The shortest time period that could be possible.
The shortest time period that could be possible.
Planck time is defined as roughly 5.39106x10^-44 seconds. It is so small, I am not even sure I could understand it so I included the wiki link.
I did see that there are other quantities of extremely short time periods such as Chronons and time measurements by a huge number of Hertz (1121015393207857.4(7)Hz for a quantum clock.) It appears chronons may be a different way of thinking/modeling short time periods, but that may be a gross error on my part.
I have never heard of Chronons and barely understand Planck time, so perhaps someone else could provide more (and better) details.
'That was tops! Who's not good at math? I was all, "Four!"' - Finn, Adventure Time.
My understanding is that if two events, A and B, occurred more than Planck time apart, it would, in principle, be possible to say which happened first, even if the time difference was far too short for our instruments to measure. (According to the linked article, 10^-17s is the current limit.)
On the other hand, if events A and B occurred less than Planck time apart, it would be meaningless to say that A was before B or vice versa. And if the events were linked in some way, it would be impossible to distinguish between "A caused B" and "B caused A".
In terms of the uncertainty principle it is the smallest uncertainty you can have in a strong measurement. I am not aware of any such constraints on weak measurements - I do wonder if it is possible to reduce the variance in the expectation value below this value in finite time? I'd guess not but I am not aware of any rigorous theoretical reasons why. That is probably my ignorance shining through though. I'm guessing once you factored in the strong QM interactions required to remake the state to make the weak measurements it would still be a limit.
My understanding of this is far from complete, but can't it be likened to the Planck Length? In quantum-mechanical models (at least, the ones I know about) you can't measure something smaller than the Planck Length because quantum effects that happen at those distances make the idea of length meaningless. Could you say something similar for time?
Imagine you took a photograph of two people, John and Susan, with a digital camera. They are quite close to you, so John, on the left of the picture, occupies several thousand pixels. Susan, on the right, occupies another several thousand pixels.
Now imagine you take a photo of them while they are standing close together, but they are so far away from you that they both occupy a single pixel. Now, from examining that one pixel, you cannot say whether it is John or Susan standing on the left.
Just because you can't say who is on the left on the basis of looking at one pixel, it doesn't follow that relative positioning is meaningless.
Going back to time, if you watch two runners in a race, and runner A finishes in 59 seconds and runner B finishes in 60 seconds, it's clear that A won, because there was a delay of about one second (~0.5-1.5s) between them.
If the delay between them was about one hundredth of a second, you probably wouldn't be able to make the distinction on your own, but if you had some very fast cameras filming the event, you'd be able to play them back at slow speed and then you could say who was first.
In principle, you could get faster and faster cameras (or other recording apparatus) to resolve shorter and shorter intervals, whether it's two people racing, particles decaying or whatever. If these events are in the same frame of reference (e.g. the two runners are the same distance from the camera) then clearly it's meaningful to say that one reached the finish line before the other.
But there's a limit to how far you can increase this temporal resolution, even in principle, and that limit is Planck time. It's the temporal equivalent of the pixel.
Here is something I was thinking about. People have said that galactic core black holes were safer to pass through (event horizon) due to the gravity well not being so immediately steep. Still, if you were to pass your hand through--you lose it in chops/slices as the particles can't wiggle back and forth to hold your hand solid.
if your spacecraft is so fast that the time it takes to cross the event horizon is less than one plank unit--you live? Because there is literally no time for the black hole to cut you--as it were.
It doesn't really work like that. An event horizon is not some point in spacetime which slices off anything that crosses it. What matters in your example is where your centre of mass is
What would your mass be if you were traveling greater than c ? Infinite?...or non-determinate? ....or zero?
And how does this relate to space itself being drawn into the black hole at > c ?
If is measures in seconds, then is measures in meters, then . To measure it we need a clock with an uncertainty of can be no larger than . Time and energy uncertainty says the product of and can be no less than
Well, actually... I am not technically right. If an object passes the lightspeed barrier, then it has infinite mass. A particle if it starts it's journey above the lightspeed barrier will then have an imaginary mass... the two are quite different.