# Classical Mechanics: Continuous or Discrete universe? [duplicate]

The question of the "continuous" or "discrete" nature of the universe is the subject of diatribe among the greatest physicists in the world. I would like to discuss the same topic, but asking a question about the aspect of continuum in classical mechanics.

The use of mathematical functions (continuous) to describe the evolution over time of quantities such as position, velocity, acceleration, energy, has been introduced since Newton's time. However, when using a calculator, the mathematical functions of physical use are subjected to a necessary discretization which involves a certain error. My question is: is the reality in which the mentioned physical quantities are discrete? Could we conceive the environment in which a body moves, with a certain trajectory, like a three-dimensional screen composed of Pixels? In this case, the use of the integral calculation would result in a mathematical error, in exactly the opposite way to the discretization process that is conducted in a computer.

My physics professor said that reality is continuous, but I do not think that this concept can be assimilated by the human mind. I do not want to come to the treatment of space-time, but I believe that the paradoxes of Zeno are sufficient to agree that the physical greatness with which we deal every day is of a discrete nature.

Quantum mechanics confirms that entities such as energy and speed should be understood as discrete (just think of the "quantum" of energy), therefore it is possible that my question can be answered already in this. However, since the school years the use of continuous mathematics is taught but not justified. Is it possible that the universe is discrete, but composed of such a high number of stencils that any error is insignificant for classical mechanics, which deals with the macroscopic world?

• It is highly possible, although once you make the universe discrete, classical mechanics won't be able to give any sufficiently correct result. Loop quantum gravity is proceeding in this direction and string theory also is trying to convince us that particles are discrete vibrating strings. Till now, experiments have not shown any deviation from a continuous universe. So your question of a classically discrete universe makes little sense. :") – Yuzuriha Inori Mar 6 '18 at 17:03
• The justification for assuming a continuous spacetime is that it fits all the observations and it is simpler than the alternative. – Javier Mar 6 '18 at 18:19

Both classical and quantum physics use mathematical models that assume space and time are continuous. Within those models, Zeno's paradoxes do not represent obstacles; assuming continuous space and time, calculus resolves the "paradoxes" with no trouble. And indeed, we can get from point $A$ to point $B$, so maybe a "correct" theory should be able to resolve such "paradoxes".