Why does everyone seem to think that moving clock appear to tick slower?

Question

I'm getting interested in special relativity and almost all people and explanations about the subject I found on the internet seem to think that when A and B would be in relative motion, they would both observe the other's clock tick slower than their own. However what I found about this is following, in § 4. (Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks) of Einstein's On the electrodynamics of moving bodies (1905):

From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity $v$ along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by $\frac{1}{2}tv^2/c^2$ (up to magnitudes of fourth and higher order), $t$ being the time occupied in the journey from A to B.

This sounds like complete opposite to what everyone seems to think.

Now this time discrepancy doesn't have anything to do with Doppler effects or isn't just some observers illusion. This is supposed to be physical fact, after stopping the traveler has physically aged less than the rest of the world.

The question: Why should the stationary clock seem slower to the traveller?

The quote i provided explicitly says that his own clock will have experienced less time. Please note that A and B can be arbitrarily close and there can be an infinite amount of such points for which the quote applies. Also the train need not stop to witness this effect

Therefore it seems to me certain that the traveller would observe the stationary clocks move faster.

Answer 1

Both observers really do see the other set of clocks as ticking slow. But the thought experiment from Einstein doesn't contradict this.

The key is that according to the person on the train the set of clocks along the track are not synchronized. They are only synchronized according to an observer standing on the ground, not for anyone in relative motion to the ground.

An example: If the person on the train looks at any individual clock they will see the clock ticking slowly as compared to their watch. Say there are two clocks anchored to the track A and B. At the moment the train passes clock A the rider's watch reads 0 sec, the time on clock A reads 0 sec and the time on clock B reads 10 sec (according to the rider; A and B are not synchronized in the rider's frame). Say $\gamma=2$ so, according to the train rider, clocks A and B tick at half the rate of their watch. The observer might take (according to their own watch) 2 seconds to reach clock B. At the moment they pass clock B it will read 11 sec (it is ticking half as fast as the watch). But the watch reads 2 sec. So even though the clocks A and B are ticking slowly clock B has "run ahead" of the watch when the train reaches B.

Answer 2

So the observer on the train ($\gamma=10$) has a clock. He looks out the window and sees a single clock (A). Let's say they are momentarily synchronized, so they both read 12:00. The instantaneous speed of the second hand on the A clock is moving more slowly than his clock (by a factor of 10), but for a brief moment, the 2 agree: it is Twelve Noon.

Ten minutes pass on the train. If the conductor sticks his head out the window, he looks back and sees the A-clock reading something like 12:00 and a few seconds. This doesn't mean much, because he knows he is looking back into the past (the A-clock is about 9'57" times $c$ far away). Anyway, when discussing distant clocks in Gedanken Experiments, light delays are never considered. "seeing" means "what he knows is true", not what delayed light looks like.

What he knows is true is that 10 minutes have passed and that the A clock is running slow by a factor of 10: The A clock reads 12:01 right now.

He looks out the window and sees the B-clock. The A and B clocks are synchronized in the track frame. The B-clock reads 1:40. We know that because in the track-frame, 100 minutes have passed since the A clock read 12:00, and the A and B clocks are synchronized in the track frame, it must show 100 minutes later. Note that he observes that the B-clock is also ticking slowly by a factor of 10. He also observes that the B clock leads the A clock by 99 minutes.

According the train conductor, each equally spaced clock (A, B, C, D, ...) leads its alphabetical predecessor by 99 minutes. It is this position dependent bias that allows both reference frames to observer the others' clock moving more slowly than his own.

If we focus on just one clock, say the A-clock, we see that as the train moves down the track, the definition of "now" at the A-clock according to the train differs more and more than "now" according to the track clocks. Again, this is not what he sees looking at the clock's light, it is what he considers "now" there. Just as we can consider "now" at the Andromeda galaxy as being very different from the 2.2 million year old light we see tonight.

Answer 3

First, your quote from Einstein's paper involves analysis from a single frame K. In frame K, clock A is in motion and clock B is not. This quote from Einstein does not consider the symmetric case of what an observer at rest with respect to clock A sees clock B doing, which is what the rest of your question is about. So this quote isn't relevant to the claim that time dilation isn't symmetric. Now, onto your ending questions.

1] Am I right in my assumption that the traveller inside the train observes the outside world go much faster, while the stationary observer outside the train would see the clock inside the train go much slower ?

No. The traveler on the train sees clocks that are at rest relative to the world as ticking slower. Similarly, an observer at rest relative to the world would see clocks on the train ticking slower. This is because there is no preferred reference frame. In either scenario, an observer sees a clock moving by them. Why should one view something different than the other?

2] Does this mean there must be an absolute speed (even if undetectable) for every object? For Example if an asteroid flies by then the universe must decide if the clock on asteroid will go faster or the clock on Earth will go faster, and so'remember' which gained more acceleration since the Big Bang.

Since the answer to the first question is no, this is invalid. SR assumes that the laws of physics are the same for all inertial observers and that the speed of light is constant independent of the relative motion between the observer and the source. The latter gives us time dilation, and the former tells us that this effect is the same for observers moving past each other. Given the experimental success of SR predictions as well as theories based on SR such as QED, I think the postulates hold true for our universe.