This is a rather entertaining article (a chapter from a book) written by Jan Zaanen on the history of the theory of high-Tc superconductivity. As everyone knows (or should know), the exact theory for this family of material is still a highly debated and contentious holy grail in condensed matter physics. It is also an area that will have wide-ranging ramifications in not only condensed matter physics, but also in many areas of physics. So knowing the development of the history of the search for this theory might be interesting and important.
Zz.
Friday, December 31, 2010
Thursday, December 30, 2010
Horsepower Versus Torque In A Vehicle
Here's an informative "basic" classical mechanics, as applied to motor vehicles. Might be something you want to read if you're shopping for new vehicles.
Don't think I want to quibble about the definition of "work" being "... moving something with some force in a certain amount of time.. ", since this probably makes no difference here.
Zz.
“Horsepower, in physics or engineering terms, is a measure of work, and work is defined as moving something with some force in a certain amount of time. Torque is a force, and can be briefly described as what force it takes to turn an axle or a rod. Horsepower and torque are related based on the speed of the engine,” says Gary Pollak, program manager for ground vehicle standards with the Society of Automotive Engineers (SAE) International.
Don't think I want to quibble about the definition of "work" being "... moving something with some force in a certain amount of time.. ", since this probably makes no difference here.
Zz.
Wednesday, December 29, 2010
In The Beginning...
This is not a bad article, written by Martin Rees. But then again, I'm a bit disappointed at how sloppy it is in some areas. I'm fully aware that this was written for the general audience, and it appeared in a regular newspaper. But still, he could have made it a bit more accurate without changing the readability of the article.
For example, he wrote this about a possible extra dimension for gravity:
While the original prediction by Arkani-Hamed et al. predicted millimeter scale compaction, it has now become sub-sub-sub-millimeter scale after several tests have concluded that the Newtonian gravity has not shown any deviation up to sub-micron length scales (or even smaller). So to me, the paragraph above gives the wrong idea that such extra dimension are of the order of just under a millimeter scale. We know quite a bit more now. There is no longer any need to stick with "under a millimeter" when we know it should be under a micrometer, which would be more accurate.
The other part is more puzzling and I don't know why he wrote it.
This, I don't understand. There are already numerous examples of QM effects in biological system. I've mentioned a lecture given by Seth Lloyd at the Perimeter Institute. And we now have many reports of QM effects in photosynthesis. Someone like Rees should be aware of such advancement. So why would he made a statement that gives the impression that quantum mechanics offers no "enlightenment" to biologists?
{scratching head}
Zz.
For example, he wrote this about a possible extra dimension for gravity:
Some have speculated that other universes could exist in tandem with ours. Imagine ants crawling around on a large sheet of paper (their two-dimensional universe). They would be unaware of a similar sheet that is parallel to it. Likewise, there could be another entire universe (with three-dimensional space, like ours) less than a millimetre away from us, but we would be oblivious to it if that millimetre were measured in a fourth spatial dimension, while we are imprisoned in just three.
While the original prediction by Arkani-Hamed et al. predicted millimeter scale compaction, it has now become sub-sub-sub-millimeter scale after several tests have concluded that the Newtonian gravity has not shown any deviation up to sub-micron length scales (or even smaller). So to me, the paragraph above gives the wrong idea that such extra dimension are of the order of just under a millimeter scale. We know quite a bit more now. There is no longer any need to stick with "under a millimeter" when we know it should be under a micrometer, which would be more accurate.
The other part is more puzzling and I don't know why he wrote it.
That said, everything, however complicated - breaking waves, migrating birds and tropical forests - is made of atoms and obeys the equations of quantum physics. But the uncertainties of subatomic physics are irrelevant to biologists; even if those equations could be solved, they would not offer the enlightenment that scientists seek.
This, I don't understand. There are already numerous examples of QM effects in biological system. I've mentioned a lecture given by Seth Lloyd at the Perimeter Institute. And we now have many reports of QM effects in photosynthesis. Someone like Rees should be aware of such advancement. So why would he made a statement that gives the impression that quantum mechanics offers no "enlightenment" to biologists?
{scratching head}
Zz.
Monday, December 27, 2010
Dubunk Quackery Using Another Quackery
A long time ago, when I found Warren Siegel's "Are You A Quack" webpage, I had quite a chuckle when I came across this piece of information.
This is not an isolated incidence. In my encounter on the web after so many years, I find that, often times, quacks can't stand other quacks, or at least, they don't want to make any effort in trying to argue with other quacks, which is understandable. After all, what VALUE is there in such discussion when a quack generally (i) doesn't understand physics and/or (ii) are set in their ways and won't want to learn why he/she is wrong.
So, in this very same spirit, I thought what would be better than using a pseudoscience to counter the argument or another pseudoscience. The pseudoscience that I want to argue against here is "ghosts" or other supernatural beings that go bump in the night. Y'know, the ones you see on either the Travel Channel where they seem to encounter some unknown "forces", "energy", or other beings almost every week, without even a bat of an eye that these things are not verified by science.
So how does one counter the validity of such ghosts? Well, we should pull out "The Secret" and apply the Law of Attraction. The fundamental idea of this Law of attraction is a bastardization of quantum mechanics. Here, it appears that you and your thoughts can somehow affect what goes on around you. Your thoughts can change your world and thus, you are in control of what is happening. This, of course, comes from the bastardization of the act of measurement in quantum mechanics, where these people are erroneously apply the fact that a measurement causes the "collapse" of a wavefunction, and how we measure things can affect the outcome.
So my argument against ghosts is that, when put in a "scary" situation, where you go into a building that you have been told to be haunted, or have supernatural occurrences, then you inevitably, according to The Law of Attraction, are "thinking of thoughts" about ghosts and other goblins. So essentially, your thoughts are the ones bringing these entities into your perception. They would not have been there if you didn't know any better, or didn't know about it. So these ghosts are not real. They are only your imagination, and they are shared by people who are there as well. I bet you, if you bring James Randi to one of these ghosts sightings, he will have a different take on what is going on.
So according to The Secret, you are the one who caused the ghosts that you experienced. How about them apples?
Zz.
Note: Long ago a professor of mine told me that he got letters from 2 quacks, so he forwarded each's letter to the other. He got back an angry letter from one saying, "Why did you introduce me to this quack?"
This is not an isolated incidence. In my encounter on the web after so many years, I find that, often times, quacks can't stand other quacks, or at least, they don't want to make any effort in trying to argue with other quacks, which is understandable. After all, what VALUE is there in such discussion when a quack generally (i) doesn't understand physics and/or (ii) are set in their ways and won't want to learn why he/she is wrong.
So, in this very same spirit, I thought what would be better than using a pseudoscience to counter the argument or another pseudoscience. The pseudoscience that I want to argue against here is "ghosts" or other supernatural beings that go bump in the night. Y'know, the ones you see on either the Travel Channel where they seem to encounter some unknown "forces", "energy", or other beings almost every week, without even a bat of an eye that these things are not verified by science.
So how does one counter the validity of such ghosts? Well, we should pull out "The Secret" and apply the Law of Attraction. The fundamental idea of this Law of attraction is a bastardization of quantum mechanics. Here, it appears that you and your thoughts can somehow affect what goes on around you. Your thoughts can change your world and thus, you are in control of what is happening. This, of course, comes from the bastardization of the act of measurement in quantum mechanics, where these people are erroneously apply the fact that a measurement causes the "collapse" of a wavefunction, and how we measure things can affect the outcome.
So my argument against ghosts is that, when put in a "scary" situation, where you go into a building that you have been told to be haunted, or have supernatural occurrences, then you inevitably, according to The Law of Attraction, are "thinking of thoughts" about ghosts and other goblins. So essentially, your thoughts are the ones bringing these entities into your perception. They would not have been there if you didn't know any better, or didn't know about it. So these ghosts are not real. They are only your imagination, and they are shared by people who are there as well. I bet you, if you bring James Randi to one of these ghosts sightings, he will have a different take on what is going on.
So according to The Secret, you are the one who caused the ghosts that you experienced. How about them apples?
Zz.
Saturday, December 25, 2010
Italy To Build Accelerator/Collider With US Parts
As further signs that the US truly is going out of particle collider experiments, an agreement has been reached for Italy's SuperB to be built with parts from the now decomissioned PEP-II accelerator at SLAC.
THe US is losing grounds on high energy physics experiments. And no one seems to be concerned about it. Might as well give these equipment to those who appreciate their importance. So Merry Christmas, Italy!
Zz.
Petronzio says he hopes that the Italian ministry will agree to a construction schedule early next year and that SuperB will start taking data around 2016. The construction of SuperB is contingent on the U.S. Department of Energy (DOE) contributing the machinery of PEP-II, which would be worth more than €100 million. However, David MacFarlane, SLAC's associate director for particle physics and particle astrophysics, says the lab and the agency are onboard with the project: "Both DOE and the laboratory are fully committed to supplying the equipment requested."
Whether U.S. physicists will be able to fully participate in the Italy project is another matter. To support such participation, DOE officials will have to find some room in the agency's already tight $810 million particle physics budget. But David Hitlin, a particle physicist at the California Institute of Technology in Pasadena who has been involved in the project since its inception, says that SuperB presents DOE with a scientific bargain. "DOE can be a major player in the project for a relatively small amount of money by leveraging the in-kind contribution" of the equipment, he says. For the moment, Hitlin says he's just happy that the project seems to be coming to fruition: "It's nice that it's real."
THe US is losing grounds on high energy physics experiments. And no one seems to be concerned about it. Might as well give these equipment to those who appreciate their importance. So Merry Christmas, Italy!
Zz.
Wednesday, December 22, 2010
Top 10 Reasons to Pursue a Career in Science & Technology
Here's the top 10 reasons to pursue a career in science and technology, from the point of view of Eric Isaacs, the Laboratory Director of Argonne.
Unfortunately, if you're an experimentalist, you can't come in to work in sandals if you're going to be doing experiments that day. :)
Zz.
Unfortunately, if you're an experimentalist, you can't come in to work in sandals if you're going to be doing experiments that day. :)
Zz.
Tuesday, December 21, 2010
More Tests Against Realism
The Leggett inequality has been violated in another experiment.
I've mentioned this test earlier in which, even invoking non-locality, certain aspect of realism still cannot survive tests that produced results consistent with quantum mechanics. Now comes a newer test that eliminated even more classes of realism. It is published in New Journal of Physics[1], which is an open access journal and should be accessible to everyone.
Abstract: We report an experimental test of Leggett's non-local hidden variable theory in an orbital angular momentum (OAM) state space of light. We show that the correlations we observe are in conflict with Leggett's model, thus excluding a particular class of non-local hidden variable theories for the first time in a non-polarization state space. It is known that the violation of the Leggett inequality becomes stronger as more detection settings are used. The required measurements become feasible in an OAM subspace, and we demonstrate this by testing the inequality using three and four settings. We observe excellent agreement with quantum predictions and a violation of five and six standard deviations, respectively, compared to Leggett's non-local hidden variable theory.
Zz.
[1] J. Romero et al., N. Jour. Phys. v.12, p.123007 (2010).
I've mentioned this test earlier in which, even invoking non-locality, certain aspect of realism still cannot survive tests that produced results consistent with quantum mechanics. Now comes a newer test that eliminated even more classes of realism. It is published in New Journal of Physics[1], which is an open access journal and should be accessible to everyone.
Abstract: We report an experimental test of Leggett's non-local hidden variable theory in an orbital angular momentum (OAM) state space of light. We show that the correlations we observe are in conflict with Leggett's model, thus excluding a particular class of non-local hidden variable theories for the first time in a non-polarization state space. It is known that the violation of the Leggett inequality becomes stronger as more detection settings are used. The required measurements become feasible in an OAM subspace, and we demonstrate this by testing the inequality using three and four settings. We observe excellent agreement with quantum predictions and a violation of five and six standard deviations, respectively, compared to Leggett's non-local hidden variable theory.
Zz.
[1] J. Romero et al., N. Jour. Phys. v.12, p.123007 (2010).
Monday, December 20, 2010
Shatter Metals With Liquid Nitrogen
More fun and educational demo from Jefferson Lab. This time, it shows how one can shatter a metal (pewter) by cooling it with liquid nitrogen. Too bad they didn't spend much time explaining why this happens.
Zz.
Zz.
Physics and Diplomacy
Thanks to PhysicsToday Science and Media news for pointing out a terrific letter written by Neil deGrasse Tyson in the NY Times regarding the late Richard Holbrook. It is worth repeating here:
I've written about this many times already on the importance of physics education. When I came up with a series of experiments to revamp undergraduate physics laboratories, I had this very thing in mind. It isn't meant to just train people to become physicists. It is meant to train everyone on how to think analytically, and that figuring out the central principle, be it a physical phenomenon or a political issue, gives one a very systematic approach on how to think things through.
A very nice letter.
Zz.
When I gave Ambassador Richard Holbrooke a personal tour of the newly opened Rose Center for Earth and Space and Hayden Planetarium in 2000, I could not help notice how fluent he was in the depth and breadth of his cosmic curiosity.
True science literacy is less about what you know and more about how your brain is wired for asking questions. Later in the tour he confessed that, as an undergraduate at Brown, he studied physics before switching to politics.
I could not resist asking him whether that exposure to physics made a difference in his career as a diplomat, especially in tense, war-torn areas of the world that are resistant to negotiated peace settlements.
He answered emphatically “yes,” citing the physics-inspired approach of sifting for the fundamental drivers of a cause or phenomenon — stripped of all ornament. To get there, one must assess how and when to ignore the surrounding details, which can give the illusion of importance, yet in the end, are often irrelevant distractions to solutions of otherwise intractable problems.
I've written about this many times already on the importance of physics education. When I came up with a series of experiments to revamp undergraduate physics laboratories, I had this very thing in mind. It isn't meant to just train people to become physicists. It is meant to train everyone on how to think analytically, and that figuring out the central principle, be it a physical phenomenon or a political issue, gives one a very systematic approach on how to think things through.
A very nice letter.
Zz.
Friday, December 17, 2010
Tuesday, December 14, 2010
Inflationary Versus Cyclic Universe
I'm guessing that most of you have heard of the battle being done on arXiv between Penrose/Gurzadyan and a number of groups disputing their conclusion. This is being reported on Nature News (which has a limited amount of time for free access).
Simply put, Penrose/Gurzadyan examined the cosmic microwave background data from WMAP and showed that there are these concentric rings of uniform temperature in the CMB. This is not in dispute. What is in dispute is that they concluded that that these are signatures of "... black holes colliding in a previous cosmic 'aeon' that existed before our Universe....", thus, giving an evidence towards a cyclic universe[1].
That led to a flurry of activities, and 3 groups have independently challenged that view[2,3,4].
Of course, that's not the end of it. Gurzadyan/Penrose has posted a rebuttal (also on arXiv)[5]. I'm sure there will be more forthcoming to rebut that one as well. People don't even wait anymore for such a thing to be published.
This, btw, is what happens when we try to deduce something using only a set of data and not in possession of other types of data. Often, in such a case, the conclusion isn't unique. You say the data is consistent with A, someone else can also say it is consistent with B. That is why we seldom accept anything to be valid until this non-uniqueness has been sufficiently removed, and Mother Nature clearly points to a single, clear description of such-and-such phenomenon. It is why science can take a very long time to come up with a valid theory of something.
Z.
1. Gurzadyan, V. G. and Penrose, R. Preprint at http://arxiv.org/abs/1011.3706 (2010).
2. Wehus, I. K. and Eriksen, H. K. Preprint at http://arxiv.org/abs/1012.1268 (2010).
3. Moss, A., Scott, D. and Zibin, J. P. Preprint at http://arxiv.org/abs/1012.1305 (2010).
4. Hajian, A. Preprint at http://arxiv.org/abs/1012.1656 (2010).
5. Gurzadyan, V. and Penrose, R Preprint at http://arxiv.org/abs/1012.1486 (2010).
Simply put, Penrose/Gurzadyan examined the cosmic microwave background data from WMAP and showed that there are these concentric rings of uniform temperature in the CMB. This is not in dispute. What is in dispute is that they concluded that that these are signatures of "... black holes colliding in a previous cosmic 'aeon' that existed before our Universe....", thus, giving an evidence towards a cyclic universe[1].
That led to a flurry of activities, and 3 groups have independently challenged that view[2,3,4].
To gauge this significance, Gurzadyan compared the observed circles with a simulation of the cosmic microwave background in which temperature fluctuations were completely scale invariant, meaning that their abundance was independent of their size. In doing so, he found that there ought not to be any patterns. But the groups who are critical of his work say that this is not what the cosmic microwave background is like.
They point out that the WMAP data clearly show that there are far more hot and cold spots at smaller angular scales, and that it is therefore wrong to assume that the microwave sky is isotropic. All three groups searched for circular variance patterns in simulations of the cosmic microwave background that assume the basic properties of the inflationary Universe, and all found circles that are very similar to the ones in the WMAP data.
Moss and his colleagues even carried out a slight variation of the exercise and found that both the observational data and the inflationary simulations also contain concentric regions of low variance in the shape of equilateral triangles. "The result obtained by Gurzadyan and Penrose does not in any way provide evidence for Penrose's cyclical model of the Universe over standard inflation," says Zibin.
Of course, that's not the end of it. Gurzadyan/Penrose has posted a rebuttal (also on arXiv)[5]. I'm sure there will be more forthcoming to rebut that one as well. People don't even wait anymore for such a thing to be published.
This, btw, is what happens when we try to deduce something using only a set of data and not in possession of other types of data. Often, in such a case, the conclusion isn't unique. You say the data is consistent with A, someone else can also say it is consistent with B. That is why we seldom accept anything to be valid until this non-uniqueness has been sufficiently removed, and Mother Nature clearly points to a single, clear description of such-and-such phenomenon. It is why science can take a very long time to come up with a valid theory of something.
Z.
1. Gurzadyan, V. G. and Penrose, R. Preprint at http://arxiv.org/abs/1011.3706 (2010).
2. Wehus, I. K. and Eriksen, H. K. Preprint at http://arxiv.org/abs/1012.1268 (2010).
3. Moss, A., Scott, D. and Zibin, J. P. Preprint at http://arxiv.org/abs/1012.1305 (2010).
4. Hajian, A. Preprint at http://arxiv.org/abs/1012.1656 (2010).
5. Gurzadyan, V. and Penrose, R Preprint at http://arxiv.org/abs/1012.1486 (2010).
Monday, December 13, 2010
Questioning The Radius Of The Proton
A brief highlight of the just published paper out of the Paul Scherrer Institut on a recently-measured proton form factor using a muonic hydrogen. You also (I believe) get a free copy of the actual paper.
It will be interesting to see how CODATA handles this new information, and whether the radius of a proton will have a change in subsequent updates.
Zz.
It will be interesting to see how CODATA handles this new information, and whether the radius of a proton will have a change in subsequent updates.
Zz.
Friday, December 10, 2010
The Physics of Holiday Decorations
... or to be specific, the Christmas tree and the Hanukkah menorah (or the Festivus pole if you wish).
PhysicsCentral has an amusing look at how unstable these items are during the holidays, especially when they are fully loaded with decorations.
Zz.
PhysicsCentral has an amusing look at how unstable these items are during the holidays, especially when they are fully loaded with decorations.
On a Christmas tree, the majority of the mass is concentrated near the floor. It has a low center of mass. The aluminum Festivus pole's mass is evenly distributed, putting its center of mass right near the center of the pole. For a menorah, with its branches at the top, it's center of mass is higher. That means the menorah would be the most likely to topple.
Zz.
Tuesday, December 07, 2010
Dear Fellow Quantum Mechanics
I try not to frequently highlight still-unpublished arXiv manuscripts. Some of them are crap and have no place else where they can go. But often, I would find something written by prominent physicists that simply demand to be mentioned. This is one such example.
Jeremy Bernstein has written an entertaining, but at the same time, rather informative view on quantum mechanics, especially on the "measurement problem". You have to read the entire article to get his argument. Along the way, he clarified the uncertainty principle based on what Heisenberg has written:
You will note that this is consistent with my earlier blog entry on the misconception of the HUP.
Still, the most fascinating aspect of this article is Bernstein's assertion about the observer based on Dyson's writing:
You also get a little provocative challenge at the very end of the article in which the scale of the Planck's time measured by a clock violates SR? Hum?
Like I said, whether you agree with the article or not, it is highly fascinating. :)
Zz.
Jeremy Bernstein has written an entertaining, but at the same time, rather informative view on quantum mechanics, especially on the "measurement problem". You have to read the entire article to get his argument. Along the way, he clarified the uncertainty principle based on what Heisenberg has written:
The uncertainty principle refers to the degree of indeterminateness in the possible present knowledge of the simultaneous values of various quantities with which the quantum theory deals; it does not restrict, for example, the exactness of a position measurement alone or a velocity measurement alone. Thus suppose that the velocity of a free electron is precisely known, while the position is completely unknown. Then the principle states that every subsequent observation of the position will alter the momentum by an unknown and undeterminable amount such that after carrying out the experiment our knowledge of the electronic motion is restricted by the uncertainty relation. This may be expressed in concise and general terms by saying that every experiment destroys some of the knowledge of the system which was obtained by previous experiments.
.
.
.
This formulation makes it clear that the uncertainty relation does not refer to the past: if the velocity of the electron is at first known and the position then exactly measured the position for times previous to the measurement may be calculated. Thus for the past times ΔxΔp is smaller than the usual limiting value, but this knowledge of the past is of a purely speculative character, since it can never (because of the unknown change in momentum caused by the position measurement) be used as an initial condition in any calculation of the future progress of the electron and thus cannot be subjected to experimental verification. It is a matter of personal belief whether such a calculation concerning the past history of the electron can be ascribed any physical reality or not.
You will note that this is consistent with my earlier blog entry on the misconception of the HUP.
Still, the most fascinating aspect of this article is Bernstein's assertion about the observer based on Dyson's writing:
My second general conclusion is that the ``role of the observer'' in quantum mechanics is solely to make the distinction between past and future. The role of the observer is not to cause an abrupt ``reduction of the wave-packet'', with the state of the system jumping discontinuously at the instant when it is observed. This picture of the observer interrupting the course of natural events is unnecessary and misleading. What really happens is that the quantum-mechanical description of an event ceases to be meaningful as the observer changes the point of reference from before the event to after it. We do not need a human observer to make quantum mechanics work. All we need is a point of reference, to separate past from future, to separate what has happened from what may happen, to separate facts from probabilities.
You also get a little provocative challenge at the very end of the article in which the scale of the Planck's time measured by a clock violates SR? Hum?
Like I said, whether you agree with the article or not, it is highly fascinating. :)
Zz.
Sunday, December 05, 2010
Science Versus Religion Battle in Israel
This is a very different battle between science and religion in Israel. If you think the battle here in the US is "complicated", wait till you read about the battle there!
It'll be interesting to see how this plays out.
Zz.
So the battle in Israel between advocates of science and advocates of Torah, surprisingly ends up to be not about an angry disagreement, but a profound agreement. Both sides agree that science education offers a road from being a Talmud scholar living on the dole who's never heard of Madam Curie to being an SUV-driving systems analyst who can't get enough of Lady Gaga.
All they disagree about is whether this is a road worth traveling.
It'll be interesting to see how this plays out.
Zz.
Saturday, December 04, 2010
"X" Marks The Spot
A lot of brouhaha has been going on this past week or so on the speculative particle called the "X" particle. The model for the existence of this particle could, in principle, explain the dark matter problem, and also the matter-antimatter imbalance of our universe.
Check out this MSNBC article, that gives you links to other articles, on this topic in case you missed it.
Zz.
Check out this MSNBC article, that gives you links to other articles, on this topic in case you missed it.
Zz.
Labels:
Cosmology,
Dark Energy,
Elementary Particles,
theory
Thursday, December 02, 2010
The Physics of X-Ray Backscattering at Airports
I'm back and severely jet-lagged. So it'll be a couple of days before I'm back up to speed with what's been happening. But yours truly got his first full-body scan at O'Hare on this past trip. Yippee!
I couldn't figure out if it was the X-ray backscattering or the millimeter wave technology. I was about to ask one of the TSA's officer what it was, but they were all rather busy at that time, and I was already "loitering" about the area for a few minutes. After giving it a thought, I decided not to risk raising suspicion about being too curious about the scanning technology and left.
Anyway, if anyone wants to look at the issue surrounding the millimeter wave technology, check out an earlier blog entry. Ars Technica has a good article covering the x-ray backscattering technology.
Happy traveling!
Zz.
I couldn't figure out if it was the X-ray backscattering or the millimeter wave technology. I was about to ask one of the TSA's officer what it was, but they were all rather busy at that time, and I was already "loitering" about the area for a few minutes. After giving it a thought, I decided not to risk raising suspicion about being too curious about the scanning technology and left.
Anyway, if anyone wants to look at the issue surrounding the millimeter wave technology, check out an earlier blog entry. Ars Technica has a good article covering the x-ray backscattering technology.
Happy traveling!
Zz.
Subscribe to:
Posts (Atom)