As far as I understand it, according to the theory of momentariness (Kshana- Bhanga, or kṣaṇa) the cause does not exist in the effect. A perishes before B arises. It arises from nothing. Even if we take the Zero energy universe model, shunyata is seen as emptiness of emptiness, and the Zero energy universe is more akin to Nirguna brahman than Shunyata. Nothing arises from nothing.

Nothing arises from Nothing is a wrong premise. All conditional conformations are impermanent but they do not lead to Nothing. They lead to suffering.

My question is -- even if we say that the cause creates the effect, with what material does it do so? For example, if A gives rise to B, where did B come from? Is it the same substance/thing as A in a different form? If not, how did B arise from A? Even if A exists after or until B arises, how can a new B arise from A (unless B is A in a different form like water turning into vapor or unless A divides its substance/material into different parts)?

Why are you clinging to A? Why do you think A gives rise to B ? It is possible that there are multiple causes which give rise to B , A being one of them. B need not be a form of A. Just as fire is produced by wood , air etc...Fire is not wood , nor it is air. Water changes in vapor but vapor is not water. All things change. All conformations are impermanent. Things come together to produce an effect but the effect is a changed state. It might be similar to cause or causes but it is also different in many ways.

Things cannot arise ex nihilo can they? If we assume that things are created anew, that is actually ex nihilo (and is also a problem that many Theists have with their God creating things from nothing)

Things can not arise ex nihilio... Every thing has a past.

I think that materialism makes more sense than the theory of momentariness for this reason? The theory of atoms perishing and then giving birth to new atoms makes no sense. Even if Atoms didn't perish until new atoms were created, this would still be impossible as new things cannot arise substantially or materially as there is only transmutation/transformation in nature.in materialism that would be eternal subatomic components.

Have you seen atoms ? Do you believe the theory of atoms is correct ? It is better if we stop this discussion and focus on suffering , origin of suffering , cessation of suffering and path leading to cessation of suffering.

Do you mean the Theravadin Abhidhamma's theory of momentariness?

That is not related to Madhyamaka's Shunyata (where all things are empty of substance or essence, including emptiness itself) or the nature of matter, or the universe. It however, relates to Theravadin Shunyata (i.e. all phenomena is empty of a self).

The Abhidhamma's theory of momentariness is applied only to the mind and mental processes. I don't fully understand it, but I see it as a quantization or discretization of mental processes into thought-moments or cittas.

This actually sounds very similar to how a computer CPU runs based on clock cycles, and its processes are quantized or discretized into processing of individual instructions (so-called instruction cycles), each taking a number of clock cycles. Each instruction has to be fetched, decoded, executed, and completed, before the next instruction can be fetched.

It is not far fetched to say that the Abhidhamma's model of mind and body is similar to the model of software and hardware in a computer. Both do not require a self or soul to function or run. And exactly, this is the point of Theravadin Shunyata i.e. sabbe dhamma anatta - all phenomena is not self.

Apparently, this is supported by scientific research. Please see "Consciousness Arises In Discrete Time Slices, Suggests Study" and "A time slice theory of consciousness suggests we’re not continually aware of our surroundings".

I quote below from The Abhidhamma in Practice by N.K.G. Mendis:

The Cittas

Awareness is the process of cittas experiencing objects. For a citta to arise it must have an object (aaramma.na). The object may be a color, sound, smell, taste, something tangible, or a mental object. These are the six external objects. Strictly speaking a mental object can be an internal phenomenon, such as a feeling, a thought, or an idea, but as forming the objective sphere of experience they are all classed as external. Corresponding to these external objects there are six internal sense faculties, called "doors" since they are the portals through which the objects enter the field of cognition. These are the eye, ear, nose, tongue, body and mind. Each of the five physical sense faculties can receive only its appropriate object; the mind door, however, can receive both its own proper mental objects as well as the objects of the five physical senses. When a door receives its object, there arises a corresponding state of consciousness, such as eye-consciousness, ear-consciousness, etc. The union of the object, the door or sense faculty, and the consciousness is called "contact" (phassa). There can be no awareness without contact. For contact to occur all three components must be present — object, door, and consciousness. If one is missing there will be no contact. The process of the arising of consciousness and the subsequent train of events is analyzed in detail in the Abhidhamma. A study of this analysis will show that only "bare phenomena" are taking place and that there is no "self" involved in this process. This is the no-self characteristic of existence.

And also:

Mind in its passive and active forms

The mind occurs in both passive and active modes. The passive gives way to the active when a stimulus is received through one of the sense doors. The passive state of mind is called bhava"nga, cuti, or paa.tisandhi, according to the occasion.

Bhava"nga. The bhava"nga citta, mentioned earlier, is the primary form of mind. It flows from conception to death except when interrupted by a stimulus through one of the sense doors. When a stimulus enters, consciousness becomes active, launching into a thought process (citta viithi). Thought processes have been analyzed in great detail in the Abhidhamma.

A complete thought process, occurring through the physical sense doors, is made up of seventeen thought moments (citta kha.na). These are:

1. A bhava"nga that flows by in a passive state when one of the five physical sense organs comes in contact with its object (atiita bhava"nga).
2. A bhava"nga that vibrates for one thought moment (bhava"nga calana).
3. A bhava"nga that cuts off the flow (bhava"nga upaccheda).
4. A citta that turns towards the object through the sense door that has been stimulated (pañcadvaara-vajjana).
5. The appropriate sense consciousness; in the case of the eye, for example, eye consciousness (cakkhu viññaa.na).
6. Next a thought moment — the sampa.ticchana citta — which has the function of receiving the object.
7. When the object has been received another thought moment, called the santiirana citta, arises, performing the function of investigating the object.
8. The act (kamma) itself, especially if it was a weighty one.

9 to 15. The object having been determined, the most important stage from an ethical standpoint follows. This stage, called javana, consists of seven consecutive thought moments all having an identical nature. It is at this stage that good or evil is done, depending on whether the cittas have wholesome or unwholesome roots. Therefore, these javana thought moments have roots and also produce new kamma.

16 and 17. Following the seventh javana the registering stage occurs, composed of two thought moments called tadaalambane. When the second registering citta has perished, the bhava"nga follows, flowing on until interrupted by another thought process.

These thought moments follow one another in extremely rapid succession; each depends on the previous one and all share the same object. There is no self or soul directing this process. The process occurs so rapidly that mindfulness has to be alert and brisk to recognize at least the determining thought moment — the vottapana — so that one can govern the javana thought moments by wholesome volition.

When the mind-door receives a mind-object, the sequence of events is a little different from that occurring through the physical senses. The mind-door-adverting citta is the same type of citta as the determining moment — the votthapana — that arises in a sensory process. This mind-door-adverting thought moment can cognize an object previously seen, heard, smelt, tasted or touched, thus making memories possible. Since the mind-object here has already been received and investigated, these functions need not be performed again and the mind-door-adverting thought moment gives way immediately to the javanas. These are, again, of great ethical significance. For example, unpleasant words previously heard can suddenly come to mind and, unless proper mindfulness (sammaa sati) is practiced, call up javana cittas rooted in hatred, i.e., unwholesome kamma.

This is essentially the question: "Does X exist?"; "Does X not exist?" which are questions the Buddha puts aside as not being helpful towards achieving the goal. Whether or not X exists, there is pain (dukkha). This is the problem that is dealt with in the Buddha's system.

The idea of 'cause', as 'hetu' and 'nidana' and 'paccaya' and a half dozen other terms are translated (including 'ahara' food!), is an error. "Hetu" the most reasonable candidate for 'cause' means 'driving force' (something like the teamster's 'giddy-up!'). Cause remains a mystery that is not dealt with as it is irrelevant to the solution of the problem of pain.

What we get in the Paticca Samuppada (and other formulas dealing with the origin and ending of things) is not a description of cause and effect (no matter how often it is translated that way -- it makes no sense as a cause-and-effect description) it is a description of causal association (aka: Bhk. Thanissaro: requisite condition; aka: proximate cause, economic cause).

Causal association can be seen.

That is the point.

We deal in this system with what we can see and know for ourselves; what we can do something about ourselves.

"It cannot exist without it" does not equal "cause."

We cannot see the 'cause' for the appearance of aging and death from birth, but we can see that without birth there would be no aging and death.

So without needing to deal with 'cause', we can know for certain that the result, whatever the 'cause' may be, can be eliminated by eliminating birth. And so on for the other causal associations.

Please read this book, the commentary addresses this exact very topic in great details:

The Rice Seedling Sutra: Buddha's Teachings on Dependent Arising

Briefly, 1) phenomena arise from gradual continuous transformation and combination of previous phenomena. 2) The act of establishing an identity (spatial/temporal/qualitative boundary) of the phenomenon and likewise delineating/identifying phenomena that served as the sources/causes of this one is an act of semiosis performed post-factum by the interpreting observer.

Related references:

Hierarchy Theory

Peirce and Biosemiotics: A Guess at the Riddle of Life