In a certain rest frame, we have a right cuboid box moving in the +x direction with velocity v. As measured in the rest frame the box has one axis aligned with the x axis and of length A and the other axes aligned with the Y and Z axes and of identical length B. At one point the center of the box coincides with the center of our coordinate system and a flash of light is emitted and bounces off a mirror at the leading edge of the box and returns to the center of the box. Also it hits a detector at the center of one of the faces parallel to the direction of the movement. Question 1. Describe all events in the rest frame if the event where the center of the box coincides with the center of coordinate system is labeled as (T, 0, 0, 0). Event O -- The light leaves the center of the cube \( O = (T, 0, 0, 0)\)Event D -- the light hits the detector in the center of a face parallel to the direction of movement. The detector starts a distance of B/2 from the origin of the light and moves with speed v in a direction initially perpendicular to the spatial separation, so from the theorem of Pythagoras: \( (c \Delta t_D) = (v \Delta t_D)^2 + (\frac{B}{2})^2\) or \(\Delta t_D = \frac{B}{2} \times \frac{1}{\sqrt{c^2 - v^2}}\) so: \( D = \left(T + \frac{B}{2} \times \frac{1}{\sqrt{c^2 - v^2}} , \quad \frac{B}{2} \times \frac{v}{\sqrt{c^2 - v^2}}, \quad 0, \quad \frac{B}{2} \right)\)(Because of the ambiguity of the specification, any of \(\tiny \left(T + \frac{B}{2} \times \frac{1}{\sqrt{c^2 - v^2}} , \; \frac{B}{2} \times \frac{v}{\sqrt{c^2 - v^2}}, \; 0, \; - \frac{B}{2} \right) , \quad \left(T + \frac{B}{2} \times \frac{1}{\sqrt{c^2 - v^2}} , \; \frac{B}{2} \times \frac{v}{\sqrt{c^2 - v^2}}, \; - \frac{B}{2} , \; 0 \right) , \quad \textrm{or} \left(T + \frac{B}{2} \times \frac{1}{\sqrt{c^2 - v^2}} , \; \frac{B}{2} \times \frac{v}{\sqrt{c^2 - v^2}}, \; + \frac{B}{2} , \; 0 \right)\) are also acceptable.) Event M -- the light bounces off the mirror in the leading direction Here, as a simple rate problem, the light catches up with the runaway mirror with a head-start of \(\frac{A}{2}\). So \(\frac{A}{2} + v \Delta t_M = c \Delta t_M\) or \(\Delta t_M = \frac{\frac{A}{2}}{c-v}\) so: \(M= \left(T + \frac{A}{2} \times \frac{1}{c - v} , \quad \frac{A}{2} \times \frac{c}{c - v}, \quad 0, \quad 0 \right)\)Event R -- the bounced light returns to the center of the moving cube This happens a time in the future of B by the amount \(\Delta t_R = \frac{\frac{A}{2}}{c+v}\) so: \(R = \left(T + \frac{c A}{c^2 - v^2} , \quad \frac{c A v}{c^2 - v^2}, \quad 0, \quad 0 \right)\) Motor Daddy's exact example is with T = 0, A = B = 1 light-second, \(v = \frac{\sqrt{69}}{13} c = \sqrt{\frac{69}{169}} c \approx 0.6390 c \approx 191.6 \, \textrm{Mm} / \textrm{s}\). So: \( O = (0, 0, 0, 0) D = \left( \frac{13}{20} \, \textrm{s} , \quad \frac{\sqrt{69}}{20} \, c \cdot \textrm{s}, \quad 0, \quad \frac{1}{2} \, c \cdot \textrm{s} \right) \approx \left( 0.6500 \, \textrm{s} , \quad 0.4153 \, c \cdot \textrm{s}, \quad 0, \quad 0.5000 \, c \cdot \textrm{s} \right) \approx \left( 194.9 \, \textrm{Mm} / c , \quad 124.5 \, \textrm{Mm}, \quad 0, \quad 149.9 \, \textrm{Mm} \right) M = \left( \frac{ 13 (13+\sqrt{69}) }{200} \, \textrm{s} , \quad \frac{ 13 (13+\sqrt{69}) }{200} \, c \cdot \textrm{s}, \quad 0, \quad 0 \right) \approx \left( 1.385 \, \textrm{s} , \quad 1.385 \, c \cdot \textrm{s}, \quad 0, \quad 0 \right) \approx \left( \quad 415.2 \, \textrm{Mm} / c , \quad 415.2 \, \textrm{Mm}, \quad 0, \quad 0 \right) R = \left(\frac{169}{100} \, \textrm{s} , \quad \frac{13 \sqrt{69}}{100} \, c \cdot \textrm{s}, \quad 0, \quad 0 \right) \approx \left( 1.690 \, \textrm{s} , \quad 1.080 \, c \cdot \textrm{s}, \quad 0, \quad 0 \right) \approx \left( 506.6 \, \textrm{Mm}/c , \quad 323.7 \, \textrm{Mm}, \quad 0, \quad 0 \right) \) But none of these calculations relate to Special Relativity which is the assertion that all inertial coordinate systems are valid descriptions of the same physics and that the speed of light is the same for all directions in all inertial coordinate systems. Motor Daddy also calculates \(v \Delta t_M = \frac{69+13 \sqrt{69}}{200} c \cdot \textrm{s} \approx 0.8849 \, c \cdot \textrm{s} \approx 265.3 \, \textrm{Mm}\) as the x-coordinate of the center of the box simultaneous with event M and \(c \Delta t_R = \frac{ 13 (13-\sqrt{69}) }{200} \, c \cdot \textrm{s} \approx 0.3051 \, c \cdot \textrm{s} \approx 91.46 \, \textrm{Mm}\) which is the difference between the position of event M and the position of event R. These calculations don't tie to any events and represent Motor Daddy's endorsement of the concept of absolute time and absolute space and complete rejection of Special Relativity.
Thank You rpenner for starting this thread and for the precise description. I want people to talk about this so they understand what I'm saying, and they can decide for themselves what's up. I'll let you all work it out in your own language and symbols. Please Register or Log in to view the hidden image!
That's the same cartoon he posted as a link to me also as proof of light slowing down and speeding up willy-nilly. It didn't work out so well for me either. The stated dimensions conflicted with the method he used to "determine" his solution and end condition. The other guy's cartoon of the bouncing balls has the same problem. At some point you just have to assume they are intentionally incorrectly applying the frames in their problems to keep the argument going,,,,, because they keep "forgetting" to apply the correct frames to the observers and the observed (over and over and over ad infinitum.)
It would help if we could read your version. I have some physics in my theory that combine special relativity with different physics. I don't usually post them in here, but this looks like more of an open discussion.
I built this theory online through interaction with other physics/math/Fraggle minded people on the net. EVERYTHING is archived in my posts. Start reading. Please Register or Log in to view the hidden image!
I walked Motor Daddy through the differences between his Newtonian box and the Einsteinian equivalent in great detail. He didn't understand most of it, and is still peddling the same nonsense years later. I think the thread was called "Relativity of simultaneity" something or other. I could dig it up...
Sorry, I didn't see the link. Well, I just wondered if I could make it easier to understand... probably not though, because it is so fractional. I would prefer a more rounded set of numbers to think about. I do it in my head, and these fractions are too hard. I always say, make the problem easy, and the hard problems will eliminate themselves.
[POST=2918091]James R's last post on "Relativity of simultaneity" thread[/POST] If Motor Daddy "admitted he was trolling" -- I don't know where to look for it -- the thread is years long and begins as a circular argument based on assuming things contradicting special relativity to prove the system is inconsistent with special relativity. But that's no way to go about doing physics. If you want evidence that Motor Daddy is not serious (which is perhaps one definition of trolling in a physics discussion):
Trolling is using intellectual dishonesty to get a rise out of other folks why wallowing in the attention you've attracted as you drive the discourse into irrelevant nonsense. Even if you don't have the intellect to evaluate you behavior you're still responsible for it.
So Motordaddy is moving the photon with the box, and keeping X the same. But the photon is moving with the background so X has to move. Is that what the argument is about?
What's it called when someone does this and nobody responds to the posts, but continues to call BS, and they have no idea what I'm saying, or what they're talking about? Insanity? ...oh, by the way, I'm f'n stupid, so it took me f'n hours! to make that, and nobody gave a damn!
It's very disingenuous to go after someone for what they said on page 40 of a .999... thread. Since .999... = 1 is settled mathematics, any such thread is by definition for entertainment purposes only. One need only read through that thread to see that it's a thread for .999... cranks; and those math-literate folks who for whatever reason, love them. One is always free to ignore such threads. But a certain subset of math-literate people love to wade in there and have it out with the cranks. Mr. rpenner is one, I'm another. But it's not a serious thread. Mr. rpenner could have picked any one of hundreds of other posts in that thread to attack. Secondly, for one poster to be applauded or encouraged for starting a thread specifically intended to demean another poster, reflects badly on this website. Nevermind that Motor Daddy is a .999... crank. He confines his posts to one specific thread that we all agree is for entertainment purposes. The moderators have not seen fit to delete Mr. Daddy's posts, nor to ban his handle. Therefore what he says is as legitimate as any other poster on this forum, even if his arguments lack mathematical sophistication. And frankly Mr. Daddy is an interesting contributor. If he's wrong, he's NOT "not even wrong." He has something to say. Nobody knows why we have a continuum of dimensionless points in math but quantization in physics. It's a mystery that all the real analysis in the world cannot make go away. And thirdly, Mr. rpenner has in that same aforementioned thread, and very recently, totally misconstrued and distorted something that I wrote. And for what it's worth, I'm one of the mathematically literate and relatively sane people posting on that thread, and I've devoted considerable time and energy here and elsewhere on the Web, to trying to explain the modern mathematical concept of the real number system to cranks and lunatics. The fact that Mr. rpenner is a kickass LaTeX expert -- I've learned a lot from his mastery of that tool -- and the fact that he seems to think he knows a little math, obscures but does not totally hide the fact that he's a very nasty attack troll. Since when is it considered fair game to deliberately start a thread on a serious section of this forum, in order to attack one single poster on a much more lighthearted and unserious thread elsewhere on the forum? And as I say, I myself was personally the target of Mr. rpenner's total lack of reading comprehension and forum manners. I haven't been around here long. But to the extent that my handle is still active, and to the extent that I have spent a couple of months now on that idiotic .999... thread ... I say rpenner should be censured, not applauded, for his misuse of this board to advance his personal agenda. Whatever that agenda may be. Showing off his LaTeX skill is my guess. And like I say, that part of Mr. rpenner's work I truly admire. It's your board, make of it what you will. You want math here, post some math. You want personal attacks, that's available too. An online forum becomes whatever its members allow and encourage. Personally I enjoy the type of freedom of expression that allows a cranky thread to remain active. I've appreciated that about the .999... thread. Most online forums typically just lock those types of threads. Myself I appreciate free speech, cranky speech, insane speech ... especially when everyone involved keeps it to one thread and stays civil. And I strenuously object to the community tolerating any poster starting a brand new thread in one subforum only to attack a specific individual participating in a different subforum. That's a bad precedent. Peace.
It's not totally pointless, I want to learn this too. I just wanted to know if the speed of light is always the same as though the box wasn't there at all. I think I know the physics, I just do not the experimental results of science so far. We are ignoring gravity I suppose?
Yes, the speed of light is always c, 299,792,458 m/s. The source that emitted the light was at that location when it emitted the light, but since it had a velocity it traveled away from that point. The point that is the center of the expanding light sphere is not capable of motion. That means the box is in motion in space, and that is what it is showing, a box in motion in space. The frames are like snapshots of time. It started at t=0. Then a snapshot was taken at t=.65...and so on...
In my scenario, I am showing you how distance and time are measured. There is no difference in ANY situation you can think of. This method is not pieced together, it is 100% absolute pinpoint accuracy at every possible scale of the infinite space that we reside in. This is not a theory, it is a fact!
That location point (0,0,0) is the center of the light sphere. There is nothing there at that point after t=0, it is simply a point in space. The blue ring is an expanding light sphere. This is how 3D+Time works.
