Why are they called "old kamma"?

Chris has given the answer the way I expected. However, I thought I look into it from a different angle. You can look at this in a Dependent Origination model as well. Vinnana paccay Namarupa : Due to old Kamma (Sankhara) vinnana create the Namarupa of this life. (say fetus) Then the fetus grows into six senses base. (as Chris noted) With the aid of six sens base (old Kamma), we create new Kamma.(ie: Namarupa Paccaya Vinnana) In a nutshell the whole Dependent Origination explains how the old Kamma become new Kamma.

People are born from their karma: that is what dependent origination teaches anyway, the abhidhamma version at least. Similarly, traditions that incorporate the 'alayavijnana' see every moment of our life as a ripening of a seed generated by past karma.

If you struggle to see how that can make sense in a scientific world view, then why not think of it as the eye that you see with, rather than some dead man's eyes, being generated by past habits and so kamma.

I think I've found one possible answer, so I will answer my own question, but I will not accept it.

The sutta quoted in the question states that the eyes, ears, nose, tongue, body and mind are old kamma, but it doesn't say WHOSE old kamma it is.

The sutta below answers that question.

So, the eyes, ears, nose, tongue, body and mind definitely arise due to old kamma, as stated in ChrisW's answer. After all, they cannot arise spontaneously - they definitely arise due to old kamma. But we cannot ask WHOSE old kamma it is. It is dependently originated - with ignorance as the condition.

This is in line with sabbe dhamma anatta (all phenomena is not self).

From SN 12.17:

“How is it, Master Gotama: is suffering created by oneself?”

“Not so, Kassapa,” the Blessed One said.

“Then, Master Gotama, is suffering created by another?”

“Not so, Kassapa,” the Blessed One said.

“How is it then, Master Gotama: is suffering created both by oneself and by another?”

“Not so, Kassapa,” the Blessed One said.

“Then, Master Gotama, has suffering arisen fortuitously, being created neither by oneself nor by another?”

“Not so, Kassapa,” the Blessed One said.

“How is it then, Master Gotama: is there no suffering?”

“It is not that there is no suffering, Kassapa; there is suffering.”

“Then is it that Master Gotama does not know and see suffering?”

“It is not that I do not know and see suffering, Kassapa. I know suffering, I see suffering.”

“Whether you are asked: ‘How is it, Master Gotama: is suffering created by oneself?’ or ‘Is it created by another?’ or ‘Is it created by both?’ or ‘Is it created by neither?’ in each case you say: ‘Not so, Kassapa.’ When you are asked: ‘How is it then, Master Gotama: is there no suffering?’ you say: ‘It is not that there is no suffering, Kassapa; there is suffering.’ When asked: ‘Then is it that Master Gotama does not know and see suffering?’ you say: ‘It is not that I do not know and see suffering, Kassapa. I know suffering, I see suffering.’ Venerable sir, let the Blessed One explain suffering to me. Let the Blessed One teach me about suffering.” “Kassapa, if one thinks, ‘The one who acts is the same as the one who experiences the result,’ then one asserts with reference to one existing from the beginning: ‘Suffering is created by oneself.’ When one asserts thus, this amounts to eternalism. But, Kassapa, if one thinks, ‘The one who acts is one, the one who experiences the result is another,’ then one asserts with reference to one stricken by feeling: ‘Suffering is created by another.’ When one asserts thus, this amounts to annihilationism. Without veering towards either of these extremes, the Tathagata teaches the Dhamma by the middle: ‘With ignorance as condition, volitional formations come to be; with volitional formations as condition, consciousness…. Such is the origin of this whole mass of suffering. But with the remainderless fading away and cessation of ignorance comes cessation of volitional formations; with the cessation of volitional formations, cessation of consciousness…. Such is the cessation of this whole mass of suffering.’”

Suppose I have a bullet mark on my shoulder, what would we call it ? A result of old kamma. Something which happened in the past but has now ceased happening. The wound has healed. In the past the bullet injury was the source of my suffering but it no more can be called a source of suffering. Similarly when looking at eye we say it is due to an old kamma. In the past the eye had a beginning..generated and fashioned by volition ,as something to be felt. Now the eye has settled to shape and size and has a defined function. It is no longer evolving like it was when it came into existence. Same applies to all the other senses. All the six senses are old kammas.

New kamma are the deeds which are still affecting our evolution(whether we will be rich or poor , man or woman , animal or human in the next rebirth).It is done by body, speech and mind.
(This is my interpretation of the sutta mentioned above.)

Why are these called old kamma (purāṇakammā)? Is it because of rebirth?

No. It appears to be the very opposite. The sutta appears to be dismissing the ordinary common view about 'rebirth', similar to AN 3.61, which dismisses the common view that happiness and suffering are due former kamma (pubbekata).

The suttas SN 35.136 & SN 12.37 literally say this kaya (group of aggregates) or these six sense organs are to be viewed as old kamma. These suttas do not say this kaya or sense organs are the result of old kamma. The group & sense organs themselves are old kamma.

Ordinarily, it is believed old kamma are actions a person personally does in the past. These suttas are actually ending this idea. These suttas are saying this present moment body & sense organs are to be viewed as old kamma and the noble practitioner should not trace further back to the past.

The above is particularly clear in SN 12.37, when it is said: "This kaya is not yours". Here, the ordinary common doctrine of personal old kamma is abolished.

In summary, SN 35.136 says three things:

1. The present moment sense organs are the oldest kamma, which is or can be something constructed & willed and which should be felt. This description is completely impersonal, namely, the sense organs are constructed from elements and from mother & father (per AN 9.15), the sense organs can be (wisely) subjected to the will if necessary and are to be felt without generating craving & self-view.

2. When these present moment sense organs are not merely felt, then new kamma is generated by craving, becoming & self-view via body, speech & mind; which is called 'new kamma'.

3. When the noble eightfold path is practised, no new kamma is created. Therefore, there is the cessation of generating or willing new kamma.

In summary, SN 35.136 & SN 12.37 appear to reject ordinary common ideas of old kamma from 'rebirth' & 'past lives'. It appears SN 35.136 & SN 12.37 are a supramundane (lokuttara) doctrine of 'old kamma'.