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I have always thought that the time is discrete (jumping), not continuous and the shortest time is Planck Time. One reason for that was the information on Wikipedia and another was the following note I read in a book:

If you throw a rock to a tree, the rock will go half the way, then half the way, then half the way and it will keep going the half of the remaining way. Therefore, the rock will never hit the tree

This could be easily applied on time. It will go half the time and half the remaining and so on. My point is:

  1. How come the self-appearing virtual particle duos live shorter than Planck Time if it is shortest possible time? The information on life time of virtual particles was in Lawrance Krauss' book titled as Universe from Nothing

  2. Is time continuous or discrete?

I know there are many posts regarding my second question but my aim was to ask, if time is continuous (as mentioned in some posts), then how do you explain the rock-tree phenomena?

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Related: en.wikipedia.org/wiki/Zenon%27s_paradox –  pfnuesel Jun 30 at 11:06
    
More on Zeno's paradox: physics.stackexchange.com/search?q=is%3Aq+zeno%27s Possible duplicates: physics.stackexchange.com/q/9720/2451 , physics.stackexchange.com/q/35674/2451 and links therein. –  Qmechanic Jun 30 at 11:06
    
Thanks for the links. I knew my question could be duplicate but since I didn't know what paradox it was, I had to ask. –  iso_9001_ Jun 30 at 11:35

1 Answer 1

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To start with you are quoting a version of Xeno's paradoxes

The conclusion to these is that the statement

If you throw a rock to a tree, the rock will go half the way, then half the way, then half the way and it will keep going the half of the remaining way. Therefore, the rock will never hit the tree

is absurd,, and patently wrong since the rock will hit the tree and its trajectory can be calculated to great accuracy.

I do not see how it could apply to time except to say again that some conclusion is absurd.

Now you start with

I have always thought that the time is discrete (jumping), not continuous and the shortest time is Planck Time

All the data we have of physics of elementary particles and astrophysics are clear that time is a continuous variable, and that is a lot of data. The statement has not been falsified. The shortest delta( time) is 0, called synchronous if it is between two events.

Paradoxes appear when one mixes up frameworks of reference. It is true that there exist mathematics where a series has an infinite number of steps. Any functional form of mathematics can be expanded in similar series. The confusion comes from thinking that because a mathematical function , a parabola in the case of the rock, describes/models a physical phenomenon, the physical phenomenon is created my the mathematical form and should materialize any expansion , series formulation automatically. Physics uses mathematics, mathematics does not create physics as far as we know .

How come the self-appearing virtual particle duos live shorter than Planck Time if it is shortest possible time?

Virtual particles are another such phenomenon. It is unfortunate they are called particles, they are just formulation under a lot of integrals. It is the end result of the calculation that has physical meaning. They are called particles, but they do not have the mass of the homonymous particle, they are off mass shell, a mathematical construct useful in calculations that carries the quantum numbers but not the mass.

So the bound is not the Planck time, a red herring in this case, but the Heisenberg Uncertainty Principle

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Thank you Ms. Anna for the detailed answer. After I posted my question, I dig deeper and found that virtual particles are not real. Another information I didn't know. Well in that case, physics rule do not apply to them I guess. But please tell me, for continuous time, it doesn't really look absurd for a non-physics guy like me that the stone (or the arrow) goes half the time and never reaches to the three. For me, if the time was discrete, it would jump just like someone jumping on the stones on the ground to pass accross the river. This makes more sense than the continuous time –  iso_9001_ Jun 30 at 11:49
    
We have managed to describe all data with continuous mathematical functions of time and space. If time were not continuous the description would fail at several points, we should observe/measure inconsistencies, which we do not. The stone is a classical example of proof by reduction to absurd. The stone reaches the tree, kills the bird. This means that your "more sense" is not fitted by the data. –  anna v Jun 30 at 12:36
    
Yes, I thought that I sounded absurd :) Thank you for your time. This clarifies everytnhing for me. –  iso_9001_ Jun 30 at 12:40

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