Showing posts with label Time Dilation. Show all posts
Showing posts with label Time Dilation. Show all posts

Thursday, December 09, 2010

Muon










The Moon's cosmic ray shadow, as seen in secondary muons generated by cosmic rays in the atmosphere, and detected 700 meters below ground, at the Soudan II detector.
Composition: Elementary particle
Particle statistics: Fermionic
Group: Lepton
Generation: Second
Interaction: Gravity, Electromagnetic,
Weak
Symbol(s): μ
Antiparticle: Antimuon (μ+)
Theorized:
Discovered: Carl D. Anderson (1936)
Mass: 105.65836668(38) MeV/c2
Mean lifetime: 2.197034(21)×10−6 s[1]
Electric charge: −1 e
Color charge: None
Spin: 12


The muon (from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with a negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton. It is an unstable subatomic particle with the second longest mean lifetime (2.2 µs), exceeded only by that of the free neutron (~15 minutes). Like all elementary particles, the muon has a corresponding antiparticle of opposite charge but equal mass and spin: the antimuon (also called a positive muon). Muons are denoted by μ and antimuons by μ+. Muons were previously called mu mesons, but are not classified as mesons by modern particle physicists (see History).

Muons have a mass of 105.7 MeV/c2, which is about 200 times the mass of an electron. Since the muon's interactions are very similar to those of the electron, a muon can be thought of as a much heavier version of the electron. Due to their greater mass, muons are not as sharply accelerated when they encounter electromagnetic fields, and do not emit as much bremsstrahlung radiation. Thus muons of a given energy penetrate matter far more deeply than electrons, since the deceleration of electrons and muons is primarily due to energy loss by this mechanism. So-called "secondary muons", generated by cosmic rays hitting the atmosphere, can penetrate to the Earth's surface and into deep mines.

As with the case of the other charged leptons, the muon has an associated muon neutrino. Muon neutrinos are denoted by νμ.

Contents

History

Muons were discovered by Carl D. Anderson and Seth Neddermeyer at Caltech in 1936, while studying cosmic radiation. Anderson had noticed particles that curved differently from electrons and other known particles when passed through a magnetic field. They were negatively charged but curved less sharply than electrons, but more sharply than protons, for particles of the same velocity. It was assumed that the magnitude of their negative electric charge was equal to that of the electron, and so to account for the difference in curvature, it was supposed that their mass was greater than an electron but smaller than a proton. Thus Anderson initially called the new particle a mesotron, adopting the prefix meso- from the Greek word for "mid-". Shortly thereafter, additional particles of intermediate mass were discovered, and the more general term meson was adopted to refer to any such particle. To differentiate between different types of mesons, the mesotron was in 1947 renamed the mu meson (the Greek letter μ (mu) corresponds to m).
It was soon found that the mu meson significantly differed from other mesons: for example, its decay products included a neutrino and an antineutrino, rather than just one or the other, as was observed with other mesons. Other mesons were eventually understood to be hadrons—that is, particles made of quarks—and thus subject to the residual strong force. In the quark model, a meson is composed of exactly two quarks (a quark and antiquark) unlike baryons, which are composed of three quarks. Mu mesons, however, were found to be fundamental particles (leptons) like electrons, with no quark structure. Thus, mu mesons were not mesons at all (in the new sense and use of the term meson), and so the term mu meson was abandoned, and replaced with the modern term muon.

Another particle (the pion, with which the muon was initially confused) had been predicted by theorist Hideki Yukawa:[2]

"It seems natural to modify the theory of Heisenberg and Fermi in the following way. The transition of a heavy particle from neutron state to proton state is not always accompanied by the mission of light particles. The transition is sometimes taken up by another heavy particle."

The existence of the muon was confirmed in 1937 by J. C. Street and E. C. Stevenson's cloud chamber experiment.[3] The discovery of the muon seemed so incongruous and surprising at the time that Nobel laureate I. I. Rabi famously quipped, "Who ordered that?"

In a 1941 experiment on Mount Washington in New Hampshire, muons were used to observe the time dilation predicted by special relativity for the first time.[4]

Muon sources

Since the production of muons requires an available center of momentum frame energy of 105.7 MeV, neither ordinary radioactive decay events nor nuclear fission and fusion events (such as those occurring in nuclear reactors and nuclear weapons) are energetic enough to produce muons. Only nuclear fission produces single-nuclear-event energies in this range, but do not produce muons as the production of a single muon would violate the conservation of quantum numbers (see under "muon decay" below).

On Earth, most naturally occurring muons are created by cosmic rays, which consist mostly of protons, many arriving from deep space at very high energy[5]

About 10,000 muons reach every square meter of the earth's surface a minute; these charged particles form as by-products of cosmic rays colliding with molecules in the upper atmosphere. Travelling at relativistic speeds, muons can penetrate tens of meters into rocks and other matter before attenuating as a result of absorption or deflection by other atoms.

When a cosmic ray proton impacts atomic nuclei of air atoms in the upper atmosphere, pions are created. These decay within a relatively short distance (meters) into muons (the pion's preferred decay product), and neutrinos. The muons from these high energy cosmic rays generally continue in about the same direction as the original proton, at a very high velocity. Although their lifetime without relativistic effects would allow a half-survival distance of only about 0.66 km (660 meters) at most (as seen from Earth) the time dilation effect of special relativity (from the viewpoint of the Earth) allows cosmic ray secondary muons to survive the flight to the Earth's surface, since in the Earth frame, the muons have a longer half-life due to their velocity. From the viewpoint (inertial frame) of the muon, on the other hand, it is the length contraction effect of special relativity which allows this penetration, since in the muon frame, its lifetime is unaffected, but the distance through the atmosphere and earth appears far shorter than these distances in the Earth rest-frame. Both are equally valid ways of explaining the fast muon's unusual survival over distances.

Since muons are unusually penetrative of ordinary matter, like neutrinos, they are also detectable deep underground (700 meters at the Soudan II detector) and underwater, where they form a major part of the natural background ionizing radiation. Like cosmic rays, as noted, this secondary muon radiation is also directional.

The same nuclear reaction described above (i.e. hadron-hadron impacts to produce pion beams, which then quickly decay to muon beams over short distances) is used by particle physicists to produce muon beams, such as the beam used for the muon g − 2 experiment.[6]

Muon decay


The most common decay of the muon
Muons are unstable elementary particles and are heavier than electrons and neutrinos but lighter than all other matter particles. They decay via the weak interaction. Because lepton numbers must be conserved, one of the product neutrinos of muon decay must be a muon-type neutrino and the other an electron-type antineutrino (antimuon decay produces the corresponding antiparticles, as detailed below). Because charge must be conserved, one of the products of muon decay is always an electron of the same charge as the muon (a positron if it is a positive muon). Thus all muons decay to at least an electron, and two neutrinos. Sometimes, besides these necessary products, additional other particles that have a net charge and spin of zero (i.e. a pair of photons, or an electron-positron pair), are produced.

The dominant muon decay mode (sometimes called the Michel decay after Louis Michel) is the simplest possible: the muon decays to an electron, an electron-antineutrino, and a muon-neutrino. Antimuons, in mirror fashion, most often decay to the corresponding antiparticles: a positron, an electron-neutrino, and a muon-antineutrino. In formulaic terms, these two decays are:
\mu^-\to e^- + \bar\nu_e + \nu_\mu,~~~\mu^+\to e^+ + \nu_e + \bar\nu_\mu.
The mean lifetime of the (positive) muon is 2.197 019 ± 0.000 021 μs[7]. The equality of the muon and anti-muon lifetimes has been established to better than one part in 104.

The tree-level muon decay width is
\Gamma=\frac{G_F^2 m_\mu^5}{192\pi^3}I\left(\frac{m_e^2}{m_\mu^2}\right),
where I(x) = 1 − 8x − 12x2lnx + 8x3x4;  G_F^2 is the Fermi coupling constant.
The decay distributions of the electron in muon decays have been parameterised using the so-called Michel parameters. The values of these four parameters are predicted unambiguously in the Standard Model of particle physics, thus muon decays represent a good test of the space-time structure of the weak interaction. No deviation from the Standard Model predictions has yet been found.

Certain neutrino-less decay modes are kinematically allowed but forbidden in the Standard Model. Examples forbidden by lepton flavour conservation are
\mu^-\to e^- + \gamma and \mu^-\to e^- + e^+ + e^-.
Observation of such decay modes would constitute clear evidence for physics beyond the Standard Model (BSM). Current experimental upper limits for the branching fractions of such decay modes are in the range 10−11 to 10−12.

Muonic atoms

The muon was the first elementary particle discovered that does not appear in ordinary atoms. Negative muons can, however, form muonic atoms (also called mu-mesic atoms), by replacing an electron in ordinary atoms. Muonic hydrogen atoms are much smaller than typical hydrogen atoms because the much larger mass of the muon gives it a much smaller ground-state wavefunction than is observed for the electron. In multi-electron atoms, when only one of the electrons is replaced by a muon, the size of the atom continues to be determined by the other electrons, and the atomic size is nearly unchanged. However, in such cases the orbital of the muon continues to be smaller and far closer to the nucleus than the atomic orbitals of the electrons.

A positive muon, when stopped in ordinary matter, can also bind an electron and form an exotic atom known as muonium (Mu) atom, in which the muon acts as the nucleus. The positive muon, in this context, can be considered a pseudo-isotope of hydrogen with one ninth of the mass of the proton. Because the reduced mass of muonium, and hence its Bohr radius, is very close to that of hydrogen[clarification needed], this short-lived "atom" behaves chemically — to a first approximation — like hydrogen, deuterium and tritium.

Use in measurement of the proton charge radius

The recent culmination of a twelve year experiment investigating the proton's charge radius involved the use of muonic hydrogen. This form of hydrogen is composed of a muon orbiting a proton[8]. The Lamb shift in muonic hydrogen was measured by driving the muon from the from its 2s state up to an excited 2p state using a laser. The frequency of the photon required to induce this transition was revealed to be 50 terahertz which, according to present theories of quantum electrodynamics, yields a value of 0.84184 ± 0.00067 femtometres for the charge radius of the proton.[9]

Anomalous magnetic dipole moment

The anomalous magnetic dipole moment is the difference between the experimentally observed value of the magnetic dipole moment and the theoretical value predicted by the Dirac equation. The measurement and prediction of this value is very important in the precision tests of QED (quantum electrodynamics). The E821 experiment at Brookhaven National Laboratory (BNL) studied the precession of muon and anti-muon in a constant external magnetic field as they circulated in a confining storage ring. The E821 Experiment reported the following average value (from the July 2007 review by Particle Data Group)
a = \frac{g-2}{2} = 0.00116592080(54)(33)
where the first errors are statistical and the second systematic.

The difference between the g-factors of the muon and the electron is due to their difference in mass. Because of the muon's larger mass, contributions to the theoretical calculation of its anomalous magnetic dipole moment from Standard Model weak interactions and from contributions involving hadrons are important at the current level of precision, whereas these effects are not important for the electron. The muon's anomalous magnetic dipole moment is also sensitive to contributions from new physics beyond the Standard Model, such as supersymmetry. For this reason, the muon's anomalous magnetic moment is normally used as a probe for new physics beyond the Standard Model rather than as a test of QED (Phys.Lett. B649, 173 (2007)).

See also

References

  1. ^ K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010), URL: http://pdg.lbl.gov
  2. ^ Yukaya Hideka, On the Interaction of Elementary Particles 1, Proceedings of the Physico-Mathematical Society of Japan (3) 17, 48, pp 139-148 (1935). (Read 17 November 1934)
  3. ^ New Evidence for the Existence of a Particle Intermediate Between the Proton and Electron", Phys. Rev. 52, 1003 (1937).
  4. ^ David H. Frisch and James A. Smith, "Measurement of the Relativistic Time Dilation Using Muons", American Journal of Physics, 31, 342, 1963, cited by Michael Fowler, "Special Relativity: What Time is it?"
  5. ^ S. Carroll (2004). Spacetime and Geometry: An Introduction to General Relativity. Addison Wesly. p. 204
  6. ^ Brookhaven National Laboratory (30 July 2002). "Physicists Announce Latest Muon g-2 Measurement". Press release. http://www.bnl.gov/bnlweb/pubaf/pr/2002/bnlpr073002.htm. Retrieved 2009-11-14. 
  7. ^ [1]
  8. ^ TRIUMF Muonic Hydrogen collaboration. "A brief description of Muonic Hydrogen research". Retrieved 2010-11-7
  9. ^ Pohl, Randolf et al. "The Size of the Proton" Nature 466, 213-216 (8 July 2010)

External links


***
Comment on Backreaction made to Steven

Hi Steven

Would we not be correct to say that unification with the small would be most apropos indeed with the large?

Pushing through that veil.

My interest with the QGP is well documented, as it presented itself "with an interesting location" with which to look at during the collision process.

Natural Microscopic blackhole creations? Are such conditions possible in the natural way of things? Although quickly dissipative, they leave their mark as Cerenkov effects.

As one looks toward the cosmos this reductionist process is how one might look at the cosmos at large, as to some of it's "motivations displayed" in the cosmos?

What conditions allow such reductionism at play to consider the end result of geometrical propensity as a message across the vast distance of space, so as to "count these effects" here on earth?

Let's say cosmos particle collisions and LHC are hand in hand "as to decay of the original particles in space" as they leave their imprint noticeably in the measures of SNO or Icecube, but help us discern further effects of that decay chain as to the constitutions of LHC energy progressions of particles in examination?

Emulating the conditions in LHC progression, adaptability seen then from such progressions, working to produce future understandings. Muon detections through the earth?

So "modeled experiments" in which "distillation of thought" are helped to be reduced too, in kind, lead to matter forming ideas with which to progress? Measure. Self evident.

You see the view has to be on two levels, maybe as a poet using words to describe, or as a artist, trying to explain the natural world. The natural consequence, of understanding of our humanity and it's continuations expressed as abstract thought of our interactions with the world at large, unseen, and miscomprehended?

Do you think Superstringy has anything to do with what I just told you here?:)

Best,

    Hi Steven,

    Maybe the following will help, and then I will lead up to a modern version for consideration, so you understand the relation.

    Keep Gran Sasso in your mind as you look at what I am giving you.

    The underground laboratory, which opened in 1989, with its low background radiation is used for experiments in particle and nuclear physics,including the study of neutrinos, high-energy cosmic rays, dark matter, nuclear decay, as well as geology, and biology-wiki


    Neutrinos, get set, go!

    This summer, CERN gave the starting signal for the long-distance neutrino race to Italy. The CNGS facility (CERN Neutrinos to Gran Sasso), embedded in the laboratory's accelerator complex, produced its first neutrino beam. For the first time, billions of neutrinos were sent through the Earth's crust to the Gran Sasso laboratory, 732 kilometres away in Italy, a journey at almost the speed of light which they completed in less than 2.5 milliseconds. The OPERA experiment at the Gran Sasso laboratory was then commissioned, recording the first neutrino tracks.

    Because I am a layman, does not reduce the understanding that I can have, that a scientist may have.

    Now for the esoteric :)

    Secrets of the Pyramids In a boon for archaeology, particle physicists plan to probe ancient structures for tombs and other hidden chambers. The key to the technology is the muon, a cousin of the electron that rains harmlessly from the sky.

    What kind of result would they get from using the muon. What will it tell them?:)

    Best,

    Friday, April 11, 2008

    The Toposense of Spacetime

    Topo-Greek, from topos, place.

    Basic Examples
    In the early 1960s Grothendieck chose the Greek word topos (which means “place”) to denote a mathematical object that would provide a general framework for his theory of étale cohomology and other variants related to his philosophy of descent. Even
    if you do not know what a topos is, you have surely come across some of them. Here are two examples:
    See: What is a Topos? by Luc Illusie

    Of course I am looking and trying to describe "Topo" in a different way. I do not want to diminish the significance of the mathematical intents. Just the realization of what we are doing with our perceptions, as we send them to extraordinary depth of of creation.



    In 1952, in his book Relativity, in discussing Minkowski's Space World interpretation of his theory of relativity, Einstein writes:

    Since there exist in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence. Albert Einstein


    Of course it was necessary to understand the evolution of Euclidean geometries to the non-euclidean, and the history associated with this. The word "Toposense" is one that becomes endearing when you realize that if your were to take to the meaning of "slide of light to heart" you would see the implications of what gravity could mean in the presence of the photon and it's explanatory revolutionary ideas about how it can encourage "Gravities Rainbow" here within context of this blog.

    "On the Effects of External Sensory Input on Time Dilation." A. Einstein, Institute for Advanced Study, Princeton, N.J.

    Conclusion: The state of mind of the observer plays a crucial role in the perception of time.


    Unfortunately the link to the article below( now shows as Intuitively Excellent) has been removed from Scientific America's data base or has changed, or, I may of copied it wrong in my search. Nevertheless, I do not have the link, but would like to conclude the remark above, in terms of those pointed out for further repercussions of that conclusiveness.

    Einstein scholars disagree, but the pretty girl/hot stove experiment also may have led to another of his pithy remarks, namely: "If we knew what it was we were doing, it would not be called research, would it?" Then again, Einstein was a bit of a wag. Consider his explanation of wireless communication: "The wireless telegraph is not difficult to understand. The ordinary telegraph is like a very long cat. You pull the tail in New York, and it meows in Los Angeles. The wireless is the same, only without the cat." This quote reportedly kept Schrödinger awake well past his bedtime.


    Summing over Histories?



    So how does all this come together into a physical theory? It turns out that the proper procedure is to construct every possible diagram allowed by the theory (for a given state of input and output particles and how they're moving) and add up the corresponding complex numbers. The result is essentially the "wave function" for that specific input-output state combination, and by squaring that number you can determine the probability that the given input will result in the given output. Doing that is how theorists at particle accelerators earn their keep.
    See: An Introduction to String Theory by Steuard Jensen

    So you look at the basis of interactions that Feynman produced in his Toy models and having some insight to the elemental consideration of those same interactions, what comes out, if we were to see the world in such a way, that continuity of expression is "the Wave that was generated in the very beginning," could have been reduce to some refractive expression of all life. The Spectrum, Hydrogen, or other wise.

    Do we then know the nature of the source, that we are all derivatives of some coherent plan that manifests toward the "cyclical nature of being?" Some Shakespearean version of, "to E or not to E?"


    Every known particle has an antiparticle; if they encounter one another, they will annihilate with the production of two gamma-rays. The quantum energies of the gamma rays is equal to the sum of the mass energies of the two particles (including their kinetic energies). It is also possible for a photon to give up its quantum energy to the formation of a particle-antiparticle pair in its interaction with matter.


    No longer Reducible and Working from the Horizon?



    How far can our perceptions be pushed? Can consciousness still remain as part of this "ability of creation," that we are still "part and parcel" of it to consider it's full scope?

    So no geometrical idealizations in sight, other then to consider the significance of a place that is far removed from our looking to the cosmos, and while thinking about it, how far it has been reduce to a fuller picture of it's reality?

    See: Colour of Gravity

    Sunday, November 12, 2006

    Graviton in a Can?

    After you consume "graviton in a can," you might never be the same? Brane thinking may then dominate your every view of the world. Then, it will all make sense?

    Imagine while we peer deeper into the subject of the "perfect fluid/soup" we find that certain aspects of the reductionist work done, has indeed lead us to speculate on how the "new physics" formed through the research and understanding currently being worked in the LHC?

    Is there some architectural design to the "Degree's of Freedom?" Why anything more then the spacetime we have come to recognize, which placed new parameters on our thinking? Moved it from the recogition of Maxwellian and Gaussian coordinates to Riemann geometries in the theory of General Relativity, to become known, as the Theory of gravity. Why "anything" more then that?


    A picture of flux lines in QED (left) and QCD (right).
    Although it didn't properly describe strong interactions, in studying string theory physicists stumbled upon an amazing mathematical structure. String theory has turned out to be far richer than people originally anticipated. For example, people found that a certain vibrational state of the string has zero mass and spin 2. According to Einstein's theory of gravity, the gravitational force is mediated by a particle with zero mass and spin 2. So string theory is, among many other things, a theory of gravity!


    I mean how are such abstract notions in the mathematics supposed to make sense, if we can not see the logic of these formulations working in some kind of reality frame of reference?


    by Jacob D. Bekenstein
    TWO UNIVERSES of different dimension and obeying disparate physical laws are rendered completely equivalent by the holographic principle. Theorists have demonstrated this principle mathematically for a specific type of five-dimensional spacetime ("anti–de Sitter") and its four-dimensional boundary. In effect, the 5-D universe is recorded like a hologram on the 4-D surface at its periphery. Superstring theory rules in the 5-D spacetime, but a so-called conformal field theory of point particles operates on the 4-D hologram. A black hole in the 5-D spacetime is equivalent to hot radiation on the hologram--for example, the hole and the radiation have the same entropy even though the physical origin of the entropy is completely different for each case. Although these two descriptions of the universe seem utterly unalike, no experiment could distinguish between them, even in principle.


    So we have these diagrams and thought processes developed from individuals like Jacob D. Bekenstein to help us visualize what is taking place. Gives us key indicators of the valuation needed, in order to determine what maths are going to be used? In this case the subject of Conformal Filed Theory makes itself known, for the thought process to hone in on what is going to be spoken too?

    Holography encodes the information in a region of space onto a surface one dimension lower. It sees to be the property of gravity, as is shown by the fact that the area of th event horizon measures the number of internal states of a blackhole, holography would be a one-to-one correspondence between states in our four dimensional world and states in higher dimensions. From a positivist viewpoint, one cannot distinguish which description is more fundamental.Pg 198, The Universe in Nutshell, by Stephen Hawking


    So we are given the label in which to speak about the holographical ntions of what is being talked about in the case of the blackhole's horizon.


    Campbell's Soup Can by Andy Warhol Exhibited in New York (USA), Leo Castelli Gallery


    While it is difficult of such images to be found displayed in the bloggery here to show what Dr. Gary Horowitz is saying you get the jest when you go right to the image of the tomato soup can.

    Spacetime in String Theory-Dr. Gary Horowitz, UCSB-Apr 20, 2005

    This year marks the hundredth anniversary of Einstein's "miraculous year", 1905, when he formulated special relativity, and explained the origin of the black body spectrum and Brownian motion. In honor of this occasion, I will describe the modern view of spacetime. After reviewing the properties of spacetime in general relativity, I will provide an overview of the nature of spacetime emerging from string theory. This is radically different from relativity. At a perturbative level, the spacetime metric appears as ``coupling constants" in a two-dimensional quantum field theory. Nonperturbatively (with certain boundary conditions), spacetime is not fundamental but must be reconstructed from a holographic, dual theory. I will conclude with some recent ideas about the big bang arising from string theory.


    Imagine containing everything we know in this can. Yet,we find that the "soup image" has somehow been translated to other factors and values that seem beyond what we know is real. Is real within the confines and boundaries, and is not evidence of the "infinities" that arise from such non containment?

    So, what of the "dilation field" that accumulates, as we speak to what the photon is in the measure of Glast. High energy photon determinations that may also be the valuation of the graviton in expression, as the photon travels through these fields?

    Such unification is important once we move into the bulk perspective and what we see of the 2d image of the brane, as a value, and discernation of the label of the soup can?


    The ALICE TPC in its clean room, where it is undergoing commissioning of all its sectors.

    One of the first cosmic-ray events recorded and reconstructed in two sectors of the TPC.
    The tests use the ALICE cosmic muon trigger detector ACORDE, as well as a specially designed UV laser system, to produce tracks in the detector. Preliminary analysis of the cosmic-ray events and the laser-induced tracks indicate that the drift velocity and diffusion of electrons liberated by traversing charged particles, as well as the spatial resolution, are very close to the design values.


    So here we are then, having graduated in perspective about what is real, as one may ask the sociological aspect of this whole adventure?



    If such missing energy is, "not accounted for" then what happens to the graviton as it is produced and causes energy to travel with them?

    For example, people found that a certain vibrational state of the string has zero mass and spin 2. According to Einstein's theory of gravity, the gravitational force is mediated by a particle with zero mass and spin 2. So string theory is, among many other things, a theory of gravity!