Mike-from-the-Bronx

forum.txt

How about something low tech like this: The switch is hidden behind a loose brick. During the day the loose brick is indistinguishable from all the other bricks that make up the building. But at night, because the interior of the building is well lit, a sliver of light shines through a crack above the brick. The protagonist would see the light, pull out the loose brick, flip the switch, replace the brick and toss some loose dirt into the crack so the bad guys would not see and follow.

I took a stab at this with my simulation program. I copied the arrangement offered by Edwina Lee. The arrangement implies a parent/child hierarchy as suggested by Bluemoon. In my simulation, the user does not declare the order of processing. The hierararchy defines it. Parent first, then child, grandchild, etc. Here's a link to a video I created from the results. http://www.relativitysimulation.com/Documents/Nested_Bowls.mp4

Oh. Then I with draw my criticism.

Oh boy. I just realized something embarrassing. When analyzing the contributions of the pans it is important to define the hanging point of the pans to be at the same elevation as the pivot point. Otherwise there will be non-offsetting torques contributed by the pans. I just added that caveat in my document.

Draw a free body diagram of the balance beam. Place a mark at the Center of Mass. Place another mark at the Pivot Point. Draw a vertical arrow through the center of mass. That’s the “f” in the formula, the force of gravity. Draw another arrow from the pivot point to the center of mass. That’s the displacement (the “r” in the formula) Torque is the cross product of those 2 arrows (vectors). That’s all there is to it. (I have done so many of these kinds of analyses it is instinctive. But to someone who only saw this kind of thing in an introductory physics class I imagine it could get confusing.)

Fair enough. I can't seem to post images here so I will try to post a link to an MS Word document with images. Hope this works. http://www.relativitysimulation.com/Documents/balancebeam3.docx

I accidentally voted this post up when I wanted to vote J.C.MacSwell up. swansont, you have displayed a lot of understanding in a lot of posts, but in this one you are dead wrong. J.C.MacSwell is dead right. Try re-posting this discussion on a classical physics or mechanical engineering forum and you will quickly be told that.

That works for me.

Post #18 is again very confusing. But the last statement (question) is valid. No analysis has yet been presented to show that a restoring torque exists on a balance beam which has been displaced from its normal horizontal position. I can't find one.

Good job studiot. (and your assessment of TakenItSeriously is spot on too)

If I understand you correctly, your conclusion would be that a Square moving at a 45 degree angle would just be a smaller square. Relativistic contraction does not work that way. (Edit: added "When....")When transforming reference frames in relativity velocities don't combine by the rules of vectors and neither does contraction. Example: If you take an object that is initially a square at rest with respect to you and transform to a reference frame that is moving northwest, the northwest and southeast corners of the square are contracted (closer to the center). The northeast and southwest corners are not effected at all. Connect the corners to determine the shape and it will be a symmetric diamond.

I am satisfied that the analysis I provided in my link in post #23 is correct and consistent with SR. But nobody’s perfect and I’ll try to stay open to the possibility that I made a mistake. I’ll be glad to go over the analysis step by step with anyone who wants. But I would ask that the requester first demonstrate their level of proficiency in SR by at least trying to solve the following 2 step problem. Given a 2D shape that is a square with proper dimensions 2 light-sec on each side when at rest with respect to reference frame S. One set of space time coordinates (common time for the 4 corners) with respect to S are; Corner a: (t, x, y) = (0, +1, +1) Corner b: (t, x, y) = (0, -1, -1) Corner c: (t, x, y) = (0, +1, -1) Corner d: (t, x, y) = (0, -1, +1) Where t is in seconds and x and y are in light seconds. Given also that there are 2 other reference frames S’ and S’’. S’ has velocity (vx, vy) = (-.6c, 0) with respect to S. S’’ has velocity (vx, vy) = (-.6c, .6c) with respect to S. Transform the shape to S’. Provide the velocity of the shape with respect to S’ and one set of space time coordinates with common time for the 4 corners. Transform the shape from S’ to S’’. Provide the velocity of the shape with respect to S’’ and one set of space time coordinates with common time for the 4 corners. Note: Task 2 is not a request to transform from S to S’’. I is a request to transform from S’ to S’’.

Well, I would not take that approach. I spent some time doing the full calculations. Link below. Interestingly, there was no rotation as I had previously predicted. I know the rotation shows up sometimes but, apparently, not for this problem. If you browse the document you will see that it is not entry level stuff. http://www.relativitysimulation.com/Documents/Square%20in%20Rectangle.htm Added this comment: I hope I copied all the numbers correctly.

I appreciate the suggestion, but Lord No. I stay away from visual effects in SR. I understand the existence of such effects but dealing with them is beyond me. I was referring to the following phenomena in SR: 1. Start in an inertial reference frame for which an object is at rest. Note the proper dimensions and (proper) shape of the object as given by the coordinates. 2. Sequentially perform multiple transformations to other inertial reference frames with different relative velocities in 2D or 3D space. 3. Transform back to a reference frame for which the object is at rest. Note the proper dimensions and (proper) shape of the object as given by the final coordinates. My experience (from doing shape transformations by the thousands) is that the final coordinates will define the original proper shape except that the shape will be rotated by some amount that is a function of the combined transformations. This SR behavior has been documented but I don't have a reference or name for it right now. studiot, in post above, suggested Thomas Precession. P.S. For any laymen reading this, note that transforming a shape, like a square, in SR is not as straightforward as just applying the Lorentz Transformation to the 4 corners. The LT will give you 4 coordinates in space for 4 different times. Relativity of Simultaneity. To determine the shape in the new reference frame, you have to adjust the spacial coordinates for one common time. If you are going to perform all 3 steps, you also have to calculate the relative velocity of the object with respect to each reference frame so that you know how to get back to zero relative velocity at the end.

Reads like you are going down the same tortuous path I went down when I first learned this aspect of SR. I'm not sure I would want to describe how I finally figured it out. But here are some hints. First recognize that velocities don't add like vectors in SR. So adding .7c in the y-direction to an existing .7c in the x-direction does not give a resultant velocity of (vx, vy) = (.7, .7). That's .99 at a 45 degree angle. Symmetrical diamond. It gives a velocity (vx, vy) of (.5, .7). So you don't get a symmetrical diamond. You can get the original dimensions (a square) back if you do all the transformations in reverse order. But what if many transformations were cascaded one after another and you don't know what they were? You are observing this strange shape moving in some strange direction. Can you just transform to a reference frame in which the object is at rest and get the square? Answer: Sort of. You will get a square but it will be rotated. At this point I am over my head and I will leave it to others to explain that.

Actually, that only applies transforming from rest to some non-zero velocity. Going from some non-zero velocity to another results in non-intuitive geometry changes. Here is a reference to a Tutorial I wrote; http://www.relativitysimulation.com/Tutorials/TutorialMeterstickAndHole.html The meter-stick-and-the-hole is a well analyzed "paradox" that was even written up in the American Journal of Physics. (Trying to find the reference now) When the problem was first given to me I went crazy. I was sure the paradox as real! What can I say. I'm a slow learner.

Yes, I grew up in the Bronx, East 223rd Street, long time ago now. I know the flavor of lead paint very well. I used to suck on it. With respect to the rectangular shape, yes, now I see that the OP intended that the angle of the velocity of the third observer contained a component that would result in the rectangle only having vertical velocity when the third observer was at rest. Good catch, twice. So now I agree with the last diagram; Rectangle at rest, square moving horizontally, third observer moving vertically. Last thing to correlate: Revised.................................................. When we switch reference frames to the third observer, the rectangle goes from rest to having vertical velocity (height contracted). The square already has horizontal velocity (already contracted horizontally) and now it acquires some vertical velocity so that its total velocity is somewhat diagonal and its contraction is somewhat diagonal. So the concern is weather the vertically contracted rectangle can still hold the diagonally contracted square. The key I would focus on is that a square contracted diagonally in 2 steps does not have the same shape as a square contracted diagonally in 1 step. That's how it still fits in the rectangle. This would be a good exercise: Start with a square and transform its shape to that observed by someone moving at .8c in the x-direction. Answer: Square is contracted by 40% in width and moving at .8c in the x-direction. Then: Transform that shape to that observed by someone moving at .8c in the y-direction. I'm too tired right now to do it. But the final velocity is not at 45 degrees and the shape does loose height.

Ok. Looks like I did not understand the initial setup. Let me try again. Initial Condition: Rectangle moving horizontally (width contracted, height unchanged). Square at Rest (fits in the rectangle, no contraction). Third observer moving diagonally (diagonally contracted). Switch reference frames to the rectangle. Rectangle at rest (no contraction). Square moving horizontally (width contracted, still fits in rectangle) Third observer now moving vertically (contraction changed). That's not a very challenging problem. Switch reference frames from initial setup to Third Observer. Rectangle now moving diagonally(with additional contraction). Square now moving diagonally (with contraction). Third Observer at rest. Let me stop here and make sure I am thinking what everybody else is thinking. If the third observer started out moving diagonally and we want to describe the world from the point of view of that observer, we are saying that observer is now at rest. Both shapes which previously had no diagonal velocity must now have some. Is that what is being said? P.S. With regard to the pole-in-the-barn paradox, there are some similarities and at first I thought, OK that's a good analogy. But there is no diagonally moving observer in pole-in-the-barn. A better analogy would be the meterstick-in-the-hole where diagonal motion is the focus. P.S. And yes I see Relativity of Simultaneity being involved all over the place in this problem.

I have a different understanding of your conundrum. It appears to me that you are not transforming the motions (hence the geometry) correctly. If your initial condition is a (1w x 1h) square moving diagonally and a (2w x 1h) rectangle moving vertically, the square will be a diamond sticking out of the compressed rectangle. OK However, if you transform to a reference frame where the square is at rest, it will become a square again, OK, but the rectangle will have diagonal motion and be a parallelogram. You don’t show that. Determining the dimensions of that parallelogram will give you a figure into which you cannot fit the square. I’m saying that on faith. I have not done the calculations. They are complicated. If you don’t feel up to doing them I could do them but I will need a few days. The important part is that, given the initial conditions, there cannot be a reference frame where the square is a square and the rectangle is a rectangle both having vertical and horizontal sides. Correction to this last statement......... There may actually be such a reference frame. But the overall dimensions of the two shapes will change such that there will be no paradox.

?????????? EDIT: Following is not part of the quote but my comments on the quote. In the original experiment, the Source of light, the Apparatus and the Observer were all at rest with respect to each other. Furthermore, the results were consistent no matter the angle at which the apparatus was oriented in space. Those conditions eliminate the possibility of either the Lorentz contraction OR the Doppler effect contributing to the results. What have you been reading?

I don't get it. We are all slightly shorter standing than when laying down. Gravity compresses us when we stand and to a lesser extent a meter stick too. Hence measuring the radius of Earth gives a slightly larger value than one would expect from measuring the circumference and applying a Euclidean formula. Even Newtonian physics tells us that. Is Feynman referring to something additional?

“Terrell Rotation” is not physical. It is a change in the appearance of an object as a consequence of viewing it from a reference frame from which is moving. The issue here is has nothing to do with appearances. Please disregard this comment ----- I thought the paradox was about a different arrangement.------- The “Bar and Ring Paradox” involves a rotation that is a consequence of transforming the geometry of a moving object to a reference frame which is moving in a direction NOT parallel to the objects original velocity. In this problem the diamonds and reference frames only have relative velocities in the X-direction. Hence the phenomenon has nothing to do with the issue described here. The resolution to this apparent paradox lies in the phenomenon of rigidity, the rigidity of the balloon. When you fall into a body of water at high speed, that water will act like a solid. It will bring you to a stop before getting out of your way, killing you. (That’s not scientifically precise, but you get the idea.) When the diamond which is moving at high speed relative to the balloon hits it, the diamond will be brought to a stop before the balloon breaks. By stop, I mean it will be accelerated/decelerated approximately to the velocity of the other diamond. Once both diamonds are at the same (or close to the same) velocity, they will have the same geometry. The balloon will break and the water will flow away in a symmetric fashion.

Let me back up a minute. If you are comfortable with freshman college physics and linear algebra, then you can handle introductory level Special Relativity. There are lots of introductions to be found on the internet or in bookstores. I believe other posters have referenced some. Many people will say that you don’t need knowledge of basic physics or linear algebra to learn Special Relativity. Speaking from experience, it would be exasperating trying to learn SR without that knowledge. Since you’ve built your own computer game I expect you already have the physics and math background. And I expect you already use a physics engine in that computer game that calculates position, orientation, velocity etc. for objects in reaction to user/system commands. That engine, whether it exists as a library, a separate chunk of your own code or many pieces spread throughout the program probably enforces the Newtonian laws of physics. If you want to enforce the laws of Relativistic Physics, you will need a Relativistic Physics Engine. (The process I provided in my last post is one superficial example of the many additions/changes that would exist in a Relativistic Physics engine.) I also expect you use some kind of Scene Graph in your game program, a hierarchical structure to manage the parent /child relationships of the objects being rendered. Again, whether it is a separate library or one of your own design, it probably manages those objects using the laws of vector algebra. I.e. child position = vector sum of (its position with respect to its parent) plus (that parent’s position). Well, relativistic physics doesn’t work that way. So you will need a separate Relativistic Scene Graph that manages the parent/child hierarchies according to the rules of Relativistic Physics. The processes that make up the Relativistic Physics Engine and Relativistic Scene Graph in my program are spread throughout the code. It’s spaghetti code! I’m in the process of organizing it now, but I am months away from being able to offer them as a usable library to anyone else. All I can give right now are the pieces as requested. In terms of passing code, I wonder if it would be better if I posted the code as web pages on my web site since it could get really long. I’ll start with a 3D Lorentz Transformation. Now where did I put that? Added some hours later: I posted an introduction to SR by David Hogg on my website at. http://www.relativitysimulation.com/Documents/SRbyDavidHogg It'spretty much the same presentation you will get from most textbooks and most members of this forum. But it does give the 3D version of the Lorentz Transformation (page 21). Credit to: David W. Hogg Center for Cosmology and Particle Physics Department of Physics New York University

Ok. So, from you original post I assume you already have the ability to display bodies/shapes in a graphical application. (2D or 3D doesn’t matter right now). And now you want to be able to modify those shapes to suit the laws of relativity. You probably already know that, in relativity, the shape of a body changes as its relative velocity changes. A cube that was sitting at rest next to you is not a cube anymore when it is moving with respect to you. You probably already know that a graphics engine renders a shape on screen based on the coordinates of its vertices. So, if you passed the engine four vertices with the following coordinates; (0,0) (1,0) (1,1) (0,1) The engine would render a square. If you want to render the body when it is moving at 87% the speed of light in the x-direction, you would have to pass the following coordinates to the engine; (.25, 0) (.75, 0) (.75, 1) (.25, 1) Or some other set that gave you x-dimensions that were half that of the square. So, you need to develop 2 capabilities. Be able to pass to the graphics engine a new set of coordinates for all the vertices of a body without having to recreate the body from scratch. (You could recreate the body from scratch but that would put an unnecessary load on the computer processor.) Be able to determine the new set of coordinates based on the relative velocity of the body. This is the hard part. You can use the Lorentz Transformation to determine the shape of the body for any relative velocity. But you will need a 3D or at least a 2D version of the Lorentz Transformation. First build the mathematical structure that is the Lorentz Transformation for the relative velocity you are using. Then pump the coordinates of every vertex through the transformation. Note that the transformation transforms events, not vertex coordinates. So you will need to convert the vertex coordinates to events, transform the events and then convert the transformed events back to vertex coordinates. It’s not as simple as it sounds. I can walk you thru it or send you some code (the code is in Java). If this post is totally off base and you really want to do something else, just disregard it.