New Clues To Solving Physics Riddle

Article written: 16 Jun , 2011
Updated: 26 Apr , 2016
by

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There are diminutive visitors to Earth. We’ve known about them and measured their presence since the 1960s. When the Sudbury Neutrino Observatory (SNO) turned on in May, 1999 the world became acutely aware of tiny particles known as solar neutrinos. The facility gathered data for seven years before shutting down and we’ve heard little in the media about neutrinos since. As we know, mass cannot be either created nor destroyed – only converted – so where did it originate? Exciting results produced by the international T2K neutrino experiment in Japan may be key to resolving this riddle.

To understand neutrinos is to understand their flavors: the electron neutrino teamed by particle interactions with electrons, and two additional marriages with the muon and tau leptons. Through research, science has proved these different types of neutrinos can spontaneously change into each other, a phenomenon called ‘neutrino oscillation’. From this action, two types of oscillations have been documented during the T2K experiment, but a new format has come to light… the introduction of electron neutrinos in a muon neutrino beam. This means neutrinos can fluctuate in every way science can possibly dream of. These new findings point to the fact that oscillations of neutrinos and their anti-particles (called anti-neutrinos) could be different. If they are, this could be an example of what physicists call CP violation. This would be a tidy explanation of why our Universe breaks the laws of physics by having more matter than anti-matter.

Unfortunately, the T2K neutrino experiment was disrupted by this year’s devastating Japan earthquake. But the team was prepared and both they – and the equipment – weathered the catastrophe. Before shutting down, six pristine electron neutrino events were recorded where there should have only been 1.5. With odds of this happening only one in one hundred times, the team felt these findings weren’t conclusive to confirm a new physics discovery and so they listed their results as an “indication”.

Prof Dave Wark of STFC and Imperial College London, who served for four years as the International Co-Spokesperson of the experiment and is head of the UK group, explains, “People sometimes think that scientific discoveries are like light switches that click from ‘off’ to ‘on’, but in reality it goes from ‘maybe’ to ‘probably’ to ‘almost certainly’ as you get more data. Right now we are somewhere between ‘probably’ and ‘almost certainly’.”

Prof Christos Touramanis from Liverpool University is the Project Manager for the UK contributions to T2K: “We have examined the near detectors and turned some of them back on, and everything that we have tried works pretty well. So far it looks like our earthquake engineering was good enough, but we never wanted to see it tested so thoroughly.”

Prof Takashi Kobayashi of the KEK Laboratory in Japan and spokesperson for the T2K experiment, said “It shows the power of our experimental design that with only 2% of our design data we are already the most sensitive experiment in the world for looking for this new type of oscillation.”

And we’re looking forward to their findings!

Original Story Source: Science and Technology.


47 Responses

  1. Matter was created by the Gawd 🙂

  2. Torbjörn Larsson says

    This has looked to me as the most promising lead to physics beyond the current for some time now (besides inflation models). AFAIU under the simplest standard model neutrinos wouldn’t oscillate in the first place (i.e. be massless), and adding it would be simpler with other types of physics than earlier standard model mechanisms.

    It would be interesting to hear lcrowell’s take, say. Meanwhile, for a layman Wikipedia has an interesting article.

    The mass mechanism, CP violation and other stuff is independent.

    And while the CP case apparently is expected, the parameter δ controlling it is “unknown”. But neutrino CP violation seems indeed to need all the oscillations to be possible (from the MNS matrix).

  3. Torbjörn Larsson says

    This has looked to me as the most promising lead to physics beyond the current for some time now (besides inflation models). AFAIU under the simplest standard model neutrinos wouldn’t oscillate in the first place (i.e. be massless), and adding it would be simpler with other types of physics than earlier standard model mechanisms.

    It would be interesting to hear lcrowell’s take, say. Meanwhile, for a layman Wikipedia has an interesting article.

    The mass mechanism, CP violation and other stuff is independent.

    And while the CP case apparently is expected, the parameter δ controlling it is “unknown”. But neutrino CP violation seems indeed to need all the oscillations to be possible (from the MNS matrix).

    • Anonymous says

      The CP violation is independent of the mass mechanism, at least within the context of the standard model. The mass of particles is given by the Higgs mechanism, at least within the standard model. CP violations are also a type of symmetry breaking, and curiously if neutrinos were more massive CP violations would less. A massless neutrino is one where you can’t ever boost yourself onto a frame with it. So if the spin vector is oppositely directed to the momentum (left handedness) it will remain so in all frames. However, since neutrinos have a mass there is a Lorentz factor ? = E/mc^2, where E is on the order of 10Mev or larger and mc^2 ~ 100ev. This is then a gamma

      ? = 10^5 = 1/sqrt(1 – (v/c)^2)

      and if you calculate the velocity you get v = .0.99999999995, where I carried this out to where the 9’s ended. So if you could boost yourself to a frame faster than this (run faster than a neutrino) the momentum and spin would be aligned. You have changed the parity of the neutrino! Of course that is not an easy thing to do. The existence of mass in fact means parity violations are not absolute. It also means that CP violations are less set in concrete the more that the Higgs mechanism gives mass to particles the less there is a parity violation.

      It is also worth noting that there is the CPT discrete symmetry CPT = 1, which means that CP = T^{-1}. The time operator is n = 2 nilpotent or T^2 = 1 and so T = T^{-1}. So CP violations have something to do with the so called arrow of time. How this is the case is not clear. It is not the case that CP violations somehow generate entropy or enough of it to explain the arrow of time and entropy.

      LC

      • Torbjörn Larsson says

        Oh. Thanks for the response, dedicated as a reply no less! Above and beyond duty.

        And it is stimulating:

        at least within the context of the standard model.

        Thanks! I goofed.

        I should have noted “could be independent”, or perhaps better, “naturally independent (in the setting of the MNS matrix)”.

        It also means that CP violations are less set in concrete the more that the Higgs mechanism gives mass to particles the less there is a parity violation.

        Interesting. I guess it is not tied to the Higgs mechanism as such, seeing your derivation from reference frames. Apparently the see-saw mechanism is slightly more natural for neutrinos specifically, so the question of mechanism for mass coupling is still dragging [sic!] the field.

        CP violations have something to do with the so called arrow of time.

        Indeed, though I note that this is the local arrow.

        In my book the global arrow of time and 2LOT are natural consequences of universe expansion.

        Putatively it devolves simply to the mechanism of inflation, which can get universes started within a certain parameter range. While in other cases they quickly revert and implode out of further consideration.

        I don’t think you even have to drag environmental selection into it due to the fundamental asymmetry. The question on that arrow’s existence becomes why not all of the multiverse (given inflation and nothing else) was inflated in the first place.

        Still, that doesn’t explain how local arrows ties into the global arrow. As you note there is no connection to entropy (that we know of; let us non-goof this =D). Either we put the question wrongly (maybe there is no inherent selection on time arrows here) or parity is more of a mystery than usually accounted for!

      • Anonymous says

        This is basically the seesaw mechanism. The parity violation is mostly apparent because the neutrino is so light.

        The problem on the “arrow of time” most likely can only be addressed with gravity or quantum gravity. The entropy of BPS and extremal black holes has some mathematical correspondences with entanglement groups. This gets into the heart of my interests, and it is very mathematical. The question about the arrow of time may have some connection with these matters. It might also involve the breaking of supersymmetry. The BPS black holes have supersymmetric charges, which at certain scales may be violated.

        LC

      • Anonymous says

        If the electron is moving at deSitte 0.9999999995 times the speed of light, should it not be flattened in the direction of the movement instead of round?

    • Anonymous says

      I can’t find the article now but there was recently news of some peculiar results regarding (IIRC) anti B-mesons where the relationship between two anti-particles wasn’t as predicted from their matter counterparts.

      The recent measurement showing the electron is very close to a perfect sphere is also interesting:

      http://www.bbc.co.uk/news/science-environment-13545453

      Of course there is also the task of finding a slot for dark matter.

      • Anonymous says

        If you look at the Feynman Lectures in Physics, the third volume has a chapter on the KK-bar system. This is similar to what obtains with the BB-bar system. The flavor eigenstates, corresponding to the numbers which give the quark types, are not diagonalized in the same basis as the Hamiltonian (energy quantum operator) for the gauge theory.

        The measurement on the “spherocity” of the electron means that up to within 10^{-25}cm (very small) the electron has no dipole moment. It is probably not best to think of the electron as some spherical ball, for that really is not quite right. There is the classical radius of the electron. This equates the E = mc^2 of the electron with its electric field potential V = (1/4??)e^2/r

        mc^2 = (1/4??)e^2/r

        and one gets the radius r = (e^2/4??c^2), which is 2×10^{-13}cm, or about a Fermi length for the nucleus. So in one sense we can think of this as a sphere that is perfect to within a trillion times smaller. However, this is not entirely correct in a quantum mechanical sense.

        LC

      • Anonymous says

        I found the original article I saw which now has me slightly confused about the numbers:

        http://www.electronicsweekly.com/Articles/2011/05/26/51135/imperial-college-reveals-shape-of-the-electron.htm

        The author’s summary is “What shape is an electron? The standard model of particle physics predicts that electrons are egg-shaped, but that the amount of distortion from a perfect sphere is so tiny that no existing experiment could possibly detect it. However, a rival theory called supersymmetry predicts that this egg-shaped distortion should be large enough to be detectable. … as far as they could tell, rather than being oval, the electron is spherical.”

        That suggested to me that the result was more “spherical” than even the standard theory predicts, however the numbers in the article suggest they only measure to 1 in 10^18 while the standard model predicts 1 in 10^28 so they are ten orders short of the testing the standard model.

        Combining that with your figure of 2*10^{-13}cm “radius” implies they have set a maximum of around 10^{-31}cm, a considerable improvement on your figure of 10^{-25}cm, while the standard model predicts 10^{-41}cm and supersymetry predicts between 10^{-32}cm and 10^{-27}cm.

        Have I got the gist there?

      • Anonymous says

        I used the figure 10^{-25}cm from memory. It might have actually been closer to 10^{-28}cm. This summary is similar to my understanding. I have not read the actual paper, but an by other means aware of this result.

        There are ways this might be overcome. The electron is ultimately a string, or so we think, where the ends of the string are attached to a D-brane with a target map to our spacetime. The string may be a sort of “tube,” and where this tube is a Taub-NUT space. The Taub-NUT space is similar to a black hole, but where time plays the role of the radius in the black hole solution. The tube is segmented into two regions, one which has closed timelike curves and another with causal timelike directions, or is chronal. There is an event horizon which separates the two regions. If this is so, the opening which is chronal attaches with a NUT-charge, while the other end has no charge. To make a long story short this would mean the gauge charges end at this opening with a diameter of 10^{-33}cm. So the electron would appear spherical.

        Physics probably ends at 10^{-33}cm. This is the Planck length, where the Schwarzschild radius of a black hole equals its wavelength. So there really probably no meaning to anything smaller than this.

        LC

      • Anonymous says

        Hmm, Google found this which might be out of date (2007):

        http://pdg.lbl.gov/2007/listings/s003.pdf

        and on page 3 there is the statement “A nonzero value is forbidden by both T invariance and P invariance.” with the value 0.069 +/- 0.074 * 10^{-26}e cm or 6.9 * 10^{-28}e cm.

        Wiki gives this very brief summary:

        http://en.wikipedia.org/wiki/Electron_electric_dipole_moment

        which is consistent.

        This page

        http://physicsworld.com/cws/article/news/46085

        says:

        “This allowed the team to place an upper limit on the EDM of 10.5 × 10^{-28}e cm with 90% confidence. … This is about 50% better than previous measurements using thallium atoms ..”

        I don’t follow how 10.5 is a tighter limit on a number which is supposed to be zero than 6.9. Oh well, never trust the press.

      • Anonymous says

        I think it is meant that the error bars are smaller for the 10,5. I pulled out the 10^{-25}cm from memory, but the 10^{-28}cm is more on tack.

        LC

      • Anonymous says

        If an electron has no dipole moment, does that mean it is a monopole?
        I remember that long time ago they were searching for the elusive monopole but if an electron is a monopole then I don’t understand what they were searching for.

      • Anonymous says

        This is an electric monopole. The search for “the monopole” involves a magnetic monopole.

        LC

      • Torbjörn Larsson says

        Of course there is dark matter.

        But it slips even further away as we write, since supersymmetry WIMPS gets more and more excluded as for now.

        Other persons will come up with different personal judgments obviously. It is good to see the different priorities and how they are reached, the more people pitch in the better I think.

        some peculiar results regarding (IIRC) anti B-mesons

        Yes, and I didn’t mean to preclude any leads to new physics.

        [For the record it is a recent result. The question of mass and now the question of mass coupling mechanism has been with the neutrinos as long as I have known them.]

        The recent measurement showing the electron is very close to a perfect sphere is also interesting:

        Personally I have to disagree, since a) it is a null result b) it is actually a result on the electron electric dipole moment, for reasons lcrowell notes.

        [As for everything minute, there are many senses of sizes and forms of systems, from nanoscale surfaces through crystals, molecules and atoms to nucleus and particles: geometric: RMS roughness, molecule positions; forces: van der Waals, electric; quantum: Compton wavelength, probability cloud; et cetera.

        However until string theory is validated it is easiest to think of the electron as geometrically point-like since the problem of the magnitude of its magnetic dipole moment vs its spin goes away. A non-point electron would have a surface velocity of its ‘spin’, in the classical sense, many times faster than light.

        Interestingly it is not _topologically_ point-like due to the same physics. Its spin value of 1/2 can be interpreted, in the quantum sense, as that you have to rotate the electron 2 full turns to get its wavefunction back to where you started.

        Quantum theory is, if not weird, surely a puzzle at times. The difference between fermions and bosons comes out of wavefunction topology (even and odd functions, rotational symmetry vs anti-symmetry if you will); easy to understand. The spin comes out of wavefunction topology (rotational symmetry vs anti-symmetry if you will); hard to grasp.]

      • Anonymous says

        The statistics of fermionic and bosonic fields is a double covering, which in group theory involves a relationship between special unitary and orthogonal groups. To throw a bit of a spanner in the picture, there is also something called the Majorana Fermion, where these is an additional “knot topology” involved with how particles are interchanged.

        There is an “end to structure” at the Planck scale. Any attempt to probe for structure on smaller scales results in probing larger scales. This is an aspect of quantum holography with black holes. To probe down to the Planck scale L_p = sqrt{G?/c^3} means putting enough energy on that scale to generate a quantum unit of a black hole. The black hole though conceals anything within it. This scale can then contain at most a quantum bit of information. How Planck volumes tessellate lattices can then define an “alphabet” for a quantum error correction code.

        The spherical nature of the electron is a bit of a puzzle, for strings are not spheres. They have certain excitation modes that correspond to elementary particles. An open string then has a dipole structure if the topological charge it contains is associated with the two open ends. The open ends are D0-branes (particles) and these are attached to higher dimensional membranes (Dp-branes). In order for there to be no dipole structure there must be some asymmetry to the string. This is not something most people receive very well in that community. As I indicated below there is the prospect for strings, on scales below the string length, to be Taub-NUT spacetimes — tubes of sorts that have one end that is achronal and the other which is chronal. This is a type of asymmetry which would associate NUT-charges on one end and the string would have a pure monopole charge structure.

        LC

  4. Anonymous says

    The first two paragraphs of this article are discombobulated.

    Most readers of this blog probably know that matter and energy can be converted into each other, and that the Big Bang (whatever it was) generated all the matter-energy we see. How does this relate to neutrinos?

    “… the electron neutrino teamed by particle interactions…”: Is “teamed” an adjective or a verb? I can’t parse this sentence at all, and it is very long.

    “a new format has come to light… the introduction of electron neutrinos in a muon neutrino beam.”: What does “introduction” mean here? Did the scientists divert electron neutrinos in on purpose? Did the oscillations occur inside the beam? Was the result unexpected? (Of course, the result was expected, but this article makes it sound very surprising.) And what were solar neutrinos doing in a beam anyway? (This experiment does not use solar neutrinos, yet the only particles introduced by the first paragraph are specifically the ones from the Sun. The source article doesn’t mention the Sun at all.)

    “This means neutrinos can fluctuate in every way science can possibly dream of.”: First, science is not a person. Second, there is probably a theory out there that postulates additional neutrinos. (If there isn’t, such a theory is possible, because theories may be incorrect.) Third, “fluctuate” simply means “change”, and there are more ways to do that than change flavors.

    Reading the sourced article, it’s clear you just rephrased it with more bombastic prose. Please, either obtain permission to reproduce the original or express what you believe to be important in your own words. This looks a bit like plagiarism, and a bit like the breathless nonsense everywhere else that drove me to this website.

    • Member
      Tammy Plotner says

      it’s my job, dude. i’m a writer and obviously not a physicist. i do not plagiarize press releases – only endeavor to take difficult text and make it more understandable to the average person. you would have far less respect for me if i simply copied this wholesale… yet it’s obvious you can’t respect another’s efforts. i applaud mr.crowell for having a deeper understanding of the subject matter than i do, therefore i appreciate what he has to say. i also feel the same way about mr. larsson’s comments and i even appreciate ivan_3_man’s corrections. if you think it is easy, then by all means… don’t let me stop you from taking over.

      • Anonymous says

        Trying to be more constructive, might I suggest replacing “.. the introduction of ..” by “.. the appearance of ..” for example would be clearer.

        Regarding the sentence on creation of matter, how about “When matter is created, it normally comes with an equal amount of anti-matter – so how did the preponderance of matter in the universe originate?”

        I hope nobody will take these comments as anything other than as they are intended: to be helpful to both sides of the debate without implying criticism of either.

      • Anonymous says

        — “When matter is created, it normally comes with an equal amount of anti-matter – so how did the preponderance of matter in the universe originate?” —

        Nu pun intended but this way of formulation sound more like what pseudo scientists would use. Also the word “created” indicates an intelligent design which is so wrong.

        Maybe this

        “When energy transforms in to matter and anti-matter, the universe should have had an equal number of matter and antimatter. But observations clearly show that only matter prevails and anti-matter is missing”

      • Anonymous says

        “the word “created” indicates an intelligent design which is so wrong”

        Not at all, as has been said before, matter is regularly created from other forms of energy in accelerators, I don’t think my version is related to the ID nonsense at all. However, adding “from energy” might reduce the chance of others making the same assumption.

        “an equal number of matter and antimatter.”

        You are using ‘matter’ and ‘antimatter’ as adjectives so you need a noun such as ‘particles’ at the end.

        Overall I agree with your comment though, it is intended as a “pop science” style of presentation (rather than “pseudo-science”), grossly simplified but hopefully consistent with the style of the genre.

        It just goes to show that nuances can be read into almost any wording however carefully phrased.

      • Torbjörn Larsson says

        Gosh. Thanks!

    • William Sparrow says

      Although Tammy did an admirable job defending herself, I’ll throw my two cents in. As she stated, she’s not a physicist but a writer, and in my opinion, a damn fine one. She offered an interesting topic for discussion, which is exactly the purpose of this site, AFAIU. I find it interesting that although you come across as very critical of Tammy’s assessment, you offer little in the way of meaningful contributions to the topic. As Tammy said, if you think you can do better, provide and example or two.

      • Sucking up to the author is worse IMO.
        As usual Tammy is mostly out of her depth, and should stick to observational material which she seems to have some knowledge.
        Frankly, mimics are easy to spot as they can offer nothing original. This be the case here.

      • Anonymous says

        I agree, this article from Tammy is far better that typical newspaper articles and still understandable for the commen person what this site should be.

  5. Anonymous says

    There are three neutrino eigenstates |?_e>, |?_?>, |?_?>, corresponding to the e, ?, and ? leptons. These have masses m_i, i = 1,2,3 for the three neutrino states. If these masses are different this means there is a degeneracy splitting of the weak interaction Hamiltonian. Equivalently, it means the perturbing energy operator (Hamiltonian) is not simultaneously diagonalizable with the weak interaction Hamiltonian. The matrix, MNS or CKM matric, takes a rather complicated form, and the reason for this I will not go into, and it is:

    c_?c_?, s_?c_?, s_?e^{i?}
    -s_?c_? – c_?s_?s_?e^{i?}, c_?s_? – c_?s_?s_?e^{i?}, c_?s_?e^{i?}
    s_?s_? – c_?s_?c_?e^{i?}, -c_?s_? – s_?s_?c_?e^{i?}, c_?c_?

    for the angles ?, ?, ? Euler angles and ? the CP phase. Matrix parentheses are assumed. The neutrino state as it evolves by this 3×3 matrix U_{ij} as

    |?_a> = sum_{aj}U_{aj}|?_j>

    where the index a is a flavor index and i is a mass index.

    This matrix is unitary and is generated by a Hamiltonian operator H that is Hermitian H = H^†. According to momentum and the Hamiltonian this matrix has the form

    U_aj}|?_j> = [exp(-i/??Hdt)exp(-i/??p*dx) |?_a>

    Now concentrate on the momentum part, which gives a phase

    ? = (c^3/4?)|r – r’|(?m_{ij})^2/E

    where r and r’ are the limits on the integration and ?m_{ij} = m_i – m_j are the mass differences between the neutrinos. To get this phase requires some calculations which I have skipped for brevity. If one evaluates the expectation for this process there is an oscillatory term that depends on this phase ? = (c^4/4?)|t – t’|(?m_{ij})^2/E, where I have converted this to time in the argument.

    This is the basic theory of neutrino oscillations. I wrote a paper last decade where I considered this on a cosmological background. Neutrinos which cross the cosmological event horizon and reach our detectors should be “frozen,” where the oscillations stop.

    LC

  6. Anonymous says

    There are three neutrino eigenstates |?_e>, |?_?>, |?_?>, corresponding to the e, ?, and ? leptons. These have masses m_i, i = 1,2,3 for the three neutrino states. If these masses are different this means there is a degeneracy splitting of the weak interaction Hamiltonian. Equivalently, it means the perturbing energy operator (Hamiltonian) is not simultaneously diagonalizable with the weak interaction Hamiltonian. The matrix, MNS or CKM matric, takes a rather complicated form, and the reason for this I will not go into, and it is:

    c_?c_?, s_?c_?, s_?e^{i?}
    -s_?c_? – c_?s_?s_?e^{i?}, c_?s_? – c_?s_?s_?e^{i?}, c_?s_?e^{i?}
    s_?s_? – c_?s_?c_?e^{i?}, -c_?s_? – s_?s_?c_?e^{i?}, c_?c_?

    for the angles ?, ?, ? Euler angles and ? the CP phase. Matrix parentheses are assumed. The neutrino state as it evolves by this 3×3 matrix U_{ij} as

    |?_a> = sum_{aj}U_{aj}|?_j>

    where the index a is a flavor index and i is a mass index.

    This matrix is unitary and is generated by a Hamiltonian operator H that is Hermitian H = H^†. According to momentum and the Hamiltonian this matrix has the form

    U_aj}|?_j> = [exp(-i/??Hdt)exp(-i/??p*dx) |?_a>

    Now concentrate on the momentum part, which gives a phase

    ? = (c^3/4?)|r – r’|(?m_{ij})^2/E

    where r and r’ are the limits on the integration and ?m_{ij} = m_i – m_j are the mass differences between the neutrinos. To get this phase requires some calculations which I have skipped for brevity. If one evaluates the expectation for this process there is an oscillatory term that depends on this phase ? = (c^4/4?)|t – t’|(?m_{ij})^2/E, where I have converted this to time in the argument.

    This is the basic theory of neutrino oscillations. I wrote a paper last decade where I considered this on a cosmological background. Neutrinos which cross the cosmological event horizon and reach our detectors should be “frozen,” where the oscillations stop.

    LC

    • Torbjörn Larsson says

      Curious. In what sense will the oscillations stop?

      [Yes, I’m, partly at least, begging for a reference of yours. Please take the opportunity! =D]

      • Anonymous says

        The paper was written in some proceedings quite a long time ago. It was not in a journal. It is buiried away somewhere. The idea goes like this. It is a similar calculation, and we start with the unitary matrix

        U = exp(-i/??Hdt)exp(-i/??p*dx),

        and where the generator of the matrix is

        (-i/?[?Hdt + ?p*dx].

        We now go to the metric for the deSitter spacetime. If we use the stationary metric

        ds^2 = Adt^2 – A^{-1}(dr^2 + r^2?^2

        for A = sqrt(1 – ?r^2/3}. The spatial ?p*dx part of this gives the phase term

        ?_{ij} = (?m_{ij}c^3/2E?)?(1/A)dr,

        where the limits (r, r’) on the integral are assumed. This gives the phase term

        ?_{ij} = (?m_{ij}c^3/2E?)[arcsin(sqrt{?/3}r’) – arcsin(sqrt{?/3}r)]

        Then from there we write

        arcsin(z) = -iln(iz + sqrt{1 – z^2})

        for z = sqrt{?/3}r. For r > sqrt{?/3} there is an analytic extension on the argand plane and the phase is

        ?_{ij} = (?m_{ij}c^3/2E?)[?/2 – iln((z +sqrt{ 1 – z^2}].

        So this is the standard result plus some imaginary term. Since the phase gives an oscillation e^{-i?_{ij}} there is then an attenuating exponential real term which mathematically damps out the oscillations.

        This means that neutrinos which arrive from the very distant universe should not be oscillating. They will be “frozen,” and detectors which measure sources of neutrinos from sources with z > 1, here z being the redshift factor, should find they do not oscillate. Of course the problem is isolating neutrinos from such sources at great distances.

        LC

      • Anonymous says

        It would be interesting if you explain what deSitter spacetime is. 😉
        I believe that this is exotic name for our normal space?

      • Anonymous says

        It is basically our spacetime. The exitence of matter perturbs it some, but as the accelerated expansion increases spacetime will become more de Sitter.

        LC

      • Anonymous says

        So it is the universe without the matter 😉
        The matter is optional.

        I just noted the distinction between matter and mass.
        We don’t know what matter really is but we do know what mass is E=mc^2 and E=-mc^2

        I have a second question.
        Energy can spontaneous materialize as matter and anti-matter. But is that always the case that anti-matter gets formed? When energy is feeded to an atom like heating it up or speeding it up. Does not only matter increase like Einstein’s formula and no anti-matter increase?

      • Anonymous says

        The universe will be pretty completely de Sitter at thermodynamic heat death. It will take about 10^{100} years to reach those conditions. At that stage matter will have been decayed away and the leptons and photons remaining will be diluted to the point there is only 1 or less in each region bounded by the cosmological horizon r = sqrt{3/?}. Beyond that time the de Sitter vacuum will quantum decay over an infinite period of time. At that “omega point” the universe will reach quantum death.

        LC

      • Colby Hayward says

        What would such quantum decay “look like”, so to speak? I mean… how does spacetime decay?

      • Anonymous says

        It is similar to the decay of black holes by Hawking radiation. The cosmological constant is ? = 10^{-56}cm^{-2}, and this defines an event horizon of sorts at r = sqrt{3/?} or at about 10^{28} cm out, or about 10 billion light years. This horizon though is not the black membrane of a black hole. An observer inside a black hole can see out beyond it, and it is maybe analogous to that. During the early inflationary period the horizon was much smaller, less than a centimeter and the exponential expansion of the universe was very rapid. There was a phase transition which occurred that dropped ? in value.

        In about 10^{100} years the universe will be largely empty and in a de Sitter configuration with this horizon. However, this vacuum is not zero and it quantum mechanically decays. The cosmological horizon will then over enormous periods of time recede off to “infinity,” as there is a quantum tunneling to a lower energy configuration. That configuration is a completely empty flat spacetime.

        LC

  7. Dark Sapiens says

    “As we know, matter cannot be either created nor destroyed”. Umm… pair production? Matter-antimatter annihilation? E=mc^2? :S

    Matter *can* be created and destroyed, from and into energy. It would be energy what can’t 😛

    • Member
      Tammy Plotner says

      thanks, DS! i’ve added a few snippets to my original opener so it makes better sense. sometimes my thoughts go faster than my ability to convert it into words! 😀

      • Member
        IVAN3MAN_AT_LARGE says

        “Relax. What is mind? No matter. What is matter? Never mind!”
        —Homer Simpson.

      • Anonymous says

        I like your joke, because it is relevant to put the mind in the equasion….

        From the MInd all phenomena appear. There isn’t an indevisible particle of matter in the universe, anyway. If there was, the solid thing “existing” on its own would not be able to interract with anything else in the universe, and in effect it would be impossible for it to exist. So, at least one of the quantum mechanics views is correct. Looking for the indivisible particle will lead people to anguish, they’ll never find it.

        Consider this: if there is this theory of a finite , solid thing existing in it’s own right—-it creates quite a lot of destructive behaviours in society. Racism, wars and any sorts of conflicts spring from us thinking that things exist as solid and disconnected from each other. It’s potentially dangerous. The mind examins the attractive properties of a thing and grabs hold of it. It examins the repulsive properties and pushes it away. It’s subjective and highly dangerous to have these views of solidity in the universe.

        Consider this: imagine one particle surrounded by six other particles of the same kind. One in each of the cardinal directions and one above and one below, all touching. Does the same part of the particle in the middle that touches the Eastern particle also touch the particle in the North?If not, then the particle in the middle has more than one part and is at least conceptually devisible.
        If, by contrast, the Eastern part does touch the particle in the North, there’s nothing to prevent it from touching particles in all the other directions as well. you can do this infinitelly….

        Thank you IVAN3MAN_AT_LARGE for the inspiration.

      • Anonymous says

        I like your joke, because it is relevant to put the mind in the equasion….

        From the MInd all phenomena appear. There isn’t an indevisible particle of matter in the universe, anyway. If there was, the solid thing “existing” on its own would not be able to interract with anything else in the universe, and in effect it would be impossible for it to exist. So, at least one of the quantum mechanics views is correct. Looking for the indivisible particle will lead people to anguish, they’ll never find it.

        Consider this: if there is this theory of a finite , solid thing existing in it’s own right—-it creates quite a lot of destructive behaviours in society. Racism, wars and any sorts of conflicts spring from us thinking that things exist as solid and disconnected from each other. It’s potentially dangerous. The mind examins the attractive properties of a thing and grabs hold of it. It examins the repulsive properties and pushes it away. It’s subjective and highly dangerous to have these views of solidity in the universe.

        Consider this: imagine one particle surrounded by six other particles of the same kind. One in each of the cardinal directions and one above and one below, all touching. Does the same part of the particle in the middle that touches the Eastern particle also touch the particle in the North?If not, then the particle in the middle has more than one part and is at least conceptually devisible.
        If, by contrast, the Eastern part does touch the particle in the North, there’s nothing to prevent it from touching particles in all the other directions as well. you can do this infinitelly….

        Thank you IVAN3MAN_AT_LARGE for the inspiration.

  8. Anonymous says

    Look guys, I’m impressed, I really am… But when are we going to get flying cars? Fusion energy? Electric vehicles? Making fart noises occur across the room? Anything? You gotta give us a bone here.

    • Member
      IVAN3MAN_AT_LARGE says

      But when are we going to get flying cars?

      Impractical — it’s bad enough already with idiots driving around on the roads, so can you imagine what it would be like with the ‘flying idiot’ problem?!

      Fusion energy?

      Er… they/we are working on it…

      Electric vehicles?

      Dude, they have been around since the mid-19th century (see: Electric car — History).

      Making fart noises occur across the room?

      That’s already available here.

      • Torbjörn Larsson says

        He, that false choice (between doing science and doing non-fundamental science) is usually something that gets my goat, even if (or perhaps precisely because) it is a stupid fallacy. And of course it was just trolling for a response.

        But as it happens, for once the electric vehicle claim was LOLable. I google:

        – Electric trains: 1837.
        – Electric boats: 1839; very popular 1880s – 1920s.
        – Electric cars: 1867; until 1900s, electric cars held the land speed record.
        – Electric bikes: 1895.
        – Electric space crafts (well, duh): 1957.
        – Electric planes: 1974.

  9. Good to see that those who now disagree with Tammy are now having posts deleted but is happy to receive ego-supporting platitudes.
    The failure here is clearly now biassed unknowing reporting
    I will be deliberately avoiding all her articles on Universe Today from now on.
    Clearly disgraceful unprofessional behaviour. 🙁

  10. Good to see that those who now disagree with Tammy are now having posts deleted but is still happy to receive ego-supporting platitudes.
    The failure here is clearly now biassed unknowing reporting
    I will be deliberately avoiding all her articles on Universe Today from now on.
    Clearly disgraceful unprofessional behaviour – especially from a presumed freedom of speech American. 🙁

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