You might have heard of the Uncertainty Principle? Basically it says that ΔxΔp ≥ ℏ/2. Well the principle is more general (look up Fourier analysis) and it can be shown that ΔtΔE ≥ ℏ/2 as well.

Have a Unicode Δ and a Unicode ℏ for your future use!

Hey, thank you. I have updated my comment :)

Cool! Then let me also offer you a ≥ in lieu of your >=.

That's a different sort of "t", isn't it? As in the lifetime of a state, rather than a measurement of duration.

It is indeed, because "time" is not an operator in QM, unlike H or x or p. But from my limited understanding of the time-energy uncertainty relation, you could (as you say) consider it a measure of lifetime - the time it takes for a change in E . So if you get a higher energy, you also should get less change in time, and thus you could probe smaller timeframes.

I might be wrong though. Someone shoot that argument down if you have to ;)

The spacetime interval should be invariant across frames, so there should be a problem there.

its badly explained, but what the first paragraph is saying is basically:

"the act of measuring time in greater detail requires increasing amounts of energy" (increasing amounts of energy dilates time because general relativity) "therefore, time-keeping devices become less precise".

time dilation implies "less precise measurements". If we assume a balance where time measurements always require more energy, then there has to be a level of precision at which increasing precision through deploying more energy increases precision by less than the increased energy decreases precision, therefore, improving precision becomes impossible.

It seems to me it is fairly analogous to how our perception of mass in relation to GR has been for a while now. It is impossible for a particle with mass to reach the speed of light because a.s it gets closer to the speed of light, it requires more and more energy to get it going faster

Why does increased time dilation imply decreased precision? If we can precisely measure the energy deployed, can't we also precisely estimate time dilation and account for it?

Now you've got two problems.

Yes, but it's a well-defined problem with known solution. As complexity goes, it's not exactly the n-body problem in an exact numerical simulation.

do you mean that literally? overcoming laws of physics is a bit more difficult than calculating the n-body problem, to be honest.

edit: to make this clear, the solution to the n-body problem is known. its just not analytical.

This isn't a matter of "overcoming the laws of physics"... what's being conjectured in the article may or may not be a physical reality.

I see, and that at least does make a certain amount of sense. By putting timekeeping into the same category as any other measurement regime you would expect to see this kind of measurement difficulty emerging. What I'm not clear on though, is whether they're saying this is a fundamental uncertainty, or a measurement problem. The latter seems likely, the former a lot less likely.

So is this basically saying that time is quantized?

Or did we know (whatever that means) that already?

I don't think it's implying that, at least, I'm not seeing it. The notion of spacetime being quantized though is very much not a proven thing, but it is very interesting. Things like QECC popping up in physical process makes it even more interesting to some.

At any rate, I think this paper applies equally well if spacetime is quantized or continuous.

In what physical processes?

Around the event horizons of black holes, would be the big one.

I think it is saying that: if it is true that more precise measurements of time require more energy, then there is a limit to how precisely we can measure time, even in theory.

That's just about exactly what John Baez said about Plank length. So hey, it's space-time that's quantized. Makes sense to me.

If we are living in a simulation, time has to be quantized... at least if the simulating computer has a clock.

Planck time?

This is one of my favorites discussion of the Planck scale, I'd strongly recommend it. https://www.physicsforums.com/insights/hand-wavy-discussion-...

Indeed, very cool. Plus, John Baez commented:

> Another way to think about the Planck length is that if you try to measure the position of an object to within in accuracy of the Planck length, it takes approximately enough energy to create a black hole whose Schwarzschild radius is… the Planck length!

That sounds familiar, here.

I guess. But IANAP. Maybe someone can comment whether Planck time is part of Ruiz et al. (2017).