it remains unresolved.
+One practical limitation is the fact that initial conditions can only be measured as accurately as our instruments allow, and after a few time steps, small inaccuracies build on each other. This means that over time, our model of the system and our predictions of its future state stray farther and farther away from the actual future state of the system. 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.
-One practical limitation is the fact that initial conditions can only be measured as accurately as our instruments allow, and after a few time steps, small inaccuracies build on each other. This means that over time, our model of the system and our predictions of its future state stray farther and farther away from the actual future state of the system. This is why iterative prediction is usually only used over small periods of time.
 [[File:determinismpooltable.png|frame|left|For an example of a chaotic system, consider a game of pool. The blue and yellow paths are the result of very similar forces on the cue ball, but the outcomes are not similar. Slight changes in the force applied to the ball result in a wildly different outcome seconds later.]]
-Another practical limitation is that we must necessarily simplify systems to be able to model them. It is impossible to account for every interaction within and outside a system, since every particle in the universe interacts with every other particle in the universe, resulting in an unthinkable number of calculations that would need to be done to accurately account for the net forces on a system. This introduces error that limits the long term accuracy of any calculations we can carry out.
-Furthermore, Newton's laws are not always sufficient. For systems with small particles, quantum mechanics comes into play. If gravitational interaction between massive objects is involved, the [[Principle of Relativity|Relativity]] needs to be taken into account. Additionally, the Heisenberg Uncertainty Principle asserts that we physically cannot know the position and velocity of a particle with one hundred percent certainty, which limits the precision of our calculations.
+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.
+These limitations prevent us from ever exactly determining the evolution of a system, but they don't necessarily say anything about the nature of the universe itself. When one moves past Newton's theory, however, the entire 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<ref> https://arxiv.org/pdf/quant-ph/0212095.pdf </ref>, that this theory will be deterministic, but we have no way to know at this time.
 ===Chaos===
-Determinism and chaos are related, almost opposite concepts. Chaos results in systems that are extremely sensitive to initial conditions. Tiny changes in initial conditions quickly lead to dramatic differences in behavior. Any system that exhibits chaos presents a challenge to deterministic theory because the future behavior of a system is so difficult to predict and varies wildly based on miniscule, imperceptible differences in initial conditions, demonstrating in an extreme way the practical limitations that hinder deterministic calculations.
-==Modeling==
-[[Image:MOTION.png|right|frame|416x192px|Position updating using Newton's laws. (from [[Iterative Prediction]])]]
 ===Mathematical Model===
+[[Image:MOTION.png|right|frame|416x192px|Position updating using Newton's laws. (from [[Iterative Prediction]])]]
 For an understanding of the mathematical equations relevant to determinism, see [[Iterative Prediction]].
-===VPython Model===
+===Computational Modeling===
+<!--
 Basic systems can be considered deterministic and calculated with some level of accuracy.
 In Physics 1, you will often use VPython to model the future behavior of systems given a set of initial conditions. The steps to do this, with given time step (deltat), initial momentum (p_initial), and initial position (pos_intiial) are:
@@ Line 44: / Line 51: @@
 Sample Glowscript code and a basic program can be found [http://www.glowscript.org/#/user/areeba/folder/Public/program/IterativePredictionExample here]. <br>
+-->
 ==Example: Weather Systems==