[ChrisLomont]

>because the universe is discrete

Many aspects of the universe are not known to be discrete, such as space, time, energy, and much, much more. It's not unreasonable that there are discrete and continuous aspects to the universe.

Many things that pop science treats as discrete, such as an electron, are most accurately described as interactions of a continuous fields via topological quantum field theories. Treating the electron as a discrete thing only works for some experiments. Treating it as a field works for all experiments.

[Chris2048]

"not known to be discrete" does not imply "It's not unreasonable that there are discrete and continuous aspects to the universe"; it is not known that anything is continuous either.

[ChrisLomont]

The theories that best model every known experiment are continuous. General relativity models large scale phenomena to incredible precision, and is continuous. Predictions made by it around 100 years ago are still being tested and found true, such as gravitational waves.

The Standard Model, which models everything else, is continuous. A specific part of it, QED, is the most accurate theory known, agreeing with experiment to better than 10 parts in a billion.

There is no known violation of these two theories, which explain all of the observable universe. There is an issue on how to glue them together, and one of the leading methods, string theory, is also continuous. I am unaware of any theory that can replace these that has no continuous parts, such as symmetries.

> it is not known that anything is continuous either

Every physics theory that we use to explain the universe is continuous, and not a single one is not, so I'm betting that there are continuous things in reality.

[Chris2048]

Other leading theories are non-continuous. LGQ example is an active area of research.

> Every physics theory that we use to explain the universe is continuous

Are you suggesting thete are no discrete models?

Any discrete model may be similar to leading continuous models, so the explanatory power of both isn't relevant unless it can only be produced by continuous models.

[ChrisLomont]

>Other leading theories are non-continuous.

Which theories discretize all variables? I'm well aware people make models all the time, but they usually fail to explain all we observe or are toy models, like 2D TQFT models, not designed to mirror reality, but to fiddle with to see if they extend.

LQG, for example, treats space as quantized at the Plank length, but this has already been disproven experimentally [1,2], forcing LQG to reassess. LQG still has continuous parameters, such as symmetry, and is based on the same continuous math as GR and TQFTs. It's simply trying to discretize (somewhat) spacetime, but it certainly has not yet succeeded at that.

Hogan's holometer experiment [3] also has shown that the scales LQG wanted to discretize spacetime at are incorrect.

So there is at least 2 different experiments invalidating a central piece of LQG. Of course LQG can simply retrench and claim scales are smaller than the Plank length.

There is no experimental evidence pointing to LGQ as reality. It has not even been shown to reproduce GR in the semi-classical limit, so it may end up simply being mathematical fantasy. LQG also has lots of other technical problems that may in the end throw it on the heap of failed theories, of which there have been many. It makes no prediction not already covered under GR.

So, yes, I realize there are people trying to discretize the universe, but so far none of these theories have reproduced what we observe in experiment, and the only theories that have reproduced all we observe in experiment are continuous.

>Any discrete model may be similar to leading continuous models, so the explanatory power of both isn't relevant unless it can only be produced by continuous models.

Which model using only discrete variables can make the same predictions of GR or SM? I cannot think of one, I cannot find one, so it may be that so far the only models that work are continuous.

Heck, even going simpler - what discrete model can reproduce only GR? LQG so far cannot, despite significant effort trying to make it do so. So that surely puts the burden of proof on showing discrete models as equivalent to continuous ones.

So I'm game for something to break current models, because that would be cool. However, nothing has, and no theories is really even close to replacing SM and/or GR.

[1] https://arxiv.org/abs/1102.2784

[2] http://hal.in2p3.fr/tel-01219651/document

[3] https://en.wikipedia.org/wiki/Holometer

[Chris2048]

> but it certainly has not yet succeeded at that

The claim here is actual "continuous" objects likely exist. How can you demonstrate this?

All continuous models can be reproduced in discrete models up to the resolution of "all current observations", How are discrete models inherently unable to match continuous ones?

[ChrisLomont]

>The claim here is actual "continuous" objects likely exist. How can you demonstrate this?

You cannot demonstrate either continuous or discrete beyond what a model shows. All of knowledge in science is from models, nothing more.

For example, all objects that you perceive as discrete are modeled as waves in QM (more specifically TQFT). Given that it seems everything behaves as a wave, how can you prove discrete items exist to the level of proof you seem to require? I doubt it's possible to do so. Your perception of discrete is wrong, according to QM. What was once wave/particle duality in the early 1900s got replaced with larger and larger systems and TQFT until now everything in QM is a field, including you, including marbles, including particles, including everything. And this view allows the theory to accurately predict all relevant experiments. Discrete you, marbles, electrons, fails experimentally.

>All continuous models can be reproduced in discrete models up to the resolution of "all current observations"

This is not true. If I recall my QCD correctly, some calculations spit out infinities if the underlying space is not continuous. I suspect there are other places that add divergences if you discretize things.

Roughly - if you perform calculations in QCD (or QED), you basically add up an infinite number of terms, each with smaller and smaller probability, to get a finite answer (which, for QED, is astoundingly accurate). If you force this infinite sum to not be allowed to go to zero spatially, then you get infinite terms that cannot shrink, and you get an infinity. If you try to fix this by only including a finite number of terms, you get other issues, such as not getting the right answer when tested experimentally.

I also seem to recall that in QED if you do not have continuous space, then the self-interaction of an electron again spits out infinities, which of course is one major impetus for developing QED to begin with.

So no, you cannot simply discretize math and get all calculations to still given the same answers you see experimentally. It's not that simple.

For example, you mentioned LQG - researchers have tried for a long, long time, with much effort, to get it to reproduce continuous GR with a discrete model, and they so far have failed. It is not as simple as simply making the discreteness smaller. There are fundamental issues in getting such things to match the continuous theories.

So, despite it being a really useful thing to do, and despite there being lots of work trying to get a discrete model to match GR or SM, I am unaware of anyone ever making it work.

Interestingly, trying to find a better way to explain it to you, I found this [1] question about the inability of anyone to make a discrete model match current continuous ones (which backs my view that it has not been done, and perhaps will be found impossible). He makes the interesting point that your view of LQG making space(time) discrete is not correct. The reason is that this would violate Lorenz invariance (which is also the thing those experiments listed) are looking at, and so far Lorenz has never been broken experimentally, to the point of pushing it below the plank limit. So the "discreteness" of LQG is much more subtle than a naïve view.

I asked for an example of a discrete theory that matches some significant piece of physics - do you have one or not? Your claim that it can be done is not matched by any evidence you have put forth, nor any that I have ever encountered.

[1] https://math.stackexchange.com/questions/186076/is-there-suc...

[q1bz2p]

I have reviewed [1] and [2] but it isn't clear to me how they prove that space isn't quantized at the Planck length.

Could you explain how these experiments disprove that?

[ChrisLomont]

Here's [1] a pop science explanation of that result (and there have been several more in the same vein since then).

A key quote from the article "And given that some quantum gravity frameworks predict that effects should be showing up at that point, perhaps those models are simply wrong, and there is no changing speed of light."

AFAIK, later experiments have even lowered the threshold, making LQG less and less likely, in the same way the LHC results have pushed back supersymmetry arguments by invalidating some versions predictions.

[1] https://www.symmetrymagazine.org/breaking/2009/10/28/gamma-r...