Consequences of time not being continuous

[YoshiMoshi]

Homework Statement

Given that the phenomena of time is non continuous, despite it often being considered as being so, what are the consequences of this? It seems that the foundation of mathematics that describes the physical world assumes that time is continuous, which we believe now to be false. I know that the difference between continuous and non continuous is very small for time, but even a little bit off has major consequences. Doing something like integration or differentiation becomes very difficult.

Or say for example analog to digital converters convert a continuous system to a discrete one, but what is actually going on is that we are converting an already discrete system to a discrete system with a higher sample time.

Homework Equations

The Attempt at a Solution

 

[FactChecker]

Homework Statement

Given that the phenomena of time is non continuous, despite it often being considered as being so, what are the consequences of this? It seems that the foundation of mathematics that describes the physical world assumes that time is continuous, which we believe now to be false. I know that the difference between continuous and non continuous is very small for time, but even a little bit off has major consequences. Doing something like integration or differentiation becomes very difficult.

The mathematical definitions of integration and differentiation are not changed. They do not depend on how the math is being applied to any particular physical situation. The truth is that the physics at that quantum level is handled with entirely different mathematics anyway.

Or say for example analog to digital converters convert a continuous system to a discrete one, but what is actually going on is that we are converting an already discrete system to a discrete system with a higher sample time.

I'm not sure what you mean here. The sample time of any analog to digital converter is much too great to require any quantum-time considerations.

PS. Is this really a homework problem? It didn't look like it so I replied here as though it is not. If it really is homework, you should show your ideas and work and we are only allowed to ask leading questionss and give hints.

 

[PeroK]

Homework Statement

Given that the phenomena of time is non continuous, despite it often being considered as being so, what are the consequences of this? It seems that the foundation of mathematics that describes the physical world assumes that time is continuous, which we believe now to be false. I know that the difference between continuous and non continuous is very small for time, but even a little bit off has major consequences. Doing something like integration or differentiation becomes very difficult.

None of this is true. I think you have picked up some wrong ideas from somewhere.

 

[Aufbauwerk 2045]

It does seem to be a rather bold statement to say "we know" that time is non-continuous. Can you define what group of physicists you mean by "we?" Of course we need to be very careful in physics about using the term "we know."

Are you perhaps thinking about some speculations that the universe is a type of computer simulation, i.e. "digital physics?" Zuse wrote the seminal paper on this decades ago, called "Calculating Space." Although fascinating as a speculation, I think it's fair to say it's not a mainstream area of physics research at this time.

In any case, here is a previous discussion from PF on a question that seems related to your question.

https://www.physicsforums.com/threads/is-time-continuous.3396/