Is Time Really Non-Existent? An Intriguing Question About Measuring Seconds

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The forum discussion centers on the philosophical and mathematical implications of measuring time, specifically the concept of a second. Participants explore the paradox of reaching one second by breaking it down into infinitely smaller fractions, questioning whether time is truly existent if it requires traversing an infinite series of numbers. The conversation concludes that despite the infinite subdivisions, time is defined and measurable in finite terms, as evidenced by the ability to sum infinite series to yield finite results.

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  • Understanding of basic mathematical concepts, including infinity and limits.
  • Familiarity with Zeno's paradoxes and their implications on motion and time.
  • Knowledge of real numbers and the distinction between countable and uncountable infinities.
  • Basic principles of time measurement, including atomic time standards like the caesium-133 atom.
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  • Study the concept of limits in calculus to understand how infinite series can converge to finite values.
  • Explore the differences between countable and uncountable infinities in set theory.
  • Learn about atomic timekeeping and how it defines the second in modern physics.
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Philosophers, mathematicians, physics students, and anyone interested in the nature of time and its measurement.

aglo6509
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So, I would like to start off by saying I know how time works and accept it for what it is, but have a curious question about it.

So we all know that 60 seconds make a minute, but how can we tell when exactly a second passed?

Let me explain ( this is all hypothetically of course):

We can break the second down into milliseconds and all that, but when looking at going from zero to 1 second from example:

0s------>1s

Doesn't time have to move through an infinite amount of numbers to get to one second? Like it has to go through 0.2s, 0.5s, 0.9s, 0.99s, 0.999999s, 0.99e900s, etc.

Since it isn't possible to go through an infinite amount of numbers, wouldn't it make sense that we could never get to one second and thus time being non-existant?

Again I know how time works in all, but this always made me curious.
 
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aglo6509 said:
Since it isn't possible to go through an infinite amount of numbers, wouldn't it make sense that we could never get to one second and thus time being non-existant?

Why isn't it possible to go through an infinite amount of numbers?
 
Mute said:
Why isn't it possible to go through an infinite amount of numbers?

Because wouldn't there always be another number to go through. Like to get through 0 to 1 second, you have to go through 0.9s then 0.99s then 0.9999999s then 0.9999999999999999999999999s all the way to infinity.

So you could never reach 1
 
aglo6509 said:
Because wouldn't there always be another number to go through. Like to get through 0 to 1 second, you have to go through 0.9s then 0.99s then 0.9999999s then 0.9999999999999999999999999s all the way to infinity.

So you could never reach 1

No, you misunderstand his point.

Just because you can break a finite task into infinite smaller tasks doesn't make the original finite task no longer finite.
 
aglo6509 said:
Because wouldn't there always be another number to go through.
The problem with this statement is that you're being vague about "always". If by "always", you mean "for every number less than 1", the answer is yes. But if by "always" you mean "for all time", the answer is no. You take less and less time to go through the numbers as you get closer and closer to 1. If you add up all those progressively smaller times, you end up with a nice, definite, finite number. Once you realize that you can add an infinite series of numbers and get a finite result, the paradox disappears.
 
Well I guess I meant there will always be a another number less then 1, because I was trying to show adding all numbers between zero and one.
 
aglo6509 said:
Well I guess I meant there will always be a another number less then 1, because I was trying to show adding all numbers between zero and one.
OK. But if you think about it, that doesn't lead you anywhere surprising. What you're saying is, "For every number less than 1, there's another number closer to but still less than 1." Fine. This is true. But there is no way that implies "So you could never reach 1".

The problem is that you've got a very strong intuition that says it's impossible to ever complete an infinite task. But you probably also have very strong intuitions that the solid Earth is not moving, and that rulers stay the same length when they move. Or you would, except that those have been beaten out of you in school. Your intuitions are not necessarily to be trusted.
 
pmsrw3 said:
OK. But if you think about it, that doesn't lead you anywhere surprising. What you're saying is, "For every number less than 1, there's another number closer to but still less than 1." Fine. This is true. But there is no way that implies "So you could never reach 1".

The problem is that you've got a very strong intuition that says it's impossible to ever complete an infinite task. But you probably also have very strong intuitions that the solid Earth is not moving, and that rulers stay the same length when they move. Or you would, except that those have been beaten out of you in school. Your intuitions are not necessarily to be trusted.

I know those other things happen. I just always had this uneasy feeling about infinity. I guess I just don't understand it yet.
 
  • #10
Don't worry about understanding infinity just yet. It takes a bit of time.
 
  • #11
first of all, what's so special about not quite getting to 1? I mean, there are infinite amount of numbers between any two numbers, in the first place...so, forget about trying to get from 0.9999999999999 to 1...how about getting out of zero to start with? how in the world do you get to 0.1? ...you would never get there either...

...that is, if you care to count...

time is not counting itself, time is continuous...

...it is us who invented numbers and are trying to count...but, for as long as we defined a second to be a certain discrete amount of time, we can just go that bit at a time...

...by the way, I think our ability to measure time came about in big chunks, first, and started to be smaller and smaller and so...it is not like we said 0.000000001 or anything like that...we simply divided time in years, then in days, then in hours, then in minutes, etc...

...anyway...just rambling...
 
  • #12
aglo6509 said:
Because wouldn't there always be another number to go through. Like to get through 0 to 1 second, you have to go through 0.9s then 0.99s then 0.9999999s then 0.9999999999999999999999999s all the way to infinity.

So you could never reach 1

But what does it mean to "go through" a number?
 
  • #13
Mute said:
But what does it mean to "go through" a number?

I'm trying to say to go through 0 to 1, you count up every number between them.


gsal said:
first of all, what's so special about not quite getting to 1? I mean, there are infinite amount of numbers between any two numbers, in the first place...so, forget about trying to get from 0.9999999999999 to 1...how about getting out of zero to start with? how in the world do you get to 0.1? ...you would never get there either...

...that is, if you care to count...

time is not counting itself, time is continuous...

...it is us who invented numbers and are trying to count...but, for as long as we defined a second to be a certain discrete amount of time, we can just go that bit at a time...

...by the way, I think our ability to measure time came about in big chunks, first, and started to be smaller and smaller and so...it is not like we said 0.000000001 or anything like that...we simply divided time in years, then in days, then in hours, then in minutes, etc...

...anyway...just rambling...

Yeah, I like your example of how it was us who made the numbers and time really has no effect by them. Just a way for us to measure it.

SteamKing said:
Don't worry about understanding infinity just yet. It takes a bit of time.

I know, it just seems so odd. Like the example if you have infinity and add one to it, it's just infinity again. To me it would seem that it would become a different inifinty, but there's only one infinity.
 
  • #14
aglo6509 said:
To me it would seem that it would become a different inifinty, but there's only one infinity.

No. Some infinities are larger than others.
 
  • #15
1MileCrash said:
No. Some infinities are larger than others.

Really? When do they get mentioned in math classes?
 
  • #16
aglo6509 said:
I'm trying to say to go through 0 to 1, you count up every number between them.

There are uncountably infinite real numbers between 0 and 1. (As opposed to containing a countable infinity of numbers).

Even if there were countably many numbers in that range, who says time flows by "counting"?

(Not to mention, how does one count the numbers if there is no time??)
 
  • #17
Mute said:
There are uncountably infinite real numbers between 0 and 1. (As opposed to containing a countable infinity of numbers).

that interval contains a countable infinity of rational numbers. but there are a lot more irrational numbers in the interval.

Even if there were countably many numbers in that range, who says time flows by "counting"?

maybe the physicists do. we count little time units. like the "periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom."
 
  • #18
aglo6509 said:
Really? When do they get mentioned in math classes?

Usually in post calculus classes. We didn't get more than a passing glance at it until college senior level, math major only classes.
 
  • #19
rbj said:
maybe the physicists do. we count little time units. like the "periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom."

That's how we measure time, but is it how time flows? (If that's even a sensible thing to ask?)
 
  • #20
nickalh said:
Usually in post calculus classes. We didn't get more than a passing glance at it until college senior level, math major only classes.

Damn, I really would love to take a course in this higher math.
 

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