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# Planck time, why cant we have a smaller unit of time?

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A Planck unit of time is about 5.4 x 10^-44 of a second , why cant this unit of time not be divided further and why cant the stuff of reality be divided infinitely smaller or larger?

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I think people are a bit cavalier about uses and implications of Planck units. The Planck mass, for example, is about 20 micrograms, and correspondingly the Planck energy is about 2 GigaJoules, but there is no question about there being smaller units of mass or energy. As one approaches the Planck scale, one needs a quantum theory of gravity if one wishes to discuss gravity. I'm not sure of the extrapolations one can make beyond that.

However, time is part of relativity, so one implication would be that you can't intelligently discuss intervals smaller than the Planck time without a quantum theory of gravity being involved, and we don't have one.

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However, time is part of relativity, so one implication would be that you can't intelligently discuss intervals smaller than the Planck time without a quantum theory of gravity being involved, and we don't have one.

That is pretty much how I would interpret it. Planck length, energy and time give you scales at which quantum effects of gravity should play an important role, or reallty the scales at which such effects cannot be ignored or considered small. But without such a theory one should take care in saying anything more.

Edited by ajb
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Plank scale is constant before beginning of the Universe? Or, after inflation Plank scale is fixed?

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Plank scale is constant before beginning of the Universe? Or, after inflation Plank scale is fixed?

Don't know how to answer the first question. What we know is that inflation started about $10^{-36}$ seconds after the big bang. Planck time is much smaller than this at $10^{-44}$ seconds. So we would not expect effects of quantum gravity to be dominant here, or lets say a classical gravity theory as a background should be okay.

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That is pretty much how I would interpret it. Planck length, energy and time give you scales at which quantum effects of gravity should play an important role, or reallty the scales at which such effects cannot be ignored or considered small.
But that of course is still very vague, given that engineers routinely work with objects way above the Planck mass and still get along nicely without a theory of quantum gravity.
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But that of course is still very vague, given that engineers routinely work with objects way above the Planck mass and still get along nicely without a theory of quantum gravity.

Some say that what we call reality only started after the first Planck Unit , to speak about anything happening before that is meaningless.

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Some say that what we call reality only started after the first Planck Unit , to speak about anything happening before that is meaningless.

They might perhaps say it is meaningless at our current level of knowledge - it certainly is not meaningless per se. To discuss physics at those energies you need a theory that combines gravity with quantum mechanics - in most situations it is easily accurate enough to either consider large scale gravity or consider small scale effects; but at these energies you need to consider both simultaneously and we cannot come up with a theory that does that.

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• 6 months later...

I remember it being explained a long time ago, that Planck time is an indivisible unit. Hypothetically speaking if one acknowledges an indivisible unit of space (Say at point A) then plank time is the distance to the adjoining unit of space (Point B) with no other distinct unit/units of space between. If the smallest unit of space can be subdivided then Planck time could be subdivided also I suppose.

A couple of hypothetical thought experiments come to mind. The first is how ancient Hindu philosophers (2nd century B.C. http://en.wikipedia.org/wiki/Vaisheshika) postulated that matter may not be infinitely divisible. They argued if a small rock is infinitely divisible then we arrive at infinite particles and with these infinite particles we can re-construct any other matter including the Himalaya's. Since this can't be, a finite indivisible entity must underlie the construction of all matter, they called this hypothetical particle paramanu, in present day Indian (Devangiri) this is transliterated to atom, however I don't believe they meant present day atom, as much as "..That smallest indivisible particle".

The other thought experiment is Aristotle's I believe (Someone correct me, if I have this wrong). I think the premise of the hypothetical experiment is when two runners run towards each other at equal speed, then they would meet in the middle. If we now had them do the same with the new halved distance then theoretically they could run into each other, half way, ad infinitum. What happens then when Planck time is reached? The runner at point A and point B can either meet up at point A or point B and not in-between, there being no space in-between to run through.

Another way of considering the query "Why can't we have a smaller unit of time?" would be "Why can't we have half or a quarter photon?"

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A Planck unit of time is about 5.4 x 10^-44 of a second , why cant this unit of time not be divided further

There is not proof that Planck time was the smallest unit of time. It is just a speculation.

and why cant the stuff of reality be divided infinitely smaller or larger?

Because stuff is made of matter and this has a discrete structure. You cannot divide an atom infinitely.

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Planck time is defined as the amount of time a hypothetical photon would take to cover a distance of one Planck length (or, as I understand it, "jump" one Planck length, as it wouldn't be able to move inbetween). Because the speed of light is a constant - and the Planck length is also derived from various uniform cosmological constants - Planck time isn't an arbitrary measurement of time like other units of time such as hours or picoseconds. The reason we do not go smaller than the Planck time (or even work in mixed fractions of time that require fractions of the Planck time) is because our current math fails spectacularly at scales smaller than the Planck units - you'd need the mathematics of a working Theory of Everything in order to work on scales smaller than the Planck units. In any case, why would you want to work on such miniscule scales? As I understand it, nothing exists at scales smaller than the Planck units.

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As I understand it, nothing exists at scales smaller than the Planck units.

I pointed out that this is wrong in post #2.

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The reason we do not go smaller than the Planck time (or even work in mixed fractions of time that require fractions of the Planck time) is because our current math fails spectacularly at scales smaller than the Planck units - you'd need the mathematics of a working Theory of Everything in order to work on scales smaller than the Planck units. In any case, why would you want to work on such miniscule scales? As I understand it, nothing exists at scales smaller than the Planck units.

We can go smaller, it is called the sub-Planck regime or scale, and it is studied by the sub-Planck physics. The math works fine, and there is no need to even mention a TOE when working at such scales.

Edited by juanrga
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Really? I must research this.

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