I don't know if this has been described in science, but I doubt it.

The closest description I can find is this:

The following article in Wired last year discusses the dependency between entities at a macro level based on quantum entanglement and the arrow of time:

In the new story of the arrow of time, it is the loss of information through quantum entanglement, rather than a subjective lack of human knowledge, that drives a (hot) cup of coffee into equilibrium with the surrounding room. The room eventually equilibrates with the outside environment, and the environment drifts even more slowly toward equilibrium with the rest of the universe. The giants of 19th century thermodynamics viewed this process as a gradual dispersal of energy that increases the overall entropy, or disorder, of the universe. Today, Lloyd, Popescu and others in their field see the arrow of time differently. In their view, information becomes increasingly diffuse, but it never disappears completely. So, they assert, although entropy increases locally, the overall entropy of the universe stays constant at zero.

“The universe as a whole is in a pure state,” Lloyd said. “But individual pieces of it, because they are entangled with the rest of the universe, are in mixtures.”

The above statement that "information becomes increasingly diffuse, but it never disappears completely" resonates with Buddha's middle way teachings for e.g. the discussion of what happens when a person dies. He does not have a permanent soul that transmigrates, according to the Buddha. The newly born person is also not the same person as the one that died, yet not completely independent. However, the "information" is not completely lost and it reappears to a certain extent in the newly born person. This is a middle path between eternalism and annihilationism. There is a description of this in the Acela Sutta and some discussion in an answer to another question. Of course, this part is only my conjecture and rebirth is not described by science.

So, the article from Wired discusses that there is no eternalism (no independent particle and no independent cup of hot coffee), yet there is also no annihilationism ("information becomes increasingly diffuse, but it never disappears completely"). It also says that everything is interdependent (“The universe as a whole is in a pure state but individual pieces of it, because they are entangled with the rest of the universe, are in mixtures"). More detailed quotes from the Wired article in another answer.

Yeah I too doubt that there's any science of rebirth in the sense of a flame lighting another torch.

I would actually find it quite depressing if there were. It's a much better metaphor on the gradualism of enlightenment IMHO.

I wouldn't be that surprised if there something on a sort of inheriting of characteristics, that isn't explicable in our normal world view - causal processes that we haven't yet identified in science.

Still minds are unaffected by mental events so maybe their effects go elsewhere; maybe this even works however the mediator is behaving. I mean It seems obvious to me that habits can have physical or real manifestations that have effects even without them creating any actual dispositions in the actor so the question is just: can meditation change our habits without changing our dispositions. If so then that's a real change that leaves us completely unchanged - so must change someone else.

And if meditators can have effects on others independent of action, then why not everyone. This is only some kind of crazy mind reading if it is deliberate or rule based.

I believe we are coming closer to an answer to this question Daly. The double slit experiment shows us that are mere perceptions actually determine the property of matter. Thus we find our tie between the physical world and the world of consciousness. But we also see evidence of this in the current multiple universe theory where in all probabilities exists around us and the universe we encounter is the one that follows our choices and Karma.

I believe these choices and the resultant Karma may actually have a physical component in the quantum world and this may be the source of consternation regarding rebirth. What happens to the chain of events created by our choices or probabilities we have affected if our body passes way before we may be affected by them? According to the Hindus and some Buddhists this is the source of rebirth. That is if we die with a karmic imbalance or resultant then it must somehow be played out in another life.

I am in the process of studying The Vedas and the upanishads as well as the dhammapada and comparing them two modern scientific theories regarding consciousness. I believe at this point we may find a scientific basis to support the original philosophies of Eastern mysticism from 4000 years ago.

"The concept of Kamma implies that information is stored in the mind (not the brain) and after the being is dead, this mind (or this data "storage") goes on and carries with it the current position of all accumulated Kamma from many previous life."

Correct. Here you are explaining the concept of the soul existing and travelling from body to a new body after death.

"Where is the information stored if there is no physical "hardware"?"

Nowhere.

How could that be?

"Information" is just a mere concept.

"Store" is just a mere concept.

"Soul" is just a mere concept.

EVERYTHING is just a dream ... an echo ... not truth.

Information is never ever stored. It's just a dream ... an echo ... not truth.

"How does this information flows?"

It does not flow.

Again.

EVERYTHING is just a dream ... an echo ... not truth.

"How a new being receives it and change its body accordingly?"

By not knowing the truth a new being receives it and changes its body accordingly.

What truth?

EVERYTHING is just a dream ... an echo ... not truth.

By not knowing the truth, volition arises and after it, everything else arises ... the mind, body and universe.

"Imagine a Kamma-Vipaka of a disease for a new born or not having a member"

Yes.

And who/what is the cause of the Kamma-Vipaka of a disease of a new born?

Not knowing the truth, a being is born in such a future destiny striken by disease after being born.

Not knowing the truth leads to suffering.

Very Good Question. Lord Buddha gives very simple example with the Deep explanation in one of the Abhidamma 7 books named "Pattana"

He asked few questions taking mango tree. If we plant a mango seed taking from the [hypothetically we say "A" mango tree] "A" mango tree. One mango we called it "B" ripen and fallen down. Once this ripen mango started decaying and the seed met with necessary requirements like Soil, Water, and Sun shine, Air to generate a new plant and it gives us "B Mango Tree"

Now A tree gives us "B" Seed and it gives us "B" Mango tree. But Is A = B? No Does B has A's qualities and similarities? Yes How it happend? Genetically A Seed carries its qualities and similarities which now B owes.

Though the fruit has fallen and though the fruit may decay the germ or the energy it has to produce another tree does not die. Once it comes into contact with the earth being nurtured by the four primary Elements – Pathavi (the earth element) Apo (the watery element) Tejo (the heat element) Vàyo (the wind element) it produces another tree of the same kind namely another mango tree.

In this manner action and re-action cause and effect death and birth, prevail and continue to prevail. It is like the tree producing the fruit and the fruit in turn producing the tree and continue to prevail as an unbroken process. We can only see it happening in the present context. But we cannot trace back to the beginning of this process nor can we visualize the end before the attainment. However much we try we would never find the first mango tree nor can we find the last mango tree but we can see how a tree produces the fruit and how the fruit produces another tree.

The separation of the fruit is like the death. Its contact with the earth is birth. There is no interval as such between the tree and the fruit and the fruit and tree. It continues to grow. Thus from the day the fruit was born by the tree and up to the producing of another tree, similarly within the human mind there is an energy to produce another being.

Similarly human being may die but the energy to be reborn does not die completely. It grows gradually. But it faces to the momentary decay and death, as (uppàda, tithi, bhaïga) genetic, static and dissolving. This energy is craving and ignorance and the resultant Karmas or action, which will continue to accumulate till one gets rid of all defilements with the rise of wisdom and the resultant cessation of craving and kamma which will put an end to rebirth ultimately reach Nibbàna.

This process can be thus elaborated :- Ignorance and craving-attachment-kamma-rebirth Wisdom-no craving-detachment-no kamma-no rebirth. This existence of beings is thus determined. Kammàvipàkà vattanti Vipakàkamma sambhavo Tasmà punabbhavo hoti Evaü loko pavattati (Visuddhi Magga)

Because of action cause and craving a being is born. After birth too he accumulates kamma craving and cause. Therefore he is reborn. Thus the Saüsàra or the continuity of life prevails. It is called the Kamma Niyama and it also related to the Citta Niyamaya.

Khandhàna¤ca patipàtã Dhatu ayatanàna ca Abbocchinnaü vattamànaü Saüsàroti pavuccati.

Saüsàra Round of Rebirth, is the unbroken chain of the five-fold Khandha-combination, or aggregates which constantly are changing from moment to moment follow continuously one upon the other through inconceivable periods of time.

Although there is a division of time into past, present and future everybody is living now. We do not live in the past or in the future. We cannot exactly say it is the present. But it moves forward as in the case of the second arm of a watch or as in case of figures that take place in an electronic wrist watch.

Thus what goes to the future is present what goes to the past is also the present. When it goes forward the mind and matter grow. When it goes backwards the mind and matter decay. So growth actually means decay. Thus from the time of birth the mind and matter decay. It is a dual process.

Yathà idaü Nàma Råpaü Paccayato bhavissati Evantãtepi nàgate Abhavittha bhavissati. ( Paññhàna)

Just as now mind and matter exist with cause, they existed even in the past, in future also they will exist.

What the dual process, one can understand by this example is someone travels from Colombo to Anuradhapura by train. When he travels by train he can see the train is moving fast forward and the trees and buildings are moving backward. The same thing happen to our mind and matter.

This is known as Anicca or impermanency. Because of the nature of impermanency there is suffering because of the presence of a mind. Where there is only matter there is no suffering because of the absence of a mind. So where there is a mind and matter there is impermanence and suffering and nothing else. There is no permanent entity in the form of soul or spirit. What prevails is Anàtma (Anicca, Dukkha Anatta).

The Buddha has also mentioned the fact that whatever kamma that we accumulate in this life are being carried over to the next.

Ya¤ca karoti kàyena Vàcàya uda cetasà Tamhi tassa sakaü hoti Ta¤ca àdàya gacchati. Ta¤cassa anugaühoti Chàyàva anapàyinã (Kosala Sanyutha)

Whatever wholesome or unwholesome (kusala, akusala) Kammas that one accumulates by the way of mind speech or action in this life are being carried over to the next.

Eso nidhã sunihito Ajeyya anugàmiko Pahàya gamanãyesu Etaü àdàya gacchati. (Nidhi Kandha Sutta)

Whatever good or bad kammas that you have accumulated, like a treasure, cannot be taken away from you. It follows you and is being carried by you to the next life. How do we carry over these good or bad kammas?

Let us now examine this and the results we derive when we carry over those Kammas to the next life. Let us take the example of the mango tree to elaborate this as well.

If the mango tree in our compound is of “Gira” variety when a fruit that is detached from the branch falls to the ground and produces another mango tree also would be of the “Gira” variety and the fruit that is born by this tree will have the same qualities of the mango fruit that originally fell from the tree. It will also have the same taste and the same shape. This shows that the taste qualities and shape are being carried forward.

Similarly beings also carry forward whatever good or bad kamma that one accumulates in this life and this kamma will determine the nature of the next life.

Suvaõõatà sussuratà Susanthàõa susråpatà âdipacca parivàrà Sabba metena labbhati – (same Sutta)

Golden complexion, softness, correct features, pleasant qualities, leadership and retinue are derived from good kammas.

Mànusikà ca sampattã Deva loke ca yàrati Yàca nibbàõa sampatti Sabba metena labbhati – (same Sutta)

Not only this all comforts and pleasures of the human world and all comforts and pleasures of the world of Devas, ultimately Nibbàna will be achieved by such meritorious actions or kusala kammas which are being carried forward from life to life.

Yàdisaü vapate bãjaü Tàtisaü harate phalaü Kalyaõakàrã kalyàõaü Pàpakàrã ca pàpakaü – (Saüyutta Nikàya)

As you saw, so shall you reap. Good action promotes good results. Bad action promotes bad results.

The mango fruit fell under the same tree. But the ground is not fertile and as such it does not grow properly. It may be a fruitless tree and that depends on the place, where the fruit has fallen.

Someone takes away this mango fruit and plants it in his garden where the place is fertile. He adds compost and waters it. It grows properly. It bears fertile mango fruit. The fertility or infertility depends on the place.

Even so according to the good and bad kamma we will be reborn in hell or heaven. The happiness and unhappiness depend on the place where he was born.

This is happening due to 24 Conditional Relationships called "Pattana"

THE TWENTY FOUR MODES OF CONDITIONAL RELATIONS

1. Hetu-paccayo - root condition
2. Arammana-paccayo - object condition
3. Adhipati-paccayo - predominance condition
4. Anantara-paccayo - proximity condition
5. Samanantara-paccayo - contiguity condition
6. Sahajata-paccayo - co-nascence condition
7. Arammana-paccayo - mutuality condition
8. Nissaya-paccayo - support condition
9. Upanissaya-paccayo - decisive support condition
10. Purejata-paccayo - pre-nascence condition
11. Pacchajata-paccayo - post-nascence condition
12. Asevana-paccayo - repetition condition
13. Kamma-paccayo - karma condition
14. Vipaka-paccayo - karma result condition
15. Ahara-paccayo - nutriment condition
16. Indriya-paccayo - faculty condition
17. Jhana-paccayo - jhàna condition
18. Magga-paccayo - path condition
19. Sampayutta-paccayo - association condition
20. Vippayutta-paccayo - dissociation condition
21. Atthi-paccayo - presence condition
22. Natthi-paccayo - absence condition
23. Vigata-paccayo - separation condition
24. Avigata-paccayo - non-separation condition.

These are twenty-four conditional relations factors that sansara keeps on going transferring the past kamma to the present and making the future kamma. Below find very important links:

1. The First one take the basic knowledge about how these conditions working CONDITIONAL RELATIONS (PATTHANA)

2. You can find all Abhidhamma 7 Books in pdf download format. Thripitaka English

Advise not to read this without knowing the Abhidamma Basics. Without knowing Universal factors it is very difficult to understand this Conditional Relations.

To Learn Basics with the circle of samsara read this site linked pages one by one to understand the Universal Factors.

3. Abhidharma Basics - Loving Kindness

May Triple Gem Bless you!!!

This is a very good question that has been answered particularly poorly in the past. The concept of karma in the early Buddhist texts does indeed imply persistence of an effect long after the condition is ceases - in our terms storage of a memory somewhere or other. And dependent arising forbids any effect to outlive the cessation of its conditions.

In my informal (as yet unpublished) writing on this I have referred to this problem as the problem of Action at a Temporal Distance. I discovered this problem independently, while study the writings of Prof Collett Cox on Sarvāstivāda Abhidharma texts. However I subsequently discovered that Nāgārjuna has also complained about this in his Mūlamadhyamakakārikā:

tiṣṭhaty ā pākakālāc cet karma tan nityatām iyāt /
niruddhaṃ cen niruddhaṃ sat kiṃ phalaṃ janayiṣyati // MMK 17.6 //

If the action remains until the time of maturation, then it would be eternal
If it ceases, being ceased, how does it produce a fruit? [My translation]

Nāgārjuna's response was to argue that all the components: agent, action, maturation, fruit, sufferer were all "like illusions" - ie. because of śūnyatā these entities have only relative and not ultimate existence. Karma only operates at the conventional level.

Now the Theravādins chose to respond to this one way: They proposed that each short lived citta that arose as a vipāka also became a kamma that was a condition for another identical citta. This introduced a number of other problems, chief amongst was how to account for moments when there was no apparent citta - such as deep sleep, experiences of cessation (nirodhasamāpatti), and (of course) death. To solve this they invented the bhavaṅgacitta to bridge the gap. The Theravādin view was only relevant in Sri Lanka and South East Asia.

The Vaibhāṣikas went about dealing the problem in an entirely different way. They reasoned that if a vipāka could be experienced in the future then the cause (hetu) must still exist as a condition in the future. And similarly for past karmas that we experience in the present. This earned them the nickname Sarvāstivādins because they believed that dharma always (sarva) exist (asti). The Sarvāstivādin view dominated North India and in China.

The Sautrāntikas opted for a similar approach in the form of a metaphor. Karma, they argued, was like a seed. The rice seed grows into a rice plant, but there is no direct connection from one to the other. This is an argument that karma is a "natural" process. Of course such metaphors are superficially pleasing, but explain nothing.

The Sautrāntika version was taken up by Vasubandhu and proposed as the solution to Action at a Temporal Distance in his Abhidharmakośa and it's autocommentary the Abhidharmakośabhāṣya (incidentally this is also the only extant source for the Sautrāntika view). And this became the Yogācāra view as well. Yogācāra exegetes did two things. They invented the alāyavijñāna as the repository of karma "seeds" and they reified the metaphor taking these images as facts. This version of karma overtook Nāgārjuna and became the standard Mahāyāna version.

Links above are to a series of essays I wrote on this problem that will also appear in my forthcoming book on Karma & rebirth.

Now unfortunately for us moderns, none of these proposed solutions really solves the problem of Action at a Temporal Distance. Karma cannot work with dependent arising. The ancients actually knew about this and we have their records of trying to fix the problem, but innovation simply stopped at some point and most of the theories died with the decline of Buddhism in India.

Discussion of this major problem in Buddhist doctrine simply ceased. The Theravādins retreated into formalism - an uncritical acceptance of whatever Buddhaghosa said and are leading the world in the production of apologetics for karma and rebirth. Similarly in the rest of the world the Mainstream became Mahāyāna and the Yogācāra view was taken on uncritically. The spirit of inquiry and problem solving simply went out of Buddhism and has yet to resurface in any major way. Regrettably not even academics seem to engage critically with Buddhist doctrine - they are in love with Buddhism it seems and reluctant to critique it. So while we get ever more refined views of history we see very little in the way of disagreement with the views in Buddhist texts - despite the fact that Buddhists of an earlier age are on record and thinking many of them demonstrably wrong.

It's misleading to suggest that the concept of karma 'implies information stored in the mind'. It's like saying that information about water is stored in the wave, which puts things out of order.

The concept of karma points at the inherent circular, self-similar, and replicate nature of the living world: a kind of homeostatic flow where things come and go, rise and fall, expand and contract, always folding back on themselves. It is cause and effect beyond the simple, linear, momentary actions we normally think of. If one wave passes and another forms, it isn't because the first wave 'carried its information' across and reformed itself; it's because the water cycled back and remade the wave that passed. If there's something like a reincarnation after death, it isn't that the mind (the self) carried itself over; it's that the world folded back on itself to make that mind (that self) again.

I could make that more scientific, obviously, but I prefer to leave it at the general principle. Not much sense in overthinking it...

"To a large extent, abhidharma thought is a systematization of the doctrine of karma"

-- Hirakawa akira

So, in this sense, an Abidhamma itself is your "detailed description" [of a particular kamma theory].

The concept of Kamma implies that information is stored in the mind

No, it does not! Information and storage are concepts. Not realities! The issue here is, we make the assumption that for causes to give an effect in the future, something needs to persist in the interim. When you commit a Kamma, the action is done and finished then and there. There's nothing stored. To give an analogy, take a stick and hold it at one end with your left hand and tap at the other end with your right. Your left hand will feel the vibration. But did any molecule travel from right to left? No! It's just that when the molecules at the place you tapped vibrate, the adjacent molecules start vibrating and then the ones next to them and so on. Then we make a concept out of it and call it a wave. But there's no wave in reality! The first molecule vibrated and stopped. It didn't go anywhere. Similarly, Kamma is also a concept given to describe a certain causes and effect process. There's nothing going from this life to the next or this moment to the next.