# Quantization of space-time

1. Jul 16, 2011

If space-time itself is quantified, and the spatial universe has, at any one time, a finite volume, would this not imply that at any one moment there are a finite number of spatial locations? (If so, then integrating over an infinite number of points would only give an approximation.)

2. Jul 16, 2011

### xts

Of course, you are absolutely right.

Integration is just much easier to perform than summing up discrete finite series.

Just keep in mind that the same argument may be used regarding any quantizied value. Try to make electronic design, counting individual electrons, rather than using 'approximation' of continous current. Or try to construct a bridge, counting every atom, rather that taking steel as a continous medium.

But, of course, in reality (whatever you mean by 'reality') steel is not continous, and consists of individual atoms, occupying their individual locations.

3. Jul 16, 2011

Thanks, xts. But in that case arguments with infinity no longer should work. For example, the cardinality argument for the Casimir effect, in which it is stated that a countably infinite number of virtual particles can appear between the plates, whereas a continuum-number of virtual particles can appear outside, hence accounting for the greater energy density outside. But both inside and outside the number of possible virtual particles should be finite, trashing that argument. No?

4. Jul 16, 2011

### xts

It would just refolmulate argument in terms of finite numbers: between plates you have some finite number of virtual particles, leading to some energy density, outside you have also finite number, but leading to different density, the pressure still is generated.

It is like with simple cylinder/piston/gas examples: you may analyse it in terms of continous gas of different pressures or in terms of different (finite) numbers of gas atoms bumping from each side. Both views lead to the same results, at least until you don't go to low with the scale, making statistical fluctuation of particle number visible.

5. Jul 16, 2011