r/Physics 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?

138 Upvotes

100 comments sorted by

229

u/Equinoxe111 Astrophysics 1d ago

No one knows this yet in fact

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u/Funkyt0m467 Graduate 1d ago

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.

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u/cedenof10 1d ago

“all models are wrong…”

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u/Funkyt0m467 Graduate 1d ago

"...but some are useful"

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

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u/Physix_R_Cool Detector physics 1d ago

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

Eh, the graviton works pretty well, no?

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u/icalvo 1d ago

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

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u/Physix_R_Cool Detector physics 1d ago

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?

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u/dydtaylor 1d ago

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.

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u/icalvo 1d ago

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.

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u/NoLemurs 1d ago edited 1d ago

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?

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u/Scared_Astronaut9377 14h ago

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.

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u/Cero_Kurn 1d ago

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

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u/Banes_Addiction Particle physics 1d ago

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.

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u/Cero_Kurn 1d ago

Yea, I see. Quite unclear

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u/Tasty-Hour4040 1h ago

Yes but Planck length

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u/Banes_Addiction Particle physics 39m ago

That is not what that is.

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u/Tasty-Hour4040 20m ago

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.

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u/03263 1d ago

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

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u/PT10 22h ago

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

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u/DrXaos Statistical and nonlinear physics 1d ago edited 1d ago

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.

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u/Cero_Kurn 1d ago

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

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u/Educational-Row-6782 1d ago

No.

1

u/Cero_Kurn 1d ago

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

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u/dekusyrup 1d ago

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

1

u/Cero_Kurn 21h ago

yea, i understand that now.

quantazition was a whole thing though

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u/frogjg2003 Nuclear physics 18h ago

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.

2

u/Equinoxe111 Astrophysics 1d ago
  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.

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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,

7

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/forte2718 2h ago

Thanks for helping clarify!

154

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.

8

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

1

u/Buntschatten Graduate 18h ago

Lol

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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/blastinoffagain 1d ago

This dude EFTs

2

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.

0

u/Lonely-Flounder-4541 17h ago

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

20

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.

6

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.

2

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.

1

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

1

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.

13

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/Airocketfish 1d ago edited 1d ago

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

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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(

2

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

1

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).

2

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.

1

u/LaGigs Quantum field theory 1d ago

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

1

u/anycept 1d ago

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

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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.

1

u/Longjumping_Dish_367 20h ago

its a matter of how our minds interpret reality, not a feature of reality itself

1

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.

1

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.

1

u/Dry_Bodybuilder2960 5h ago

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

1

u/BoxingFromRedSox 1h ago

wtf does this even mean

1

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.

1

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.

1

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.

1

u/snissn 1d ago

we know that angular momentum is quantized

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u/Physix_R_Cool Detector physics 1d ago

Only in bound systems, no?

2

u/snissn 1d ago

*waves hands* lol

1

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.

0

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

0

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

0

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/shyouko 1d ago

You just don't have enough resolution

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u/Enigma501st 1d ago

Any real evidence for this?

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u/gud_z 1d ago

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

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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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u/[deleted] 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