Peter Schwarz, a 67 year old male from Toronto asks on June 1, 2011,

I understand that even in a finite volume, there are an infinite number of points. Why does the Planck area not apply here?

viewed 6101 times

Yes, any volume has an ifinite number of points. That is an aspect of mathematics of the real numbers. If you represent the volume as a part of R^{3} (the 3-dimensional space of reals) it is trivial to show that it has an infinite number of points.

Now, the question can be asked as to whether or not R^{3} is a good model of a volume, whether a manifold captures the essense of the physics of a spatial volume. That is where the Planck scale comes in. Does the best model of space have something like quantization of spatial volumes in terms of planck scale volumes, or is the Manifold structure a better model? No one knows. There is a suspicion that the former is somwhow true, but we have no adequate mathematical model which would tell us. The loop quantum gravity people would argue that their results suggest that there is a minimal volume and that any volume, if you measure it somehow, would give a finite number of something like planck volumes. String theory suggests there is a complementarity between volumes (or any dimensions) and energy, such that if you try to measure to smaller and smaller scales, you will need more and more energy in the string, which wil then correspond to more and more curved spacetime which makes the concept of the volume become more and more problematic. But the "right answer" is liable to be even weirder.

Note: All submissions are moderated prior to posting.

If you found this answer useful, please consider making a small donation to science.ca.

- Canadian Nuclear Safety Commission Educational Resources
- National Inventors Hall of Fame
- JUMP Math
- Society for Canadian Women in Science and Technology
- SciQuest e-Solutions for Science
- Natural Sciences and Engineering Research Council of Canada
- Manning Awards for Innovation
- Royal Society of Canada
- Geological Survey of Canada
- Canadian Networks of Centres of Excellence
- Canadian Landscapes at Natural Resources Canada
- Canadian Association of Physicists
- A Century of Innovation
- Understanding Science
- AlphaGalileo
- National Film Board of Canada Youth Science
- PICS Climate Insights 101
- Canadian Association for Girls in Science
- Virtual Library for the History of Science
- The Chemical Institute of Canada
- Canadian Biotechnologist 2.0
- ISI Highly Cited Scientists
- Deep River Science Academy
- Journal of the History of Canadian Science
- Wikipedia
- Innovation Canada
- Mars Society
- Nobel Prize Archive
- science.gc.ca
- Online Science & Engineering Encyclopedia
- CurioCity
- Canadian Nuclear FAQ
- Association of Science Communicators
- Astrofiles
- Wilderness Astronomy