I am interested in the synthesis and characterization of new magnetic oxides. As a former faculty member of Florida State University, I am currently supervising several graduate students in my synthesis and crystal growth lab there. I am also in the process of establishing a solid state chemistry lab at the University of Winnipeg.
I am primarily interested in what are called strongly correlated electron systems, or materials which have unusual magnetic or electrical behavior. These include functional materials, such as new solid state batteries, multiferroics, or superconductors, but they also include systems of theoretical interest, such as geometrically frustrated magnets, low dimensional compounds, and heavy fermion compounds. As an experimentalist, my main methods of characterization include diffraction techniques such as x-ray scattering and neutron scattering, but the bulk of my time is spent on the synthesis and crystal growth of these new materials here at the University of Winnipeg.
Define the quantity, m, as the quantity such that, in an inertial frame, mv is conserved. Call this quantity "mass" (some call this "relativistic mass")
For tardyon's (particles which move at speeds less than c) the mass is a function of speed, i.e. m = m(v).
Certain quantities are observer dependant. The mass of a particle, m, as defined above, is one of them. Each observer will meausure the mass of a particle and obtain a quantitity which will depend of the relative velocity of observer and particle. That is what is called an "observer dependant quantity."
The norm of a 4-vector remains unchanged by a change in coordinates and is thus is an invariant. The scalar product of two 4-vectors also remains unchanged by a change in coordinates and thus is also an invariant.
Now consider the quantity P*U_obs/c which is the scalar product of the 4-momentum of a partricle and the 4-velocity of the observer divided by c, the speed of light. Since this is a scalar product of two 4-vectors it is an invariant. It can be easily shown that
And thus the magntiude of this scalar product, m, is an invariant. This is overly obvious since U_obs represents the observer and thus its not surprising that U_obs dotted with a quantity will be observer dependant.
However the components of a 4-vector change upon a change in coordinate system so in that context "mc" and thus "m" is not an invariant.
Example from Euclidian geometry - The dot product the position vector, R = (x,y,z), and the unit vector in the x-direction, "i", is an invariant. i.e.
In the new system R = (x',y',z'). The dot product of the vector with the new unit vector will now be R*i' = x' which will in general be different than R*i = x. However i and i' are quite different vectors and therefore i != i'. The quantity R*i is a Euclidean scalar and has the value of x.
Thus x can be interpreted in two ways, one way as the component of a vector (and as such not an invariant) and another way as the component of R along a given direction - the quantity then being invariant.
Thanks for the great diagrams, working back through the traditional astronomical jargon was going to be tedious!
Perhaps the diagram could be made less'busy' using an "exploded view" where the plane of the Earth-Moon system ,
is shown as a smaller part of the plane of the Solar System , it self a smaller part of the plane of the Milky-Way !
with origin based on the multi-million solar-mass black-hole at the'centre' of the Milky-Way Galaxy (ie ours);
The natural co-ordinate system which suggested itself was actually a cylindrical one with the our star (Sol ?)'s;
distance to that centre as one co-ordinate, it's hieght above or below the galactic plane (or angle subtended at the origin) another;
and finally the whole co-ordinate system rotating with the Milky-Way by setting Sol's 'longitude' to zero degrees !
Unfortunately the location of the exact center of the Milky Way is not known due to a number of issues. From wiki:
An accurate determination of the distance to the Galactic Center as established from variable stars (e.g. RR Lyrae variables) or standard candles (e.g. red-clump stars) is hindered by countless effects, which include: an ambiguous reddening law; a bias for smaller values of the distance to the Galactic Center because of a preferential sampling of stars toward the near side of the Galactic bulge owing to interstellar extinction; and an uncertainty in characterizing how a mean distance to a group of variable stars found in the direction of the Galactic bulge relates to the distance to the Galactic Center.
The supermassive black hole is almost certainly not at the center though, but probably lies a few thousand light-years off from the center. It's a bit like how the Sun isn't always the center of the solar system (as defined as the barycenter, or center of mass).
That 3D TV & Film never really worked out - at least in its latest iteration - is a topic beyond the scope of this thread. Nevertheless, it would be an ideal way to represent the orientation (and motion) of the solar system in relation to the Milky Way, especially if it included 'zoom' controls. Such a fully immersive apprehension-at-a-glance technology will probably be a visual treat reserved for the next generation. Saying that, I did once undertake a slow tour of the solar system via Oculus VR, and that was tremendously impressive. Sticks in the memory, even now.
I made this diagram using the drawing tools Microsoft Word believe it or not. The reason I made it was to avoid using a lot of words, which wouldn’t really give people a clear idea idea of what I was trying to convey. And in all honesty, I don’t really understand what you’re saying. I would suggest, if you’re trying to get your idea across, that you use pictures and drawings (worth thousands of words).
Amazing thread! Thank you very much for the pictures. They are great! They say a lot more than reading.
Hard to imagine if this is even a pertinent question, but i couldn't answer it myself. What seems to confuse me is the large spans of time and space involved.
From what i got from this thread, it appears solar system crossed galactic equator around 3Mil years ago. Was that the moment that could be considered as an equinox?
Also, to me it seems a little strange, that ~3 million years number. Kind of coincides with homo erectus location in time, more or less.
The term 'equinox' means that for Earth, both North and South hemispheres are receiving the same amount of sunlight.
The galactic center does not emit any radiation that makes any difference for the circumstances of Earth, or the Sun.
I presume that wavey trajectory of the sun is waving around a center line that matches galactic disc.
Is it correct in diagram 1 that the summer and winter solstice occur closest to the center of the galactic plane and equinoxs occur when the earth is farthest from the galactic plane? If this is the case, then wouldn’t the North Celestial Pole be misrepresented in this 2d model?
It's important to bear in mind the scale of what you are describing. The Galaxy is around 1000LY thick and the solar system is only about 30 AU across (1AU is around 1/6000 LY). So the solar system is minute in terms of the layout of the galaxy. The "Galactic Plane" is far too fuzzy to use the geometry that you seem to be using. The 'tilt' of the plane of the ecliptic relative the the galactic plane is a pretty random and irrelevant quantity.
I was more interested in which angle the tilt of the earth (celestial axis) is compared to the galactic plane. It would appear to tilt outward away from the galactic center more than it does north or south of the galactic plane. I assume this because the winter/summer solstice are at or near the galactic plane at this time and equinoxes are above and below the galactic plane. Does this sound correct? Just trying to give myself a relative perspective.
But, whatever it is, it's surely just arbitrary. There will be systems with an ecliptic that is almost at right angles to the galactic plane, systems that are right near the lateral edge etc. etc. so what would make their orientation of any interest at all?
I was more interested in which angle the tilt of the earth (celestial axis) is compared to the galactic plane.
Don't the fig. 2 and fig. 3 in post #1 answer this question? The angles given are between axes or planes, but it's just a matter of subtracting them from 90 degrees if you want an angle between an axis and a plane.
It would appear to tilt outward away from the galactic center more than it does north or south of the galactic plane.
I think you're describing the angle between the celestial axis (celestial north) and the galactic plane, but it's larger not smaller than the previous one (it's the 62.9 degrees from before).
I think the issue he has with the diagram is with where the nodes between the ecliptic and celestial planes are located. In the diagram, the Earth is shown as being near the winter solstice, but the direction the Earth's axis is shown as pointing, relative to the direction of the Sun, looks closer to what you would expect during an equinox.
Yes this was my intent. I may not have expressed that clearly. I was simply trying to discover the angle of the earth’s Celestial axis in relation to the direction of the travel of the sun. I may have complicated the question by using a inprecise variable such as galactic plane. I am assuming since the earth is near galactic plane (as illustrated) at the time of summer solstice, then the axial tilt of the earth would be in the direction of the sun and not to the galactic north. Is this a correct assumption? I’m not criticizing the great work. I am just trying to clarify my understanding of the earth’s orientation in relation to the sun’s direction of travel.
I am assuming since the earth is near galactic plane (as illustrated) at the time of summer solstice, then the axial tilt of the earth would be in the direction of the sun and not to the galactic north.
Ah. You're right. Well spotted. It does look like it's pointing in the wrong direction, and should indeed be deflected towards the reader rather than in the plane of the picture.
Maybe @fizixfan will stop by and take a shot at correcting it. Although I imagine it might be difficult to render it clearly in two dimensions.
I've been following this thread since Loki sullivan started posting, but I've been unable to fully understand what's being said. This may not answer your question, but the Earth's Axis of Rotation is tilted "away" from the Sun in the Winter, which is why it gets colder in the Northern Hemisphere during winter (you probably already know that), and tilted "toward" the Sun in the Northern Hemisphere in the Summer. The Earth is also situated between the Sun and the Galactic Center in the summer (Sun - Earth - Galactic Center). That's why we have such great viewing of the Milky Way in the summer months - because the Sun isn't in the way at night and we're looking toward the Galactic Center. In winter the Sun is between the Earth and Galactic Center (Earth-Sun-Galactic Center), so no viewing of the Milky Way in Winter from the NH.
The Earth, in a physical sense, is about 50 light years north of the Galactic Equator, so change in position of 186 million miles from over the course of a year isn't going to change our position with respect to the Galactic Plane. What does change is our point of view, since we are on a tilted, spinning sphere orbiting the sun.
The axial tilt of the earth does not vary relative to the Galactic North on a seasonal basis or even during a human lifetime - although it does precess (Google that term if necessary). But for the purposes of this discussion let's just say the North Celestial Pole (Earth's Axis of Rotation) and the North Galactic Pole (Milky Way's Axis of Rotation) do not vary. The angle between the NCP and NGP is 62.9°, although this can only be determined using spherical trigonometry, since the Celestial Equator, Ecliptic Plane and Galactic Plane do not intersect at a single point. See Figures 2 and 3 in my original post. I'm including another crude drawing I did that may help. Words are really kind of hopeless in explaining three different celestial coordinate systems - which is why I prefer pictures.
It might also help if you read all the posts in this thread, but especially, I would encourage you to go to a place where there are dark skies during the summer months and look up. I recently purchased a telescope for my camera, and have found some amateur astrophotographers to hang out with. I would also recommend uploading Stellarium - a free planetarium program for your PC, and Skywatch for you mobile device.
Let me first say, thank you for sharing your work. I have learned much from your illustrations. As far as my inquiry, I hope you understand I am not criticizing your work but seeking clarification for my own understanding. I DO understand the axial tilt of the earth and its affect on seasonality. My question was referring to the direction of axial tilt of the earth. In the illustration, the angle of the earth axis in relation to galactic plane is apparent, but the axial tilt direction appears to be towards the sun when near the winter solstice. If I am understanding that the northern hemisphere is shown to the left, then wouldn’t the direction of axial tilt be away from the sun at winter solstice? It may just be a misinterpretation due to the nature of 2D renderings, so I ask for clarification for my own understanding.
Looking at the Sun's direction of travel arrow on fizixfan's 'Motion of Earth & Sun around the Milky Way' diagram, does this mean then that the solar system is orbiting the Galaxy in a clockwise direction? Also, which hemisphere of Earth's is (mostly?) facing the direction the solar system is taking during its orbit round the galactic disc? North or South? Or do they each take turns during the course of a terrestrial year? I can't quite put it all together it somehow.
You'll be interested to know that, since the Earth's equator is inclined so steeply (60.2 degrees) to the plane of the Milky Way, that there are features of the Milky Way, such as the Galactic Center and Galactic Bulge, that can only be seen from the Northern Hemisphere, and features such as the Coalsack Nebula and the small and large Magellanic Clouds, that can only be seen from the Southern Hemisphere!
i have heard that there exists an anomaly in amount of neutrinos coming from sun. are there any explanations around? how is the presence of jupiter sized planets near stars have been explained?
I believe there are some unexplained questions regarding this. For example, why has Jupiter not spiraled into the sun? Why is our system apparently stable?
It seems that in other systems there may possibly be a lot of crud and debris which by collision and turbulence gradually drain energy out of planet orbits so that the giant planets, more often than not, creep in closer and closer to the star. Almost as if
Perhaps these systems did not start off with as much angular momentum as ours. Anyway it does seem that we were rather lucky.
If Jupiter were to start squandering its own angular momentum and energy in gradually cleaning out the asteroid belt, and catapulting one asteroid after another out of the system, by the gravity-slingshot type of encounter, then it would lose energy and gradually creep in somewhat closer to the sun. this would be a major screwup. Bad things can happen in a complex orbital system----but we (thanks be to Allah the all-merciful) have apparently not suffered the worst that nature can deal out.
i have heard that there exists an anomaly in amount of neutrinos coming from sun. are there any explanations around?
Yes the anomaly has been resolved. An acquaintance of mine was on the team that ran the big tank of Heavy Water in Canada that detected the missing neutrinos. These devious neutrinos had, with devlish elusiveness, been evading detection by changing into other types of neutrinos which the earlier detectors couldn't see. The whole point seems to be that there are three types (and three corresponding antineutrino types for a total of 6) and that the normal type-----electron-neutrino or electon-antineutrino----that the sun makes can change during flight into other types that are harder to detect because they do not undergo the same reactions. This is admittedly confusing but doubtless it is all for the best
have heard that there exists an anomaly in amount of neutrinos coming from sun. are there any explanations around?
There are three kinds of neutrinos. The reactions in the sun generate electron neutrinos. The older experiments looked for electron neutrinos and didn't find enough. More recently they have found, by looking for all three kinds, that there are enough, assuming that neutrinos can change from one kind to another. Under this assumption, it is necessary to assume that neutrinos have mass. That is the current state of neutrino theory.
Many astronomers think that giant planets in close to a star is the norm, and it is our star system that needs explaining. One theory called, http://www.space.com/scienceastronomy/solarsystem/jupiter_elements_991117.html [Broken] has gained considerable popularity. It claims that jupiter formed very close to the Sun, "as most giants do", and then moved outward later.
Yes, neutrinos are now known to have mass; the SNO and Super-K experiments confirmed this a few years ago. We do not yet know their actual masses, we just have data on the mass differences. But it appears highly probably that neutrino masses will only make up a tiny portion of the missing dark matter.
It seems to mean that the distribution of elements within our solar system matches the distribution one would expect to find without planetary migration. If the solar system did indeed form from an amorphous cloud of dust particles and gas molecules pulled together by gravity, one would expect to find the heavier elements near the gravitational "bottom" (the center). And that is exactly what we do find; rocky planets made of carbon and various metals occupy the center of our system, while the outside is the domain of the "gas giants". There is even a belt made of rocky asteroids marking the borderland between the two zones.
For the planetary migration model to work, we would need some excuse as to why the innermost part of the solar system was originally composed of lighter elements. To me, this seems to oppose Occum's Razor.
Could it be that the protoplanet's initial velocity was the major factor in it's present location? We know that (for circular satellite orbits) it's mass has nothing to do with it's orbital radius. It's orbital radius is totally dependant on the tangential velocity and mass of the object it is orbiting (assuming it is orbiting a much more massive object than itself.) I wouldn't expect many of these planets to have circular orbits, but probably close enough to presume that the planet's mass has little correlation to it's position.
I wonder if Kepler's Laws hold for these extrasolar planets? Probably don't have accurate enough metrics on them yet.
Tidal friction could be the "sling" to propel heavy planets (usually up to higher orbit, but in some cases interplay of angular momentum of star vs planet can propel it inward too).