I’m struggling with an apparent contradiction of special theory of relativity (STR) that I cannot resolve.
Imagine two twins flying by each other in space along the same straight line but in the opposite direction. Say their relative speed is 1/3 c (one third the speed of light). Their trajectories of are right next to each other, so that at one point in space-time they will fly right by each others noses.
Moreover, in both twins’ inertial frame of reference, right along the line of the other twin’s trajectory, there are many clock/camera devices extending very far in both directions. For each frame, these devices are synchronized with each other. They display clearly the time of their clocks, and they continually take photos around them, putting a time stamp corresponding to their internal clock into every photo. This means that each of the two lines of devices will be constantly taking a picture of the devices flying by them in the other inertial frame of reference, and at very close distance. The photos of the other device will show the time displayed on those devices.
Finally, let’s assume that when the twins fly by each other’s noses, the time for all devices in both reference frames shows t=t’=0. So this happens and now the devices are flying by each other each constantly taking photos of the devices flying by them in the straight line.
According to STR postulate, each reference frame measures time dilation (slower clocks) in the other reference frame. The situation is symmetrical. But given the setup I outlined above, in either reference frame, each device will show a photo of the clock in the other reference frame with the time it’s showing, as well as its own time stamp when the photo is taken.
Now, if all devices show the same time stamp on the photo and the time shown in the photo from the device in the other reference frame, there is no time dilation, and STR fails. Otherwise, if a device shows a higher time value in its time stamp than the time it captured on the photo, then the time in the other reference frame runs slower. However, this must mean that the other device, whose picture was taken, recorded a LOWER time stamp value than the value displayed by the device IT took a picture of, which means that from this second device’s frame of reference, the time was seen as moving faster in the reference frame moving relative to it, and this again violates the STR postulate that BOTH devices should observe time dilation in the other reference frame.
