How can calculus help us understand the time index function across the universe?

[mundane]

Hi, I have to write a "thesis" (short paper using only calculus and no philosophical concepts) about a very big and ambiguous concept, and I was hoping some of you could point me in the right direction.

It says...

"We can assume that at any moment every location in the universe observes the passage of time in one and only one way. We can assign that observation a value based in the observer's location. While any two different locations might observe the passage of time in the exact same way or in different ways, any specific location will only observe time in one way, and no more. Therefore the time index values, based ln physical location in the universe, form a function. Using calculus, explain the analytical process one would use to understand the passage of time throughout our universe. Specifically pay attention to the dimensions of the range and domain of the time index function and discuss the characteristics we can determine about the time index function using calculus techniques. Logical calculus techniques should be discussed with complimentary discussion Of supporting math concepts.



Can somebody maybe push me in the right direction? I was thinking about illustrating a graph and talking about how taking derivatives illustrates the acceleration/velocity etc. but I really don't know how I should go about this.. Any thoughts? It's obviously very open ended but worth over a letter grade...

Thanks in advance!

 

[haruspex]

What would the "time index function" be a function of? What derivatives therefore may be of interest?
Perhaps a consideration is that at one location there will be awareness of neighbouring locations, communicating at speed of light, leading to some sort of consistency rules. Just guessing here.

 

[mundane]

Thanks for the reply... The professor will not tell us... He is purposely being very vague, and I just need something to set up that I can then try some calculus on or talk about what would happen if calculus were done to it... He said we should get no numbers, just a vague illustration/explanation.

What do you mean by "awareness of neighboring locations communicating at the speed of light)?

I am way too lost to even begin... please help :/

 

[haruspex]

OK, but first please try to answer my questions. I think you should be able to answer these: What would the "time index function" be a function of? What derivatives therefore may be of interest?

 

[mundane]

OK, but first please try to answer my questions. I think you should be able to answer these: What would the "time index function" be a function of? What derivatives therefore may be of interest?

Sorry, I thought you were actually wondering that, :P

As far as I can tell, it might be a function of location in the universe against the speed at which one perceives time? That's the direction I was heading... but I am not sure of myself. If that were the case, would I get an instantaneous velocity by taking the derivative at some point and then acceleration if I derived further?

 

[phinds]

... it might be a function of location in the universe against the speed at which one perceives time?

Just to clarify something here, there is EXACTLY ONE way in which you perceive time and that is at a rate of 1 second per second. In your own frame of reference you are always at rest. Other people observing you might think your time is running at a different rate than theirs, if that's what you mean.

 

[mundane]

Indeed... I understand, I am just lost on how to create a function out of it...

 

[haruspex]

The only way I can see to proceed is to assume some (indeterminable) 'real' time and express the local time index as a function of that and location. You might then be able to encode rules like 'time doesn't flow backwards anywhere'.