# If time isn't continuous, what is the best-known upper bound on the length of time intervals?

There have been several questions about whether time is continuous or not and it seems like the answer isn't currently known. I know quantum mechanics treats time as continuous and any mathematics that involves integrating over some time interval treats time as continuous too.

Surely though there are experiments that are quite sensitive to discrete time with large intervals. It seems the shortest laser pulse so far is only 67 attoseconds ($67 \times 10^{-18}\: \mathrm{s}$) but wouldn't this experiment actually constrain time intervals to much less than that? Are short laser pulses even a good experiment to determine if time is discrete or not?

So, assuming time isn't continuous, what is the best-known upper-bound on time intervals? Also, which experiments have done the best to constrain how non-continuous time could be?

• It seems the light pulse may have been improved to 12 attoseconds: phys.org/news192909576.html – Brandon Enright Dec 12 '13 at 4:13
• – Brandon Enright Dec 12 '13 at 4:13
• I am assuming that the answer greatly depends on the model used for such discreteness. Do you have any particular models in mind? – user23660 Dec 12 '13 at 5:32
• Take, for instance, numerical integration of DE. It is not enough to specify 'time step', one has to give at least the type of algorithm to make prediction as to how well it interpolates continuum model. The same should be true for discreteness (only in reverse): when will the physics start to exhibit the artifacts of underlying discreteness greatly depends on what type of discreteness it is and not just on time step. – user23660 Dec 12 '13 at 7:24
• See for instance Lubos's answer to physics.stackexchange.com/a/9721/26076 : some pretty impressive lower bounds on discretisation lengths and times are seemingly motivated by recent observations. – Selene Routley Dec 23 '13 at 2:06

The lifetimes of the W and Z boson and top quark are each on the order of $10 ^ {-25}\,\rm{s}$ .
The Z-boson lifetime is $2.64 \times 10^{-25}s$ from a decay width of $2.495 \pm 0.0023 \, \rm{GeV}$. Decay width for the W-boson is $2.085 \pm 0.042\, \rm{ GeV}$
If time were not intervals of less than this order of magnitude ($10 ^ {-25}\,\rm{s}$), I would expect narrowing of line width (longer lifetime) and maybe distortion of line shape.
• If your argument holds, then the Higgs decay rate could give us also some information. The SM prediction is around $5\,\rm{MeV}$ and maybe this will be measured at the LHC or the ILC. – Melquíades Apr 28 '14 at 22:02