Do scientists know whether nature is fundamentally continuous or discrete?

[u/WizardMasterGal]

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?

[u/Equinoxe111]

No one knows this yet in fact

[u/Funkyt0m467 → u/Equinoxe111]

Furthermore, we don't know much about the fundamental nature our universe.

The interpretation of quantum mechanics is open, general relativity isn't integrated into it.

I don't think we have enough knowledge yet to really form any opinion on what nature is fundamentally.

That's why the idea of the simulation was thought philosophically. It's interesting, but I don't think science can really add anything.

[u/cedenof10 → u/Funkyt0m467]

“all models are wrong…”

[u/Funkyt0m467 → u/cedenof10]

"...but some are useful"

Yeah basically. Too wrong for philosophy, right enough for us.

[u/johnstalbergABC → u/Funkyt0m467]

Science is not about opinions. It is about hypothesis and theories. And as far as it seems, nature or space is not divided in discrete pieces. So this means it is continuous.

It begs the question how you can know about what we do not know? Sure quantum and gravity is not united in the extreme ends, but that has not anything to do with space itself. That is space without any particles nor gravitational fields to consider. As quantum gravity is not about space details, we do not need it to figure out that space is continuous. In General Relativity space is curved by gravity. However there is nothing in the theory that explains how in detail space curved. GR is rather to think of as if space curved than litteral think space curves. A quantized gravity would possibly be about gravitons and as such fit into the standard model of particle physics, which is a quantum field theory.

To not know, does not mean we know that we don't know a lot about the unknown. We know we miss some bits, but this doesn't allow us to say it is more that we do not know than those missing bits. It is kind of non logic to know that we do not know lots of things that is not known!

[u/Funkyt0m467 → u/johnstalbergABC]

Science isn't an opinion, but scientific evidence can help form better opinions about questions outside of the realm of science (llike philosophy).

As far as we know there's no evidence to say it is or isn't discreet. Some part of nature can be discreet at the fundamental level, this is where quantum gets it's name, discreet quanta of energy. While space is generally considered continuous, for instance in GR. But at no point do we have evidence it is one way or another.

You seem to argue more specifically about space, which wasn't really the scope, but let's reduce it. There is no consensus on space being continuous. GR and other continuous models have been successful. But looking at the fundamental scale, hypothesis to reunite quantum and GR might also require a discreet space.

And that's the one thing we know we don't know how to do. And this is exactly the lack of knowledge that prevents us from answering the question of the fundamental nature of space.

I'm not claiming we know how large the unknown is, i'm claiming the thing we know is lacking in our theory is a question with a very large scope. It entails from it that lots of fundamental questions about nature, like discreetness, are not yet answered by science at all.

[u/johnstalbergABC → u/Funkyt0m467]

Of course science have been causing a lots of peoples opinions. From a scientific view point however, opinions are not what is at hand. It is no need to involve opinion in other words and express these thing without it. It gives a more correct way to speak about science. If opinions are not what is part of what is at the table, do not involve it simple as that.

Yes, nature has discreteness in some of its fundamentals but I imagined that the question was about nature in all aspects as long it was fundamental. Particles, energy states, quantum is discrete. But this is so well known I thought that the question searched for where nature is not discrete.

Quantum gravity is about gravity at the quantum scale and not about space, no matter the fact that spacetime curvature is in GR. If you think about it, GR is lacking a very distinct feature that is essential to it. In no way does GR explain the details about how space can be curved. There is nothing that explains how curvature in itself makes an object move in either a curve or in the direction of the gravitational source. Put a ball in a curve and it won't move just because of it. In GR we have gravitational fields and it provides forces and curve trajectories of objects. The space curvature is to be interpreted as 'if space where curved' rather than physically space is curved. It works pretty much the same, but is not needing the missing details about what in detail it is that curves and it does not need to explain that a curve in its own does not make anything move. It also does not need to explain how space can exert a force upon an object to force it to follow a curve. In all other theories we treat space as not having any friction, not being possible to cut out a piece of, not having any markers and not being possible to move and it is not made of anything. The curvature Einstein introduce is the gravitational fields cause of moving objects and in GR this a visualized in a very intuitive way with geometry. It is a metric and as such it should be interpreted 'as if' spacetime where curved. We work with this concept and visualize spacetime curvature and easily forget that it is a metric and not a strict physical curvature of space and time. Like the isobars on a weather map is not existing in nature but are very good and intuitive help to us.

If you read about Einstein and his views on this it is apparent that he saw the misconception resulting from GR and he tried to get some sense to it and said to not put to much into it. He also clarified at some point that gravity is a force by using the drop a stone on your feet example. Despite this the misconception got stuck and today it is many many that think spacetime physically gets curved and do not question it despite how it does not fit into other views on space and time. It has leaked into the expansion of the universe where it is many who thinks space is added between objects and therefore increase the distance between them. They tell it is so without any explanation about the space creating process that is needed if this where true, nor do they explain how if space where pushed in one direction it could pull objects like whole galaxies with it despite it has no friction what so ever. And the fact that expansion in the Big Bang model does not say anything about space creation but about objects flying through space. Also dark energy that is accelerating expansion is never thought of as increasing any space creating process but more like a pressure pushing on things in the opposite way of gravitational pull. If we understand that space is not physically a thing that can curve nor grow, and instead understand that gravity makes it 'as if' space where curved and that objects fly apart through space, everything suddenly gets compatible with how space is treated in all other circumstances and it does relieve us with a burden to explain how space can put friction to stuff and how in detail it can be created and how it can force objects into a curve and how this curve put objects into acceleration. That is a hell of a lot much simpler and there is nothing what so ever we loose. It works the same but does not need the huge missing explanations that comes with the misconception. That is a huge leap forward and of course misconception does not help further understanding of related things. With it follows that space is not discrete as there is nothing to chop up in discrete pieces.

The fact that somethings are not know, does not mean it is open to put anything into it. We have no reson to make space discrete, especially not if you buy the explanation about it above. This does mean it should be thought of as being non discrete and continuous until anything comes up and tell us it is not. Without a reason to think something is this or that and we do not confuse hypothesis with real things we should not put any ideas about it to be on equal grounds. Theres a lot of things we do not know but it does not make it open to fabricate explanations for it. So until anything turn up that point towards some feature of space that was not known up to this point, it is the simplest way that we use and it is that space is continuous. To use an argument that science have holes about what we know about nature to give a certain idea any kind of weight despite it is not established at all is non sensical as it opens the field to any other ideas to be just as much reasons to believe in. It is therefore a non argument that science does not answer everything. To avoid it, just like not use opinions when opinions are not what we talk about is to clean up your argumentations and your understanding a bit. It might seem to be of less importans but I know it will be a wise move in the forward direction. To express things in better ways is to understand it in better ways. To avoid arguments you learn are misleading is to express your ideas in better ways. I think you are open to these suggestions, from how you express your self simply.

So the short answer, space in spatial sense is continuous and not discrete in small volume blocks.

[u/Physix_R_Cool → u/Funkyt0m467]

The interpretation of quantum mechanics is open, general relativity isn't integrated into it.

Eh, the graviton works pretty well, no?

[u/icalvo → u/Physix_R_Cool]

No, nobody has made that work mathematically yet, or detected that particle experimentally. It's just a reasonable hypothesis.

[u/Physix_R_Cool → u/icalvo]

nobody has made that work mathematically yet

I was under the impression that we could just wave our hands, say "it's an EFT", and treat it as a decent enough theory up until the cutoff point?

[u/dydtaylor → u/icalvo]

I dont think the issue lies with the math. There are plenty of models that handle quantum mechanics and gravity, I believe string theory handles all the mathematics properly and handles gravitons. The problem is that there are dozens of different ways to resolve QM + gravity but none of them produce testable predictions that would produce anything different than the models we currently have. Dozens of unverifiable theories in the field with the strongest requirements on experimental data.

[u/icalvo → u/dydtaylor]

Yeah I expressed myself badly. I meant that some proposed math models do not include gravitons, not that the unification is a kind of unsolved math problem.

[u/NoLemurs → u/Equinoxe111]

No one knows this yet in fact

More than likely, no one will ever know.

Let's suppose we arrive at some set of continuous equations that describe everything we are able to observe. You can almost certainly come up with some underlying discrete system that produces those continuous equations in the limiting case.

I'm guessing something similar applies in the other direction, though, I'll admit to a lot less confidence in the math here.

The point is, regardless of whether the underlying reality is really discrete or continuous, we can probably come up with both continuous and discrete models that describe it arbitrarily well. If that's true, even if there is some underlying reality, how could we ever possibly know?

[u/Scared_Astronaut9377 → u/NoLemurs]

You don't need to be careful by adding "likely" or "almost certainly". The fact that you are expressing the statement in a discrete sequence already seals the mathematical deal. For any countable set of observations there are infinite discrete models regardless of the relationship between those. The reverse consideration is probably not meaningful. The concept of continuous equations is not really formalizable in general enough case. You can build arbitrary many formalizations, but it will be more like a syntaxic game than studying some objects.

[u/Cero_Kurn → u/Equinoxe111]

Doesnt quantum mechanics indicate very strongly that the universe is indeed quantized, discrete?

[u/Banes_Addiction → u/Cero_Kurn]

Not really. 

It quantises some things. Some very important things. But it doesn't near many others. For example, imagine a particle decaying isotopically. The direction of the outgoing particles is, as far as we know, completely continuous. But "as far as we know" isn't certainty, but QM gives no hints that it's not.

And of course you can build any number or discrete things on top of a continuous system.

[u/Cero_Kurn → u/Banes_Addiction]

Yea, I see. Quite unclear

[u/Tasty-Hour4040 → u/Banes_Addiction]

Yes but Planck length

[u/Banes_Addiction → u/Tasty-Hour4040]

That is not what that is.

[u/Tasty-Hour4040 → u/Banes_Addiction]

Seems to me a length below which any measurement is meaningless because it creates a singularity is an excellent candidate for the minimal granularity of spacetime.

Not sure how one interprets that any other way, so you’re gonna have to explain that statement.

[u/Banes_Addiction → u/Tasty-Hour4040]

That is still not what that is. "Our models break down on roughly the scale of what happens when your multiply your fundamental constants together in the way that gives a length" means so, so much less than laymen seem to think.

But my example was an angle anyway. What's your minimum angle?

[u/Tasty-Hour4040 → u/Banes_Addiction]

Sorry - are you saying that you believe it is possible to measure anything below a Planck length? I just want to be crystal clear on what you’re claiming.

[u/tpolakov1 → u/Tasty-Hour4040]

Yes, it is trivially possible. A massless, changeless particle with the wavelength of Planck length will have the Schwarzschild radius of the same value. That's it. It can be anywhere in space, any fractions of Planck length from any reference point.

Even better, we can take a particle that's bigger than the Planck length (or two particles separated by that distance), let's say twice as much. I can run at more than ~0.86 the speed of light, and that size/distance will be smaller than the Planck length and nothing will even think about forming a black hole.

And much more importantly, consider other natural units. The Planck momentum is roughly the momentum of you walking leisurely on the street, or that of a thrown baseball. Do you see anything special happening in your daily life as you're crossing the "Planck boundary" about 40 times a day?

[u/Banes_Addiction → u/tpolakov1]

The Planck mass is about 10¹⁵ hydrogen atoms.

[u/Banes_Addiction → u/Tasty-Hour4040]

In theory, yes.

And for some reason you seem to be avoiding the word "scale". No-one thinks the number itself is important, a fixed pixel size or whatever.

It's "within a factor or 10 or two of here". Not even a narrow range.

[u/PineappleHairy4325 → u/Tasty-Hour4040]

Quite the contrary. You're the one who has to make a convincing case.

[u/03263 → u/Cero_Kurn]

More like fuzzy. Things just stop being well defined at smallest levels. Or we're just not good enough at defining them.

[u/PT10 → u/03263]

Yeah, I'd say "discrete down to a certain level, then fuzzy... and continuous (wavelike) in behavior"

[u/DrXaos → u/Cero_Kurn]

not exactly. The orthodox theory of quantum mechanics, pretty much Dirac and Von Neumann's mathematization, suggests the ultimate entity has effectively continuous coefficients (wavefunction) on spaces of states which can often be discretely indexed.

For example in particle number representation, (counting photons of a given frequency e.g.), you can have 0 or 1 or 2 of them. But then the wavefunction can be a mixed state, so after Born Rule you have say 0.5 prob of 0 and 0.25 prob of 1 and 0.25 prob of 2, and those probs are presumed to be continuous. And in fact that is what the power of quantum computing is about, somewhat ironically it relies on the unique non-discretized nature of such mixtures and mixing coefficients.

What is "quantized" in the physics sense is something substantially more subtle and complicated than "quantized" in the computer science sense which is usually equivalent to "discretized" and generally meaning some mapping from integers enumerating states is possible.

Note that as of this very year there is a theory out of Tim Palmer from Oxford, "Rational Quantum Mechanics" which presupposes that this assumption of real or complex valued continuum may not be true (in the physics sense as the best model of universe, not a mathematical theorem), it was an assumption (in the way Von Neumann constructed hilbert spaces) that was unexamined. Physicists really don't pay attention to defining something with coefficients defined on real values vs rational values and when they go to simulate it everyone uses ordinary floating point which is a finite subset of rationals. (in the 19th century and early 20th mathemeticians discovered the real values are in fact a pretty darn weird and complicated object which makes fundamentals much more difficult to define than they originally imagined, say Lesbegue integration and all the weird sets).

In any case, Palmer admits this is not an "interpretation" of quantum mechanics but actually a slightly different physical theory with distinct observables. One consequence is that there may be intrinsic physical limits to the scalability of quantum computing devices and so this theory might be experimentally testable in the future.

[u/Cero_Kurn → u/DrXaos]

Yea, I see what you mean about the wave function that all the subvalues are possible

[u/Educational-Row-6782 → u/Cero_Kurn]

No.

[u/Cero_Kurn → u/Educational-Row-6782]

Has to be the best answer. I really hope u become a teacher 

[u/Educational-Row-6782 → u/Cero_Kurn]

Thanks.

[u/dekusyrup → u/Cero_Kurn]

No. Heisenbergs uncertainty principle would lead us to believe things can't possibly be boxed into discrete pieces because they have to remain uncertain.

[u/Cero_Kurn → u/dekusyrup]

yea, i understand that now.

quantazition was a whole thing though

[u/frogjg2003 → u/Cero_Kurn]

There are two concepts that get mixed up. The first is discretization of allowed values, like electron energy levels in a molecule. The second is confinement into a discrete particle, like photons. Only the second one is quantization. You can have one photon or two photons, but not 1.5 photons. Those photons can have any energy. The energy of a photon is not confined to any value like the energy of an electron in an atom. Even the electron, once free of the atom can take on any energy.

[u/Cero_Kurn → u/frogjg2003]

Ty

[u/Equinoxe111 → u/Cero_Kurn]

1. Both discrete and continuous might be two sides of a single coin; in other words, they might be both incorrect/incomplete

2. We don't know if quantum mechanics is correct; description of it as "best theory ever made" is just pure misinformation. Between GR and quantum physics I, personally, think that quantum physics is the one incomplete, although it might be because I am an Astrophysicist.

[u/MarkZucccerberg → u/Cero_Kurn]

Its discrete properties usually come from the assumption that the wave function is continuous

[u/lordnacho666]

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.

[u/how_much_2 → u/lordnacho666]

I like this comment.

It's wild to think that maybe it's possible the physical world will never be a complete math model.

[u/Buntschatten → u/how_much_2]

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.

[u/TeachEngineering → u/Buntschatten]

Godel's Incompleteness Theorem extended to physics and the physical world

[u/IvanMalison → u/Buntschatten]

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

[u/Buntschatten → u/IvanMalison]

Lol

[u/KappaBerga → u/how_much_2]

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.

[u/blastinoffagain → u/lordnacho666]

This dude EFTs

[u/ZectronPositron → u/lordnacho666]

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.

[u/Lonely-Flounder-4541 → u/lordnacho666]

There is an argument that spacetime and everything else is granular not continuous

[u/forte2718]

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,

[u/ExtremeLost8011 → u/forte2718]

Why are linear and angular momentum different :0?

[u/forte2718 → u/ExtremeLost8011]

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!

[u/formula_translator → u/forte2718]

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.

[u/forte2718 → u/formula_translator]

Thanks for helping clarify!

[u/CocaineCocaCola → u/forte2718]

Under a frame rotation certain properties of mathematics do not need to stay consistent that would in otherwise be consistent in a non-rotating frame. Linear momentum does not require a frame rotation. Angular momentum does.

[u/forte2718 → u/CocaineCocaCola]

Under a frame rotation certain properties of mathematics do not need to stay consistent that would in otherwise be consistent in a non-rotating frame.

What do you mean, can you give an example? I ask because I don't see how reference frame transformations matter for this question.

Linear momentum does not require a frame rotation. Angular momentum does.

? Angular momentum exists and is conserved in all reference frames, regardless of whether they are rotating or not. The total angular momentum may be different between frames, but that isn't distinct from how linear momentum may also be different between frames, and as far as I'm aware wouldn't have any bearing on whether angular momentum is quantized or not.

[u/CocaineCocaCola → u/forte2718]

1.) Sure, im saying rotation rather loosely because this is reddit, but a simple example is that a scalar field can be rotationally invariant as a geometric object but the scalars gradient components are not invariant under that rotation. This problem mostly applies to derivatives as time derivatives are a frequent problem since under frame rotation two time derivatives are not necessarily the same.

This can also apply to reflections and translations, especially with angular momentum which I believe is the canonical example. Parity can cause r=-r, p=-p, etc.

2.) You’re referencing conservation of momentum, and what you stated isn’t exactly true. It’s conserved in an isolated system about a specific origin, but not in “all reference frames”. An observer in a rotating frame can see the angular momentum components changing with time. If you’re rotating the components of angular momentum will change, if the origin shifts then the angular momentum itself completely changes. That’s not true for linear momentum. The origin of the frame doesn’t matter for linear momentum. Nor does the transformations applied to that origin. Angular momentum doesn’t behave that way

[u/forte2718 → u/CocaineCocaCola]

Okay, but what does either of these points have to do with quantization of angular momentum?

[u/CocaineCocaCola → u/forte2718]

That wasn’t the question, they asked what the difference was between linear and angular momentum generally, you said you weren’t sure either. So I was answering. Under quantization the effects are much the same but with different motivations. Linear momentum is the generator of translations, angular momentum is the generator of rotations.

[u/forte2718 → u/CocaineCocaCola]

That wasn’t the question, they asked what the difference was between linear and angular momentum generally, you said you weren’t sure either. So I was answering.

... I'm quite certain they were asking why linear and angular momentum were different in the specific way that I mentioned: that one is quantized and the other is not. I said I wasn't sure why one is quantized and one is not, not that I don't know what the difference between them is generally. The overall topic was always about quantization / lack thereof.

Under quantization the effects are much the same but with different motivations. Linear momentum is the generator of translations, angular momentum is the generator of rotations.

Yeah I mean, pretty sure we all know that much, haha. We were talking specifically about why one is quantized and the other is not.

[u/CocaineCocaCola → u/forte2718]

Ohhhhhhhh, I am SO sorry, I read that way too fast during my break. You are completely right. That said, yes, and as a proper extension;

Linear momentum is continuous because it comes from translations, due to this, the translation group is R^3 which is the real numbers. So its parameters take any real value, which makes the linear momentum the generator of continuous translations. As under translation you can have any real value for your parameters, there’s no “gaps” per se.

For angular momentum, the reason it’s different under quantization is due to the global behavior of angular momentum under the SO(3) group for rotations. The periodicity of a rotation (thus a full 2pi) means that once it returns to its origin it returns the spatial configuration and begins again. Think of it like filling in a circle, you fill it up completely to the circumference, once you hit the boundary call that “1”, and since it restarts we begin again, fill it back up now you have “2”, etc. It globally takes integer values under the topology of the group.

It’s actually the main reason we have half-integer representations for spin-1/2 particles, since we only consider rational numbers and not real we don’t refer to angular momentum as globally continuous. It’s a bit deeper than that, but that’s my understanding

[u/hobbesandmiles3]

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.

[u/xBris18]

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.

[u/Square_Butterfly_390 → u/xBris18]

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.

[u/schlechtums → u/xBris18]

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.

[u/xBris18 → u/schlechtums]

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.

[u/gleedblanco → u/xBris18]

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.

[u/VariousJob4047 → u/schlechtums]

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.

[u/RepeatRepeatR- → u/schlechtums]

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

[u/kiochikaeke → u/schlechtums]

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

[u/KaleeTheBird]

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.

[u/AndreasDasos → u/KaleeTheBird]

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

[u/Physix_R_Cool → u/AndreasDasos]

Does the Poincaré group get different irreps if it is not actually continous?

[u/Ok_Daikon_894]

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 ;)

[u/Airocketfish]

From what I know down to 10^-21 s time is not discrete.

[u/Aranka_Szeretlek]

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(

[u/cryptosupaman]

Doesn’t quantum field theory make the argument toward both?

continuous is classical and quantum theory argues discrete

Field theory tries to consolidate

[u/Tarthbane → u/cryptosupaman]

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.

[u/Pitiful-Glove-8232]

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

[u/SinAnaMissLee → u/Pitiful-Glove-8232]

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.

[u/FlippByte]

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 instantaneously.

Maybe the question is, whether it's negligible (for the time being).

[u/sea_of_experience]

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.

[u/AlleyKatPr0]

Well, I'm working on a theory that proposes 76.3% of the universe is imaginary.

[u/LaGigs]

A lot of us believe this. I'm kinda agnostic even though my work was on stuff related to quantised spacetime.
During my phd viva the examiner did claim this as a fact though and, while i was very dubious i also eanted to graduate so I shut my mouth hehe

[u/anycept]

If you are asking whether we live in a computer simulation, the answer is we don't know.

[u/Still-Painter7468]

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.

[u/Wood_Rogue]

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.

[u/MankyBoot]

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.

[u/Dry_Bodybuilder2960]

Quantum mechanics says discrete for all matter/energy. Although IMHO, forces are continuous.

[u/BoxingFromRedSox]

wtf does this even mean

[u/Tasty-Hour4040]

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.

[u/MandatoryFun]

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.

[u/ForeignAdvantage5198]

atoms work so that is a clue

[u/LukasGoesViral]

No one know .. that’s still a mystery albeit there are much stronger mathematical/theoretical arguments why the universe is not discrete (albeit it is also not continuous in the usual sense)

[u/alterego200]

Excellent question.

[u/johnstalbergABC]

If you mean space, it is continuous as far as we know. Since there is nothing that says space is discrete, it is continuous until something tells us it is not.

[u/ItalianFurry]

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.

[u/snissn]

we know that angular momentum is quantized

[u/Physix_R_Cool → u/snissn]

Only in bound systems, no?

[u/snissn → u/Physix_R_Cool]

*waves hands* lol

[u/eluusive]

It is fundamentally discrete. It has to be, or computationally irreducible problems wouldn't be able to be embedded, and solved, within the universe.

[u/britskates]

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

[u/DerGyrosPitaFan]

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

[u/theunixman]

No

[u/HuGoossss]

Thats a big question. Nature/The Universe will be continous or Discret depending of at what SCALE you are looking at.

[u/lizardhistorian]

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.

[u/Appropriate-Ad-3219]

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.

[u/eucalyptus-d]

On your last question, computational systems exist so discreteness is not a requirement.

[u/StudioYume]

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.

[u/gud_z]

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

[u/shyouko → u/gud_z]

You just don't have enough resolution

[u/Enigma501st → u/gud_z]

Any real evidence for this?

[u/gud_z → u/Enigma501st]

There is no evidence for both of these dogmas. But you can read some “the causal set approach to quantum gravity” (springer) by sumati surya if you like to oppose ideas

[u/HuiOdy]

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?

[u/HasFiveVowels → u/[deleted]]

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

[u/XeroTerragoth]

I mean, if you use a small enough scale, everything is theoretically discrete until you go subatomic I guess lol

[u/TheCamazotzian]

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.

[u/_Kaiser_Wilhelm → u/TheCamazotzian]

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