Planck length, planck time, and spacetime

[UNFFwildcard]

I was wondering if one of you guys could help me out with something.

I know that planck length and time represent fundamental limitations to the accuracy in which we can measure something. You cannot measure something more precisely than the planck length, and you cannot measure a period of time shorter than the planck time (planck time being the amount of time it takes for a photon to traverse 1 planck length). My question is whether this problem is ontological or epistimological in nature. Can spacetime be divided infinitely, with us being able to only measure something with precision not exceeding 1 planck length (assumably because of some limitation of the photon or whatnot), or is spacetime itself quantized into packets of 'Planck volumes', and the reason why you cannot measure something smaller is because space cannot be infinitely divided (unlike what is typically assumed in classical geometry)?

Thanks for the help!

 

[AndroidAR]

From what I can understand, the universe IS infinitely divisible, but the Planck length is as precise as we can get, because (as you mentioned) it is a limitation of the photon (which is about 10^20 Planck lengths wide).

(I'm summarizing The Wiki here, so sue me.)
In order to measure an object, electromagnetic radiation (in the form of photons) is bounced off the target. In order to get a more accurate measurement, the energy of the photon must be increased. If the photon's energy is increased enough so that it could get a precision of less than one Planck length, the resulting collision would, in theory, create a microscopic black hole, swallowing the photon, and thus ruining the measurement.

http://en.wikipedia.org/wiki/Planck_length

The Planck mass is the mass for which the Schwarzschild radius is equal to the Compton length divided by π. The radius of such a black hole would be, roughly, the Planck length. The following thought experiment illuminates this fact. The task is to measure an object's position by bouncing electromagnetic radiation, namely photons, off it. The shorter the wavelength of the photons, and hence the higher their energy, the more accurate the measurement. If the photons are sufficiently energetic to make possible a measurement whose precision is less than 1 Planck length, their collision with the object under study would, in theory, create a minuscule black hole. This black hole would "swallow" the photon and thereby make it impossible to obtain a measurement. A simple calculation using dimensional analysis suggests that this problem arises if we attempt to measure an object's position with a precision equal to 1 Planck length. However, this black hole could, at least in theory, produce Hawking Radiation by "swallowing" other photons. Therefore, this radiation could be measured.

So to answer your question from my understanding, yes, the universe is infinitely divisible, but we simply cannot see anything smaller than the Planck volume. Thus, the Planck length is our current theoretical "pixel" of reality, with the observable universe having a "resolution" of 5.4 × 10^61 Planck lengths wide.

 

[Squawk]

There is a hypothesis, not in favour but certainly in existence with some experimental evidence, that we live in a holographic universe that would have a minimum length.

This idea is out of favour atm, but it is not beyond the bounds of possibility and has, AFAIK, not been ruled out.

I don't claim to know much about it and you can google it as easily as I can. Google Holographic Universe, and look for the findings of the gravity wave detectors which found a source of interference that was predicted by a guy working separately, on this very hypothesis.

The simple answer is that we don't know.

 

[blinddesign]

What about Zeno's paradoxes? If units of time are infinitely small then these paradoxes are truly paradoxes, which is a logical impossibility. If we agree upon a 'shortest time', Planck length, then I believe that these paradoxes are just a matter of human perception of motion and time.

 

[aeroeng314]

What about Zeno's paradoxes? If units of time are infinitely small then these paradoxes are truly paradoxes,

No they aren't.

 

[Pulsar]

What about Zeno's paradoxes? If units of time are infinitely small then these paradoxes are truly paradoxes,

No they aren't.

That's still a matter of debate. Some argue that calculus doesn't address the essence of Zeno's paradoxes, which is motion: if time and space are infinitely divisible, how can you reach the next point (see wiki)? In other words, is motion a supertask? And are supertasks physically possible? I personally think that the answer to both questions is no, and that there really is a smallest unit of time and space, so that they are not a continuum.