Continuous vs discrete Universe

[Lynch101]

TL;DR Summary

Trying to understand the issue of continuity vs discreteness.

I've come across the question of continuity vs discreteness in different articles, discussions, etc. but I'm not sure that I am 100% clear on what the precise question is.

My basic interpretation of it is a question of whether the Universe is made up of lots of separate entities which all interact with each other, or if it is just one single continuous thing. To us the analogy of a jigsaw puzzle, it would be like questioning whether the Universe is more like the completed jigsaw puzzle, with all the different pieces fitted together to give the complete picture, or if it is more like the picture on the box that the puzzle comes in, a single, continuous entity not made up of lots of different parts.

The idea of the Universe as being made up of lots of discrete parts would seem to follow naturally from the subatomic picture of the world, where the world is made up of atoms or subatomic particles all interacting with each other.

Is it more precise to say that the question relates to spacetime i.e. the question is, more precisely, is spactime continuous or discrete? To my mind this would, essentially, be the same question as asking whether the Universe is continuous or discrete. Is there a nuance that I am perhaps missing out on there? Could the jigsaw puzzle analogy still be applied in this instance?
I've also heard that the question of discreteness applies more to energy quanta and need not, necessarily, imply a lack of and underlying continuity. This idea is better articulated in this article: Nova - Are space and time discrete or continuous?

While almost all approaches to quantum gravity bring in a minimal length one way or the other, not all approaches do so by means of “discretization”—that is, by “chunking” space and time. In some theories of quantum gravity, the minimal length emerges from a “resolution limit,” without the need of discreteness. Think of studying samples with a microscope, for example. Magnify too much, and you encounter a resolution-limit beyond which images remain blurry. And if you zoom into a digital photo, you eventually see single pixels: further zooming will not reveal any more detail. In both cases there is a limit to resolution, but only in the latter case is it due to discretization.

I would take this to, effectively, be an argument in favour of a continuous spacetime/Universe. Would that be an accurate interpretation?

 

[jambaugh]

There are implicit assumptions built into your question that need resolving before arriving at an answer. My view is that space-time is a parametric construction we use to relate phenomena. It is meaningful in how we use it but not as an ontological (physically real) object. Thus it isn't, in and of itself, inherently discrete or inherently continuous. Space and time coordinates are, as we use them, continuous as they are the parameters for the *Lie* group of transformations on objects. So they are no different from angles which parameterize rotations but can also be utilized to describe the orientation (angular position) of a physical system relative to some ad hoc default position. You may find that utilizing sufficiently small discrete angular, durational, and distance parameters makes no difference that we can physically observe at the scale of current experiments. But increasing our domain of observation will only push the question further down, "maybe my unit distance is too large but should still be discrete". After-all we only actually carry out real measurements to a finite level of precision. So in another sense, we experimentally always work in discrete units of measurement albeit many different degrees of precision. The continuum is convenient in that it is agnostic of our limits in precision. This may be fortunate or unfortunate as a choice depending on circumstances.

When we invoke Einstein's geometric model for General Relativity one must remember it is a model (in the sense of physics) and not the theory itself. The theory states that the geometry is indistinguishable from a class of dynamics we imagine as gravity as a "physical dynamic force". The "relativity" in its strongest form means we shouldn't actually say "gravity is just curved space-time" because you can't take the role of the omniscient observer and assert the geometry. We can only infer geometry relative to an assumed dynamics or vis versa.

It is beautifully tempting to make too strong an assertion in the case of gravity in that we can, according to Einstein's theory, choose a frame of description (model) where "all is geometry" but asserting a fixed compatible geometry and then overlaying additional dynamic gravitational forces can be asserted as no less valid a model predicting exactly the same phenomena. It's just not as elegant. But that's in the classical domain. The reverse (allowing for non-trivial gravitational dynamics) may very well lead to a more elegantly expressed quantum theory of gravity. I suggest the possibility this might be a reason for lack of progress in the field of quantum gravity.

In short don't over reify space-time.

 

[Lynch101]

space-time is a parametric construction we use to relate phenomena. It is meaningful in how we use it but not as an ontological (physically real) object. Thus it isn't, in and of itself, inherently discrete or inherently continuous.

Thanks jambaugh. I understand the point you are making here. Does it represent the consensus among physicists, that spacetime is not an ontological/physically real object, or is opinion divided on that?

In short don't over reify space-time.

If we ignore the question with regard to spacetime, I believe (if I remember correctly) I have seen the same question posed with regard to the Universe itself: is the Universe continuous or discrete.

This might be seen as stemming from atomic (and subatomic) physics which says that all matter is made up of discrete particles. This would suggest a picture of the Universe analagous to a jigsaw puzzle, made up of lots of discrete parts stuck together. Are there some theories, or physicists who advocate a different picture of the universe; a single continuous entity/structure?

 

[PeterDonis]

Does it represent the consensus among physicists, that spacetime is not an ontological/physically real object, or is opinion divided on that?

Opinion is divided. Some physicists view it as @jambaugh does. Others view the fact that in GR spacetime is dynamical--the spacetime geometry is determined by the distribution of matter and energy, and in turn determines the motion of matter, per the Einstein Field Equation--as an indication that it is real.

 

[Lynch101]

Opinion is divided. Some physicists view it as @jambaugh does. Others view the fact that in GR spacetime is dynamical--the spacetime geometry is determined by the distribution of matter and energy, and in turn determines the motion of matter, per the Einstein Field Equation--as an indication that it is real.

Thanks Peter. I wasn't really aware that there were those who didn't take spacetime to be physically real. With regard to those that do consider it to be physically real, is opinion pretty evenly split when it comes to the question of whether or not it is continuous or discrete; or are there more in one camp than the other?

Is the question of the Universe being continuous or discrete effectively the same question, would you say, or is there a slight nuance to it? For those that don't consider spacetime to be a physically real structure, would the question of the Universe being continuous or discrete would supplant that?

 

[PeterDonis]

With regard to those that do consider it to be physically real, is opinion pretty evenly split when it comes to the question of whether or not it is continuous or discrete

I don't know. Nobody has a model that makes actual predictions in which spacetime is discrete; the only model we have of spacetime that makes predictions is GR, in which spacetime is continuous. So I'm not sure how much anyone's opinion on the question is worth anyway.

 

[PeterDonis]

Is the question of the Universe being continuous or discrete effectively the same question, would you say, or is there a slight nuance to it?

I don't understand what "the Universe" being continuous or discrete even means, if it's supposed to not be the same as spacetime being continuous or discrete.

 

[Lynch101]

I don't understand what "the Universe" being continuous or discrete even means, if it's supposed to not be the same as spacetime being continuous or discrete.

The way I would interpret it, is as a question of whether the Universe is made up of discrete particles and/or fields, or if there is only one single field (or substance perhaps) with different properties.

 

[Lynch101]

I don't know. Nobody has a model that makes actual predictions in which spacetime is discrete; the only model we have of spacetime that makes predictions is GR, in which spacetime is continuous. So I'm not sure how much anyone's opinion on the question is worth anyway.

Ah, cool. Thanks. I didn't realize that all models [thus far] treat spacetime as continuous.

 

[PeterDonis]

The way I would interpret it, is as a question of whether the Universe is made up of discrete particles and/or fields, or if there is only one single field (or substance perhaps) with different properties.

You seem to be confusing two different meanings of "discrete".

In our current Standard Model, there are multiple fields: the quark fields, the lepton fields, the gauge boson fields. So the model has "discrete" fields in this sense--as opposed to just having one field, it has a number of fields which is an integer greater than 1.

But each of the fields in the Standard Model is defined on a continuous spacetime manifold and can take a continuous range of values (actually, fields in QFT are operators, not numbers, so we really should be talking about things like their expectation values, but the point is the same). There are no "discrete" fields that only take discrete values. Certain observables can have discrete (quantized) values under certain conditions (e.g., the energy observable for a bound state), but that doesn't make the underlying fields discrete.

As far as the question of whether there could be only one single field "with different properties", I don't think this makes sense. "Different properties" means different fields. At least, that seems to me to be a better choice of words. If you are willing to make "different properties" broad enough, you could say our current Standard Model is a theory of just one field with "different properties", but I don't think that's a useful way of looking at it.

 

[Lynch101]

You seem to be confusing two different meanings of "discrete".

Thanks Peter. I am familiar with the different meanings of the term "discrete" - or more accurately, I am familiar with the idea that it is used in two different ways and I think I have a fairly basic understanding of both. The meaning of the term I'm trying to get at here is the one which refers to separate, or perhaps distinct, parts of something.

In our current Standard Model, there are multiple fields: the quark fields, the lepton fields, the gauge boson fields.
...
But each of the fields in the Standard Model is defined on a continuous spacetime manifold and can take a continuous range of values.
...
"Different properties" means different fields. At least, that seems to me to be a better choice of words. If you are willing to make "different properties" broad enough, you could say our current Standard Model is a theory of just one field with "different properties", but I don't think that's a useful way of looking at it.

I understand what you are saying here but I think it might be helpful for me to use an analogy to try and clarify the question I am trying to get at - incidentally, me clarifying the question still doesn't necessarily mean that it will be a useful way of looking at things.

You mention the various fields above, quark, lepton, and gauge boson and you say that this is defined on continuous spacetime manifold. If we consider spacetime to be a physically real thing, then we might view the three fields and spacetime as 4 pieces of the jigsaw puzzle that make up the Universe. This would mean that we have 4 discrete parts of the Universe. Or perhaps we might think of it in terms of a patchwork quilt stitched together from 4 discrete patches.

In the context of the question of continuity vs discreteness (the meaning mentioned above), while the discrete picture would be that of a patchwork quilt, the continuous picture would be that of a single sheet with say, different textures. If that makes sense.Again, it might not be a useful way of looking at it, it's just a question that I had with regard to continuity vs discreteness.

 

[PeterDonis]

The meaning of the term I'm trying to get at here is the one which refers to separate, or perhaps distinct, parts of something.

Unfortunately, this is not the meaning that most discussions of "continuous vs. discrete" in a physics context are interested in. Most discussions (including, as far as I can tell, the ones you refer to in your OP) are interested in the other meaning.

it might not be a useful way of looking at it

Unfortunately, I don't think it is. See above.

 

[PeterDonis]

In the context of the question of continuity vs discreteness (the meaning mentioned above), while the discrete picture would be that of a patchwork quilt, the continuous picture would be that of a single sheet with say, different textures. If that makes sense.

It doesn't make sense to me. It looks to me like you are just waving your hands and using vague intuitive pictures with no grounding in actual physics.

 

[vanhees71]

I'd simply define an observable to have discrete values if and only if the corresponding self-adjoint operator representing it has a discrete or partially discrete spectrum. Then there's at least no doubt what we are discussing about.

 

[Lynch101]

It doesn't make sense to me. It looks to me like you are just waving your hands and using vague intuitive pictures with no grounding in actual physics.

It is hand wavy, unfortunately because I am trying to illustrate an intuitive idea that I'm not sure is grounded in any physical theory.

Unfortunately, this is not the meaning that most discussions of "continuous vs. discrete" in a physics context are interested in. Most discussions (including, as far as I can tell, the ones you refer to in your OP) are interested in the other meaning.

I may have misinterpreted this, but it sounded like it was making the distinction between discrete parts (or chunks) as opposed to discrete values:

While almost all approaches to quantum gravity bring in a minimal length one way or the other, not all approaches do so by means of “discretization”—that is, by “chunking” space and time. In some theories of quantum gravity, the minimal length emerges from a “resolution limit,” without the need of discreteness. Think of studying samples with a microscope, for example. Magnify too much, and you encounter a resolution-limit beyond which images remain blurry. And if you zoom into a digital photo, you eventually see single pixels: further zooming will not reveal any more detail. In both cases there is a limit to resolution, but only in the latter case is it due to discretization.

Unfortunately, I don't think it is. See above.

The two pictures might be indistinguishable from each other, in any case, so it probably wouldn't be a useful way of looking at it, in terms of a physical theory. As I said, I thought that was what the above section of the article was getting at (and other articles I have read), but I may have misinterpreted them.

Thanks Peter.

 

[PeterDonis]

I may have misinterpreted this

You have.

 

[Lynch101]

You have.

Ah cool. Thank you.

The particular question I was getting at then, isn't one that is a consideration in physics?

EDIT: does M-theory suggest that the Universe is a single continuous membrane?

 

[PeterDonis]

The particular question I was getting at then, isn't one that is a consideration in physics?

It doesn't seem to be, no.

does M-theory suggest that the Universe is a single continuous membrane?

I have no idea what this means.

I think you are trying to understand physics the wrong way. Physics is not done in vague ordinary language. Physics is done in math. If you want to understand how a particular model in physics, whether it's M-theory or anything else, works, you have to understand the math. Throwing around vague ordinary language words is not a good approach, but that's what you are doing.

 

[Lynch101]

I think my misinterpretation may partly stem from articles like this one:

There are fundamental, indivisible, energy-carrying quanta that make up the matter and energy we know of. But quantized doesn't necessarily mean discrete; you can be quantum and continuous as well.
...
Discrete means that you can divide something up into a localized, distinct sections that are inherently separate from one another. The counterpart of discrete is continuous, where there are no such division.

Following the logic from atomic and subatomic theory, that all matter is made up of discrete/individual particles, this would lead to the idea that the Universe is made up of a multitude of discrete/individual particles. For simplicity sake, if we replace particles with fields, then we would have a Universe made up of a multitude of discrete/individual fields. It was probably my misinterpretation of the continuous vs discrete question with regard to spacetime that lead me to question whether the Universe (or all matter/fields in the Universe) is continuous or discrete - in the sense referred to in the linked article.EDIT: I just read your latest reply and this is probably case-in-point.

 

[PeterDonis]

I think my misinterpretation may partly stem from articles like this one:

I think you've been around PF long enough to know the response to this: don't try to learn physics from pop science articles. They do the same wrong thing you are doing: they throw around vague ordinary language instead of giving you the actual math. The rest of this post of yours is just more of the same.

 

[Lynch101]

I think you are trying to understand physics the wrong way. Physics is not done in vague ordinary language. Physics is done in math. If you want to understand how a particular model in physics, whether it's M-theory or anything else, works, you have to understand the math. Throwing around vague ordinary language words is not a good approach, but that's what you are doing.

I appreciate that point. I've made a start at re-learning mathematics but it'll be a very long time before I'm fully able to understand the mathematics necessary to understand physical theories. I guess I'm trying to get as good an understanding as I can, until I learn the mathematics. But I'm also interested in the philsophical consequences that our physical theories have and I'm keen to understand those too.

 

[PeterDonis]

I'm also interested in the philsophical consequences that our physical theories have

You need to understand the math to understand those too. Philosophers like to say that philosophy can be done using ordinary language, but that's not really true. When you actually dig into it, you find that philosophers are always redefining ordinary language words to have precise technical meanings, because they understand that precise technical meanings are required in order to do precise reasoning as they are trying to do. Physicists use math for precise reasoning because it's a much better tool for the job for any problem domain that it can be applied to. Philosophy tends to deal with problem domains for which it's much harder to apply math as a precise reasoning tool, so they have to make the best of what they have. But when philosophy deals with a problem domain like physics, where math can be applied, they should use it.

 

[Morbert]

What you would probably be most interested in is projects that try to understand QM in terms of a primitive ontology. E.g. https://arxiv.org/pdf/1406.0732.pdf . What you are looking for sounds a bit like a Bohmian unified field theory of some kind.

Most physicists emphasise observables and their expectation values over 'beables' and their ontic status.

 

[Lynch101]

You need to understand the math to understand those too. Philosophers like to say that philosophy can be done using ordinary language, but that's not really true. When you actually dig into it, you find that philosophers are always redefining ordinary language words to have precise technical meanings, because they understand that precise technical meanings are required in order to do precise reasoning as they are trying to do. Physicists use math for precise reasoning because it's a much better tool for the job for any problem domain that it can be applied to. Philosophy tends to deal with problem domains for which it's much harder to apply math as a precise reasoning tool, so they have to make the best of what they have. But when philosophy deals with a problem domain like physics, where math can be applied, they should use it.

I would 99% agree with this but I would say that a certain level of understanding can be arrived at without detailed knowledge of the mathematics. Although I could not work through a a problem pertaining to Bell's theorem, I have seen them worked through in videos and I can understand that there is a discrepancy between what classical physics would predict for the correlations of the measurements and what is actually observed.

I couldn't work through the mathematics pertaining to the EPR paper but I can understand that what the EPR paper was proposing was ruled out by experiment and that quantum systems do not necessarily have the properties of position and momentum prior to measurement.

Although I cannot calculate the predictions for a run of quantum experiments, I can understand that QM makes statistical predictions which thereby challenge the notion of determinism.

I can't verify the claims that people might make wrt to QM but it is possible to follow the logical consequences, assuming that what is being stated is correct. In the thread on anti-real interpretations for example, I was misinterpreting what was meant by "anti-real" interpretations of QM but through discussion there I was able to understand where the misinterpretation lay and correct it.

 

[Lynch101]

What you would probably be most interested in is projects that try to understand QM in terms of a primitive ontology. E.g. https://arxiv.org/pdf/1406.0732.pdf . What you are looking for sounds a bit like a Bohmian unified field theory of some kind.

Thanks Morbert. I'll check that out.

Most physicists emphasise observables and their expectation values over 'beables' and their ontic status.

I was familiar with the notion of observables, such as the energy values of electrons, taking discrete values as opposed to continuous values but some articles I read seemed to suggest that there might also be a question about whether spacetime has a discrete structure in the sense of being comprised of discrete particles, or is continuous.

 

[PeterDonis]

I would say that a certain level of understanding can be arrived at without detailed knowledge of the mathematics.

How do you know? You give a bunch of examples where you think you have arrived at a certain level of understanding; but how do you know you have? How could you possibly tell?

 

[Lynch101]

How do you know? You give a bunch of examples where you think you have arrived at a certain level of understanding; but how do you know you have? How could you possibly tell?

As I said, I can't verify the claims that others make but I can accept what they say in good faith and go from there. I get the impression that there are members on here who are very knowledgeable when it comes to physics and QM in particular. Now, I could be completely wrong about that and I have no way of actually verifying it, but on the balance of evidence that I can evaluate, that certainly seems to be the case.

If someone on here tells me that the EPR paper proposed a thought experiment which aimed to demonstrate that QM was incomplete because the position and momentum of entangled particles could be predicted by measuring the reciprocal for each particle, but that Bell came along and developed a theorem which showed that if this were true then experimental results would conform to a mathematical inequality but that actual experimental results violate this equality, then I can accept that at face value and follow the consequences of that.

If someone on here tells me that the statistical predictions of QM challenge the very notion that we live in a deterministic universe, I can accept that at face value and follow the consequences. Likewise, if someone tells me that there are deterministic interpretations of QM also.

If someone on here tells me that "anti-realist" interpretations of QM only say that the mathematical structure of QM doesn't correspond to an underlying ontology, as opposed to saying that there is no underlying ontological structure at all, then I can accept that at face value and follow the consequences.

If If someone on here tells me that , according to"anti-realist" interpretations of QM, the mathematics of QM only makes predictions about what outcomes will be observed on classical level devices, I don't need to be able to calculate what those predictions are to reason what the mathematics doesn't tell us (if it only predicts the outcomes of experiments).

 

[PeterDonis]

I can accept what they say in good faith and go from there.

I don't see how, since just accepting what they say doesn't help you understand what it actually means. Physics is not done in ordinary language. It's done in math. So if all you have is someone's ordinary language statement, and not the math, and you don't already know the math, you have no way of "going on from there", because you don't have a valid basis for further reasoning.

 

[Lynch101]

I don't see how, since just accepting what they say doesn't help you understand what it actually means. Physics is not done in ordinary language. It's done in math. So if all you have is someone's ordinary language statement, and not the math, and you don't already know the math, you have no way of "going on from there", because you don't have a valid basis for further reasoning.

It's a bit like understanding how a card trick works. If someone shows you how its done you can understand how it is done and how the apparent illusion is just that, an illusion. Simply seeing the card trick once, however, doesn't necessarily mean that you will be able to do the card trick yourself. That doesn't mean you can't understand how the card trick is done. It is similar with some of the issues in QM. I have seen the mathematics worked through, in explanations of Bell's inequality and I can understand how actual experimental observations deviate from what classical physics would predict. Just because I cannot work through problems independently, to calculate the correct predictions for a Bell test, that doesn't mean that I can't understand [some of] the consequences of QM.Without knowing the mathematics of other physical theories, it's possible to have an understanding of what determinism is,as it's a pretty intuitive idea. Simply knowing that QM makes indeterministic predictions and that these predictions are hugely successful means that I can understand that the idea that we live in a fundamentally deterministic universe is challenged by QM. Do I know, definitively, that QM makes statistical predictions for an ensemble of similarly prepared systems? No, I don't. But, there certainly seems to be an abundance of evidence which points to this fact. So, without even knowing that QM does actually make statistical predictions, I can understand that this thing which I have read a lot about, which people refer to as QM supposedly makes statistical predictions and this QM, if it is indeed a majorly successful scientific theory - something I have not verified - then it challenges the notion of determinism with which we are all familiar. The alternative, of course, is that I am being mislead and QM isn't this hugely successful theory.

We don't need to understand the mechanics of an engine to understand that pressing on the accelerator will make the car go faster, given certain other conditions. It's also possible to be shown how an engine works and have an understanding of it, without necessarily being able to assemble one.

 

[PeterDonis]

It's a bit like understanding how a card trick works.

You can pile on analogies all you want, it still isn't convincing me of your claim.

We don't need to understand the mechanics of an engine to understand that pressing on the accelerator will make the car go faster

But the whole point of physics is understanding how the car works. There is no analogy in physics to understanding how to drive but not understanding how the car works. That just means you don't understand the physics, period. Understanding that a particular physical theory makes accurate predictions is not understanding the physics. It's certainly better than not understanding that a particular physical theory makes accurate predictions, but it's still not understanding the physics.

Just because I cannot work through problems independently, to calculate the correct predictions for a Bell test, that doesn't mean that I can't understand [some of] the consequences of QM.

If you can't use the theory to make predictions, you don't understand it. You might understand that it makes good predictions, but you don't understand how, and the "how" is what you need to understand to understand the physics. You might understand what the physics says, because you've been told, but that's not the same as understanding the physics. Understanding the physics means you can use your knowledge to make correct predictions about new cases without anyone else telling you what the theory's predictions are for those cases.