Philosophy Professor on Physics? :s

[nonequilibrium]

In my philosophy course it says: (translating it into English, don't mind typo's)

"The school example of emergence is found in chemistry, namely water: the structure of H20 seems so elementary that one would expect to be able to derive its characteristics from the individual atoms that it is composed of. Yet nothing of it let's predict that once composed into H20, the characteristic 'fluid' should come up. It's an actual new feature that by the way only emerges once a critical amount of number of molecules is reached. So there is no reduction possible to the level of constituent particles: 'the whole is more than the sum of the parts'."

Isn't this very wrong? If you only had the particles (H's and O's) and were able to analyze the force fields around them, wouldn't you perfectly be able to predict that there would be something as a liquid as a result when forming the molecules and putting them together closely?

 

[ZapperZ]

At the risk of restarting the debate with Vanesh (grin), this is a common idea based on emergence versus reductionism.

If you do a search on this, or on Robert Laughlin's name, you'll find several discussion already on this issue. The most obvious would be to start with Laughlin's Nobel Lecture, where he essentially said the same thing in describing superconductivity, i.e. you can't derive it based on accounting for all the interactions at the single particle scale.

Zz.

 

[nonequilibrium]

Oh I didn't suspect this had already come up, my apologies.

I must say I'd be baffled if there's actually a case of emergence (bad choice of words? :p) in physics... I don't know anything substantial about superconductivity, so I'd have to take your word on it, but I'll be sure to read the other thread then.

But I must say, it just seems too improbable (of course not that that's any sort of valid argument)

EDIT: but anyway, the quote I cited is very wrong in its choice of example, still, no? :/

 

[ZapperZ]

I'm not so sure it is wrong.

Here, look at the first page of Laughlin's lecture. You'll see that he is saying almost the same thing:

http://nobelprize.org/nobel_prizes/physics/laureates/1998/laughlin-lecture.pdf

Zz.

 

[Academic]

Here is something along this vein that I read years ago. I honestly don't remember much about it, I am going to read it again today.
http://www.ctnsstars.org/conferences/papers/The%20physics%20of%20downward%20causation.pdf

 

[nonequilibrium]

Interesting articles! (Skimmed them so far)

But one thing I don't understand: even the qualitative Vanderwaalsgas equation alludes to something like a gas turning into a liquid, purely by adding the assumption that gas particles have size and a potential field to the ideal gas law. Now I think it would be fair to assume there are quantitative models possible and thus it wouldn't be emergent?

 

[alxm]

EDIT: but anyway, the quote I cited is very wrong in its choice of example, still, no? :/

It would seem to me to that that's the case. Without knowing almost any physics, and just a little mathematics, we can say the following:
- The chemical properties of an atom derive primarily from the properties of its electrons, including their motion/kinetic energy.
- Electrons repel each other.

So without much further knowledge, one can deduce that the motion/energy/etc of every electron is interdependent on that of every other electron. Regardless of your physical theory (classical mech or QM), it's a many-body problem. I.e. described by a non-linear differential equation. By the very definition of 'non-linear', the properties of any single electron cannot be correctly described without taking the other ones into account.

In other words: The chemical properties of an atom is literally not the sum of the properties of its individual electrons and nucleus. And by the same argument, it follows that the chemical properties of a molecule is not the sum of its constituent atoms. Since molecules also interact, again, the property of many molecules cannot be described as the sum of its constituents. In short, it seems quite naïve to assume that the bulk properties of interacting objects could be literally thought of of a sum-of-parts.

Should all non-linear behavior be described as 'emergent'?

It's true that non-linear systems are difficult to solve mathematically; They can exhibit chaotic behavior and be difficult to predict. But I think it seems philosophically 'weak' to claim that A cannot be reduced to B, merely because our current state of mathematics and computational power do not allow us to accurately predict A in terms of B.

You cannot describe the motion of the planets accurately in terms of planets moving individually. (However it's a decent approximation) But with Newton's laws (and now, GR) we can still solve the equations numerically and predict this motion to very high accuracy. So is their motion 'emergent behavior' or is it reducible to relativistic mechanics?

 

[nonequilibrium]

Well that is definitely not what I would call emergent.

In the case of the atoms: if you have a physical theory explaining the fields around the atoms and then can theoretically make your differential equation that characterizes your distribution when you mentally place all the particles where they'll be in reality, then it's already out of the realm of emergency, no? The solution is already there (albeit just hard to solve, or only numerically, but at least the solution exists in the mathematic equation you wrote down, it exists and we know it exists), it's not as if nature alone can predict what is going to happen when it actually happens, which is what I would call emergent.

If emergent is actually defined as a more practical thing, I'd be far less concerned with the matter...

 

[alxm]

Well, doing quantum chemistry, I can tell you there's fairly little dispute that chemistry can be reduced to quantum mechanics, at least in principle. (Something your experimental chemist will be quick to point out) Given enough computing power we could exactly predict every chemical property of everything to a sufficient degree of accuracy.

Thing is, exact quantum mechanics is almost "too powerful" a microscope. If you ask why substance A is more stable than substance B, then shrugging your shoulders and saying "That's what solving the Schrödinger equation resulted in" isn't a satisfactory answer to a chemist! So, even though you have more accurate methods, approximate models are still necessary to provide a conceptual framework to rationalize the more accurate results.

What I'd (somewhat fuzzily) define as 'emergent' phenomena are those which are so far removed from their underlying causes, that they can be regarded as more or less distinct phenomena. For instance, intermolecular forces are quantum-mechanical in their origin, but once they are known, most of the properties of a gas of that substance can be derived independently using only classical physics. Evolution and natural selection stands out as an even better example of this, as the fundamental ideas are completely independent of the exact nature of how traits are passed on, and how the selection occurs.

In other words, I'd say an emergent phenomenon is not one which can't be derived from its basic constituents, it's a phenomenon doesn't need to be.

 

[cesiumfrog]

Well that is definitely not what I would call emergent.

Isn't emergence the idea that there exist phenomena foreign from the behavior of the atomic constituents in isolation, not that the phenomena can not be determined by modelling large numbers of atomic constituents interacting? Otherwise (at least presuming we adopt the reductionist approach inherent to physics) nothing would be emergent?

Edit: agree with alxm.

 

[Q_Goest]

Hi mr. vodka,

If emergent is actually defined as a more practical thing, I'd be far less concerned with the matter...

One thing I’ve noticed is that many people use the term “emergent” without having a good definition of what that means. Laughlin for example, uses the term but fails to define it. His definition of emergent is mostly created by example. Protein folding is one he uses to help his audience ‘define’ what emergence means. I think that’s the same thing your philosophy professor is doing; defining by example.

There are some good definitions of emergence such as “weak” and by contrast, “strong” emergence as defined for example by Bedau who is often quoted in a number of papers. Bedau is only in favor of weak emergence. I don’t think Laughlin however, would agree with this definition. I think the definition of emergence has to address two key issues, causation and separability.

The first (causation) regards how parts of a physical system might be influenced by other parts of the system. Obviously, a point on wheel rolling down a hill for example (per RW Sperry, Nobel Laureate) travels through a rather unique path dictated by it’s location on the wheel and influences of the environment on the wheel. But this kind of emergence isn’t particularly interesting IMHO. The point on the wheel is simply following straightforward, classical physics. Emmeche et al. however provide a decent set of definitions regarding downward causation of which they define three types - strong, medium and weak. The definitions however really only boil down to 2 IMO, strong and weak. Either something within the system is overtly influenced by the system it is in, or that something is only influenced by local causes. And that’s where I think the second issue picks up.

The second issue of emergence regards separability. One can define “nonlinear systems” as being “emergent” because of the (imagined) mathematical restrictions on a system or because they are in some way, physically not separable.. Alwyn Scott was a big proponent of nonlinear systems being emergent because they are inseparable (mathematically?). That’s the only criteria he uses as far as I can tell. Scott would lump rivers and tornadoes as being emergent along with folding proteins for example. He has no interest in separating systems that are classical in nature or are fundamentally described using quantum mechanics. In the paper provided by Davies (link above) for example (part of a book called “Re-Emergence of Emergence”), Davies talks about Benard cells which have by some people, been described as emergent systems. Davies ridicules the idea of Benard cells being emergent, pointing out that the molecules of liquid making up the Benard cells are only being influenced by the push and pull of the other local molecules. One might argue this is a 3 body problem, so all molecules are somehow influenced by every other, but clearly this line of thinking fails when it one considers that a force field (gravitational or electric) is only the summation of individual fields.

Another philosopher who picks up on a nice definition of emergence is Paul Humphreys who suggests that the key feature of emergence is that a unified whole cannot be represented in terms of separate causal effects. He uses the term “fusion” of properties to indicate that the properties of the whole are not in some way a summation of the properties of the parts. This definition would follow the “example” used by your philosophy professor. The properties of water such as surface tension, are not properties of the individual parts (ie: the attraction between the H20 molecules). This definition also leaves a bit to your imagination I think.

Humphreys was quoted by Kronz and Tiehen in a paper that suggests that quantum mechanics is inseparable but leaves open the possibility of classical systems potentially having inseparable properties. Kronz suggests that there are nonseparable states in quantum mechanics but, “Because the direct sum is used in classical mechanics to define the states of a composite system in terms of its components, rather than the tensor product operation as in quantum mechanics, there are no nonseparable states in classical mechanics.” Here’s where I think it gets interesting. I don’t think classical mechanical systems, even those that are nonlinear systems as described by Scott, can create emergent phenomena. Note the term “phenomena” here. I also think we need to understand that emergence regards what occurs, as opposed to merely what properties can be measured.

Conclusion I have is that emergence really needs to be properly defined before you go hunting for it. Your definition should touch on the points of 1) downward causation and 2) separability. Feel free to ask for papers I’ve quoted.

 

[cesiumfrog]

The properties of water such as surface tension, are not properties of the individual parts (ie: the attraction between the H20 molecules).

No? But surely if we knew the attraction between a type of molecules, we can predict the surface tension of a liquid of that type. Either I'm still misunderstanding your stronger definition, or I think the class you propose labeling by it is empty.

 

[alxm]

The properties of water such as surface tension, are not properties of the individual parts (ie: the attraction between the H20 molecules). This definition also leaves a bit to your imagination I think.

Obviously there's a difference between bulk properties and the properties of individual molecules. But as Cesiumfrog alludes to, a full knowledge of the properties of a single water molecule (e.g. in this case its geometry, dipole moment, polarizabilities), is enough to tell you everything about its bulk behavior. This is not even a theoretical argument, since such modeling is actually done in practice. And since we're on the topic, it's worth mentioning it's used for protein folding as well.

Humphreys was quoted by Kronz and Tiehen in a paper that suggests that quantum mechanics is inseparable but leaves open the possibility of classical systems potentially having inseparable properties.

Having looked into the paper, what they're talking about there is primarily entanglement. And yes, by comparison quantum mechanics has "inseparable states" in that respect, where classical mechanics does not. But, they also point out that classical mechanics has inseparable Hamiltonians. (i.e. nonlinear systems)

I don't feel the difference here is that significant. In the quantum case, you cannot know the state of two entangled things, A and B independently, in the classical case, there's no such restriction. But the thing is, you're not generally interested in the situation where you know the state, you're interested in knowing what happens next. If they interact, the fact that you know the state of both A and B doesn't mean you can determine both states independently of each other at any other time.

Also, looking at that paper, there are some minor errors on QC which I'll skip, but I really can't let this pass:

For example (one of numerous examples), no one has a clue as to how to use quantum mechanics to explain the different isomers (different molecular structure that correspond to the same chemical formula) of C6H6 (Woolley 1991). At best, this is a semi-classical theory, meaning that a good bit of classical structure of the nuclei [sic!] (bond lengths, bond angles, dihedral angles of rotation about single bonds) must be put in before quantum structure (of energy levels and orbitals) comes out

It's simply not accurate to say that QC cannot predict structure. It's true that isomers have the same molecular Hamiltonian. (within the BO-approximation framework, one can view them as different valleys on the same 'potential energy landscape') It's true that QM does not directly supply us with any convenient means to find these structures. But you can still evaluate whether a structure is stable, and arrive at that structure from a rough guess, by minimization. So you could conceivably simply find isomers from simple brute-force. Or better, use a rough approximate method to find candidates and then do a full QC minimization.

But naturally it's much much more convenient to simply apply basic chemistry to guess plausible structures, and then use QC methods to refine and verify these guesses. I don't see how that makes it 'semi-classical'. I don't even know what 'semi-classical' is supposed to mean in this context. There is no 'classical' theory of chemistry! All modern theory of chemistry (beyond the octet rule taught to high school students) is based on quantum mechanics. Prior to that, there was (for instance) no understanding of why methane is tetrahedral.

 

[nonequilibrium]

Thank you all three for your replies.

Q_Goest: I'm not sure if I find a solid difference between downward causation and seperability (they're both about how one particle is influenced by its environement, right?). But I'll try to give a clear definition of what I see as emergent.
For this let me first quote a line out of cesiumfrog's post:
"Otherwise (at least presuming we adopt the reductionist approach inherent to physics) nothing would be emergent?"
And that's exactly it, the main characteristic of an emergent phenomenon, for me, would be a refutation of the reductionist view. That is why I take the existence of emergent phenomenona very seriously, because if they are possible, that would mean the core of the reductionist view (which surely 99% or more of all physicists believe in as self-evident) would be wrong. More concrete: An emergent phenomenon is a characteristic of something which even in principle cannot be deduced from purely analyzing the parts it is made of (their constitutions, their force fields, etc...). Separability is not an issue, as when trying to deduce the property, you can theoretically place all the particles together and work out how they should react according to your theory (again, in principle, of course).

I hope that is a satisfactory definition of how I see it?

Now while skimming over one of the earlier papers linked to (cf. ZapperZ), Laughlin talked about how he found himself cruel that every year he gave some of his students as an assignment to deduce the properties of superconductivity from its constituent parts: this made him evil, because according to him superconductivity is a purely emergent phenomenon which cannot be deduced. Maybe I'm paraphrasing him wrong? This seems to be a VERY BIG claim. (Maybe alxm knows what this could refer to?)

This is a very interesting discussion.

 

[ZapperZ]

To address the point being made that people such as Laughlin used the word "emergent" but without clearly defining it, this is clearly false. If people think that the reference that I gave earlier is the ONLY place where this is discussed, that would be a severe error. There have been plenty. Laughlin even wrote a whole book on this topic (read "A Different Universe: Reinventing Physics from the Bottom Down").

I can give many other references to this. Below are some of them:

http://www.pnas.org/cgi/reprint/97/1/28.pdf
http://www.pnas.org/cgi/reprint/97/1/32.pdf
http://arXiv.org/abs/hep-th/0210162

But really, the impetus for all of this is Phil Anderson's "More is Different" article in Science from many years ago, which I would say is a good starting point to read. One might also want to read a more recent study on this very concept:

http://arxiv.org/abs/0809.0151

Zz.

 

[Q_Goest]

Emergence can be defined in different ways. For what it’s worth, bulk properties such as temperature, surface tension and many more are often viewed as emergent properties. But perhaps the use of Laughlin’s example of superconductivity is less controversial. Regardless, I’d like to go over the definition of emergence, especially strong emergence and strong downward causation.

If I had to define emergence for Laughlin, I’d say he’s looking to say that an emergent phenomenon is one that can’t be predicted, even in principal, from the underlying processes. That’s not an uncommon definition (Chalmers for example, “Strong and Weak Emergence”) but it’s insufficient. The concepts of strong and weak emergence have to be considered when coming up with a definition for emergence.

Here's a definition for strong emergence (and strong downward causation) by Emmeche:

… a given entity or process on a given level may causally inflict changes or effects on entities or processes on a lower level. This idea requires that the levels in question are sharply distinguished and automonous. …
The theory of strong downward causation [a hallmark of strong emergence] is thus based on a constitutive irreductionism [such that] higher level entities do not (only) consist of lower level entities; they possesses a substantial existence qualitatively different from the lower level entities.

I’d like to add to that the concept of physical laws and how they are influenced by strong emergence including “strong downward causation”. I can see two possibilities:
1. The physical laws at a lower level are superseded by physical laws at a higher level.
2. The physical laws at a lower level are augmented by additional physical laws at a higher level.

To pursue this, we need to go on a tangent regarding separability for a moment. If there is a phenomena governed by some physical laws at a given level, we either find that these physical laws ALWAYS apply, regardless of what system we find the occurrence in, or we find that these physical laws ONLY apply for specific systems. For example, we might apply known physical laws and expect that physical state A changes to physical state B due to causal actions A’. However, we may find that physical state A instead changes to physical state C due to causal actions A’. If we find such a phenomenon to occur (A -> B or A-> C) depending on the system it is in, then we have a system that is not separable. This inseparable feature of the system can then be correlated with what physically occurs and we can say that we have identified a case of strong downward causation and thus strong emergence. But remember, that the system has to be inseparable in the sense that what occurs depends on what system a given ‘part of a system’ is found in.

There are numerous, specific examples of this concept of strong downward causation. Here’s one I’d like to touch on. The paper by Davies listed above talks about Benard cells. Davies writes:

Thus we are told that in the Benard instability, where fluids spontaneously form convection cells, the molecules organize themselves into an elaborate and orderly pattern of flow, which may extend over macroscopic dimensions, even though individual molecules merely push and pull on their near neighbours (see, for example, Coveney & Highfield, 1995). [also Bishop, 2008] This carries the hint that there is a sort global choreographer, an emergent demon, marshalling the molecules into a coherent, cooperative dance, the better to fulfill the global project of convective flow. Naturally this is absurd. The onset of convection certainly represents novel emergent behaviour, but the normal inter-molecular forces are not in competition with, or over-ridden by, novel global forces. The global system ‘harnesses’ the local forces, but at no stage is there a need for an extra type of force to act on an individual molecule to make it comply with a ‘convective master plan.’

I’d agree with Davies to the degree that any phenomena that can be described using classical mechanics can’t support strongly emergent phenomena; only weakly emergent phenomena are supported by classical mechanics. I think Davies might actually go along with this, but certainly it seems Kronz would. Classical systems are separable so by definition, strong emergence isn’t possible – what occurs in and can be described using classical mechanics will not vary depending on what system you find the occurrence in. Quantum mechanical systems however, can be inseparable, so those systems may support strong downward causation. That said I don’t really know enough about QM to make that judgment. I’d love to hear a bit more from you folks on what bulk properties might be considered strongly emergent or not, or any other phenomenon you think might be considered strongly emergent (other than consciousness, let's leave that out for now).

 

[alxm]

I’d agree with Davies to the degree that any phenomena that can be described using classical mechanics can’t support strongly emergent phenomena; only weakly emergent phenomena are supported by classical mechanics. I think Davies might actually go along with this, but certainly it seems Kronz would. Classical systems are separable so by definition, strong emergence isn’t possible – what occurs in and can be described using classical mechanics will not vary depending on what system you find the occurrence in. Quantum mechanical systems however, can be inseparable, so those systems may support strong downward causation.

Well, I'm still not convinced emergent phenomena, as defined, actually exist in any form. I just can't see any meaningful fundamental distinction between quantum and classical mechanics with respect to emergent phenomena. Yes, QM and CM are fundamentally different. QM has entangled states etc, and particles can 'lose their individuality'.

But in QM, a system of two entangled particles is a single, inseparable system. In other words, it's not meaningful to consider it the same system as the same two particles in a non-entangled state. This is counterintuitive (hence the EPR paradox!), but if you simply accept it at face value, I don't see how this is so much different from classically different systems. In classical mechanics, it would be silly to assume that two balls connected by a string would act the same way as two balls and a string which were not connected.Even though they have the same components, their behavior is entirely different. They are different systems. So, telling someone to "explains superconductivity", in terms of individual electrons - despite that in a SC situation the electrons do not act as independent particles, is to me not unlike asking someone to explain the action of the balls-on-a-string in terms of independent balls!

Since the formalism of QM is mathematically more difficult than classical mechanics, It's easy to get the idea QM behavior is more complex than classical behavior. But this isn't necessarily the case. To take an example, the Helium atom (the simplest quantum many-body problem of significance). It's not analytically soluble, but it's far from intractable, and was solved (1929) to a high degree of precision even without computers. On the other hand, if you build a semi-classical model of Helium, 'colinear Helium' (with electron-nucleus-electron on a rotating axis) It exhibits rich and complicated dynamics which are strongly chaotic. It requires math and computation on a whole different level. (for which reason it only got studied properly starting in the 1990's, despite that the ideas involved came about just after the Bohr model)

So the unique properties of quantum mechanics do not necessarily lead to less predictable or more chaotic systems - it can be the opposite as well. Seems worth noting since some seem to imply chaos is an 'emergent' phenomenon. The Benard instability is of course a wonderful example of nonlinear dynamics. But I can't for the life of me see how it's not predictable from the underlying processes. (Just take a look at the Navier-Stokes equations)

From a physics perspective, such 'emergence' seems impossible almost by definition. If you cannot predict the behavior of a system from its constituents, then something's wrong with your model. The examples against it seem naïve to me (á la balls-on-a-string). Basically nothing is separable. Even classically, practically everything interacts with everything else to some extent. Some things are separable, if you consider abstract isolated systems, or 'ideal' cases, etc. We do this because it's conceptually and mathematically easier to deal with discrete noninteracting entities. But it's just an approximation. And whenever you consider an ensemble of objects, you have to assess whether that's a good approximation or not, rather than blindly assuming the components will act separably.

 

[Q_Goest]

Hi alxm. That’s a great lead into another point about emergence. What you’re arguing for is called “weak emergence”. Bedau is one of the best authors on this topic IMO. You can read one of his articles here:
http://people.reed.edu/~mab/publications/papers/principia.pdf

Also, Emmeche et al whom I’ve quoted have described “medium” and “weak” downward causation that would generally go along with what you’ve described. Strong downward causation is generally not accepted from what I’ve seen. That’s not to say strong downward causation in all its forms is not accepted. It’s hard to tell if Laughlin for example, proposes strong downward causation at or below the mesoscopic level, but it seems to me he’d probably suggest that:
2. The physical laws at a lower level are augmented by additional physical laws at a higher level.

Don’t quote me on that, I’m not absolutely sure and he doesn’t seem to define what he means exactly by emergence in his article “The Middle Way”. I haven’t read his book but maybe Zz could shed some light on what he’s written there.

Note also that Kronz is arguing in favor of some kind of emergence like this for quantum mechanical systems by saying those systems are not separable. More on that in a moment.

In classical mechanics, it would be silly to assume that two balls connected by a string would act the same way as two balls and a string which were not connected.Even though they have the same components, their behavior is entirely different. They are different systems.

This is perfect. I’m going to talk a bit about classical mechanics here, so this will not apply to QM which I’ll explain in a moment... Consider two balls on a string twirling around in space (or in a gravitational field, it doesn’t matter). Now consider cutting the string and applying the same force as that created by the other ball. Apply this force with any means you’d like. Put a magnet on the end and apply a magnetic field that duplicates the force on the string for example. You can do this with any classical system. One can, in principal, apply the same boundary conditions to a (CM) system without actually putting that system into the larger system. When you apply the force on the string that’s attached to the ball, the ball undergoes the same exact motion as it had when it was attached to the other ball. People do this all the time using controlled experiments. They also use this basic technique when using 3D numerical modeling methods such as FEA, CFD or multiphysics software programs that look at finite elements. If we apply duplicate boundary conditions on a classical system, we can duplicate what happens to that system. Any such classical system is then seen to be separable, and as such, can only be found to exhibit weakly emergent behavior. It CAN’T exhibit strongly emergent behavior.

Now the question comes in, can we perform this same operation on any quantum mechanical system? From the definition of separable that I’ve used for classical systems, the answer I think is NO; quantum mechanical systems are not separable. That isn’t to say they necessarily exhibit strongly emergent behavior. We haven’t shown that yet. But it IS to say that they are not separable in the sense that we can’t duplicate boundary conditions on parts of the system and expect the same behavior from the system. Take for example water molecules. Let’ cut off one of the hydrogen atoms and leave the OH. There’s no way to duplicate the boundary conditions on the OH such that it exhibits the same properties as the H2O molecule. It is not physically separable in the same way a CM system is. This is how I'd interpret Humphrey's notion of "fusion" that Kronz is writing about. That may seem like a fine point or one that isn’t pertinent, but the issue of separability is (IMHO) a fundamental issue. Once we find a system that isn’t separable (by applying identical boundary conditions), there is a chance that system will exhibit strong emergence and strong downward causation.

Now go back to protein folding or superconductivity. Could either of these phenomena possibly exhibit one of the two possible signs of strong emergence that I provided earlier? Why aren’t these phenomena predictable as described by Laughlin? Consider even more complex systems such as DNA. Can any such molecular system exhibit either of the following?
1. The physical laws at a lower level are superseded by physical laws at a higher level.
2. The physical laws at a lower level are augmented by additional physical laws at a higher level.
Note here that the higher level would be at the molecular level and the lower level would be at the individual particle level.