From a lot of time discussions about SRT ant Relativity in this forum are circling, as I see it, around one and the same mis-interpetation - the relative relocity. I will try to explain this with the only purpose to decrease amout of posts about SRT n this forum (take care, the database can crash again Please Register or Log in to view the hidden image! ) First, how can be defined 'Frame of Reference /FR/', when two objects are in one and the same FR. For example if we have three objects A,B and C and : A B---------->v C--------> v A v<----------B v<--------C it is known that B and C are going away or are approaching tio A with one and the same velocity B and C are in one FR. What will happens however in the following case: v<----------B A C----------> C and B are moving in opposite directions? Are they in one and the same FR? The answer is yes, B and C are again in one and the same FR. Evaen if they move with the speed of light they are in one and the same FR no matter in what direction they are moving wrt A. This is very important because the velocity v which is included in gamma is not the same mechanical velocity which is used in classical mechanics, in another words it is possible two frames to move one wrt other with velocity bigger then c (in the above case) but their relative velocity used by SRT will be 0! the relative velocity between two frames can be found only if we has third FR in rest, then: VBC(relative) = |VAB| - |VAC| the modul velocities - |VAB| and |VAC| are the magnitudes of velocities of frames B and C wrt A not caring of direction of movement. In the same way as we calculate kinetic energy T we are not caring about the direction of movement only by the magnitude! Please try to understand what 'relative velocity' means in SRT.
I thought that nothing can move faster then c, no matter what frame your in. "2. Second postulate (invariance of c) The speed of light in vacuum, commonly denoted c, is the same to all inertial observers, is the same in all directions..." http://en.wikipedia.org/wiki/Special_relativity Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image!
Hi XGen, That's an interesting misconception! You've reached that conclusion by knowledge of how length contraction and time dilation are calculated, right? There's more to special relativity than you know! Think about this: If B's velocity is v, then C's velocity is -v, and vice versa. This makes a big difference. If you look at the Lorentz transform, you'll see that the gamma factor is not the only factor involving v. In fact, the relative velocity predicted by SR between B and C is 2v/(1+v<sup>2</sup>/c<sup>2</sup>)
You have just quoted a modified version of the Velocity Addition Formula. It predicts the terminal velocity of a missle fired from a shuddlecraft as viewed by the stationary mothership observer. You have taken v and u being equal as being mathematically equilvelent to 2v. Which is acceptable mathematically. w = (v + u) / ( 1+ (vu)/c<sup>2</sup>). In addition to that fact you are incorrect. Where two objects are launched in opposite directions the relative velocity between them as viewed by them is the collective velocity. If you want to argue this point I suggest you provide direction to SR's rules on just how you know which formula to apply when you come across two objects in relative motion and know nothing about the origin of that motion. Please Register or Log in to view the hidden image!
Xgen, I read your post to mean that two FR's could not measure their relative velocity with no other references needed? Radar reflections or transponders are commonly believed to be able to measure the relative motion wrt two inertial frames. Did I err here? A three frame problem to analyze Xgen. Let me know what you think. Thanks Geistkiesel Please Register or Log in to view the hidden image!
I find this interesting. 1 - You start by saying you are going to correct all us confused anti-relativists. 2 - You end by repeating my claim that there is no time dilation between B and C. (One which James R and many others have chastized me and called me names saying I don't understand relativity, etc). 3 - You justify this by claiming their motion is not relative. Please Register or Log in to view the hidden image! I ask you to comment on my statement that "Given a relative velocity between two objects in space you cannot compute time dilation". You'll make some song and dance about B and C don't have relative velocity. Well they damn sure do. Instead of launching B and C in opposite directions we'll launch them simultaneously from points D and E which are in line, at relative rest to each other and to A and seperated from A with A being at the mid point. Now when B and C collide at A, if they have no relative velocity please compute for me the kenetic energy disapated in the crash. Please Register or Log in to view the hidden image! B and C have relative velocity but you cannot determine relavistic affect without knowing their respective velocities to their common rest frame.
Not meaning to be deragatory but you are acting like a tard. Please Register or Log in to view the hidden image! I'll note for others you just misrepresented my posts by typing your own and making it appear as a MacM quote. I never wrote that. Does anybody else out there not understand what it means to say a "Common Rest Frame"? Is english your native language?
I made the comment knowing full well you'd make an appropriate reply comment. But all kidding aside, I really do want you to define completely and without any room for interpretation as to what exactly you define as a "common rest frame". What is significant about this "common rest frame"? Do two objects in relative motion only have one "common rest frame"? If not, why don't you refer to it as "common rest frames"? I'm awaiting answers.
"Common Rest Frame" is a term that MacM uses to mean "The frame in which the average velocity of these objects is zero" (at least, that's what I think he means. One can never be sure). He appears to think that Special Relativity relies on this concept in some way.
I don't think MacM would agree to this - which isn't saying much because he never agrees with anyone as far as I can tell Please Register or Log in to view the hidden image!. Anway, I think MacM would raise the same problem if you launched A at .3c and B at .6c such that they had a relative velocity greater than .8c.
You may be right... Perhaps he means "The frame in which the objects were last at rest with respect to each other"???
In another thread, I wrote this: Suppose I launch spaceship A at 0.866c away from Earth. Ship A carries spaceship B inside it. Ship A travels for a while at this constant speed, and then, while still going at constant speed, launches spaceship B at a speed of 0.866c away from A (and still away from Earth), where the 0.866c is measured relative to A. Questions: 1. Is it even possible to launch ship B at a speed of 0.866c away from A? Would that mean that B would be going at 0.866c + 0.866c relative to Earth? 2. If it is possible, what would the speed of B be, relative to Earth? 3. What would B's final gamma factor be, relative to Earth? 4. What would be the final relative rates of the clocks on Earth, A and B, after B was launched? 5. Is the "common rest frame" of A and B the frame of A, or the frame of Earth? MacM hasn't answered, so far.
Edit: I replied thinking you meant what Pete first said. Anyway, with this new definition, we must assume that the frames undergo acceleration. This isn't good. What if two frames (objects) were never at relativity rest? What is their "common rest frame"?
I sure as hell did. If it isn't there somebody deleted it because I did respond. But in any case. 1 - Certainly 2 - 0.9897391706c 3 - 6.998592267 4 - Earth = 1,000 ticks; B = 142.8857431 ticks 5 - Since you know A,B and Earth were all at common rest it is a primary referance including earth, however A is also a common rest point for calculation between A and B.
Find one. Case that is. That is just as impractical as asking you what is the time dilation between B and C if you don't know the common rest point. They have one but you weren't there when they were launched, I was. Hence I know if their seperation at 0.866c , apparent relative velocity, has time dilation or not, you don't.
