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While working on physics simulation software, I noticed that I had implemented discrete time (the only type possible on computers).

By that I mean that I had an update mechanism that advanced the simulation for a fixed amount of time repeatedly, creating a continuously changing system.

I was a bit intrigued by the concept. Is the real world advancing continuously, or in really tiny, but discrete time intervals?

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Why don't you use a timer (for each item in your array) that is set to fire at the desired time? instead of firing the timer every 60 seconds. Assuming the app would be running all the time. –  user11951 Sep 5 '12 at 12:36
    
Hey, I appreciate the comment and all, but this doesn't really answer my question. I asked about the real, physical world, and provided my simulations only as a source of that curiosity. –  jco Sep 5 '12 at 13:09
    
Also, I'm not sure what do you mean. I do have timers, but I advance the world in discrete time intervals. –  jco Sep 5 '12 at 13:09
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I would also add that using n timers to run a simulation is a terrible design. –  C. Lawrence Wenham Sep 5 '12 at 15:02
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Time is an illusion - Lunchtime doubly so. ;) –  Wayne Werner Sep 6 '12 at 0:00
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9 Answers 9

up vote 29 down vote accepted

As we cannot resolve arbitrarily small time intervals, what is ''really'' the case cannot be decided.

But in classical and quantum mechanics (i.e., in most of physics), time is treated as continuous.

Physics would become very awkward if expressed in terms of a discrete time.

Edit: If time appear discrete (or continuous) at some level, it could still be continuous (or discrete) at higher resolution. This is due to general reasons that have nothing to do with time per se. I explain it by analogy: For example, line spectra look discrete, but upon higher resolution one sees that they have a line width with a physical meaning.

Thus one cannot definitely resolve the question with finitely many observations of finite accuracy, no matter how contrived the experiment.

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I disagree that it's necessary impossible to distinguish discrete from continuous time: discretization even on the smallest scale can impact large scale measurements. Recall the impact of Planck's quantization of radiation energy that impacted black body radiation and the rest of Physics in the most profound way. With the discretization of time too, it's possible that it would have significant statistical implications. –  Michael Jan 14 at 19:56
    
@Michael: Quantization of radiation energy is, in today's terms, not a phenomenon of discretization - the energy spectrum remains continuous. And all of quantum mechnaics is based on a continuous time! –  Arnold Neumaier Jan 16 at 9:02
    
Given fixed radiation frequency $\nu$, the energy of that radiation is discrete, at least in QM, $E=Nh\nu$ for integer N, I believe. But that wasn't quite the point: I was just saying that it's not inconceivable that a discretization, even on the tiniest scale, would have a macroscopic effect. Therefore I disagree with the assertion that one cannot possibly tell continuous time (or any other parameter) from very finely discretized one. –  Michael Jan 16 at 17:17
    
@Michael: But any discrete structure can be approximated by a continuous structure, and conversely, arbitrarily well, so macroscopic evidence is always ambiguous whith respect to deciding between discrete and continuous. For example, quantum jumps, that were once successfully understood as discrete, can nowadays be continuously resolved so that one can see a gradual ''jump''. –  Arnold Neumaier Jan 22 at 15:55
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I'd say there's no conclusive evidence, but in quantum physics, Planck time is sometimes cited as a possible smallest unit of time.

The source for my data is Quantum Gods: Creation, Chaos, and the Search for Cosmic Consciousness by Victor J. Stenger. In there, he goes into a lot of detail about this in one chapter.

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From Wikipedia: Within the framework of the laws of physics as we understand them today, for times less than one Planck time apart, we can neither measure nor detect any change. So it's not necessarily the smallest unit of time, just the smallest one we're capable of using. –  Brendan Long Sep 5 '12 at 14:34
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@BrendanLong - Except there's the philosophical question of "If there's no way to measure it, does it even exist?". Largely, for example, the answer for Heisenberg's uncertainty principle is that the information about a particles position and velocity don't actually physically exist simultaneously. So, if we can't measure a unit of time smaller than Planck time, if it's physically impossible, then perhaps it doesn't even exist. –  Omnifarious Sep 5 '12 at 15:17
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My interpretation of the Planck Time is that it's the smallest meaningful unit of time. Time itself is continuous, i.e. intervals shorter than the Planck Time exist. But these shorter intervals are trivial, so time may as well be discrete. Additionally, if time is discrete then distance as well must be discrete. It's weird to think of the universe as pixelated... –  chharvey Sep 5 '12 at 23:25
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-1. Quantum Mechanics regards spacetime as continuous, and that includes time too!. –  Dimensio1n0 Jun 22 '13 at 14:16
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I think it's important to note that quantum or quantized time is not equal to discrete time. For instance, we have "quantized" space. By this we mean that it receives quantum treatment. But the underlying coordinates still form a continuum. So even if you live on a finite circle and only consider wavefunctions so that you get a countable set of basis functions from which to form all the others, you can still in principle measure incidence of particles at any point, again forming a continuum. Therefore, if we take quantum time in analogy to quantum space, we would have to conclude that quantum mechanically it would still form a continuum.

Of course none of this proves how the universe really works, which is your question. The only honest answer direct to your question is "We don't know". Physical theories do not describe how the universe actually works, the only thing we know is that their predictions match experimental results we currently posses. So even if the best physical theories we currently posses use a continuum of temporal coordinates, we cannot by any means conclude that the way the universe actually works matches our description.

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We have quantized space? News to me. We do have quantized angular momentum and other variables, which behaves the way you describe quantized variables as working. –  Peter Shor Jun 18 '13 at 22:28
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I just mean that there exist quantum observables corresponding to position, and their outcomes in general form a continuum. Time is another issue. –  SMeznaric Jun 19 '13 at 20:38
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What you are talking about is similar to the problem of quantum gravity. Since gravity is an effect of the curvature of spacetime, to have a quantum theory of it, you need to quantize the spacetime manifold. This is done with spin foams which are little units of volume in spacetime that have spins associated to them. They connect together like total angular momentum and build up into various kinds of geometry. This is just a theory, but comes from the very real problem of "what is the quantum field theory of gravity". Also, it answers the question "Higher power is needed to resolve smaller dimensions (sizes). To resolve small enough distances, the power eventually gets large enough to couple to the metric of space time. How do we talk about spacetime when the uncertainty in the injected energy transfers to uncertainty in the metric."

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The answer to this question is not known presently. Current physics is, as stated by other answers, based on fully continuous mathematical models, which particularly assume spacetime to be continuous. On the other hand you could argue that these models are isomorphic to discrete constructive models, with the general view that the continuous is the limit of the discrete. Some modern spacetime theories assume an underlying network/relational structure, and are fully discrete.

My personal belief is that continuous structures do not exist in the physical world. This is however just a belief.

See also: Is the universe finite and discrete?

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My understanding of the fundamental issue of time is that if we base it upon physical transactions, then we are (not only) dealing with a discretized system (e.g. quantum interactions) - but that moreover time then may have geometric properties that further confound the question.

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There is no continuous time or space. Only events are happening. Suppose if you are reading this answer is an event. And then looking on the roof is another event. So combine these two based on the measure of time elapse,will get the actual motion of events. same as that in the movies.

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To those downvoting this, I'd like to point out that it is not completely without merit. The work 'Science without Numbers' and the resulting research efforts have successfully formulated various fields of physics without reference to any mathematical objects (numbers, functions, sets, categories, calculus etc.) and, with relevance to this post, without coordinatising space. See also Tarski's axioms (euclidean geometry without sets) and these notes goo.gl/vxYtOA from a lecture by Prof Frank Arntzenius. –  ComptonScattering Sep 11 '13 at 23:17
    
Was this also suggested by you yourself ? . –  Dimensio1n0 Sep 13 '13 at 1:50
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@ComptonScattering: But this is non - mainstream . –  Dimensio1n0 Sep 13 '13 at 1:51
    
The edit was not proposed by me. Also I disagree that geometric constructions of science are in any sense fringe if that is what you are suggesting. They are the accepted works of respected scientists. It was merely an exercise to show that algebra, though useful, is not fundamental to what science does, and so one should not promote algebraic to the status of existential when attempting to interpret a theory. In other words, something that was invoked to do a calculation cannot reasonably be said to therefore exist. –  ComptonScattering Sep 13 '13 at 8:14
    
@ComptonScattering: I was asking wilfred, not you . –  Dimensio1n0 Sep 13 '13 at 12:15
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Obviously space is continuous, so is time. What is not continuous is the conception of numbers which we are using in computers and measurments. There is no reason for something so fundamental to be descrete, since continuity is more general (and amazing) than discreteness.

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Hmm, I'd need some argumentation. And personally, I like discreteness more than continuity. –  jco Sep 6 '12 at 20:14
    
Is your thinking process continuous? If so, so is universe and its time. There is always something inbetween descrete stuff, this emptiness makes whole system continuous. Descreteness is always embedded in continuity, since it needs a separator. –  Asphir Dom Sep 6 '12 at 20:27
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That's quite contradictory. Also, you cannot objectively judge your thinking process. It might appear continuous, although neural activity does have steps, but that's not the proof that it is continuous. –  jco Sep 6 '12 at 21:47
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By the very fact of calling it time (i.e. assuming division), infinity appears as discrete. Otherwise, it is continuous. Same for space, since it's the other side of the same coin.

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Please go into more detail about your assumptions and how they leads to your conclusions. As it stands, this doesn't really answer the question. –  Benjamin Hodgson Oct 17 '12 at 22:20
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protected by Qmechanic Sep 11 '13 at 9:52

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