ghwellsjr said:
Darwin123, my comment in the above quote from post #50 was directed at indirachap, not at you. Since he had acknowledged that there was a difference in the accumulated age of the two twins, one of which traveled at high speed, I just wanted to make sure he also agreed that the clocks they carried with them would indicate the same difference in accumulated time because I then wanted to direct him to the Hafele–Keating experiment done with slow speed clocks which is a direct confirmation of Einstein's prediction of time dilation so I'm surprised that you would then say that "there never has been a direct test of relativity".
My definition of direct was very narrow. I am sorry that I said it this way.
What I meant to say is that the experimental tests of relativity did not use two symmetric "observers". There has been no test with two twins.
For example, consider one possible test of time dilation using mesons. A cosmic ray hits an atom in the atmosphere. A photomultiplier on the ground detects the flash of light, a scintillation counter with other gadgets detects a meson from the event and measures the mesons velocity. Many such events are recorded. Statistical analysis shows that the Lorentz time dilation formula "works".
I don't have references. I don't know how many times it was actually done this particular way. However, I think that it is clear to everybody that this method validates the Lorentz time dilation formula from the point of view of an observer at rest with respect to the surface of the earth.
This experiment did not validate the Lorentz time dilation formula from the point of view of an observer traveling with the meson. Hypothetically, suppose there was a photomultiplier and a scintillation counter with the same gadgets at rest with respect to the meson. The atom in question is hit by the cosmic ray at the very moment when the PMT and counter are passing the atom. The two detectors travel with the meson until it decays. The two detectors are then hoisted back into the atmosphere and accelerated to do the measurement again.
The principle of relativity says that a statistical analysis of the second procedure should validate the same Lorentz time dilation formula as the experiment where both detectors are fixed on the ground.
The second procedure would be prohibitively expensive. Aside from accelerating the detectors to near light speed relative to the ground, one would have to do something to prevent the detectors from hitting the ground near the speed of light. However, this experiment could hypothetically be done.
Comparing the results of this experiment, where the detectors are moving relative to the ground, with the results of the traditional experiment, where the detectors are fixed relative to the ground, is what I call a direct test of relativity. The direct test would validate the Lorentz time dilation formula twice with detectors that are identical but for their state of motion.
What I meant by a direct test of special relativity is where two experiments are done twice with nearly identical detectors in different inertial frames. One set of detectors is moving at high speed relative to the other set of detectors. The same process is being examined by both. This experiment would be testing the relativity part of relativity.
The experiment where the Lorentz time dilation formula was validated once is sufficient proof for me. I can follow the simultaneity argument, unlike some other people. However, not everybody follows the simultaneity argument. The simultaneity argument is logical, but it takes too many steps.
This is why the OP asked for a "simple explanation". There is an implication in some of the responses that special relativity is based on circular reasoning. He needs a "simple" experiment, by which he means symmetric observers, to convince him that there is no circular reasoning.
My point is that no test of special relativity has used "symmetric observers" in two different inertial frames. The theory of special relativity has been validated many times using just one observer in one inertial frame. The Lorentz time dilation formula has been validated many times.
You brought up the Hafele-Keating experiment as an experiment that validated special relativity. The HK experiment did not use "symmetric observers" in two inertial frames. In fact, none of the detectors used in the HK experiment were part of an inertial frame. What the HK experiment involved was actually three frames that were accelerating relative to the inertial frame.
Some people have claimed that the HK experiment is a test of general relativity, not special relativity. They argue that any test that involves both acceleration and gravitational mass has to be a test of general relativity. I have argued with some of these people on line. However, I have argued that it really is a test of special relativity.
My argument is that the direction of travel (East-West) in the HKE was chosen in such a way that gravitational mass canceled out. Furthermore, the results of the experiment could be analyzed from the point of view of an inertial frame located on the Earth's axis. Therefore, it is a test of special relativity. However, I admit that my argument is a bit tenuous.
In the HKE, none of the detectors was in an inertial frame. So some would argue that this was not a "direct" test of special relativity. The results were consistent with special relativity, using mathematical analysis. However, The HKE was not an experiment that used identical detectors in two different inertial frames.
I don't think any such "direct" test is practical. In actual practice, all the tests of relativity will involve at most one inertial frame. If you know of any direct test using detectors in two completely different inertial frames, then tell us. I don't need it for myself, but it would relieve a lot of other people.