Godel and the end of Physics - by S.W. Hawking 2002 - Article review

This document contains article review "Godel and the and of Physics" by S.W. Hawking written in 2002
To order to read the article select: https://www.hawking.org.uk/in-words/lectures/godel-and-the-end-of-physics



1. Our picture of the Universe.

Dirac showed how the work of Erwin Schrodinger and Werner Heisenberg could be combined in new picture of reality, called quantum theory.
Okay. However this sentence is not complete. More detail is required to describe quantum theory.
In quantum theory, a particle is not characterized by two quantities, its position and its velocity, as in classical Newtonian theory.
In Newton's theory a particle is described by three positions in time (at regular intervals). As a result velocity and acceleration are calculated
Newtonian theory also requires the concept of mass.
Instead it is described by a single quantity, the wave function.
The wave function, as being defined as a description of a particle, most probably includes many parameters or quantities.
The size of the wave function at a point, gives the probability that the particle will be found at that point, and the rate at which the wave function changes from point to point, gives the probability of different velocities.
This raises the question how the wave function in detail is calculated. Which observations are involved.
One can have a wave function that is sharply peaked at a point.
My understanding is, that in that case, the size of the wave function is small.
This corresponds to a state in which there is little uncertainty in the position of the particle.
Does little uncertainty imply that the speed of the particle is low? This is the same when the speed of an object is considered.
However, the wave function varies rapidly, so there is a lot of uncertainty in the velocity.
And also with the position.
Similarly, a long chain of waves has a large uncertainty in position, but a small uncertainty in velocity
See next sentence.
One can have a well defined position, or a well defined velocity, but not both.
The problem is, as mentioned before that a velocity requires 2 positions.

This would seem to make complete determinism impossible.
This requires a clear definition of the concept of determinism. See also next sentence. It is advised to start any dicussion about determinism not with the wave function. Determinism and inderterminism came first.
If one can't accurately define both the positions and the velocities of particles at one time, how can one predict what they will be in the future?
The accuracy of your predictions depend on the accuracy of your observations and the calculations involved to make your prediction.
It is like weather forecasting.
It is like all processes. The further in the futher, the more inaccurate.
However, in quantum theory, it turns out one doesn't need to know both the positions and the velocities.
Why? This sentence is not clear.
If one knew the laws of physics and the wave function at one time, then something called the Schrodinger equation would tell one how fast the wave function was changing with time.
This sentence starts with a big If. The problem is that the laws of physics, the schrödinger equation and the wave function are all descriptions of identical processes. All these descriptions are based on observations. These observations including experiments, come first. The calculations to make predictions, come second.

Reflection 1 - Comparing Newton Mechanics with Quantum Mechanics

General speaking it is difficult to compare Newton mechanics with Quantum Mechanics.
Quantum Mechanics is the study of elementary particles. Newton mechanics is the study of objects, collections of particles.
My understanding is that it is almost impossible to predict the future position of an individual particle. For a star this of a lesser problem. In both cass you must know the position at a sequence of equally spaced distances. The problem is that any measurement will influence the position of the object you want to measure. For elementary particles this is relative large, for photons almost impossible for photons implying that it is more difficult to predict the future of induvidual elementary particles as for larger objects.

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Created: 1 June 2022

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