Student Blog: Quantum Physics III – Predicting the Future


Determinism is the theory that all events, including moral choices, are completely determined by previously existing clauses.

Due to the uncertainty principle, determinism seems impossible at first sight. Because the more accurately we measure the position, the less accurately we can determine the velocity, and vice versa, right? The Laplace version of scientific determinism stated that if we knew the positions and velocities of particles at one time, we could determine their positions and velocities at any time in the past or future. But the uncertainty principle prevents us from making any start as we cannot know both concepts at the same time. 

Nonetheless, the new quantum mechanics theory, which incorporates the uncertainty principle, have meant that we can, roughly speaking, accurately predict half of what we would expect to predict in the classical Laplace point of view. 

wave function is a number at each point of space that gives the probability that the particle is to be found at that position. The rate at which the wave function changes from point to point tells how probable different particle velocities are. If a wave function has a sharp peak, it means that there is a high probability that the particle is there – low uncertainty in the position – and if there is a wider wavelength, there is large uncertainty. Similarly, if there was a rapidly changing wave function (i.e., not many waves – just one as the example below) then there is a large velocity uncertainty as the probability distribution for the velocity is spread over a wide range. 

However, now imagine a continuous train of waves, there is large uncertainty in positionbut small uncertainty in velocitysatisfying the uncertainty principle. The wave function is all that can be well defined. 

Schrödinger Equation

The Schrödinger equation gives the rate at which the wave function changes with time. If we know the wave function at one time, we can use the Schrödinger equation to calculate it at any other time, past or future. Therefore, though it is on a reduced scale, there is stilldeterminism in quantum theory. The Schrödinger equation allows us to predict the wave function, which in turn can be used to work out either the positions or velocities. In conclusion, in quantum theory, the ability to make exact predictions is just half what it was in the classical Laplace worldview (all planets move in the same direction around the Sun). 

Though the Schrödinger equation shines hope on being able to predict the future, it relies on that time runs smoothly everywhere, forever. However, the special theory of relativity overthrew the concept of absolute time, where time was just one direction in a four-dimensional spacetime. In special relativity, spacetime is smooth, the quantum version of determinism works

Black Holes

In contrast, in Einstein’s new, and more widely accepted theory of general relativity, spacetime was curved and distorted by the matter and energy in it. In places like our Solar System, where curvature of spacetime is so light, that it doesn’t interfere with our usual idea of time however, once we increase the scale and spacetime can be curved, there is a possibility that it may have a structure that doesn’t admit a time that increases smoothly for every observer – as everyone has their own measure of time. 

It is because of black holes that scientists think time will not increase for every observer. Black holes have massive gravitational strength, so strong that not even light can escape from them. This is because a black hole has an escape velocity (lowest velocity needed to escape the gravitational attraction of a body) that surpasses even the speed of light(300,000 km per second). 

This is a black hole, a region of space bounded by an event horizon, from which it is impossible for anything, including light to escape from. A black hole is formed when any sufficiently heavy nonrotating star runs out of nuclear fuel, and it will necessarily collapse to a perfectly spherical Schwarzschild black hole. 

Schwarzschild was a German astronomer who managed to incorporate a spherical black hole into Einstein’s theory of relativity: 

As stars run out of fuel to burn in nuclear fission, they do not release much energy, so they lose heat and the thermal pressure that supports them against gravity. As a result, the stars begin to shrink. Those twice the size of the Sun will not have sufficient pressure to stop the contraction. They will collapse to zero size and infinite density, forming a singularity – a point of infinite density and gravity. 

As seen in the previous page, the paths of light rays from its surface will start out at smaller and smaller angles to the vertical. When the star reaches a certain critical radius, the paths will be vertical on the diagram which means that the light will hover at a constant distance from the centre of the star, never getting away. This forms a surface known as the event horizon, which separates the region of spacetime from which light can escape from the region from which it cannot. Any light emitted by the star after it passes the event horizon will be bent back inward by the curvature of spacetime. 

If black holes emit no light, how do we know they exist? Scientists search for black holes by monitoring bodies around them that seem to be orbiting an invisible massive object. 

If an astronaut was to fall into a black hole and hits the singularity, time will come to an end for them. However, in general relativity, you are free to measure time at different rates in different places. 

As seen above, the surface of constant values of this new time would be all crowded together at the centre, below the point where the singularity appeared. Given that, they would still agree with the usual measure of time in the nearly flat spacetime far away from the black hole. 

You could use this time in the Schrödinger equation and calculate the wave function at later times if you knew it initially. There is still determinism. Although, it should be noted that at late times, part of the wave function is inside the black hole, where it can’t be observed by someone outside. Meaning, an observer outside the black hole cannot run the Schrödinger equation backwards and calculate the wave function at early times. To do that, they would need to know the part of the wave function that is inside the black hole, which contains information about what fell into the hole.

Conclusion

Quantum physics is about particles and their nature in everyday life. Research in quantum physics is crucial for our future and the development of humankind as I have explored in this essay. Quantum physics could be the key to answering all our questions.  Hey, maybe one day you’ll discover the Theory of Everything! 

Written by Dinuli, a Year 10 Student at Harris Academy Bromley


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