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I am having difficulty understanding time at the most fundamental level, especially I am wondering whether there exists an indivisible unit of time (i.e. whether time at some fundamental level is discrete). If the question is non-nonsensical, please help me with how to think about time.

Research for and against this notion are very welcome.

Qmechanic
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Toke Faurby
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  • Time does not flow for photons. Their unit of time is $\epsilon$? or perhaps zero? – Yashas Mar 19 '17 at 09:42
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    Keep in mind that 'atomic unit of time' normally refers to the time unit in the atomic system of units, i.e. the time it takes to advance by one Bohr radius if you're going at velocity $\alpha c = \frac{1}{137}c$. That's independent of your question but it will derail your googling attempts with those keywords. – Emilio Pisanty Mar 19 '17 at 11:05
  • Possible duplicates: http://physics.stackexchange.com/q/35674/2451 , http://physics.stackexchange.com/q/9720/2451 , http://physics.stackexchange.com/q/89975/2451 and links therein. – Qmechanic Mar 19 '17 at 16:07

2 Answers2

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At this point, nobody knows.Certainly there is no experimental evidence in favor of such an unit. On the other hand, there is no evidence against it, except that we have been unable to find it, yet.

However, by putting together $G$ (Newton's constant of gravity), $h$ (Planck's constant) and $c$ (the velocity of light), we can compute the smallest meaningful time coming at about $10^{-44}$ second. At this scale, quantum effects should be dominating gravity and hence, because Einstein's theory links gravity and time, dominating the ordinary notion of time. Simply put, any 'time' smaller than this would hold no meaning according to our notion of time.

peterh
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Prabhdeep Singh
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    Augmentation: You're referring to the Planck time . If we assume time to be quantized, too ( a fair assumption) then there could be a "minimal unit of time" - whether it is the Planck time is, afaik, unknown. – Nox Mar 19 '17 at 10:49
  • @Nox No, that is not a "fair" assumption. The currently accepted quantum theory, i.e. quantum field theory, does not quantize time and space - both are continuous. – ACuriousMind Mar 19 '17 at 13:09
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    @ACuriousMind Is it possible to make time or space discrete and be Lorentz-invariant? I've always assumed not. –  Mar 19 '17 at 15:26
  • @ACuriousMind I am well aware that time as well as space are assumed to be continuous in QFT.What I meant by "fair" is that having arrived at a quantized description of matter it is fair to try ang quantize time and space themselves. If memory serves me right there's a theory which actually assumes that at least space is quantized and derives from that assumption that distant $\gamma$-ray bursts should have a delay between "blue" and "red" when arriving at earth. – Nox Mar 20 '17 at 13:04
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The question can be answered in two ways -

  1. Is time discrete for us? Yes, it is. How discrete? will depend upon the smallest event we can use to measure the time. If we can not measure time with higher precision than that, then it does not make sense to talk about smaller units of time than that as there is no way we can measure it. Just like how high the temperature can be - as high as we can measure.

  2. Is time discrete in nature? No! that can not be true. Simply because - suppose there is a smallest unit of time in nature. That smallest unit has to belong to the smallest possible event in nature. That means all such events in the whole universe have to be synchronized, otherwise, you can come up with a smaller event by intersecting boundaries of two such events.

Also, suppose there was a smallest unit of time in nature, then what would wake up the nature when that time is elapsed? That means, there has to be a more precise nature underlying the nature, eventually making it a continuous nature.

kpv
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  • I don't think the whole universe would have to be synchronized. Einstein's theory links gravity and time, and allows for time to be stretched and compressed. – Toke Faurby Mar 20 '17 at 04:43
  • I don't understand your 'wake up' metaphor. – Toke Faurby Mar 20 '17 at 04:43
  • @TokeFaurby: Yes, and time stretching/compression is another reasoning that time can not be discrete, – kpv Mar 20 '17 at 16:02
  • @TokeFaurby: For the smallest unit of time, we need a wake up mechanism. For example, if our smallest time is a heart beat, then we can not differentiate within a heart beat and can only observe one beat to another. That is the wake up metaphor. Why we set the alarm? To wake us up as we can not tell when that particular time will be. Same way, if nature has a minimum time interval, then nature needs to know when that interval is over and then something more precise needs to monitor when that interval is over. – kpv Mar 20 '17 at 16:05