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In all religions that ever existed, there is a soul and a God - two intangible things. From physics we know that there is no difference between a particle without the electrical charge, mass and energy and a non-existing particle - neither of them can affect anything in the universe. And supposing the chemical and physical properties of brain don't somehow bring the molecules to life, it isn't a physical thing that could affect anything.

How can res cogitans and res extensa interact?

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    Through the pineal gland, obvs – Joseph Weissman Sep 14 '14 at 15:20
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    All religions? Clearly you haven't studied enough religions. – Dave Sep 14 '14 at 16:42
  • @Ransack Minimally God - that is even the best definition of religion, we don't need soul for this. – Probably Sep 14 '14 at 16:45
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    Joseph Weissman actually gave you the answer - Descartes' answer to that problem. And the answer is (as you pointed out) a joke. But Descartes really never came up with a better answer. It is a tough problem to his theory. One might say, he never solved it. – Einer Sep 14 '14 at 16:52
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    This appears to be the thorny question of the relationship between the observer and the observed, a question so problematic for modern physics. – Nick R Sep 14 '14 at 21:36
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In all religions what ever existed there are soul and God

Hinduism doesn't have 'God'; it does have Brahman, which is sometimes identified with it; since in this sense it is a monotheistic aspect of Hinduism, as for example exemplified in the Upanishads; but this doesn't mean the same thing. For example the Catholic doctrine of the Trinity as a description of God is not found in Hinduism.

Nor is the Hindu concept of soul atma similar; in Advaita Vedanta (non-dualism), an Indian philosophical school, the atma is identical with Brahman; in Dvaita Vedanta distinguishes, at least partly between the two.

Still, in a broad sense you are right; one can distinguish notions in most religions that correspond in some sense with the distinction that you make.

From physics we know that there is no difference between particle without eletrical charge, gravity, mass and energy and non-existing particle - both of them can affect the universe as well - they can not.

Sure: In the physical sciences; one aspect of truth( and a large part of it) is instrumental; we know a particle exists when it has an effect; and by depriving them of charges - electric or gravitational; so that they do not interact with anything; it can't be distinguished from a particle that is not there at all.

What you receive better: a universe in which God has no ability to affect anything or universe in which anything does not make sense, because something without any physical properties can not influence anything.

This appears to be a personal declaration disguised as a rhetorical question

How can interact res cogitans and res extensa?

There are quite a number of different theories. Descarte wrote in Passions of the Soul, his last book that:

We need to recognize that the soul is really joined to the whole body, and that we cannot properly say that it exists in any one part of the body to the exclusion of the others.

For the body is a unity which is in a sense indivisible because of the arrangement of its organs, these being so related to one another that the removal of any one of them renders the whole body defective.

And the soul is of such a nature that it has no relation to extension, or to the dimensions or other properties of the matter of which the body is composed: it is related solely to the whole assemblage of the body's organs.

This is obvious from our inability to conceive of a half or a third of a soul, or of the extension which a soul occupies. Nor does the soul become any smaller if we cut off some part of the body, but it becomes completely separate from the body when we break up the assemblage of the body's organs”

This conclusion (if not the argument) was already in St Augustine, in his book On the Trinity:

In each body the whole soul is in the whole body, and whole in each part of it

For Descarte the soul is not the principle of life; but the principle of thought. Taking into all his other account, at least twelve other different accounts of his solution to the mind-body problem has been put forward.

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For monists, such as Plotinus or Spinoza, they are but different versions of the same essence. Plotinus for example would hold the res extensa to be "gross spirit", and the res cogitans to be "rarefied matter". In other words, both would spiritual/material, just on a spectrum. For Spinoza too, they are simply different descriptions of the same thing: God. They are the two accessible substances (for humans), but Spinoza does not mean to imply that they are the only ones.

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