Why is that unlikely? After all, today we can understand that there are certain substances in the brain that are responsible for these things; for example, falling in love is the secretion of a certain hormone (I think). And in addition—what exactly, in your view, exists in a person besides matter?

That is a categorical confusion, though a very common one. Substances are not related to the issue in any way. The substances may perhaps be causes of mental phenomena, but my question is what those phenomena themselves are, not who causes them. Substances are not endowed with consciousness, desire, thought, and so on. Falling in love is not the secretion of a hormone. The secretion may perhaps cause the feeling of being in love.

I understand, and regarding the second question I asked: what exactly exists in a person besides matter? How can one define the spiritual part (?) that exists in a person other than as “non-physical”?

Do you know how to define physical/material? If not, then there is no difference. If so, then the definition of the spiritual is whatever does not meet the definition of the material. There is no problem with that definition.

One can define physical—say, something perceived by one of the senses. How does the Rabbi define physical?

Is an electron physical? It is not perceived by any sense. It has indirect effects, but so does the soul. I do not have a clear-cut definition, but perhaps something that obeys the laws of physics (and even that is somewhat circular, because one can ask how the laws of physics are themselves defined).

That is not similar. An electron is not perceived by the senses because of technical limitations, but it has mass, and therefore one could feel its weight or see it if our senses were sharp enough for that.

Yes, and it is also round. So what? If we had suitable senses, we would perceive souls too.
And how do you know it would be perceived? Maybe there are no electrons at all and you are imagining them?

So maybe the difference should be phrased like this: ultimately, the building blocks of matter (an electron or any other structure—I do not think that matters for our discussion here) take up space. That is to say, once there are many building blocks in one place and matter is formed at the macro level, say a cup, then it takes up space and you cannot put an infinite amount of it in one place. Regarding consciousness/experience/emotion/memory, we do not think that is true. You can put an infinite number of experiences into our brain and it does not create any density; or, going back to mass—a person with experiences does not weigh more than a person without experiences.
I hope the Rabbi will not give up on the discussion, because it is important to me to arrive at a definition, and then it will be possible to discuss whether there really is something in the world that is not material.

I gave up on it long ago. Everything has already been answered here, and the question of definition does not add or subtract anything.

So what is the meaning of the sentence, “Simply because I experience things that are unlikely to be material,” which the Rabbi wrote above, if there is no clear definition of matter?

I already answered everything. You talk about matter without defining it, and I am not allowed to talk about spirit without defining it?
I am done.