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Time dilation and muons = April 2016 webinar

Discussion in 'Mitochondrial Rx' started by Jack Kruse, Jun 28, 2021.

  1. Jack Kruse

    Jack Kruse Administrator

    The effect of time dilation is particularly vivid on unstable particles which live much longer in the lab frame than in their own rest frame. An early demonstration was seen in muons in 1941. These are heavier, unstable, versions of the electron. They decay into an electron, together with a couple of neutrinos, with a half-life of t = 2 x 10^-6 s.

    Muons are created when cosmic rays hit the atmosphere, and subsequently, rain down on Earth. Yet to make it down to sea level, it takes about t = 7 x 10^-6 s, somewhat longer than their lifetime. Given this, why are there any muons detected on Earth at all? Surely they should have decayed.

    The reason is they undergo time dilation. Muons experience a change in time. The reason that they do not is that the muons are travelling at a speed v = 0.99c (99% the speed of light), essentially giving v = 10. From the muon’s perspective (relativity), the journey only takes t1 = t/v 7 x 10 ^-7 s, somewhat less than their lifetime.
    JanSz likes this.
  2. Jack Kruse

    Jack Kruse Administrator

    Note that elementary particles are, by definition, structureless. They’re certainly not some clock with internal machinery. The reason that they live longer can’t be explained because of some mechanical device that slows down: it is time itself that is running slower.

    In biology, times runs slower when deuterium is depleted in the right places in molecules cells use to transform energy in metabolism.

    Remember that mitochondrion reverse photosynthesis.

    This means that both processes are linked to General and Special relativity.
    JanSz likes this.
  3. Jack Kruse

    Jack Kruse Administrator

    During time dilation moving clocks run slow and moving rods are shortened.

    The Geometry of Spacetime makes Einstein relativity hard to fathom. Consider the quote below

    "The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

    Hermann Minkowski, 1908

    It is clear now that time is relative, length is relative, simultaneity is relative. Is nothing sacred anymore? Well, the answer is yes: there is one measurement that all observers will agree on.

    the invariant interval is that case. The problem is that it is hard to fathom.

    The spacetime of special relativity is topologically R4. When endowed with the measure of distance, this spacetime is referred to as Minkowski space. This version of space is not like space you learned about in 3rd grade. Although topologically equivalent to Euclidean space, distances are measured differently. To stress the difference between the time and spatial directions, Minkowski space is sometimes said to have dimension d = 1 + 3. (For once, it’s important that you don’t do this sum!).

    Usually, if two points are separated by zero distance, then they are the same point. This is not true in Minkowski spacetime: if two points are separated by zero distance, it means that they can be connected by a light ray. Nuts.
    JanSz likes this.
  4. Jack Kruse

    Jack Kruse Administrator

    This fact also allows us to clarify one of our original postulates of special relativity: that the speed of light is the same for all inertial frames. You may wonder why the propagation of light, an electromagnetic phenomenon, is singled out for special treatment. The answer is: because the photon – the particle of light – is massless. In fact, a better way of stating the postulate is to say that there is an upper speed limit in the Universe, which is the same for all inertial observers. Any massless particle must travel at this speed limit. All massive particles must go slower.

    We know of only two types of massless particles in the Universe: the photon and the graviton. Both of these owe their particle-like nature to quantum mechanics (actually, this is true of all particles) and have a classical analog as light waves and gravity waves respectively. You’ve all seen light waves (literally!) and individual photons have been routinely measured in experiments for more than a century. Gravitational waves were observed for the first time in 2015, although compelling indirect evidence had existed for decades. There appears to be no hope at all of detecting an individual graviton, at least within our lifetimes.

    Until the late 1990s, it was thought that neutrinos were also massless. It is now known that they have a small, but finite mass. (Actually, there’s a caveat here: there are three different types of neutrino: an electron neutrino, a muon neutrino, and a tau neutrino. The differences between their masses are known to be of order of 0.01 - 0.1 eV and there are constraints that limit the sum of their masses to be no greater than 0.3 eV or so. But the absolute scale of their masses has not yet been determined. In principle, one of the three neutrinos may be massless)

    Higgs boson has mass (m)h x c2 = 125 GeV . It mostly decays into two photons. Here is an example of something with mass that becomes massless. Also hard to fathom.
    JanSz likes this.
  5. Jack Kruse

    Jack Kruse Administrator

    Pauli's Exclusion Principle states that no two electrons in the same atom can have identical values for all four of their quantum numbers. In other words, (1) no more than two electrons can occupy the same orbital and (2) two electrons in the same orbital must have opposite spins
    JanSz likes this.
  6. Jack Kruse

    Jack Kruse Administrator

    It also means that too much deuterium in the place of hydrogen also speeds time up...............
  7. JanSz

    JanSz Gold

    In the tropics there is more deuterium in the water and in the air we breathe. Except for some cenotes water.
    Daily we breathe in over 2 liters of water.
    Josie Thomson likes this.
  8. JanSz

    JanSz Gold

    Last edited: Jun 29, 2021
  9. Jack Kruse

    Jack Kruse Administrator

    Lead has relativistic effects too: these effects account for 1.7–1.8 V in a standard 2-V lead-acid battery cell. This implies, “cars start due to relativity”
    JanSz likes this.
  10. Jack Kruse

    Jack Kruse Administrator

    Relativistic effects are generally not observable in Nature in the sense of the usual observables of quantum theory such as position, momentum, energy, etc. However, manifestations of relativistic effects in the chemistry and physics of heavy elements compounds are ubiquitous. Gold is yellow, Hg is a liquid, and lead is really dense.

    In the case when an atomic or molecular property vanishes in the nonrelativistic limit (such as spin-orbit coupling or electronic g-shifts (deviations from the free-electron g value)), then the consequences of relativity are directly observable.

    At the size scale of atoms and molecules, and given the small masses of protons, neutrons, and electrons, gravitational effects on chemical phenomena can be neglected. In relativistic quantum chemistry, one deals with Einstein's special relativity. The effects become apparent as the velocities of the particles approach the speed of light c. Consider a free electron in a far-away orbital from the nucleus.

    One may speculate, that relativistic effects on the chemical properties of heavy atoms are small because their valence shells are subject to small effective (screened) nuclear charges. This turns out to be incorrect; valence orbitals in heavy many-electron atoms have comparatively small orbital energies but may have very large kinetic and potential energies.

    Depending on the desired accuracy of a calculation, relativistic effects may be required even for light elements (H, C, N, O, etc., with C, N, and O curiously sometimes termed “heavy atoms” in the computational chemistry literature). For truly heavy atoms such as I, Cs, Pt, Au,Hg, Pb, U, and so on, (Z/c)2 reaches an appreciable magnitude, and relativistic effects may alter the chemical and physical behavior qualitatively. The chemistry of light elements is well described by nonrelativistic quantum mechanics, whereas heavy elements require a relativistic theory. In particular, in the lower third of the periodic table, the chemical characteristics of the elements are strongly influenced by relativity. This may be the reason why few heavy atoms are used in living systems.

    Iodine and selenium being two examples.
    JanSz likes this.
  11. Jack Kruse

    Jack Kruse Administrator

    For example, lighter group 13 and 14 elements such as Al, Ga, Si, Ge, tend to favor oxidation states of III and IV, respectively, whereas the heaviest members of the groups, Tl and Pb, favor the oxidation states I and II, respectively. The rationale for such changes in the chemical behavior when going down in the group is the particular energetic stabilization of the valence "s" orbital in Tl, Pb, and other heavy 6th row elements due to relativistic effects, creating the 6s “inert pair” effect.

    There are also well-known “heavy atom effects” in spectroscopy. For instance, in NMR spectroscopy the presence of a heavy halide (Br, I) bound to a light atom causes the chemical shift of the light atom to be more negative (more shielded) than in an analogous compound with Cl or F. Think about the Grothaus mechanism

    This so-called normal halogen dependence has been known for quite some time to be caused by spin-orbit (SO) coupling, which is a relativistic effect. SO coupling also leads to the splitting of multiplet levels that would be degenerate according to nonrelativistic theory, and it is therefore directly observed in atomic spectroscopy.

    Grotthuss, I believe is another relativistic effect that augments proton conduction in water.

    The Grotthuss Mechanism is the mechanism by which an 'excess' proton or protonic defect diffuses through the hydrogen bond network of water molecules or other hydrogen-bonded liquids through the formation/cleavage of covalent bonds.

    In his seminal 1806 publication “Theory of decomposition of liquids by electrical currents”, Theodor Grotthuss proposed a unique theory of water conductivity. Grotthuss envisioned the electrolytic reaction as a sort of ‘bucket line’ where each oxygen atom simultaneously passes and receives a single hydrogen atom. It was an astonishing theory to propose at the time since the water molecule was thought to be OH not H2O and the existence of ions was not fully understood.
    JanSz likes this.

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