How can time exist? In the space between 10:00 and 10:01, there

>>8016791
>what are convergent series

>>8016791
What's really weird to think about is that time isn't really passing at the same rate ever

There's not an infinite amount of time in one minute. There's one minute in one minute.
You can split this minute into infinitely small fractions of a minute, but there's not infinite time in one minute.

>>8016809
I like the idea from the movie Valentine, where one second on earth could be forever in hell.

>>8016809
Halve a minute and you have 30 seconds. Halve 30 seconds and you have 15. Continue the process, and you would theoretically never reach 1 minute, nonetheless anything after a minute.

>>8016823
How about taking >>8016794's hint and realizing that [math]\sum_{n=1}^\infty \frac{1}{2^n} = 1[/math] ?

>>8016791
>there is an infinite amount of time
Infinite moments aren't the same as infinite time. If you can't measure it, you can't differentiate it from zero or even infinity.

>>8016823
If what you're thinking were the case, no definite integral could have a finite value, yet somehow many do.

>>8016791
>implying time isn't actually discrete
>implying time isn't just successive steps in this numerical simulation we call the universe
>implying future states of the universe don't affect the current ones since some of the subroutines of the universe don't use implicit PDE solving methods

>>8016881
>desiring a self-consistent simulation after the activation point of the same simulation

>>8016791
Clearly time, like space, is not infinitely divisible

This is a heinously incorrect analogy, but it helps when thinking about it a bit.

try to think of time as an infinite amount of 'frames' passing infinitely quickly.

>>8016945
you can still divide a planck unit.

>>8016990
Then its not the smallest possible unit of time

>>8016991
It is.
You can divide an atom into its components and lose the properties asociated with atoms.
Just because it loses its properties doesn;t mean you can't divide it.

>>8017000
Its either not divisible, or not the smallest possible unit of time. It cant be both by definition, pick one

>>8017011
Planck time is the time light takes to travel one Planck length. Theoretically, this is the smallest time measurement that will ever be possible. Smaller time units have no use in physics as we understand it today.

>>8017000
But division DOES cause property loss.

>>8017033
It does.
Anything smaller than the smallest time unit won't be time anymore. But it is still divisible.
Like with the atoms. You can divide an atom into its constituent parts, it is divisible but the emergent properties, such as the atomic orbitals, dissappear.

>>8016809
yoke-assed bitch

>>8016791
Okay you two go stand up against that wall on the far side of this nice big room. The experiment is going to be to see if you can walk to the wall on the other side of the room. Now go. Congratulations you did it on your first attempt! Easy right? Now reset and we're going to try again but this time with a challenge.
This time, each time I say go you are only allowed to walk halfway to the wall from where you are. Understood? Good. Now go. Wow look at that. You're already halfway there. Pretty easy challenge eh.
Go. Hmm well that was still a pretty good job but it wasn't as impressive as last time. Go. Well that wasn't so good and we've already had three attempts. Go. Uhoh. You two are really slowing down. Go. That was the 5th and now you're barely moving at all. Right so wait there for a second.

>>8017496

Op knows the Achilles and Tortoise paradox you retard

>>8016858
[math] \displaystyle
\sum_{n=1}^\infty \frac{1}{2^n} = 1
[/math]

Infinity in between seconds is stopped when a certain amount of time is passed

This is meme tier.
Interaction happens fluidly.

File: Fuck me Dr Physux.jpg (15KB, 480x360px) Image search: [Google]

15KB, 480x360px

>Ideal time happens like real time

>>8017045
Yes, you can subdivide a Planck time
No, it does not stop becoming time

Planck time is just the smallest thing that we could ever measure, that doesn't mean things don't exist or happen on shorter timescales

>>8016791
>Plank second

>>8019093

>Planck time is just the smallest thing that we could ever measure, that doesn't mean things don't exist or happen on shorter timescales


It's very important to be specific with the semantics here. Planck time is the smallest time measurable by any system that interacts with time (i.e. not just humans with stopwatches -- any rock falling requires time to do so). If a unit of time is no longer measurable by a system, can you really say that some events occur within it?

>>8017582
>muh topological assumptions

File: 1437598757909.png (296KB, 500x375px) Image search: [Google]

296KB, 500x375px

>literally this entire thread
>[math]\mathbb R[/math]
>infinite sets

How does sec^2 even make sense relativistically? Is a second a constant? No, I don't think so. Seconds can be short or long, depending on who you ask.

File: mb5mS4b.jpg (120KB, 750x812px) Image search: [Google]

120KB, 750x812px

>>8017584
>Fuck me Dr Physux
hahahahaha

>>8019470
>Planck time is the smallest time measurable by any system that interacts with time (i.e. not just humans with stopwatches -- any rock falling requires time to do so).
planck time is defined only in a few models

>>8017028
>Theoretically, this is the smallest time measurement that will ever be possible.
Within about an order of magnitude, the smallest unit of distance possible to measure isn't exactly the planck length, it's about a factor of 10 out.

>>8016791
What if time moves in discrete steps and the universe has a frame rate?

>>8020109
Isn't that what the Planck units stand for?

>>8020112
not entirely i think. Plank units are just the smallest steps measurable, it doesnt mean that there are no smaller steps. If I understood it correctly

>>8020112
>>8020145
You're both wrong

Planck units are just units of measurement defined from fundamental constants. You know how the metre is essentially just defined by some rod they keep in France somewhere? Some people wanted to make some less arbitrary units so they got some constants that we know the values and dimensions of and decided to define lengths, times and masses in terms of them. They're all extremely small, far smaller than anything we can measure directly with our current technology but there is nothing to suggest that they are the smallest units it is possible to measure. There is some way of defining the smallest distance possible to measure but the result you get is not the Planck Length.

What they are good for is for simplifying certain equations because a bunch of constants take on the value 1 when expressed in these units.

>>8020168
>planck length is the pixel size of the universe

When will this meme die?

File: image.jpg (55KB, 487x515px) Image search: [Google]

55KB, 487x515px

if you think about it, time "passes" at the speed of light. In 1 second we have a 1 light-second length of space-time (4d). Divide it by the plank length and you will theoretically get how many units of time 1 second has.

>>8016794

A topic in mathematics that probably has no relation whatsoever to the way time actually works.

>implying our universe is a purely logical, smooth, continuous manifold.

>>8016874

This isn't exactly right. When we take definite integrals, we aren't physically adding up infinitely many values, as that would take forever. Rather, an integral is a limit of partial sums, which is a just a fancy way of saying "if we had an infinite amount of time to add up these infinitely many of these values, we would achieve such and such a result".

>>8016990

No you cant.

>>8020212
Yes you can, Planck units are not the smallest anything can get, they are just tiny units defined using fundamental constants. There is nothing to suggest that they are the smallest anything.

>>8020215
what's half a planck unit then?

>>8020216
The value of the planck unit divided by 2

>>8020159
But the Planck scale is the point where quantum gravity becomes essential to describing reality, so if spacetime does have a shortest distance it will probably be around the Planck length. In some quantum gravity theories there is no shortest length, such as string theory where spacetime is smooth. The length of a string is about a Planck length though, so it is still the scale at which stringy, quantum gravity effects become all-important. That is, if you had a Planck length magnifying glass (i.e a very powerful particle accelerator) you couldn't ignore the fact that particles are actually strings at these distances, though these effects might be noticeable before that.
Compare this with the Compton wavelength in QFT - the scale at which you can't pretend particle number is fixed.

More or less.

>>8020223
>But the Planck scale is the point where quantum gravity becomes essential to describing reality, so if spacetime does have a shortest distance it will probably be around the Planck length
Sure why not.

It's still all a big IF though. There's nothing concrete to suggest that planck units are the smallest anything.

idk about string theory, I don't think anyone on /sci/ does

>>8016791
So in your opinion numbers can't exist either? as between 1 and 2 there are an equally infinite number of possibilities.
The same goes for distance, or anything measured in the inherently ifinitely divisible numbers.

> infinite amount of time

>Failing to realize that the continuum is nothing more than theoretical tool that allows us to reasonably approximate processes that are discrete but relatively small.

>Failing to realize that reality is ridiculously more complex than any shitty model humans have produced.

>>8020216
It has no meaning.

>>8020200
It has everything to do with why an arbitrary time interval (such as one second), while it theoretically can be subdivided indefinitely, still is finite.