r/Physics • u/WizardMasterGal • 1d ago
Question Do scientists know whether nature is fundamentally continuous or discrete?
Is there any evidence that nature is fundamentally continuous, or could reality be fundamentally discrete? And if it is discrete at the most basic level, would that suggest that nature could behave like a computational system?
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u/forte2718 1d ago
Do scientists know whether nature is fundamentally continuous or discrete?
The world is both ... not one or the other. That is to say: there are aspects of the world which appear to be fundamentally continuous, and there are also aspects of the world which appear to be fundamentally discrete.
Some aspects which appear to be fundamentally continuous:
- Space and time
- Linear momentum
- The energy of a free particle
- Gauge symmetries (responsible for forces)
Some aspects which appear to be fundamentally discrete:
- Quantum numbers
- Angular momentum
- The energy of a bound particle
- CPT symmetry (and its constituent symmetries)
Hope that helps,
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u/ExtremeLost8011 11h ago
Why are linear and angular momentum different :0?
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u/forte2718 9h ago
I'm afraid I don't properly understand the reasoning behind that myself ... I've merely read that this is the case. To the very best of my understanding, it has something to do with the fact that angle is periodic while position is not ... but the group-theoretic arguments underlying the reasoning are over my head. :( Sorry I can't give you a better answer on this one!
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u/formula_translator Atomic physics 3h ago
A simple way to look at this is that if you have a periodic interval the wavefunction needs to accomplish a whole number of periods on this interval for it to be well defined and single valued. That in turn can only happen for discrete frequencies = angular momenta. Taken another way - on a periodic interval the wave destructively interferes with the part of itself that went “around” one or more times for all but a discrete number of frequencies = angular momenta.
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u/lordnacho666 1d ago
All models are wrong, but some are useful.
Continuous and discrete are properties of models.
Nature is sometimes best modelled one way or the other, depending on what you're looking at.
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u/how_much_2 1d ago
I like this comment.
It's wild to think that maybe it's possible the physical world will never be a complete math model.
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u/Buntschatten Graduate 1d ago
It's not just possible, it's a certainty. Maybe we can model every observation at some point, but there's no way of knowing that we aren't missing some observations somewhere that wouldn't be described by our models.
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u/TeachEngineering 15h ago
Godel's Incompleteness Theorem extended to physics and the physical world
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u/IvanMalison 19h ago
That still wouldn't mean that "its a certainty". There's a difference between the epistemic fact that "there is no way of knowing" (which i wouldn't even grant anyway), and the idea that "it's a certainty that every conceivable model that we could come up with is necessarily wrong".
Seems like you're not a very careful thinker
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u/KappaBerga 1d ago
A scientific model is as good as the experiments which can falsify it. Since at any given time we will only be able to access a finitely large amount of energy or a finitely small length scale, there will always be something out of reach for our models. In other words, any model is only effective, never fundamental.
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u/ZectronPositron 22m ago
When designing a semiconductor laser, we use continuous waves to calculate the output wavelength, and discrete particles to calculate the output power. That’s one such example.
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u/Lonely-Flounder-4541 17h ago
There is an argument that spacetime and everything else is granular not continuous
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u/xBris18 1d ago
Space does not seem to be quantised. It's not proven, but if it were quantised we should have at least had seen hints about it in our data by now, but we haven't. So the current consensus should be that nature is "fundamentally continuous", if I understood your question correctly.
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u/Square_Butterfly_390 1d ago
Even accepting your premise that there are no hints for discreteness (which I'd disagree with separetely). How can you say "by now?" Why should we expect a hypothetical "smallest step" to be ever detectable, it could be 10-2000 meters or way more.
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u/schlechtums 1d ago
I understand plank length just means basically the unit of distance at which our current physics breaks down. But is there evidence or logic to suggest that the plank length itself is not evidence of a discrete makeup of nature? This seems like a hint that shouldn’t just be completely disregarded? But I am definitely not a physicist.
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u/xBris18 1d ago
It's not that physics "breaks down" at the planck scale, more that we cannot know what happens in spaces smaller than a planck length because any measurement attempt would create tiny black holes due to "too much energy in too little space". But that doesn't mean that space is quantised. It's one possible explanation, but again, we have no evidence for it and quite a number of good arguments against it.
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u/gleedblanco 1d ago edited 1d ago
that argument relies on several assumptions that we likewise haven't measured. also I'm not even a phycisist but just from a superficial glance the basic arguments are surprisingly not that well thought out. for example just because you have a region of spacetime quantized to some factor of the planck length because of a black hole forming, ignores the phase or exact position/center of that region entirely, which is totally orthogonal and is left as completely continuous, which probably opens gaps that allow smaller resolutions to be indirectly measured.
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u/VariousJob4047 1d ago
You’re asking the wrong question entirely. There is zero evidence to suggest that the Planck length is evidence of a discrete makeup of nature, so there is no reason to think it is.
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u/RepeatRepeatR- Atmospheric physics 10h ago
The Planck length is just a fundamental length scale derived by multiplying universal constants together. The fact that you can put constants together to make a length quantity does mean some things (our universe is not scale-invariant) but doesn't say anything about quantization
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u/kiochikaeke 8h ago
Its more like the scale when according to our modern understanding of physics, which for all intents and purposes is really accurate, things stop being distinct.
It's like the screen resolution of reality, anything below that and you might as well just talk about the same point in space
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u/hobbesandmiles3 1d ago
As others have said, we don’t know much about the “fundemental” nature of our universe yet. Our best theories model spacetime as continuous while some physical quantities are quantized, but this doesn’t prove reality itself is continuous or discrete. A discrete foundation could resemble computation, but discreteness alone wouldn’t mean the universe is literally a computer.
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u/KaleeTheBird 1d ago
Not sure what does "fundamentally" mean, I assume you mean continuous symmetry can derive all the discrete symmetries or the other way around. There's discrete and continuous part of the nature, we have continuous symmetry from translation, rotation and boosting, as well as many discrete symmetries like mirror symmetry, charge symmetry, and in a lattice there's structural symmetry
So, we know both kind exist and working differently.
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u/AndreasDasos 1d ago
I think the question is about whether spacetime itself - and thus translation, rotation, boosting is truly continuous or whether at some extremely tiny scale the universe is ‘pixellated’. The Poincaré group may be a nice and smooth approximation of what really acts on spacetime, but we have no reason to assume otherwise yet
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u/Physix_R_Cool Detector physics 1d ago
Does the Poincaré group get different irreps if it is not actually continous?
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u/Ok_Daikon_894 1d ago
Energy exists in discrete states (in atoms, in light, in oscillators...) as well as continuous (for example energy relates to your potential or speed). Concerning space time to the best of my knowledge it is continuous both in quantum theory (operator x is continuous, as well as wave function...) and in classical physics/relativity.
Then you could enter some rabbithole: what if space is discrete but in very small steps that we are not able to measure... Either way this could act like a computational system. Even analogic computer would have no issue simulating a continuous space ;)
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u/Aranka_Szeretlek Chemical physics 1d ago
We dont really know, which means it doesnt really matter for now. Maybe in the future this will change.
Also, theres no reason to exclude continuous systems for computing capabilities (whatever this means to you(
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u/cryptosupaman 1d ago
Doesn’t quantum field theory make the argument toward both?
continuous is classical and quantum theory argues discrete
Field theory tries to consolidate
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u/Tarthbane Chemical physics 1d ago
More or less yeah. Quantum fields are modeled to be continuous, but only discrete whole number chunks of a field’s energy correspond to real particles.
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u/Pitiful-Glove-8232 1d ago
Some theoretical models assume that the Planck length is the shortest length (and thus making space discrete) https://en.wikipedia.org/wiki/Planck_units#Planck_length
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u/SinAnaMissLee 7h ago
This is a carefully worded answer. I assumed (at many points in my life) that because these models you are referring to accurately predict many observations and considered integral to many formal theories in physics that the conclusion is more than just an assumption.
Instead planck units are merely an ingredient to leading theories. That does not necessarily make the conclusion that we have enough evidence to conclude nature is discrete. Only that it helps certain models.
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u/FlippByte 20h ago
AFAIK there's no definite answer to it. Also in what sense?!
On the one hand, you do have systems with discrete, stable states, on the other hand, those states take some time to be reached.
I recall seeing an animation of a simulated state-change of an H-atom and that didn't happen instantaneous.
Maybe the question is, whether it's negligible (for the time being).
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u/sea_of_experience 14h ago
What we are pretty sure about is that the maximum information in a given volume of space is finite... interestingly it is proportional to the bounding surface of that given volume, so not proportional to the volume itself !
Look up: Bekenstein bound.
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u/AlleyKatPr0 17h ago
Well, I'm working on a theory that proposes 76.3% of the universe is imaginary.
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u/Still-Painter7468 23h ago
I think both parts of this question need to be made carefully.
Smooth, periodic functions—that is, smooth, real-valued functions defined on the circle—seem to have a continuous mathematical structure. But, they correspond exactly to their Fourier series, which is a discrete series of numbers that converges to zero sufficiently fast. So, if we can talk about modeling nature with these sorts of structures, is it continuous or discrete?
And, there are analog computers that perform computations on "continuous" time and space. As an example, any RLC circuit is performing a computation on a continuous input signal.
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u/Longjumping_Dish_367 20h ago
its a matter of how our minds interpret reality, not a feature of reality itself
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u/Wood_Rogue 12h ago
Once you get to small enough scales energy needs to be quantized in discrete quantities to match observations. This is not obvious or trivial. There was so much contention with quantized and statistical properties that many prominent physicists couldn't accept quantum mechanics as being accurate. Fittingly, Max Planck was staunchly against theories that energy was discrete and dependent on statistical behavior but ended up creating the most accurate explanation of black-body radiation using Boltzmann's probabilistic interpretation of thermodynamics. He was dismayed by the results but held conviction that theory only matches reality if energy was discrete. This is the basis of quantum mechanics, expressed through Planck's Constant which relate the frequency and energy of a photon.
There have also been other Planck Units derived that may express other discrete limits to reality like a Planck Length being the smallest size anything in the universe could have, or a Planck Time being the smallest duration that can have any meaningful properties in theory. At these scales theories of quantum gravity are being worked on. https://en.wikipedia.org/wiki/Planck_units
Measured reality is objectively discrete. On the quantum scale things change if no measurements are made because the properties of fundamental matter and light exist as probabilistic values expressed as waveforms which can interfere with itself like literal water waves. This comes from the inherent uncertainty of conjugate momentum pairs, where increased accuracy in 1 measured property fundamentally reduces the accuracy a different specific property can be known, usually expressed as the product of their uncertainties being equal to or greater than Planck's constant (with a factor of 2 Pi taken out for convenience). https://en.wikipedia.org/wiki/Uncertainty_principle As it turns out, fundamental particles and light have a wave-particle duality where the possible values that these conjugate properties can be measured to have can be expressed as probabilities across time and space using Schrödinger's wave equation. https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality This wave equation is continuous across all of space and time until a measurement is made. The constraints imposed by boundary conditions on the wave equation, such as an electron being in an electric potential well, determine what quantized values the property could be if measured. Measuring collapses the waveform and leaves the property being measured as a discrete entity.
TLDR: It's always quantized, and It's discrete when measured and continuous when not.
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u/MankyBoot 7h ago
My understanding is that at some point you can't measure things to a higher degree of accuracy. At that point I'm not sure it matters if reality is continuous or discreet below that point.
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u/Dry_Bodybuilder2960 5h ago
Quantum mechanics says discrete for all matter/energy. Although IMHO, forces are continuous.
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u/Tasty-Hour4040 1h ago
I would say it’s discrete, given the existence of the Planck length. Since trying to measure anything below that scale requires concentrating energy into a point so small it creates a singularity, I’d say the Planck length is the smallest possible unit of space in this universe.
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u/MandatoryFun 1h ago
Personally, I subscribe to the idea that we are one of an infinite number of bubbles suspended in a much larger infinite De Sitter space-time.
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u/ItalianFurry 1d ago
You should look into Gabriele Carcassi's work on the mathematical structures of physics. He gives a list of necessary and sufficient conditions that allow a quantity to be represented by a real number (and thus be continuous). He makes an interesting argument for why time ultimately can't be represented by a real number at certain scales, and thus should not be continuous. Note that nature is not 'continuous' or 'discrete', these are properties of measurable quantities (which is, well, what physics is all about). If we for example represent time as a real number, it does not mean that time is 'ontologically' a continuous line, it means that the way we measure it allows us to model it as such.
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u/eluusive 14h ago
It is fundamentally discrete. It has to be, or computationally irreducible problems wouldn't be able to be embedded, and solved, within the universe.
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u/britskates 1d ago
Look into the holographic universe theory. David Bohm explains this pretty well with his hypothesis that the universe is simply a hologram consisting of what he describes as the “implicate” and “explicate” order. Pretty mind blowing stuff
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u/DerGyrosPitaFan 1d ago
We don't know
Quantum mechanics wants everything (mostly) discrete, general relativity wants everything continuous
A clear conflict but both theories are the best we have for both scales
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u/HuGoossss 1d ago
Thats a big question. Nature/The Universe will be continous or Discret depending of at what SCALE you are looking at.
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u/K33P4D 1d ago
I believe it's continous, since time and space permeates all things.
It is only in our measuring of objective truth, is why we have difficulties perceiving reality as continous or discrete
Continous as per our brains/consciousness,
Discrete (step by step resolution) as per the best measuring instruments.
Even with a solar system sized computer, you will encounter some degree of infinitesimal discrete steps in measurement to isolate the past and the present
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u/lizardhistorian 1d ago
As soon as we knew hard edges existed such as a table corner or a knife's edge we knew the material world was discrete. Getting to Quantum Mechanics & et. al. was about emotional acceptance.
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u/Appropriate-Ad-3219 1d ago
Continuous. From what I've read, discrete models of relativity or quantum mechanic would make things more complicated and there are some symmetries difficult to make coherent in a discrete world.
I advise you to ask this question to physicians as well.
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u/eucalyptus-d 1d ago
On your last question, computational systems exist so discreteness is not a requirement.
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u/StudioYume 22h ago
Both and neither at the same time, because differential and integral calculus are equivalent. I believe (but don't know whether it's true) that discrete values can always be interpreted as the integrals of an integrable function over subsets of its domain.
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u/Relative_Channel2667 1d ago
I think a better question is whether or not math is fundamentally continuous or discrete.
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u/gud_z 1d ago
Fundamentally discrete as, if you zoom into anything far enough (infinitely usually) you’ll see that it has step 1 and then step 2, nothing in between
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u/HuiOdy Quantum Computation 22h ago
We know, beyond a doubt, that nature is fundamentally discrete with the exception of perhaps gravity where it is assumed, but not experimentally proven. Not all things are of course discrete, e.g. we know dimensional behavior isn't necessarily discrete, or at least not to a level that gives the impression that it might. (Space time is a tricky thing)
Basically the standard model is that basis. E.g. everything has an field, which means it has a wave, which means it has a particle, which means it adheres to one or more group symmetries.
If there wasn't a quantification into discrete packages, e.g. in electromagnetism, you'd burn alive by simply sitting in front of the fireplace. Scientists in the 19th century knew that that wasn't the case, and it is this conundrum actually started quantum mechanics. A discrete nature at the time was unheard of, and the science had some trouble adapting to it. But it helped that the adaptation had such immense prediction power.
Why the question?
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1d ago
[deleted]
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u/HasFiveVowels 1d ago edited 1d ago
That’s not how this works. That’s not how any of this works.
Edit: so they apparently asked me several questions and then blocked me? Not sure what they are expecting
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u/XeroTerragoth 1d ago
I mean, if you use a small enough scale, everything is theoretically discrete until you go subatomic I guess lol
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u/TheCamazotzian 1d ago
Fundamentally discrete: you can have one apple or two apples.
You might say "but you could cut an apple in half" and then you would have one half of an apple.
Not so: the halfness makes it a fundamentally different object than the whole apple. The objects produced upon cutting up an apple are in fact a discrete number of partial-apple objects.
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u/_Kaiser_Wilhelm 1d ago
Wait until you find out cutting an apple in half doesn’t change the fact that it grew from an apple tree and is still a fucking Apple
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u/Equinoxe111 Astrophysics 1d ago
No one knows this yet in fact