I thought the mantra of quantum physics was "anything that can happen, does happen". So the short answer is yes. Few physical processes are irreversible. Consider the 'photoneutrino process' then imagine situations in which time can be reversed. I'm not surprised I'm the first to answer. This is an important question but if you really want an answer you might have to battle the tedious men in black. Good luck!

Ales, there are no specialists discussing this on the internet and you have been badly misinformed. The cross-section for scattering tells you next to nothing about the annihilation rate. In the case of annihilation it is necessary to know the ambient neutrino concentration (which is irrelevant for scattering). Also, one would like to know whether the neutrinos are degenerate or not. Most other civilisations will appreciate that things get very interesting for gravitationally condensed nonrelativistic neutrinos, but those that have poor survival prospects will not - just as it should be.

 Thanks all ^_^ , And Robin I liked your answers . 

Rawaa, I don't know what led you to consider neutrino annihilation but it turns out this is one of the most important questions someone could ask. There are physically realistic situations in which neutrinos entering a planet will not emerge the other side: they are likely to annihilate on the way through the core, transferring their energy to the outermost electron of an iron atom. An oceanic planet need only consume about one gram of neutrinos per second to provide a very comfortable, efficient and long-term habitat for aquatic life. Calculations find this to be viable if neutrinos collect on galactic scales. Neutrino cross-sections have to be tiny (think a light year of lead) in order to prevent the orbital decay of planets on relevant timescales (1025 years or so). You will find here three novel explanations for the long-standing mystery of extraterrestrial silence, a plausible explanation for the dark matter of galaxy clusters and a mechanism for the decay of dark energy to dense neutrino haloes in about 60 billion years. There are three main articles describing the physics and the implications, listed below.

Article Planetary Heating by Neutrinos: Long-Term Habitats for Aquat...

Article A cosmological hypothesis potentially resolving the mystery ...

Preprint A Non-anthropic Solution to the Cosmological Constant Problem

Thanks a lot Robin ,  what led me to consider neutrino annihilation that I asked my proff. In the class : can we transfer the neutrino to photon ? Then he said : I don't know, can you search for it and bring us the results . I agreed  . And then I asked my proff in physics and he said that any particle/ antiparticle could yield photons and that what we call annihilation . In the end I put this question here and you answered me .I will keep searching for this . ^_^ and  I will read your articals which I planned to read them before you put them here .what made me surprise that your specialization isn't physics ^_^ . I'm interested in physics too .

Rawaa, thanks for explaining your interest. There's quite an old paper I cite which has considered the annihilation of a pair of neutrinos in vacuum. It's impossible for this to yield a single photon due to the need for momentum conservation. It turns out that the production of three photons is the most likely possibility, rare as it is. Of course, it needs to be rare, otherwise energy that could sustain aquatic life would be squandered in empty space. As it happens, this consideration places an important constraint on the neutrino mass and has a big influence over the duration for which the universe can efficiently sustain life. By the way, nobody is born a specialist, and I am still resisting the pressure to be labelled one - so I take your comment as a compliment! Perhaps I should point out that this work began by simultaneously pondering the Fermi paradox, what we know of dark matter and the fact that much of the fine-tuning of physics has no credible anthropic explanation. I suspect the same conclusions could have been reached 60-70 years ago if the academic community had more respect for multidisciplinary science rather than its obsessive focus on reductionism and specialism.

Ales, I have no idea what you think I'm suggesting but your criticism is very wide of the mark. Why not familiarise yourself with the articles before making these seemingly random comments? The internal temperatures of the planets would be thermally regulated at levels that, to a good approximation, compensate for variations in planet size/mass. A temperature gradient would exist between the core of the planet and space. The power deposited by the neutrinos would be rapidly converted into heat which gradually percolates from the core to the surface, ultimately escaping into space in the form of infrared radiation - biologically spent energy. The thermal flux through the ice-capped oceans would be remarkably consistent across a wide range of planet masses, a fraction of a Watt per square metre. Complex megafauna, I suspect, are unlikely to evolve in these dark, anoxic habitats. That is not a drawback of the model or the cosmic arrangement, but a strength. To understand why you might need to spend a lot of time thinking about the ethics of reproduction and the impressive safeguards the universe has implemented against incompetent colonists.

I really liked your answer Robin because I agree you in not being a labelled one . And I want to know a bout every thing but people around me always said  that I must focus on one subject to be in the " right way " and I hate that . Thanks Robin ^_^ 

Robin : How could they are incompetent colonists while the scientists reproduce them for their good characteristics ?

note: that's not meaning I'm with reproduction ^_^ 

Rawaa, I was trying to explain that these oceanic planets, whose formation proceeds until stellar activity ceases (each supernova can make almost a million of these planets) will in time be very tranquil (non-volcanic) but rather sterile worlds. There would be a need for advanced civilisations to populate them using skills we do not possess. Notice that there are no human communities living in the oceans yet, we lack the necessary sophistication to adapt ourselves to watery environments. We don't even have a base on the Moon. You may ask why would anyone bother adapting now to life in an ocean if these water worlds take tens of billions of years to form? Well, we would be free to go wherever we like, explore all 3 dimensions of space, there would be no need for expensive accommodation, food would be freely available and there would be no need to work. The galaxies where aquatic life could thrive well into the distant future are anticipated to possess around 1020 oceanic planets, so there is a great need to ensure that colonisation standards are not compromised. This consideration leads to two of the three novel resolutions of the Fermi paradox. The third has to do with the welfare of lifeforms of differing ethical and technological advancement.

Okay , I got it ^_^ . Robin didn't you think that the answer of the fermi paradox is parallel unevirse theory or they are related to each other ? 

Rawaa, I'm aware that the strange belief in parallel universes is fashionable these days but I don't see what it has to do with science. It was mainly concocted to try to downplay the evidence that the universe is more conducive to life than our own existence can account for, it is just a symptom of an irrational belief system now pervading academic science. If you're asking what I used to think about the Fermi paradox before taking a close look at neutrinos I suppose I was leaning towards the alarming view that intelligent life is rare on galactic scales, probably due to some combination of it actually being rarer than we once expected and due to things like exhaustion of resources, political stupidity and military holocaust. It is still plausible I think that only, say, one in a million technological civilisations evades the risk of self-destruction. The model is silent on this but can predict the rarity of stable civilisations to an accuracy of about a factor of two.

Thanks Robin ^_^  we won't find as beautiful as earth far away from political wars and the rivers of blood  that flow all over it ... 

Dear Rawaa,

to me it seems you have not yet got a proper answer. Let me try to do the job.

For neutrinos to oscillate into anti-neutrinos, both would have to be "the same" particle. How can this be when we call them differently? The answer is that, experimentally, we only observe "left-handed" neutrinos (it's not the perfect name, but left-handed refers to a certain quantum property called chirality), which are those which e.g. are produced in orbital electron capture of atoms or in beta^+ decays, and "right-handed" anti-neutrinos, which are emitted e.g. in beta^- decays.

The reason for this distinction is that the weak interaction only couples to left-handed particles and right-handed anti-particles (that's not 100% precise, but for neutrinos it's perfectly correct). Thus, if "right-handed neutrinos" or "left-handed anti-neutrinos" existed, we would not know about it at least by the experiments we have been able to do so far.

Thus, at the moment, we don't know whether neutrinos are identical to their anti-particles (in which case they would be called "Majorana fermions") or not (in which case they would be called "Dirac fermions"). Up to now, we have observed elementary DIrac fermions in Nature (e.g. the electron has a distinct anti-particle, the positron) and we have also observed non-elementary ("quasi-particle") Majorana fermion-like states in condensed matter systems (in graphene to be precise). However, for neutrinos we don't know at the moment.

What would in any case be needed for neutrinos to be Majorana is "lepton number violation". We are actually searching for reactions which violate lepton number (the most promising being "neutrinoless double beta decay"), but we have found none so far.

From the theory side, we have indications that lepton number is violated, but we don't know for sure without experimental proof:

-We know that neutrinos are massive, and from the theory side, there are many more possibilities for this to happen if the neutrinos are Majorana fermions.

-We know that the Standard Model (SM) itself does *not* conserve lepton number. This is often stated incorrectly in textbooks, because at the perturbative level, the SM does conserve lepton number: it is not possible to write down any SM-Feynman diagram that violates lepton number. However, on the non-perturbative level there are certain types of reactions called "spahlerons" which are known to violate lepton number.

Both these arguments are good motivations to make an experiment to look for lepton number violation, but both do not tell us for sure.

And now we are finally ready to answer your question: *if* neutrinos are identical to anti-neutrinos, *then* we could have oscillations between neutrinos and anti-neutrinos. In fact, such an oscillation is part of one particular Feynman diagram that would transmit neutrinoless double beta decay. This oscillation would be hugely suppressed by the small neutrino mass, making it quite hard to observe experimentally, but in principle it would exist. In fact, even the very first paper on neutrino oscillations by Bruno Pontecorvo studied neutrino/anti-neutrino oscillation - at that time we did not know of more than one neutrino. But we have not found these oscillations experimentally (maybe: yet).

I hope this answers your question.

Best regards,

Alexander

 Thanks Alexander ^_^ 

Alexander, your rather lengthy post addresses the possibility of neutrino/antinuetrino oscillation but fails to say whether this might have some connection to the mutual annihilation of neutrinos.

Rawaa, nonrelativistic neutrinos can be trapped by a gravitational potential. It is not appropriate to label the individual neutrinos of a galactic halo as being either left-handed or right-handed, they can be either depending on the frame of reference. This is a simple consequence of neutrinos travelling slower than light (definitely not faster!) due to their non-zero mass. The neutrinos produced by most astrophysical processes are, in contrast, ultrarelativistic and so their behaviour is more easily described.

Dear Robin,

if neutrinos are identical to their antiparticles, they could annihilate with each other. While I did indeed not say that in my post, this was also not part of Rawaa's original question.

The problem with your statement about changing the frame of reference is that you are referring to "helicity", while the coupling of the weak interaction is based on "chirality". Unfortunately, both these quantities are put into categories called "left-handed" and "right-handed", which is a stupid ambiguity of technical terms and causes a lot of confusion.

Thus, while the weak interaction does only couple to left-handed neutrinos and right-handed anti-neutrinos, in terms of chirality, this does not forbid to "overtake" a neutrino by changing the frame of reference - in which case its *helicity* would change.

Best regards,

Alexander

So, I think you both talk close to each other but to be honest Robin answers convinced me more . Alexander I will keep thinking of your answers and I will see what I get . 

Thanks all and I loved this discussion  maybe I will be an active part of it in the future but now I have a lot of studying waiting me ^_^ . 

Robin : I told my Proff. the result and he knew that I will get these answers . ^_^ 

Alexander,

The photoneutrino process produces a neutrino/antineutrino pair. Its time reversal would allow a neutrino and an antineutrino to annihilate, so there is no strict necessity for neutrinos to be Majorana fermions. I take your point about the chirality/helicity difference, but you did not specify the circumstances in which the neutrinos were produced.

Just a short comment (maybe rather a question): a neutrino-antineutrino annihilation would yield photons correspondind to the neutrino mass, so at very low energy. Would we even notice such a weak signature? Or, asking an experimentalist's question: what would be the observable in this case?

The sum of the masses would give a lower bound only, below 1eV and the photons would be in the IR range. Most neutrinos (other than relics from nucleogenesis) have relativistic velocities and much higher energies.

Dear Robin, dear Erik,

let me answer your questions one by one.

-Robin:

Sorry, I think I misread the question at first (reading "oscillation" instead of "annihilation"). You are right that annihilation can process whether neutrinos are Dirac or Majorana. In the first case, we would have one neutrino annihilating with one anti-neutrino, while in the second case we would simply have two neutrinos annihilating. It does not really matter how the neutrinos have been produced, as long as they have a chance to meet often enough. However, this requirement makes this process happen not very often in the Universe, because the density of neutrinos is too small and the rates are simply too small.

-Erik:

You're right that the energy of the photons would be of the order of the neutrino mass, at least if both neutrinos are nearly at rest. This may not always be the case, but at least for the cosmic neutrino background it would be a good approximation. The main reason we cannot see these photons is however the rate of the process (it hardly ever happens). The mere energy is not so much of a problem, because eV-scale masses would still correspond to visible light, or maybe IR, but certainly nothing too low to be detected energy-wise. Thus, if we had many more neutrinos in the Universe, we could actually search for their annihilation lines and possibly measure the neutrino mass this way. However, Nature has not been kind enough.

Best regards,

Alexander

IceCube has a useful chart of the neutrino energy spectrum.

https://masterclass.icecube.wisc.edu/sites/default/files/images/neutrinos-energy.png

https://masterclass.icecube.wisc.edu/en/learn/detecting-neutrinos

Thanks George  ^_^

Alexander, I think civilisations elsewhere will have a rather more nuanced and informed perspective on this particular topic. I expect they will have properly considered the possibilities and performed the necessary calculations. It may be that their approach to science is not hindered by intellectual intransigence, bizarre belief systems and academic "peer" review.

Robin what do you think those civilization are ? 

Intelligent, ethical, post-evolutionary, ancient and wise.

Yes, nu and anu annihilate into Z0 boson. 

Yes, charge conservation requires it to be the Z boson, whose mass is far geater than the combined neutrino mass. So this is only a temporary and extremely rare outcome for annihilation in vacuum.

Annihilaton primarily proceeds, however, when mediated by matter. For the case of nonrelativistic neutrinos the opportunities are almost exclusively restricted to the ultra low energy 4s to 3d electron transitions in iron at pressures encountered within planets. Here, the annihilation is less prompt. The collision of an incoming electron antineutrino with a 4s electron creates a W- boson via the uncertainty principle. This then looks for an electron neutrino and, in the presence of a degenerate dark matter halo of neutrinos, rapidly finds one since, by definition, the wavefunctions of the consitutent halo particles saturate the space within the halo.

Under these circumstances, the rate-limiting step for neutrino annihilation is the frequency with which electron antineutrinos encounter iron's receptive 4s electrons to within the range of the weak force - or to be more precise in this case, the Compton wavelength of the W- boson (roughly 10-18 metres).

Dear Fumihiko,

I am sorry, but your answer does not make sense in my opinion. Of course there is a vertex of two neutrinos (or neutrino and anti-neutrino in the case of Dirac particles) into a Z-boson, but - as Robin correctly pointed out - the Z-boson is by far too heavy for the neutrinos being at rest. Apart from this, 2-to-1 annihilation has an infinitesimal in phase space, due to the kinematic restrictions.

Neutrinos are the second-to lightest particles in the Standard Model, apart from photons. (In fact, also gluons are massless, but one cannot annihilate into physical gluons because they need to hadronise due to colour neutrality, which is forbidden by kinematics.) Thus, two neutrinos can either annihilate into two lighter neutrinos (which probably was not the point of the question) or into two photons.

The latter case does however not proceed via Z-boson exchange: if two neutrinos turn into a Z, it would then need to convert into two photons by a fermionic triangle loop. However, this is forbidden by the requirement of the triangle anomaly having to vanish. For the same reason, the Z-boson as produced at LEP did not annihilate into two photons.

The analogue triangle diagram would be allowed for a Higgs, however, the coupling of the Higgs to two neutrinos is (presumably) tiny, so we can forget about this, too. Thus, the only remaining possibility is a loop with W-bosons and charged leptons, but this will equally be highly suppressed by the loop and by the large masses inside.

Again the conclusion stays the same: while neutrinos at rest (or with very small velocities) can in principle annihilate (into two photons, which is the only possibility), the rates will be tiny, beyond any real detection.

Differently, if neutrinos are highly energetic, the Z-boson channels into massive final states are open. E.g., we could have diagrams like nu + anti-nu -> Z-boson -> electron + positron, but this would only happend in environments where the neutrino energy is sufficiently large. The early Universe would be a good example. However, with neutrino sources we have available nowadays, it is hard to make this happen: either the energies are too low (e.g. for solar neutrinos, reactor neutrinos, geoneutrinos, or the cosmic neutrino background) or the number of neutrinos is too small to possibly observe such processes (e.g. for atmospheric neutrinos or accelerator neutrinos).

Best regards,

Alexander

The vacuum annihilation of neutrinos to three photons has been studied by de Graaf and Tolhoek (Nuclear Physics B 81, 596). They concluded that a neutrino halo would lose negligible energy by this process over a timescale comparable to the age of the universe. If the neutrino mass scale does not lie much below 0.05eV, which is compatible with current constraints, this same conclusion should also hold for the anticipated 1025 years over which electron-mediated neutrino annihilation can sustain aquatic life. Calculations have shown that for this neutrino mass an ambient neutrino density of 1 picogram per cubic km would suffice to maintain internally warmed planets with deep liquid oceans. Calculations have also found that this density is physically attainable with about 3 orders of magnitude to spare, a useful safety margin guarding against the gravitational implosion of neutrino haloes. These facts, and others, herald the future decay of dark energy to neutrinos, and provide a long-sought resolution of the cosmological constant problem that completely dispenses with anthropic reasoning.

Wow , Robin If I decided to "battle the tedious men in black" like you said . Could you suggest some books to start with ? 

Rawaa, the publishing industry is alas largely under their control! I suppose there could be more illuminating books on other worlds, but the universe has taken the sensible precaution of making it difficult for civilisations of our advancement to explore deep space. In case we might be in any doubt of that strategy, it has also ensured that all stars capable of cultivating life terminate their lives as incandescent red giants that purge formerly habitable orbiting planets of life, even microbial life several km below the surface. Our species is a relative newcomer and other civilisations may have histories a million times lengthier than ours. Science here is hardly being taken seriously. Some spectacularly premature and wayward conclusions have already been reached. My advice would be to study nature and the clues it provides, and think for yourself instead of blindly accepting whatever is written in the textbooks.

Robin,I agree you in what you said And I'm donig it from 3 month ago because that's when my proffessor in Arabic Comunication skilles toled me that there are no Postulates and I must work hardly to reach what I want .

Thanks Robin and Ales ^_^ 

Hello, Alexander, 

Since the question does not specify the energy nor final state, I guessed the simple answer might be for what Rawaa actually questioned. 

Boltzmann factors tell us about the probability of finding particles at a certain energy E given some temperature T. The relationship if E ~ kT where k is the Boltzmann constant whose units can be expressed as Joules per Kelvin. Combine this with Einstein's celebrated E=mc2 and you get kT ~ mc2. We can now translate a mass into a temperature.

Water has been dubbed the 'matrix of life'. All known living organisms are primarily composed of water. Water is liquid at room temperatures, around 300K.

We know that nuclear fusion is a rather inefficient source of energy, stars cannot convert more than 1% of their mass into energy. Also, habitable planets only intercept about one billionth of the radiation from their host stars. But ordinary matter only makes up 5% of the universe, and supernovae are very efficient at making oceanic planets - if we allow sufficient time.

The annihilation of matter with antimatter can liberate energy very efficiently. If the annihilation occurs in the vicinity of habitats for life then temperatures compatible with the presence of liquid water might be possible. If there is some thermoregulation system in operation, we can obtain a rough guess of the mass of the required annihilating particles.

Using m ~ kT/c2 ~ 300k/c^2 we get a mass scale resembling that of the neutrinos. Until now it has been a puzzle as to why neutrinos do not have a much larger mass, similar to that of an electron (as Pauli anticipated), or exactly zero (as dictated by the Standard Model). Neutrino oscillations have demonstrated that neutrinos do possess some mass - the only known departure from Standard Model physics which has ever been experimentally observed. Furthermore, neutrinos are the only dark matter candidates that are known to exist in nature.

I think extraterrestrial civilisations would be very surprised that our scientific community is so reluctant to consider how neutrinos might efficiently fuel aquatic life.

Ales, it is extremely likely we would have to check many other planets and different environments before we found other examples of life. My model does not rely on abiogenesis and lengthy evolutionary processes occurring in dark, anoxic subglacial oceans. Quite the opposite, it predicts the need for responsible and skilled colonists if these habitats are to be populated.

Life has adapted to some harsh environments here but visit central Antarctica and you will be hard pressed to find any complex life. Similarly, there are many deserts where neither plant nor animal life exists. Temperature is a key determinant of the likelihood of finding life, and it obviously controls whether substances can exist in the liquid state so as to allow for biochemical interactions.

The universe is in its infancy. There is a need for life to establish itself but it is extremely unlikely that evolution alone will give rise to ethically responsible colonists. Precautions are therefore needed. I've already pointed out that red giants are extremely effective at eradicating lifeforms too primitive to spread out across space, but there are other precautions too. The deferred delivery of neutrinos via dark energy decay (some 60 billion years hence) prohibits widespread colonisation until stars have had a chance to cultivate advanced forms of life.

The more unethical civilisations face the real risk of self-destruction via warfare, terrorism and environmental calamity. We have known for some time that we are related to other animals and it is self-evident that no lifeform can be blamed for their own DNA. It is worse than cannibalism if you understand that the lifeforms you exploit and devour are your own relatives, that they are on your menu by pure accident of birth, that they are helpless to defend themselves and they are afforded no legal rights - hardly an ideal outcome in a universe configured for life. I might also mention numerous examples of how we fail to prioritise the welfare of future human generations and compromise the environments they must live in. I think the universe tries to restrict opportunities for lifeforms such as ourselves beyond the stelliferous era (which is very brief compared to the annihilation timescales for neutrino haloes).

Other obstacles that must somehow be overcome for ongoing survival include long-range relocation (in our case, we would need to traverse ~ 50 million light years in order to arrive at a location where a dense neutrino halo is anticipated to form via dark energy decay). Were we to succeed in this, we could hardly expect a warm welcome. There are likely to be hundreds of advanced civilisations already at the destination, wondering why we did not pause to properly comprehend the arrangement of the universe before setting out. At the very least, we could expect to be quarantined and, if we failed to advance further, we would have no prospect of contributing to the future colonisation effort.

With a network of collaborating colonists well-versed in genetics and reproductive ethics, internally warmed oceanic planets should provide comfortable, predation-, war- and exploitation-free environments for aquatic life long after the (temporary) pandemonium of the early universe is over.

> in our case, we would need to traverse ~ 50 million light years in order to arrive at a location where a dense neutrino halo is anticipated to form via dark energy decay .

what if we worked at time scale lesser than ( 10^-15 _10^-18 ) ? Can that help more than waiting the universe to expand and reach this location because time become faster when the universe keep expanding . So if we can work at the time scale that will be notice easily after 50 million light years . Could that happen or it's just imagination ? I mean Is there any research for working at lowering the time scale we work in . 

And sorry for my bad English . 

Rawaa, are you asking if we can buy ourselves more time? The life-cultivating (class F, G, K) stars are not very long-lived (about 70 billion years max). They expire at about the same time as dark energy needs to decay to produce well-stocked neutrino haloes of about 1021 solar masses. The halo mass cannot be higher without risking implosion so there's not much flexibility on the timing of dark energy decay.

Colonisation would probably get underway as soon as the neutrino haloes are dense enough to sustain liquid oceans. I doubt that other civilisations would be willing to wait for us, especially if we have little to offer. All we can do with relativistic effects is decrease the time it takes to arrive at future events.I don't think the  expansion of the universe is really the issue, although the longer we wait the further we would need to travel (only really an issue if there is a delay of a billion years or so).

At 10% of the speed of light we could tackle relocation in ~500 million years. This seems long but it's still shorter than the 60 billion year wait for dark energy to decay. For an almost immortal lifeform, it may hardly be an inconvenience. However, advanced civilisations might impose restrictions on their own lifetimes until after they have tackled the relocation bottleneck.

I think every thing is possible but in this moment I hope the life on earth reach the end fastly because it's full of pain . 

Thanks Robin that's what I want "buy ourselves more time" ^_^ OR made things such technology to keep some extra time . Who could say that one day we traveled for long distance  to get answers for our Q's and today we make a disscusion with out need to travel . ^_^ 

The most beautiful theory must be verified by experiments, of course. In the present topic, one has to know at least the flux of the neutrinos.

Some problems related to the measurement of the neutrino flux only are described in the paper

O. Yu. Smirnov (speaker, representing 97 authors): Measurement of neutrino flux from the primary proton-proton fusion process in the Sun with Borexino detector. International Workshop on Prospects of Particle Physics: ”Neutrino Physics and astrophysics”, JINR, INR. 1 February - 8 February 2015, Valday, Russia

Personal remark: I'm afraid, we have to wait some time for the reports on parallel measurements of the neutrino and antineutrino flux (and the reaction rate of their collisions...).

It is interesting to consider the case of annihilating low energy degenerate neutrinos at the microscopic level. The Feynman diagram below is from http://arxiv.org/abs/astro-ph/0309564v2 which discusses the photoneutrino process. The time-reversal of this interaction is relevant to planetary heating. An electron antineutrino "collides" with a receptive 4s electron orbiting an iron atom. A virtual W- boson then arises, annihilation proceeding when it makes contact with an available electron neutrino. The initial 4s electron is replaced by a mildly excited 3d electron which goes on to warm its surroundings.

There are two vertices involving the W boson. The first involves the W boson coupling to the initial electron and the incident antineutrino. This coupling is only possible if the antineutrino approaches the electron to within a distance comparable to the Compton wavelength of the W boson (some 10-18 metres, the range of the weak force). This is the crucial rate-limiting step.

To understand why annihilation is then very likely to proceed remember that the neutrino halo is made of neutrinos whose wavefunctions are somewhat overlapping - this gives rise to the degeneracy pressure that supports the halo. The neutrino wavefunctions automatically adjust their size according to the pressure, and there is guaranteed overlap between the wavefunction of the W boson and the wavefunction of a neutrino for the second vertex.

The W boson is virtual, its huge mass can only be borrowed for a short time. The neutrino has a tiny mass, about one trillionth that of the W boson, and so its de Broglie wavelength (which is inversely proportional to the neutrino's momentum) is at least a trillion times larger than the W boson's Compton wavelength. If we were to take an instantaneous snapshot in time, the chances of the neutrino (in the sense of a point particle) being inside the wavefunction of the W boson would be extremely small. However, even though the W boson is not present very long, its existence is more than momentary. In that brief interval the neutrino is able to explore the region defined by its wavefunction sufficiently that it will find the W boson offering the chance for it to annihilate.

In other words, once the antineutrino approaches a receptive electron to within the range of the weak force, annihilation should normally proceed. The second vertex is not a hindrance: its range is governed by quantum mechanics and the low momentum of the neutrino, not by the weak force. This simplifies the calculations and clarifies why it is foolish to discount neutrino annihilation as a ludicrously rare event. Furthermore, at the nonrelativistic energies of interest, the mass of the neutrinos should be neglected.

A planet could expect to receive ~ 0.1 micro Watts per cubic metre of internal heating. It is therefore conceivable that the energy imparted by low energy neutrino annihilation to receptive electrons could one day be measured, but it might take some experimental ingenuity. I doubt that the anticipated neutrino concentration can be realistically achieved in a laboratory setting, so highly sensitive instrumentation and a lengthy integration time may be needed to compensate.

Robin : what do you think about that ?

"If the neutrino rest mass is only a few eV, this might result in sufficiently

greater gravitational force that could eventually stop the expansion and contraction will begin". 

Rawaa, this idea was popularised by people such as Dennis Sciama back in the 1980s after it was realised that a neutrino mass of about 30eV could provide a reasonably good fit for dark matter and, perhaps, "close the universe" i.e. prevent indefinite expansion.

We now have direct experimental measurements showing that the active neutrinos cannot have a mass exceeding about 2eV. Cosmological constraints are tighter still, perhaps a tenth of that. However, the fact that neutrinos do have mass tells us that there is unknown physics beyond the standard model. Potentially, there could be mixing between active and inactive species, with sterile masses being far higher than the 1.5eV which Nieuwenhuizen obtained from fitting gravitational lensing data for a galaxy cluster.  He has suggested a production mechanism for sterile neutrinos which occurs at higher energies.

Such scenarios could assist the fuelling of aquatic life in the future universe. For instance, the tandem production of active and sterile neutrinos via the Unruh effect at the centres of the largest galaxies could be (and I would say most probably is) the primary mechanism by which dark energy decays, and might automatically achieve an optimal balance between the active and sterile neutrino population, helping to maximise biotic efficiency.

Now that we know the expansion of the universe is accelerating, and the properties of neutrinos offer the only coherent explanation for why that is, it seems to me highly unlikely that the universe will begin to contract within the next 1025 years. Anyone can hazard a guess as to what happens after that. Perhaps the "operating system" somehow gets switched off and physics reverts to a more natural state incompatible with biology.

Ales, I didn't state that the accelerating expansion would continue forever, nor that it had always accelerated at the same rate, I was simply responding to Rawaa.

Thanks Robin ^_^ 

Rawaa, I should point out that now we know the universe is dominated by dark energy, the figure 30eV no longer has the relevance it once had. Even if it were much larger, dark energy would still determine the outcome.

It's interesting to consider how long after the big bang the accelerating expansion became discernible to the earliest civilisations. It is likely that a few arose prior to the acceleration becoming evident - and I imagine they would have been confused to discover that neutrinos have the properties needed for efficient planetary heating, but that their abundance is woefully inadequate in that regard.

We may not be alive at a particularly good time, and this civilisation may not have the best survival prospects, but things could have been even worse!

Interesting, I must read and think more about that ^_^ 

A standard model process is that two neutrinos annihilate in a S-channel collision. They  produce a virtual Z boson, which finally decays to two fermions.

Because we do not know whether neutrino is a Dirac or a Majorana particle, at the moment we cannot say whether it is neutrino-neutrino interaction or neutrino-antineutrino interaction.

 Thanks Biswajoy ^_^ 

Rawaa, although a pair of neutrinos might annihilate in a vacuum to produce two other fermions, the lightest fermions besides the neutrinos are the electrons. The mass gap spans about 7 orders of magnitude. So this is only possible if the annihilating neutrinos are ultrarelativistic. When the kinetic energy is less than 10 million times the rest mass energy of the neutrinos, the virtual boson can only decay to the original neutrinos (if fermions are produced). The universe can therefore avoid squandering neutrino energy in empty space, good news for the aquatic lifeforms of the future.

In discussions of the weak interaction a propagator involving the mass of the W boson appears and a simplification is normally used in which the momentum of the neutrino is taken to be negligible compared to the mass of the W boson.

However, in the detailed calculations that follow on, the neutrino momentum p is almost invariably assumed to be much larger than the neutrino mass. This is because it simplifies the equation E2 = m2c4 + p2c2 to E = pc  (note that for small p, the famous E=mc2 is recovered).

This simplifcation is inappropriate in the case of nonrelativistic neutrinos, but I have yet to see any mention of that caveat in a textbook. Remember that the de Broglie wavelength represents the scale of a particle's wavefunction and that annihilation requires some overlap of the wavefunctions of the two neutrinos. At very low energies, the volume of the wavefunction grows as the inverse cube of the neutrino velocity, greatly enhancing  the opportunities for neutrino annihilation which science here has been overlooking.

Thanks Robin ^_^ 

Rawaa, as this is a matter of global importance I've prepared a very short, single page article providing what should be a very easy to follow calculation of the power obtainable through neutrino annihilation, for a fairly typical case (a planet of about 3 Earth masses).

Technical Report The annihilation of gravitationally trapped neutrinos

Ales, we would have to be immortal inhabitants of an ininitely old universe to have any chance of knowing anything for certain, so the answer is no. However, Pauli originally postulated neutrinos in 1930 to rescue energy-momentum conservation and the conservation of spin in beta decay: a particle of half integer spin was required. Although it took many years for the existence of these particles to be experimentally confirmed, no experiment has ever found evidence that neutrinos are not fermions.

Thanks Robin ,That's really kind of you , I will read it today ^_^ 

Ales, it's true that like charges repel but that's not what gives rise to the degeneracy pressure that supports white dwarves, neutron stars and neutrino condensations. Quantum mechanics tells us that the probability of two identical fermions occupying the same state is zero, irrespective of the attributes of the fermions.