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| Thursday, October 9th, 2008 | 9:59 pm
[saber_rider]
 |
Scale Symmetry and the Conservation of.... what?
What happens if you take, say, a box, and increase the lengths of all sides from a to 2a. Well, your box is now eight times bigger, but it's still a box. In fact, you scale all lengths of an object by the same amount, and you'll still have the same object, just of a total different size. This gets more interesting if you have two boxes, both of the same size initially. Put them against a plain background, take a picture, and scale one of the boxes, leaving the other untouched. Now take a second picture. Provided you don't get any hints from other parts of the photo, there's no way to tell in a second photo if one box has been scaled up, or the other has been scaled down. It would seem that scale is a very good symmetry.
Now, of course, you may think of a large animal, such as an elephant. Scale it up, and you get a larger elephant. But weight scales as length cubed, but area only as length squared. It would seem the pressure in the poor animal's legs scales up now as the length (l^3/l^2), and when you're a big animal like an elephant, this is going to be more pressure than your skeleton can handle. So, perhaps, scale is not such a good symmetry after all. But all we did was scale the elephant. What if we scale earth along with it? Well, mass still stays the same, but the distance to the center will increase. Hence the weight will scale down as 1/length^2, and we don't recover our same elephant, but one with lighter weight on it's feet!
These kinds of symmetries are very important, especially in quantum mechanics and high energy physics. A good symmetry implies, via something called "Noether's Theorem" a conserved "charge" of some sort. Electric charge is one such conserved charge, but we can deduce conservation of energy, momentum, and angular momentum, too. These arise from phase, translational, and rotational symmetries, respectively. So what does scale symmetry imply?
Let us imagine a very simple universe consisting of only two point particles. They are some distance apart, but what of this distance? How are we to tell if it is one micron, or one hundred light years? We cannot. Distance only has meaning as a reference to other distances. Now add a third particle. It can be anywhere, but it will certainly have a distance to the other two particles. Now, finally, it seems distance has some meaning. Taking our original pair to define a length metric, we can now say that the third particle is some multiple of this metric away from each of the original two particles.
So given this triangle configuration, let's assume we have gravity. Gravity is proportional to the product of the masses, and inversely proportional to the square of the distance between particles. The proportionality constant is what we call G. You can probably guess where this is going. Let us scale all distances by the same amount. We have the same triangle, four times the size, but of otherwise identical geometry. But what of the forces? Each force, between the same pairs of masses, ought to degrease by a factor of four. Whoops, maybe scale really isn't such a good symmetry. But what is a force? We don't measure forces, really, but accelerations. Accelerations are calculated from distances and times. But what is time? The only way we have of keeping track of time is to track the motion of some reference objects. In our scale now, we have universally reduced G to G/4. But the motion of each particle relative to each other is STILL the same; this proportionality constant is really just arbitary. In our three particle universe, we may as well just set it equal to unity.
I would think this kind of argument would apply to other forces, and in a universe with more particles.
So, my question is, is scale a good symmetry of the universe, at least globally? And if so, what does it conserve? I did the math to figure out the conserved current of scale, as a homework, but the professor wouldn't tell us what the conserved current was, nor could a few other professors whom I've asked. | | Tuesday, October 7th, 2008 | 7:19 pm
[pmax3]
 |
Equality of gravitational and intertial mass Ok I've been putting off asking this question for a long time now, because the anomaly seems so straightforward to me that I am probably mistaken in a very stupid way, but I'll overcome my hesitation and ask it now: Why is such a big deal made out of gravitational and inertial mass being equal? Isn't it the case that we have defined the universal gravitational constant G in such a way that using the (inertial) mass in the equation for gravitational force between two bodies gives us the, well, gravitational force between them? We reverse the same equation and get the (gravitational, so called) mass from the same equation, which has to be equal to the inertial mass because we used it in the first place, and then we wonder how the "two" are equal! What am I missing here? Thanks a lot for your answers. Current Mood:  good | | Sunday, October 5th, 2008 | 1:58 pm
[calysto]
 |
Why? Before I ask this question, three important caveats: - I don't believe in coincidences
- I have a keen interest in physics, but zero training :(
- I tried to google the answer to this but it has too many common search terms to be useful, so... I did try to RTFM.
With those caveats in mind, here's my question: Why is E exactly equal to M multiplied by the square of the speed of light? Or to look at it in a way which illustrates the point of the question more keenly, why does light travel at a speed exactly equal to the square root of mass' relationship to energy? I understand that many of nature's basic laws have no "why" they just are, but there has to be a reason for a correlation involving such a specific number. | | Thursday, October 2nd, 2008 | 7:40 pm
[cjwade]
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Cha Cha Slide As a Physics Lesson This is of a different level of inquiry than some entries but it is still True Physics at Heart. I teach physics to a Diploma Plus High School in Indianapolis on the campus of Arsenal Technical HS. We are a projects based curriculum. Our current project was for my students to create lesson plans so that they could teach outsiders how we analyze motion in a physics class. We were exploring (okay playing, I believe best lessons are based on phun) using sonic rangers to create motion graphs and have people match the motion. They were getting frustrated & bored as they tried to understand enough so that they could teach it. I suggested they think of it as a dance, so naturally someone asked if they could match it to a dance. I was like, sure if the dance was linear. A quick discussion led to us exploring how to use the song "Cha Cha Slide". And yep, sure enough using iTunes and the motion analysis program we were quickly matching motions and discussing what you had to do (sliding, accelerations, directions to turn, standing still, etc) and the students hated errors in their motions, such as signals that were bounced to floor or ceiling and figured out ways to minimize these errors. And trust me, it was priceless to see our brand new Social Worker, our Academic Dean, and our "slightly older" secretary all come into the class and try to match the motions as well. Easily, best lesson that I was a part of in the past three years! I gotta stay creative. Current Mood: excitedCurrent Music: Wake Up Alone, Amy Winehouse | | Wednesday, October 1st, 2008 | 8:47 pm
[dlakelan]
 |
Flash game for physics geeks Fantastic Contraption Can you get past level 13 "Big Ball"?? I'm impressed at the physics simulation. But flash is really cranking hard... Warning, you will spend hours working on this. | 6:25 pm
[krilltish] |
Momentum I was recently wattching a show about physics and it focused primarily on pe-Relativity history.
In it, they state that someone (I forget whom) realized that momentum was not p=mv as Newton said, but really p=mv^2.
However, I always thought that momentum was more accurately described as: p=(1/sqrt1-(v^2/c^2))m{i}v.
Where (1/sqrt1-(v^2/c^2)) is the Lorentz factor and m{i} is the invariant mass. I figure that the newer equation is more correct, but how correct? What is the history of the older equation? Any additional information would be useful as well, of course.
Thank you all.
Current Mood:  pensive | | Thursday, October 2nd, 2008 | 2:22 am
[pmax3]
|
Penrose Hello! I seek your help in resolving some issues regarding free will that I have been grappling with. I don't know where Roger Penrose stands on the issue. I know his work has been used to support and explain free will but here [ http://psyche.csse.monash.edu.au/v2/psyche-2-23-penrose.html] (see section 13), he seems to be saying that there is some kind of mathematics that "PRECEISELY DETERMINES" human behaviour, and yet goes on to say it may be compatible with our "(feelings of)" free will. Is he making sense? Does he agree with the existence of (libertarian) free will or is he just another compatiblist like Dennett in disguise? Your inputs are much appreciated, thanks! | | Wednesday, October 1st, 2008 | 3:05 pm
[gammameta]
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Atoms I have what's probably a silly question, but I can't find an answer online or in the books I've searched. Hoping someone more knowledgeable can help. Atoms - why do they form the way they do? What are the forces at work that make them want to form orbitals instead of just being 'blobs' of matter? There is the force of attraction (the protons, neutrons, and electrons all have mass) and of charge. The electrons certainly repel each other, and that force is stronger than the attraction of mass. However - the protons repel each other, and they are in much closer proximity together in the nucleus. The electrons are attracted to the nucleus itself. Why don't they 'glom' on to the outside of a nucleus? Why do they orbit around it? If electrons were similar in mass to protons, would they still form orbitals? Can we at all liken this to orbiting planets? I've been able to find a lot of equations that explain how to calculate the energy level of an electron orbital. But I'm after the fundamental forces at work that explain that configuration in the first place. Is there a physical explanation for this I'm missing? Thanks for any fb you might have. Current Mood:  confused | | Tuesday, September 30th, 2008 | 12:01 am
[zigurdu]
 |
Fourier integral Hi. I'm calculating the probability amplitude for a simple scattering process in QFT to first order. On the way I was intrigued by our given result for a three-dimensional Fourier transform of the Coloumb potential:  Here, q = p_f - p_i is the momentum transfer vector. I'm trying to reproduce this result, but I'm out of ideas. I switched to spherical coordinates, called the absolute value of the x vector r, aligned q with the "z" axis and integrated wrt. the spherical angles:  If the minus sign between the exponentials had been a plus, the integrand would be symmetric and the whole thing would be a delta function (which I don't want, because q HAS to be different from zero if it's a scattering process). Anyway, I simply don't know how to solve this. Even using the residue theorem brings trouble because you have to change from r to |r| if extending the integral to negative infinity. The result being given, I don't have to solve this, but I'd prefer to be able to. Thanks for any help. | | Monday, September 29th, 2008 | 12:18 am
[calysto]
 |
Another Problem with Time Travel
Say I build a time machine... it successfully sends me back ten years... I arrive in exactly the same place ten years earlier... and I'm hanging in empty space because the Earth isn't located here yet.
Space-time being a single fabric with both a space coordinate and a time coordinate, that is.
I am quite sure I am not the first person to realize this, so why haven't I heard anyone mention this before? (realizing, of course, that I am not a scientist, so I'm only exposed to X amount of actual science in the din) | | Sunday, September 28th, 2008 | 1:02 am
[allmhuran]
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Expansion of space, gravitational mass, inertial mass I have a few questions on these topics. I'd like to point out first up that I am not knowledgeable of the mathematics. My study of physics ended in second year university. I am interested in the subject and therefore stay in touch with the broad concepts, especially when it comes to cosmology, which I find particularly interesting. I'm hoping to find people who know much more than I do who can help me with some thoughts. ( With that out of the way... ) | | Friday, September 26th, 2008 | 6:00 pm
[castusalbuscor]
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Assignment help - Fortran program Hey, me again I managed to get Fortran working on my Mac, however I believe I am getting the wrong answer. The question is to find the Black-body power flux per unit wavelength using the following equation: From 3000Å to 8000Å at two temperatures 6000K and 8000K 10000K. Then we have to graph it, which gives: I was showing it to fellow class mate and he told me there is supposed to be a peak according to Wien's Law, for the 6000K it should be at 4830Å which it does not do so in my graph. Here is a link to my code, it is by far not the most elegant code, I am sure there is something missing in there that's just too simple and is going to cause me to bang my head against a wall once I figure it out. I guess what I am asking is: My code seems right, but the output is not, am I using the wrong units? Current Mood: confused | | Wednesday, September 24th, 2008 | 8:15 am
[bob_the_normal]
 |
LHC Delayed Again
I'm sure most of you have heard about this, but I thought I'd post it for the people that are too busy to regularly check CERN's site (like me!).
The LHC commissioning will be pushed back until next year due to what is suspected to be a mechanical failure between two magnets. You can read more about it at CERN's website.
Another year to wait. =/
Later. | 12:49 am
[castusalbuscor]
 |
Fortran In one of my Physics courses the prof wants us to hand in the next assignment in bloody fortran, except I don't have a fortran complier on my Mac (running OS X 10.5.5). Mac Ports proved to be useless in that front (we have to use fortran 77). I guess the question is where do I get a f77 compiler for my Mac? Thanks guys Edit: I got g95 running, and I don't care if it does not compile in f77, the prof can just shove it to put it in a polite way. I also have Ubuntu on a virtual machine just in case g95 does something strange Current Mood:  aggravated | | Tuesday, September 23rd, 2008 | 5:45 pm
[red_handed]
 |
A Few LHC Icons There are four of them and a silly 'Love' bar I made behind the cut. Take 'em, use 'em, credit me if you want. ( the LHC is love ) | 6:48 pm
[kenonline]
 |
| | Wednesday, September 24th, 2008 | 3:29 am
[sindragosam] |
Friction and tops
I was playing with a top just now, and I suddenly thought that if I spun a disc with the same weigh and Moment of Inertia on the floor, it would come to rest almost immediately. So obviously the reason that the top remains spinning for so long is that it's tiny point minimizes contact with the floor.
But I remember reading that friction only depends on the weight, and not on the area of contact. So why should this be a factor? Or could it be that the laws for friction in angular motion and for linear motion are not the same?
Thanks. | | Tuesday, September 23rd, 2008 | 4:38 am
[luxmacabre]
 |
Problem help
Hello Physics community :)
Hope a homework help post is okay? I'd like any input on how to approach this problem:
A baseball thrown at an angle of 60.0 degrees above the horizontal strikes a building 18.0 m away at a point 5.00 m above the point from which it is thrown. Find the initial and final velocity. Ignore air resistance.
I've been plugging and chugging for a few hours now and am still not getting answers consistent with the answers provided in my text. I'm also taking an introductory physics course if that is of any relevance.
TIA! | | Monday, September 22nd, 2008 | 2:39 am
[sbil]
 |
The Way to TOE Before I leave science for some period I decided to write an article about TOE. How I was creating TOE almost in all details: * motivation * the process of creation (as it was for me) * what TOE should cover * and more. This post is not about internals of TOE, but about everything around TOE. With an example of how to create TOE. Now you have everything around TOE except the TOE itself. Maybe someone will want to join me. Maybe I will release it later. The article is here: http://sbthebasics.com | | Saturday, September 20th, 2008 | 11:03 am
[chamcha]
 |
quantum mechanics?
At my institution, mathematics students are required to take four science courses beyond intro mechanics and e-mag/optics. (Yes, I am a mathematics student - NOT physics.) I was thinking about taking an intro to quantum mechanics as one of them. Advanced classical mechanics (Hamilton's principle, rigid body rotations, vibrations/waves, central force problems, etc.) is the only physics listed pre-requisite, which I have taken. But I was wondering I would be putting myself in a bad position having not taken modern physics. It's not listed as a pre-requisite, but maybe it's understood that a physics student would have already had modern by then?
For reference, the topics covered in quantum here are: Origins of quantum theory. Uncertainty principle. Schroedinger equation for simple systems, including hydrogen atom. Perturbation theory. Spin. Identical particles.
And the topics in modern physics are listed as special relativity theory, black body radiation, photons and electrons; wave particle duality, elements of atomic theory, nuclei and fundamental particles.
Of course I don't know if any of the latter are necessary before studying the former, which is my question to you. |
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