Posts tagged: physics
Here is something to think about that was only casually mentioned in passing in the recent video that was posted.
The sunlight you may or may not have experienced today finally managed to reach you after a ~100,000 year long journey since it was originally created at the Sun’s core!
Since the speed of light is finite, about 300,000,000 meters/second (or about 671,000,000 miles/hour), it takes time for it to travel from one point in space to another.
Given that the distance from Earth to the Sun is about 150,000,000,000 meters (about 93,000,000 miles) it takes about 8 minutes for light to reach us!
But this is just the time it takes light to reach us from the surface of the sun.
The light coming from the surface of the Sun is itself created as a by-product of nuclear fusion occurring deep in the Sun’s core.
Once light is created at at the Sun’s core it begins its journey to the surface of the Sun some 700,000,000 meters (430,000 miles) away from the core.
One might assume that this light takes the shortest path and heads straight to the surface, which would only take a couple seconds of travel time.
However, this is not the case because there is all kinds of star stuff that gets in the way.
An actual photon may only travel a mere fraction of a centimeter (anywhere between .01 and .3 centimeters depending on how close it is to the surface) before it makes a collision with other matter thereby diverting its path to some other random direction.
Photons continue moving in these seemingly random trajectories, bumping into other particles along the way, and don’t actually reach the surface until about 100,000 years later (give or take an order of magnitude)!
This kind of behavior characterizing the photons motion is modeled by something called a random walk, and is illustrated in a few different instances in the animations above.
Random walks have widespread applications through out the sciences and mathematics. The idea of random walks are even used in some computer algorithms to allow for more efficient solutions to some problems.
One particular application of personal interest, and a rather abstract generalization of the idea, is the quantum random walk, in which the superposition principle of quantum mechanics is used to put the trajectory into a combination of multiple possible trajectories to assist quantum computers in solving problems. The workings of Grover’s search algorithm can be thought of in this way. This isn’t the only instance that relates quantum mechanics to the workings of the Sun (see here).
Anyway, next time you are out in the relentless light of the Sun you may wonder what was going on some 100,000 years ago when that light first originated in the Sun, or maybe even where you’ll be 100,000 years from now when the light being created in the Sun at this moment finally reaches Earth.
(GIFs created from this Java app)
The secret lives of invisible magnetic fields are revealed as chaotic ever-changing geometries . All action takes place around NASA’s Space Sciences Laboratories, UC Berkeley, to recordings of space scientists describing their discoveries . Actual VLF audio recordings control the evolution of the fields as they delve into our inaudible surroundings, revealing recurrent ‘whistlers’ produced by fleeting electrons . Are we observing a series of scientific experiments, the universe in flux, or a documentary of a fictional world?.(via Magnetic Movie)
This video, by Semiconductor, is an artistic rendering exemplifying the dynamics of electromagnetic phenomenon happening around us and through out the universe. The animations are set to audio from VLF radio-wave recordings produced from real ambient sources such as weather systems, electrical storms, the Earth’s core, the upper atmosphere, and solar wind traveling to us all the way from the Sun.
Also, be sure to check out one of my favorite blogs, spooky(abstr)action, over at spookyactioncollective.tumblr.com where you can find quality posts ranging on topics like science, math, and technology amongst many other intriguing and peculiar things.
![albanhouse:
Hey guys, look what I did!
Which is to say that I wrote a Mathematica notebook which, given a Lagrangian, derives the canonical equations of the system. The test run (pictured) is a pendulum under the influence of gravity (V=mgh) where the mass m can move up and down the massless pendulum rod but is connected to the origin by a spring with spring constant k and rest length R.
The amazing thing is how wild non-linear systems can be; the graph shown is for k=0.8, m=0.8, R=1, g=0.2, released from rest at π/2 from the vertical (where θ=0), but playing around with these constants morphs the trajectory in various different ways and you can get a lot of different but interesting plots.
A quick educational bit: the Hamiltonian dynamics happens in phase space, Γ, but since this system has two degrees of freedom dim(Γ)=4 and you and I can’t visualize it. Nevertheless, there’s a trajectory γ[t] parameterized by the time that runs through Γ which the particle will follow given initial conditions. The graph here is the projection of that curve onto the configuration space, Q, so information about the particle’s momentum is lost here.
Some more background information here.](http://24.media.tumblr.com/tumblr_lv0z2iNS3Q1qzxsbbo1_1280.png)
Hey guys, look what I did!
Which is to say that I wrote a Mathematica notebook which, given a Lagrangian, derives the canonical equations of the system. The test run (pictured) is a pendulum under the influence of gravity (V=mgh) where the mass m can move up and down the massless pendulum rod but is connected to the origin by a spring with spring constant k and rest length R.
The amazing thing is how wild non-linear systems can be; the graph shown is for k=0.8, m=0.8, R=1, g=0.2, released from rest at π/2 from the vertical (where θ=0), but playing around with these constants morphs the trajectory in various different ways and you can get a lot of different but interesting plots.
A quick educational bit: the Hamiltonian dynamics happens in phase space, Γ, but since this system has two degrees of freedom dim(Γ)=4 and you and I can’t visualize it. Nevertheless, there’s a trajectory γ[t] parameterized by the time that runs through Γ which the particle will follow given initial conditions. The graph here is the projection of that curve onto the configuration space, Q, so information about the particle’s momentum is lost here.
Some more background information here.
“Until very recently, general relativity was taught only in postgraduate mathematics or physics courses, because the mathematical foundations of the theory were regarded as much too demanding for undergraduates. But the Liebers possessed an astounding, Promethean faith that a much larger audience could learn Einstein’s theories—the genuine article, not watered-down explanations. They believed that Einstein’s work, the deepest understanding of space and time yet conceived, belonged to all of us and should be made accessible to anyone who wanted to learn it. We share that belief. The first editions of this book were homemade by the Liebers (Hugh Lieber colored many of the illustrations by hand). After some years, a publisher took a chance, and kept the book in print for fifteen years. It has been out of print ever since, despite substantial efforts by the book’s fans to get it republished. This new edition has made the dream of decades come true for us.” (via 50 Watts)
A reason to believe that you don’t have to be good at doing index gymnastics to understand the theory of relativity.
More illustrations at 50 Watts.
Caption: Field ion micrograph of atoms of iridium. The tiny dots are the locations of individual atoms; the ring-like patterns are facets of a single crystal of the metal. The image was made by superimposing successive micrographs, taken with different col- our filters, to show small changes on the surface. The red dots are atoms which have evaporated or corroded away, while the green ones are probably atoms of gas which have been absorbed. Field-ion microscopy involves placing a tiny needle of a substance like iridium in a gas-filled chamber & passing a high voltage through it. The drifting gas ions hit the charged atoms & are repelled at right angles to form this pattern on a screen.
Credit: PROF. ERWIN MUELLER/SCIENCE PHOTO LIBRARY
I just want to explain what I mean when I say that we should try to hold on to physical reality. We are … all aware of the situation regarding what will turn out to be the basic foundational concepts in physics: the point-mass or the particle is surely not among them; the field, in the Faraday-Maxwell sense, might be, but not with certainty. But that which we conceive as existing (“real”) should somehow be localized in time and space. That is, the real in one part of space, A, should (in theory) somehow “exist” independently of that which is thought of as real in another part of space, B. If a physical system stretches over A and B, then what is present in B should somehow have an existence independent of what is present in A. What is actually present in B should thus not depend the type of measurement carried out in the part of space A; it should also be independent of whether or not a measurement is made in A.
If one adheres to this program, then one can hardly view the quantum-theoretical description as a complete representation of the physically real. If one attempts, nevertheless, so to view it, then one must assume that the physically real in B undergoes a sudden change because of a measurement in A. My physical instincts bristle at that suggestion.
However, if one renounces the assumption that what is present in different parts of space has an independent, real existence, then I don’t see at all what physics is supposed to be describing. For what is thought to be a “system” is after all, just conventional, and I do not see how one is supposed to divide up the world objectively so that one can make statements about parts.
The notion of nonlocality in quantum mechanics has been a topic of much interest over the past several decades since the conception of quantum mechanics. Nonlocality is the idea that particular systems which are spatially separated can exhibit instantaneous correlations which seemingly violate certain principles of classical physics such as faster-than-light travel. This phenomenon deeply bothered Albert Einstein, and has even led to some metaphysical claims of quantum mysticism.
Experimental evidence of such “nonlocal effects” is by no means doubted in the field. However, the idea of nonlocality may conflict with some of our models and interpretations of the world.
David Deutsch has recently posted a pre-print in which he argues a claim that he made over a decade ago: that reality is not nonlocal as believed by many.
Einstein’s (1949) criterion for locality is that for any two spatially separated physical systems S1 and S2 , ‘the real factual situation of the system S2 is independent of what is done with the system S1 ’. A previous paper (Deutsch & Hayden (2000)) included a proof that quantum physics satisfies this criterion. The method was first to prove that every quantum computational network satisfies it, and then to infer the same for general quantum systems by appealing to the universality of such networks.
Note that Deutsch’s proof makes use of the theory of quantum computation, which gives reason to believe that this theory may deserve a more fundamental role in our understanding of the world. It is also interesting to note that Deutsch is a strong advocate for the many-worlds interpretation of quantum mechanics, and thinks that this interpretation is the natural setting to understand quantum computation.
This makes me wonder what Einstein would of thought about later ideas like quantum computers and the multiverse. I, in my opinion, think he would have liked them.
(via anthonyh555)
Quantum Tunneling
According to Quantum Mechanics, a particle has a definite probability of being anywhere in the entire universe. Although any real distance from the particle’s expected classical path is infinitesimally small, since Quantum Mechanics is a statistical theory those small probabilities must be counted!
Quantum Tunneling is a fascinating effect that arises out of these small probabilities. This effect allows particles to occasionally pass right through obstacles that it would not normally have the proper energy to overcome, or an electron to escape the ‘pull’ of the nucleus without having enough kinetic energy to do so.
Although it’s fairly obvious that atoms are not just randomly going through every barrier, but this is because the probability of that happening is astronomically small because the barriers in our everyday world are rather thick. If made thin enough (approximately 1-3 nm,) the chance that a particle will spontaneously pass through becomes noticeable. A particle can effectively ‘borrow’ energy from the system that it’s acting in, pass through a barrier, and then spontaneously lose it. Mathematically, this can be explained using Heisenberg’s uncertainty principle, which limits the amount of information that can be known about any particle.
Quantum Tunneling is responsible for many interesting happenings throughout our universe, including enzymes in our own bodies. However, we can thank Quantum Tunneling for the sun’s heat. The sun is massive - very massive. However, in order to produce the temperatures necessary to activate nuclear fusion, the sun should be mathematically be much more massive! Due to Quantum Tunneling, there is a small chance that a Hydrogen atom will spontaneously undergo nuclear fusion without the proper temperature. However, since the sun has a tremendous amount of Hydrogen atoms in it, this small chance is converting about four million metric tonnes of Hydrogen each second!
So basically you would not exist here today because stars would not behave the way they do if it wasn’t for quantum mechanics!
Transverse plane wave
Propagation of a transverse spherical wave in a 2d grid
Plane pressure pulse wave
Representation of the propagation of an omnidirectional pulse wave on a 2d grid
Spacetime is assumed to be a branched 4-dimensional manifold embedded in a 6-dimensional Minkowski space. The branches allow quantum interference; each individual branch is a history in the sum-over-histories. A n-manifold embedded in a n+2-space can be knotted. The metric on the spacetime manifold is inherited from the Minkowski space and only allows a particular variety of knots. We show how those knots correspond to the observed particles with corresponding properties. We derive a 2-term Lagrangian. The Lagrangian combined with the geometry of the manifold produces gravity, electromagnetism, weak force, and strong force.
The abstract, topological properties of mathematical knots are related to the properties of elementary particles in the physical universe.
The interested reader can view the paper as a .pdf here.
(via introqft)
There is a useful quantum algorithm for quantum computers discovered by Lov Grover which pertains to the problem of searching large unstructured databases. Think of this problem as having to search through a large list or table of entries (like names and phone numbers) trying to find one particular entry. Like the factoring problem, the best a classical computer can do in searching a large unstructured database for a particular item is to proceed by brute force and exhaust all the possibilities. Grover’s search algorithm, though it does not provide an exponential speedup as in the case of factoring large integers, offers a quadratic speedup in searching such databases. However, this still has practical benefits.
Consider a database consisting of N entries that needs to be searched through. It can be shown that the best known classical algorithms, on average, can find a given entry in N/2 computational steps. On the other hand, Grover’s algorithm allows this to be accomplished in √N steps on a quantum computer.
As an illustration, imagine some future quantum computer that is performing Grover’s search algorithm with a processing speed capable of performing 108 computational steps per second—a realistic processing speed for classical computers. Suppose it is engaged in a particularly arduous search through a space of N = 1030 entries looking for a single unique entry. How long will it take? Well, it would require √N = 1015 computational steps, which at a rate of 108 steps per second, would take 107 seconds, or about 4 months. Though this may seem like a long time, let us calculate how long it would take a classical computer to search through the same database with the same processing speed of 108 computational steps per second. It would take N/2 = 5×1029 steps and thus require 5 × 1021 seconds, or very nearly the age of the universe (13.7 billion years)! That is the size of the practical benefit of the quantum search algorithm over the classical. In general, the larger the search is, the larger the gain the quantum computer has over the classical.
The theoretical implications of these algorithms are even more mind-boggling, because of the way quantum computers work. In the example of Grover’s search algorithm, the quantum computer is not just doing 1015 computational steps in parallel, which can be mimicked classically by making all the computers on Earth work on nothing but this problem. The quantum computer is doing 1030 possible computations in parallel every time a computational step is invoked. If all the silicon in the whole of our planet were made into microchips, and they were all set performing different computations, there would still be fewer distinct computations going on in that giant parallel computer than there would be in a single quantum computer performing Grover’s algorithm. That is a measure of the complexity, structure, and the process that exists in ordinary matter just beyond our perception since quantum processes are, of course, going on all the time everywhere. In a quantum computer, some small part of nature’s complexity is put to good use!
What is the Hamiltonian of the whole multiverse? Traditionally, fundamental physics has been about what types of systems exist in nature, what their observables are, and what their Hamiltonians are. That’s what elementary particle physicists call the theory of everything, but there is another way of looking at what is elementary or fundamental. Instead of asking what types of Hamiltonian are found in natural systems, which means what sorts of changes can occur in elementary systems over an infinitesimal time, one could go all the way to the bottom line and ask which transformation can be realized in nature by some quantum system evolving for some time and which cannot. The short answer is all changes, in which observables of the system undergo unitary evolution with every observable undergoing the same transformations so as to preserve their algebra, can occur in nature and nothing else can. Every unitary matrix is the evolution matrix for some quantum system evolving over some time. Or at least we think it is, because it turns out that the vast majority of these possible evolutions can only be realized in a very special type of physical system: a universal quantum computer. They don’t occur naturally because they require a complex computer program to bring them about. So, here is a fascinating situation. In terms of Hamiltonians the laws of physics are very finely tuned. The multiverse has its Hamiltonian and subsystems of the multiverse only have very special Hamiltonians. Most Hermitian matrices cannot be realized in nature as Hamiltonians. But when we ask a slightly different question: which unitary evolution operators can be realized in nature? The answer is all of them if a universal quantum computer can exist. This special type of object, the universal quantum computer, in a sense contains within itself all the diversity of nature. No other system does, except perhaps systems that are capable of constructing a universal quantum computer. Suddenly we find ourselves unavoidably playing a role at the deepest level of the structure of physical reality.
Super-kamiokande Cherenkov detector, near the village of Higashi-Mozumi, Gifu, Japan.
(via sneakystratuses)
