I don't think it's confusing at all. Nugatory gave a very simple explanation in the very first response on this thread:
And in fact, that's exactly the same process that could be used for a space-like Lorentz interval where an inertial observer passes through one of the two events in question...
Yes. And all you really need are the two events A and B. The two worldlines are irrelevant except to let us know that the second frame is moving at 0.3c with respect to the first one.
You could assign the coordinates xA=0, tA=0 and xB=5, tB=0 then transform to a speed of 0.3c and get the new...
Is the reason you say "given two specific events" to allow for non-inertial worldlines? If the two worldlines are inertial, do you still need two specific events? And are there two events on each worldline for a total of four?
I'm really having trouble understanding this so I would appreciate...
You misunderstood. When I said in post #27 that the velocities were negative, I was talking about the velocities of Red and Blue. The term "v" is the speed of the moving frame relative to the stationary frame. It's the value that we plug into the Lorentz Transformation equations which I will...
That's almost correct. B does not deduce when the reflection occurs by this method, he defines when it occurs. Do you see the difference? Simultaneity is not something that nature provides for us that we have to figure out, instead, it is up to us to figure out a convenient and satisfying but...
I presume you mean this diagram which I have redrawn with the units you are using (seconds and light-seconds rather than nanoseconds and feet). I'll explain later why I have extended the Red and Blue wordlines:
But now we have a problem because in this diagram, the RB distance (if by that you...
I made this diagram to illustrate why you don't want to take shortcuts in transforming IRF's, you should always apply the Lorentz Transform. The reason why I made the tick mark black when the R clock reaches 6 was to show that it doesn't have any significance to R, it is only a calculation that...
Wikipedia's article on Proper Time makes it clear that the clock has to follow the world line, that is, it has to travel the path of the object, so I don't know where you are seeing a possible conflict. Where did you get that quote?
Since time according to the precepts of Special Relativity is defined as what a clock measures, time cannot apply to a photon because no clock can travel at the speed of light. If you use the space time interval between two events that start out as time like and you continually move one of the...
Good question. I think some spacetime diagrams may help to answer your question.
Let's take a scenario where an observer sends out a light pulse to a reflector 6 feet away and measures with his clock how long it takes for the reflection to get back to him. Since light travels at 1 foot per...
Finally, we get to Peter's zig-zag scenario:
TT can use radar coordinates just like before to construct this diagram but here I show some of the significant radar signals that TT employs:
And from that data he will construct this non-inertial frame:
I think some spacetime diagrams might help to illustrate the two scenarios specified in this thread. The first one comes from post #55:
HT is shown in blue and elapses 20 years while TT is shown in red and elapses 12 years (the dots mark off 1-year increments of Proper Time for each twin)...
That's a good summary of what really happens to muons but it's not what is of concern in this thread as the OP stated approximately the same relevant facts in his first post. Keep in mind that my diagrams use a speed of 99.8c and a lifetime of 3.3 microseconds.
I'm treating the muons' lifetimes to be 3.3 microseconds (1 light-kilometer) just so that my drawing program can show the time intervals as either coordinate times or Proper Times for all muons (moving or at rest) as indicated by the interval between a pair of dots on a worldline.