I How does time add up to 1 second with infinite smaller amounts of time?

[Gondur]

Hello.
I have a question.
Time can be divided into smaller amounts of time.
So, 1 second can be divided into 1/2, 1/4, 1/6 etc seconds
SO, 1 second can be divided into 1 / infinite amount seconds
So, it follows that this will yield an infinitely small amount of time.
So, given that there is an infinite amount of 1/ infinite seconds that make up one second.
How does time go from 1 second to another because surely 1 second will never be reached?
I think this would display as an asymptotic curve - when the curve (time) never actually crosses the axis, but always tends towards it?

Do you understand my question?
Thank you.

 

[phinds]

Hello.
I have a question.
Time can be divided into smaller amounts of time.
So, 1 second can be divided into 1/2, 1/4, 1/6 etc seconds
SO, 1 second can be divided into 1 / infinite amount seconds
So, it follows that this will yield an infinitely small amount of time.
So, given that there is an infinite amount of 1/ infinite seconds that make up one second.
How does time go from 1 second to another?

Do you understand my question?
Thank you.

https://en.wikipedia.org/wiki/Zeno's_paradoxes

 

[Gondur]

https://en.wikipedia.org/wiki/Zeno's_paradoxes

Yes that's what I thought, but he applied it to distance.
I apply it to time.
So, how does time go forward?
Surely since the creation of the universe till now, not one second has passed - we are still living in a time of 1/X amount of seconds?

 

[phinds]

Yes that's what I thought, but he applied it to distance.

Irrelevant. It's the exact same principle.

 

[fresh_42]

Hello.
I have a question.
Time can be divided into smaller amounts of time.
So, 1 second can be divided into 1/2, 1/4, 1/6 etc seconds
SO, 1 second can be divided into 1 / infinite amount seconds
So, it follows that this will yield an infinitely small amount of time.
So, given that there is an infinite amount of 1/ infinite seconds that make up one second.
How does time go from 1 second to another?

Do you understand my question?
Thank you.

Whether there is a smallest possible amount of time isn't clear, yet, as far as I know. But this isn't important here. What is important is, that you treat this like $\dfrac{1}{\infty} = 0$ which doesn't make sense. The limit process doesn't apply, because you can always only calculate with a finite amount. So what's left is the so called Zeno's paradox. There are many versions of it, e.g. https://en.wikipedia.org/wiki/Zeno's_paradoxes#Achilles_and_the_tortoise

 

[A.T.]

So, how does time go forward?

At one second per second.

 

[jerromyjon]

So, given that there is an infinite amount of 1/ infinite seconds that make up one second.
How does time go from 1 second to another because surely 1 second will never be reached?

Infinity times 1/infinity = 1

 

[CWatters]

Without a human to define it there is no such thing as a second. So Seconds and fractions of a second etc are not a fundamental property of the universe.

We don't actually know if time moves in little steps (eg is quantized) or if it just rolls along smoothly (continuous)..

https://www.scientificamerican.com/article/is-time-quantized-in-othe/

 

[jerromyjon]

https://www.scientificamerican.com/article/is-time-quantized-in-othe/

From that link:
"One could, however, ask the question in a slightly different way. By putting together G (Newton's constant of gravity), h (Planck's constant) and c (the velocity of light), one can derive a minimum meaningful amount of time, about 10^-44 second."

 

[phinds]

From that link:
"One could, however, ask the question in a slightly different way. By putting together G (Newton's constant of gravity), h (Planck's constant) and c (the velocity of light), one can derive a minimum meaningful amount of time, about 10^-44 second."

But there is no indication at all that this would in any sense be a MINIMUM possible amount of time any more than the Planck length is a minimum possible length.

 

[gianeshwar]

Without a human to define it there is no such thing as a second. So Seconds and fractions of a second etc are not a fundamental property of the universe.

We don't actually know if time moves in little steps (eg is quantized) or if it just rolls along smoothly (continuous)..

https://www.scientificamerican.com/article/is-time-quantized-in-othe/

So should we assume tgat time is subjective and not a fundamental physical quantity?

 

[jerromyjon]

But there is no indication at all that this would in any sense be a MINIMUM possible amount of time

The key word was minimum MEANINGFUL amount of time, which seems to me to address our macroscopic view of things, but there must still be smaller divisible portions to address subatomic physical time scales... or I may be wrong and Planck time is in the magnitude of subatomic processes. Either way it still is not a known quantifiable parameter.

 

[phinds]

So should we assume tgat time is subjective and not a fundamental physical quantity?

No, our PERCEPTION of time is subjective. Local time, as measured by a valid clock, doesn't care what we think of it it just moves along and one second per second.

 

[MarekKuzmicki]

SO, 1 second can be divided into 1 / infinite amount seconds
So, it follows that this will yield an infinitely small amount of time.

It can not.
We are inside the box named as universe. Our perception of time is perception of counting events. Even theoreticaly, if there is no events time is frozen for us. Of course if you can look outside the box, this may not be true, but we are in the box, so we can not say that.

 

[Dale]

Yes that's what I thought, but he applied it to distance.
I apply it to time.

It is still Zeno’s paradox. Both time and distance are represented by real numbers (continuum). Zeno’s paradox and its solution work for any continuum.

 

[Nugatory]

Infinity times 1/infinity = 1

That is not right - it is undefined. Any attempt to treat infinity as a number that can be subjected to arithmetic operations to yield meaningful finite results will lead quickly to unpleasant contradictions.

Further discussion of this digression should happen over in the "General Math" subforum.

 

[russ_watters]

Time can be divided into smaller amounts of time.
So, 1 second can be divided into 1/2, 1/4, 1/6 etc seconds
SO, 1 second can be divided into 1 / infinite amount seconds
So, it follows that this will yield an infinitely small amount of time.
So, given that there is an infinite amount of 1/ infinite seconds that make up one second.
How does time go from 1 second to another because surely 1 second will never be reached?

In order for the math to work, they MUST add up to 1 second:
1/2+1/2=1
1/3+1/3+1/3=1
Etc.