# Is there an equivalent of the Planck length for time?

Is there an equivalent of the Planck length for time? I'd just like a term I may use (high-level) for a similar "unit of time"? I am not looking for a debate on how discrete time might be, but if there is a term I can use that complements Planck's constant for space, I'd like that.

This doesn't help at all.

• If there is a minimum length and a maximum speed it follows that there's a minimum time, the time for that really fast thing to go the minimum distance, however I'm unwilling to commit to this :P – Alec Teal Jan 23 '16 at 10:36
• Mikey, I made kind of a radical edit to your question because it seems like what you really want to know is whether there is something like the Planck length, but for time. We don't usually make such edits, but in this case I think it makes the question better and also makes the existing answers fit your question better. Please check it and if this doesn't reflect what you want to ask, change it so that it does. I took out all the stuff about "smallest unit of time" because that is an entirely separate matter from Planck units. – David Z Jan 24 '16 at 18:05
• @DavidZ - it certainly does help; and I appreciate it. I'm not in Physics, and I did not know how to phrase the question so succinctly. I hope that the last sentence of the question doesn't come across disparaging - I meant only to say this is not a duplicate. – Mikey Jan 25 '16 at 0:12

Planck time - the amount of time it would take a photon (or other particle travelling at the speed of light) to cross a planck length - the fastest known speed travelling over the shortest known distance. Time, as distance divided by speed, doesn't get much smaller than that.

It is about 5.39 x 10-44 seconds

Which can be expressed as 0.0000000000000000000000000000000000000000000539 seconds

Or rounded to one ten million billion billion billion billionths of a second

• At least not hypothetically... – CuriousOne Jan 23 '16 at 10:33
• @Amphibio is the Planck length less than the diameter of a photon ? – N.S.JOHN Jan 23 '16 at 10:49
• @n.s.john, this is a guess so please correct me - would the planck length be equal to one wavelength of light at its highest possible energy state / frequency? – Amphibio Jan 23 '16 at 11:03
• @Amphibio Actually I have no idea. – N.S.JOHN Jan 23 '16 at 11:55
• en.m.wikipedia.org/wiki/Planck_time shows a value of $5.39\cdot10^{-44}~\rm{s}$ - might be more helpful than all those zeros. – Floris Jan 23 '16 at 13:05

There is a smallest measurable time interval, known as Planck time, which is the time required for light to travel the smallest measurable length which is known as the Planck length, $$\ell_\mathrm{P} =\sqrt\frac{\hbar G}{c^3} \approx 1.616\;199 (97) \times 10^{-35}\ \mathrm{m}$$.

So, the Planck time will be $t_\mathrm{P} = {\frac{\ell_\mathrm{P}}{c}}\approx 5.39106 (32) \times 10^{-44}\ \mathrm{s}$.

If two points are separated by a length less than the Planck length, we would be unable to tell the difference between those two points. Spacetime geometry itself might not be meaningful below the Planck length (we don't know yet what happens below the Planck length).

The Planck length limit comes from the assumption that neither quantum mechanics or relativity fails. So we don't know what happens below that length as the physics is not quite up to the handling at that scale.

• "smallest measurable timeinterval / length" – What tells you that it's the smallest? And what tells you that "If two points are separated by a length less than the Planck length, we would be unable to tell the difference between those two points."? So far my impression has been that the Planck units are mere numerology and noone knows what their meaning is. (Other than "they're really small/big and QM and GR probably break down at these scales.) – balu May 23 at 20:30