Do laws governing science allow us to predict the future? The short answer no, and yes. In principle , the laws allow us to predict the future. But in practice the calculations are often to difficult.
In Ancient times, it must have been very difficult to predict the future course of event. Natural phenomenon like volcano eruption, rain, storm, lightning seemed unpredictable. In absence of scientific knowledge people took to worship Gods and held them responsible for such event. However, with the advent of scientific revolution we were able to predict some event in advance and mitigate the disastrous outcomes. Still the very question remains stood: Can we predict the future?
When it was found natural events follow scientific laws. This led to the idea of scientific determinism. Which seems to have been first published by French scientist Pierre-Simon Laplace. The argument put forward by Laplace was: If we knew the positions and speeds of all particles at one instance we predict their future course of events. But is not as good as it sounds. The equations dealing with such an idea contain a factor what is known as Chaos factor. A tiny disturbance at one place can lead to major change at another. A butterfly flapping its wings in Australia can cause rain in Mumbai. And the factor is not same as that before, the outcome may be different this time. Chaos is what is responsible for unpredictable weather event.
The Quantum View
The idea of scientific determinism prevailed till early 20th century. Quantum Mechanics changed it all. In 1927 German Physicist Werner Heisenberg gave his Uncertainty principle stating clearly that both the positions and speed of a particle cannot be simultaneously determined with accuracy. An accuracy in one causes uncertainty in other. Many notable physicists including Albert Einstein did not agree with the view. Einstein quoted “God does not play dice”. But experiments have confirmed the uncertainty principle time to time and it is well established as a founding rock of Quantum mechanics.
What quantum mechanics says instead that we have a wave function which gives us a set of possible values a system may have. From this wave function we can extract information about the system. Although quantum mechanics leads to uncertainty when we try to predict both the position and the speed, it still allows us to predict, with certainty, one combination of position and speed. However even this degree of certainty seems to be threatened by more recent developments. This problem arises because gravity can wrap space-time so much that there can be regions of space that we can`t observe. Such regions are the interiors of black holes.
To summarize the above discussion, scientific determinism, first proposed by Laplace, suggested that if we knew all particle positions and speeds, we could predict the future. However, chaos theory introduced unpredictability due to tiny disturbances. Quantum mechanics, with Heisenberg’s Uncertainty Principle, challenged determinism. It revealed wave functions offering sets of possible values for a system, allowing some predictions. Yet, the extreme gravity of black holes could create unobservable regions, threatening even this limited certainty. Despite scientific advancements, true complete prediction of the future remains elusive, as uncertainty and complexity persist.
References: Brief Answer To The Big Questions by Stephen Hawking