Not at all clear examples of special relativity (rectangle in motion and coming to rest)

[Hak]

I have always had certain difficulties in correctly understanding the theory of special relativity; I often apply it to certain situations and they fall apart...

Imagine there is a rectangular object placed with its long sides parallel to the ground and its short sides perpendicular to it, moving at a certain constant speed with the same direction as the long sides. There are 2 observers, one on the object (moving with it) and the other outside, on the 'stationary' earth. From the centre of the rectangle, 2 photons depart in the direction of motion, one in one direction, the other in the opposite direction, and exit the 'rectangle'.

According to the observer in solidarity with the rectangle, in order to exit the rectangle, the photons take 2 paths with the same length, i.e. half the long side of the rectangle (since the photons start from the centre). According to the (2nd) postulate of special relativity, the speed of light is always C for every reference system, so the 2 photons take the same time to exit the rectangle, i.e. L/C (L= half the long side of the rectangle), so they exit at the same time.

According to the external observer, the photon that is going in the same direction as the rectangle is moving, has to travel a greater distance than L to exit the rectangle, because in the meantime the edge of the rectangle that the photon must pass through to exit it is moving in its own direction, moving away from where the photon started. On the other hand, the other photon, moving in the opposite direction, and exit the 'rectangle'.

According to the observer in solidarity with the rectangle, the photons take 2 paths with the same length, i.e. half the long side of the rectangle (since the photons start from the centre), to exit the rectangle. According to the (2nd) postulate of special relativity, the speed of light is always C for each reference system, therefore the 2 photons take the same time to exit the rectangle, i.e. L/C (L= half the long side of the rectangle), so they exit at the same time.

According to the external observer, the photon that is going in the same direction as the rectangle is moving, has to travel a greater distance than L to exit the rectangle, because in the meantime the edge of the rectangle that the photon must pass through to exit it is moving in its own direction, moving away from where the photon started. On the other hand, the other photon, which is moving in the opposite direction to the speed of the rectangle, will have to travel a shorter distance than L, since the edge of the rectangle that it must pass through is coming towards it, approaching the place where the photon started. The speed of the 2 photons must be the same, C, so the first photon, having to travel a greater distance, will take longer to exit than the other photon, which has to travel a shorter distance. So, for the external observer, the two photons leave at two different times... but for the internal observer, they leave at the same time!

Thus we have 2 different universes, one in which the photons are one in which the photons came out at the same time, and another in which they came out at 2 different times. So I asked my physics professor for an explanation, and he roughly replied that, as becoming progresses, things settle down, and it just seems that the universes are different just because the observers are different.

Subsequently, another idea came to me. Let us place 2 circles at the ends of the rectangle, near the short sides, just where the photons come out; these circles are divided into many (numbered) segments and are arranged in such a way as to accommodate the photons in their segmented compartments when they hit them. We rotate the two circles, connecting them (with a tube) in such a way that they rotate together, so that when one circle is in a position to receive the photon coming at it from the rectangle in a given segment, the other circle also receives a possible photon in the same segment.

With such a device, the observer integral with the rectangle, seeing that the photons leave the rectangle at the same instant, captures the 2 photons, in the 2 rotating circles, always in compartments with the same numbering. On the other hand, for the external observer, seeing that he sees the 2 photons leave at 2 different instants, by arranging everything appropriately, the 2 photons will be captured by 2 compartments with different numbering, since in the time lapse that the lagging photon takes longer to leave, the circle that must capture it still rotates a little bit by changing segments. The rectangle stops and the 2 observers meet: one shows the other that the photons are in the same segment (or at least shows the segments with more energy, due to the photon that hit them), the other that they are in different segments... but while there are 2 observers, the reality (at least for sympathetic observers) is 1!

I hope I have been sufficiently understandable... if you find any missteps I will be very grateful: I have not found a solution for some time. Thank you very much.

 

[Nugatory]

Thus we have 2 different universes, one in which the photons are one in which the photons came out at the same time, and another in which they came out at 2 different times.

You and I are standing facing one another. A rabbit runs between us, and you observe that the rabbit is running from your left to to your right. I observe that the rabbit is running from my right to my left. So far so good, that’s just how “left” and “right” work for people facing in opposite directions.

But suppose that I then jump to the conclusion that we have two different universes, one in which the rabbit is moving from left to right and another in which the rabbit is moving from right to left. You would say that that is absurd, and you would be right. We don’t have two different universes, we have two different meanings of “left” and “right”, unsurprising because those words are defined relative to the different directions we are facing.

The absurdity of the two different universes claim is obvious when we’re disagree about whether the rabbit is “really” moving from left to right or from right to left. It’s less obvious when we disagree about whether the two flashes of light left the rectangle at the same time or different times, but the fallacy is the same.

 

[Ibix]

Thus we have 2 different universes, one in which the photons are one in which the photons came out at the same time, and another in which they came out at 2 different times.

You and I are sitting on opposite sides of a table and an ant crawls across it. I say the ant is moving left-to-right. You say it is moving right-to-left. Are there two separate universes here? Or just two different descriptions of one universe?

One of the things people seem to struggle with in relativity is accepting that "these two things happened at the same time" can be as subjective as "the ant is moving left-to-right". But that is how it is.

 

[Ibix]

A rabbit

an ant

Now if I see an ant and you see a rabbit, there was either something in the water or there really would have to be two different universes!

 

[Hak]

You and I are standing facing one another. A rabbit runs between us, and you observe that the rabbit is running from your left to to your right. I observe that the rabbit is running from my right to my left. So far so good, that’s just how “left” and “right” work for people facing in opposite directions.

But suppose that I then jump to the conclusion that we have two different universes, one in which the rabbit is moving from left to right and another in which the rabbit is moving from right to left. You would say that that is absurd, and you would be right. We don’t have two different universes, we have two different meanings of “left” and “right”, unsurprising because those words are defined relative to the different directions we are facing.

The absurdity of the two different universes claim is obvious when we’re disagree about whether the rabbit is “really” moving from left to right or from right to left. It’s less obvious when we disagree about whether the two flashes of light left the rectangle at the same time or different times, but the fallacy is the same.

You and I are sitting on opposite sides of a table and an ant crawls across it. I say the ant is moving left-to-right. You say it is moving right-to-left. Are there two separate universes here? Or just two different descriptions of one universe?

One of the things people seem to struggle with in relativity is accepting that "these two things happened at the same time" can be as subjective as "the ant is moving left-to-right". But that is how it is.

Thank you very much. I had thought that the delicate point was what happens when the rectangle stops. I have read that this objection has also been raised for the twins paradox. The rectangle cannot stop instantaneously for either the fixed or the mobile observer (it is presumed that they would be different instants) and so it seems to me that there is nothing to prevent one from thinking of a traumatic recomposition of the two universes and the two realities: like, it is said, the sudden ageing of the wandering twin. Thanks to those who will clarify these points for me.

 

[Nugatory]

We rotate the two circles, connecting them (with a tube) in such a way that they rotate together, so that when one circle is in a position to receive the photon coming at it from the rectangle in a given segment, the other circle also receives a possible photon in the same segment.

The bolded text is the problem. If they are rotating together in the frame in which the rectangle is at rest, they won’t be rotating together in the frame in which it is moving. So everyone will agree about which segments receives the flashes of light, but the two reception events only happen at the same time in one frame.

This isn’t all that surprising when we consider that your rotating rings are literally clocks - put a mark on one of the segments, call it the “sweep seconds hand” and we have an old-fashioned analog clock with hands moving around the dial. And we know that clocks synchronized in one frame won’t be synchronized in another.

But, you say, we have mechanically connected the two rings to force them to rotate together….
We start with the two rings rotating together in the frame in which the rectangle is at rest (I’m setting it up this way to avoid having to accelerate anything or spin the rings up, which would bring in all sorts of unnecessary complications involving the rigidity of the connecting tube). Now our lab assistant mechanically connects segment zero of one ring to segment zero of the other in an attempt to keep them synchronized. But if the two rings were both lined up at the same time using the frame in which the rectangle is at rest, they aren’t lined up at the same time in the other frame and the connecting tube is skewed.

 

[Nugatory]

I had thought that the delicate point was what happens when the rectangle stops. I have read that this objection has also been raised for the twins paradox.

Changes of speed are completely irrelevant to understanding the moving rectangle, and considering them just brings in some horrifying and unnecessary mathematical complications (Google for “Born rigid motion” and “Ehrenfest rotating disk” to see what I mean - you do NOT want to go there).

The instantaneous or non-instantaneous change of speed is also a red herring in the twin paradox - it’s usually presented as instantaneous because it simplifies the math without losing any of the essential physics.

So don’t take on problems involving acceleration until you have a solid grasp of the simpler case of straight-line constant speed motion. It’s a necessary foundation.

 

[Hak]

Changes of speed are completely irrelevant to understanding the moving rectangle, and considering them just brings in some horrifying and unnecessary mathematical complications (Google for “Born rigid motion” and “Ehrenfest rotating disk” to see what I mean - you do NOT want to go there).

The instantaneous or non-instantaneous change of speed is also a red herring in the twin paradox - it’s usually presented as instantaneous because it simplifies the math without losing any of the essential physics.

So don’t take on problems involving acceleration until you have a solid grasp of the simpler case of straight-line constant speed motion. It’s a necessary foundation.

Thank you, very much. So, could it be said that a photon can change compartment? For that, shouldn't there be a cause that moves it? I don't think the outside observer can influence the change of compartment: who knows how many outside observers there are. Nor can decelerating move a photon from one compartment to another, since it would have to do so at random; for example, decelerating does not indicate whether the photon should move clockwise or counterclockwise in the compartments. However, to remove any doubt, the observer on the rectangle could separate the segments before decelerating, so that they cannot communicate.
Thank you for any further clarification...

 

[Dale]

So, for the external observer, the two photons leave at two different times... but for the internal observer, they leave at the same time!

Yes, this is the relativity of simultaneity.

the 2 photons will be captured by 2 compartments with different numbering

The two photons will be captured by two compartments with the same numbering in both frames. In the “moving” frame the compartments are not synchronized. They do not have the same number in position at the same time.

We rotate the two circles, connecting them (with a tube) in such a way that they rotate together

Suppose you draw a straight line along the length of the tube in one frame. In the other frame that line forms a helix due to the relativity of simultaneity. The pitch of that helix is such that the photons enter the like-numbered compartments at different times.

So, could it be said that a photon can change compartment?

Why should it change compartments. It enters the like-numbered compartment in both frames.

 

[Hak]

Yes, this is the relativity of simultaneity.

The two photons will be captured by two compartments with the same numbering in both frames. In the “moving” frame the compartments are not synchronized. They do not have the same number in position at the same time.

Suppose you draw a straight line along the length of the tube in one frame. In the other frame that line forms a helix due to the relativity of simultaneity. The pitch of that helix is such that the photons enter the like-numbered compartments at different times.

Why should it change compartments. It enters the like-numbered compartment in both frames.

Thank you very much. After your explanation, I thought of another possible theory: it is absolutely not true that the traveller stops and shows the other where the two photons WERE. After he stopped the reality must be the same and therefore the photons must have the same location as the twins, previously different, are now equally old. So, according to this hypothesis, now reality is the same for the two as the measure of the instant of stop, which MUST be the same for the two (they are in the same reference system). Before, on the other hand, there were two realities and two times which were perfectly justified by theory and not contradictory, because to be surprised by this would be like being surprised by the different lengths the two attributed to the rectangle.

Then, if I understand correctly, it is a known fact in special relativity: two events that happen simultaneously in one reference system do not happen simultaneously in all other reference systems. This is counter-intuitive but to be accepted as it is.

The system of rotating circles is a method of measuring time and, as I understand it, one finds the same measurement in one reference system and two different measurements in the other system. The creative description I gave in previous posts seems to have the sole effect of making the result even more counter-intuitive. I am convinced that things happen exactly so that the two equivalent sections of the circles are illuminated in the first system, two different sections are illuminated in the second. I still think there might be some effect when we stop the rectangle, but I don't quite understand what it is, perhaps we have to accept this as it is, as you have told me. Where am I going wrong?

 

[FactChecker]

Then, if I understand correctly, it is a known fact in special relativity: two events that happen simultaneously in one reference system do not happen simultaneously in all other reference systems. This is counter-intuitive but to be accepted as it is.

This should be intuitively obvious. IMO, you should try as hard to understand the correct theory as you try to come up with your own counter-examples.

 

[Hak]

This should be intuitively obvious. IMO, you should try as hard to understand the correct theory as you try to come up with your own counter-examples.

Why is it intuitive?

Anyway, I understand your point of view, but I am making counter-arguments precisely to try to understand the main theory, which does not seem so readily understood. I can never be at the level of you and the experts on these topics. At first I thought this: first there are 2 reference systems, therefore 2 realities. The rectangle stops and the 2 observers become integral, so we only have 1 reference system: one would therefore expect there to be only 1 reality (present) equal for both. However, it must be shown how 1 of the 2 observers (or both) can see their own reality transform into that of the other (or into a 3rd), so that the (present) realities of the 2 observers, once they have reached the same reference system, match.

Then, I thought: let's consider the twins' paradox in which just the traumatic stop, about which the theory can say NOTHING, would bring the two realities to match and, as the traveller's hair from black becomes white like that of the stationary twin, so the two photons go to the places considered by the stationary observer. According to this hypothesis, which still convinces me, the problem (of the two meeting in the 'fixed' system after the stop and showing different results on the position of the photons) therefore makes no sense.

Incidentally, the matching of the two realities ultimately occurs between perfectly symmetrical systems, none PRIVILEGED; in fact, according to the traveller is the fixed one that moves, that loses simultaneity, that observes the Lorentz contraction. The travelling twin envies the fixed one that, according to him, ages less. Therefore, if one does not consider, as one is inclined to do, the fixed one as privileged, the reunion of the two realities appears 'natural': it is not that the point of view of the one moving MUST ADAPT to the other, the reverse is also true. Which is the black-haired twin during the journey of one of the two?

What do you say?

 

[Dale]

I thought of another possible theory

Personal theories are not permitted here. We are not in the business of debunking personal theories, only in the business of explaining the mainstream scientific theory.

At first I thought this: first there are 2 reference systems, therefore 2 realities. The rectangle stops and the 2 observers become integral, so we only have 1 reference system: one would therefore expect there to be only 1 reality (present) equal for both. However, it must be shown how 1 of the 2 observers (or both) can see their own reality transform into that of the other (or into a 3rd), so that the (present) realities of the 2 observers, once they have reached the same reference system, match.

This is completely useless. There is only one reality. There are simply multiple descriptions of that one reality. Just like two people facing other and one says the thunder came from the right and the other says the thunder came from the left. There are not two realities with two different thunders, just two descriptions for the same reality. Speaking of multiple realities transforming is nonsense and will get you nowhere.

The system of rotating circles is a method of measuring time and, as I understand it, one finds the same measurement in one reference system and two different measurements in the other system. The creative description I gave in previous posts seems to have the sole effect of making the result even more counter-intuitive. I am convinced that things happen exactly so that the two equivalent sections of the circles are illuminated in the first system, two different sections are illuminated in the second.

This is wrong. I already explained why.

I still think there might be some effect when we stop the rectangle, but I don't quite understand what it is, perhaps we have to accept this as it is, as you have told me. Where am I going wrong?

Usually the place that new students go wrong is in understanding the relativity of simultaneity. This is the most counter-intuitive concept in relativity. I suspect that is the case here.

In particular, you seemed to gloss over the statement I made that a straight line in one frame becomes a helix in another frame. This is not a material deformation, but simply a consequence of the relativity of simultaneity.

I am making counter-arguments precisely to try to understand the main theory

This is not a productive approach. You should be trying to make arguments, not counter-arguments. Many students have attempted your approach here on this forum. I have yet to see one succeed with that approach.

 

[Hak]

Personal theories are not permitted here. We are not in the business of debunking personal theories, only in the business of explaining the mainstream scientific theory.

I did not explain myself well. I don't think it's a personal theory that I want to prove, but my initial thoughts on the topic at hand. It's just a matter of semantics that created a misunderstanding, I know very well that this is not the space to discuss personal theories. Sorry again if I did not express it well.

 

[Hak]

This is not a productive approach. You should be trying to make arguments, not counter-arguments. Many students have attempted your approach here on this forum. I have yet to see one succeed with that approach.

I understand. You are right. I am highlighting the topic that I had developed on my own, without your help. No one can say anything about the causes of the two realities coming together in the same reference system, because otherwise there would be no paradox, of twins or photons. I spoke of an objection to the paradox of twins, a paradox that consists precisely in the fact that the twin returning from the trip is younger, has black hair. In this case the paradox is that the photons are in the segments with the same number in one case and different numbers in the other. (It is not true, in my opinion, that hair can more easily go 'back and forth').

What would be the cause that causes the traveller to age in the stop? It is not known. Just as it is not known what cause would bring the pair of photons back to the right place. That is why it is a hypothesis. On the other hand, those who believe in the paradox would argue that after the stop one is younger and, in the case at hand, they would argue that after the stop they are in different pairs. As you see, those who believe in the paradox accept the contradiction. Those who, like me, are inclined not to accept it claim that when they are in the same reference the reality must be ONE but do not know the causes that lead to collimation.

In conclusion, if you accept the paradox you must tolerate the contradiction. If, like me, you do not accept it, you must endure ignorance of the causes that eliminate it.
I know that much of this statement is wrong, do not point at me for this. I would just like to understand how to adjust them in the light of what you have said, because at the moment I cannot. Thank you so much.

 

[Dale]

In this case the paradox is that the photons are in the segments with the same number in one case and different numbers in the other.

I already told you twice now that this is false. The light pulses are in the segments with the same number in both cases.

I spoke of an objection to the paradox of twins ... that hair can more easily go 'back and forth'

Let's stick to one scenario. I have no idea what you are discussing with hair going back and forth. If you want to discuss that then make a separate thread where you can describe it in sufficient detail to understand. As it is, this is incomprehensible.

I would just like to understand how to adjust them in the light of what you have said, because at the moment I cannot.

I have also explained this twice. If you draw a line on the rod connecting the bins, that line is straight in one frame but it is a helix in the other frame due to the relativity of simultaneity. So in the "moving" frame at any given time the bins are not aligned. Because of that misalignment, when the light pulses arrive at different times, they wind up in the same-numbered bins.

In conclusion, if you accept the paradox you must tolerate the contradiction. If, like me, you do not accept it, you must endure ignorance of the causes that eliminate it.

One of the problems that we are having is that instead of engaging with follow up questions on the explanation, you are simply going back to repeating the question. If you ignore the explanations then yes, you will endure ignorance. This is not because an explanation does not exist, but because you simply ignored it, repeatedly, when it was offered.

 

[Sagittarius A-Star]

No one can say anything about the causes of the two realities coming together in the same reference system, because otherwise there would be no paradox, of twins or photons.

There exists only one reality.
The twin "paradox" is not a paradox, although it's usually called so. It is experimentally verified with muons in a particle storage ring.
https://ui.adsabs.harvard.edu/abs/1977Natur.268..301B/abstract

 

[FactChecker]

Why is [the relativity of simultaneity] intuitive?

Start with the experimentally demonstrated result from experiments like Michelson-Morley and others. The measured speed of light is the same no matter how the inertial reference frame is moving. How can clocks be synchronized throughout an IRF to make that happen?
Suppose that I am "stationary" and another observer at the center of a train in a different IRF travels past. Suppose that when that observer is right beside me, light beams are sent forward and backward in the train. How can his clocks measure the arrival time at the ends of the train to be identical? What does that tell you about how those clocks are set? Compare those clocks to mine.

IMO, you should think hard about that until it is second nature.

 

[Hak]

I already told you twice now that this is false. The light pulses are in the segments with the same number in both cases.

Let's stick to one scenario. I have no idea what you are discussing with hair going back and forth. If you want to discuss that then make a separate thread where you can describe it in sufficient detail to understand. As it is, this is incomprehensible.

I have also explained this twice. If you draw a line on the rod connecting the bins, that line is straight in one frame but it is a helix in the other frame due to the relativity of simultaneity. So in the "moving" frame at any given time the bins are not aligned. Because of that misalignment, when the light pulses arrive at different times, they wind up in the same-numbered bins.

One of the problems that we are having is that instead of engaging with follow up questions on the explanation, you are simply going back to repeating the question. If you ignore the explanations then yes, you will endure ignorance. This is not because an explanation does not exist, but because you simply ignored it, repeatedly, when it was offered.

Thank you very much. I am not ignoring your explanations, in fact I am paying attention to them. I am still approaching relativity, so I have a lot of difficulty understanding it. I think I understand now, but still, this is the topic I developed on my own, without your help, as I said. It was only meant to answer the question of 'develop your own argument, abandoning all counterexamples, which are not a good approach'. It was not my final argument, which matured after your answers. I hope everything is clear and that I have not offended anyone. Thank you very much for your comprehensive replies.

 

[Hak]

Start with the experimentally demonstrated result from experiments like Michelson-Morley and others. The measured speed of light is the same no matter how the inertial reference frame is moving. How can clocks be synchronized throughout an IRF to make that happen?
Suppose that I am "stationary" and another observer at the center of a train in a different IRF travels past. Suppose that when that observer is right beside me, light beams are sent forward and backward in the train. How can his clocks measure the arrival time at the ends of the train to be identical? What does that tell you about how those clocks are set? Compare those clocks to mine.

IMO, you should think hard about that until it is second nature.

Thanks. According to your suggestions, assume that the observer on the train and the observer on the ground have synchronized their clocks at the moment they pass each other. This means that both observers agree that their clocks show the same time when they are at the same location.

Now, when the light beams are sent forward and backward in the train, the observer on the train will measure the arrival time at the ends of the train to be identical, because he is at rest with respect to the train and the light beams travel equal distances at the same speed. However, the observer on the ground will measure a different arrival time for the light beams, because he sees the train moving and the light beams traveling different distances at different speeds.

For example, if the train is moving to the right, then the light beam going to the left will have to travel a longer distance and a slower speed than the light beam going to the right, as seen by the observer on the ground. Therefore, he will see the light beam going to the right reach the end of the train before the light beam going to the left.

This difference in arrival time implies that the clocks at the ends of the train are not synchronized according to the observer on the ground. In fact, he will see that the clock at the front of the train is ahead of the clock at the back of the train by a certain amount that depends on how fast the train is moving: this would be time dilation, which means that moving clocks run slower than stationary clocks. The observer on the train, however, will not notice any time dilation, because he is in his own inertial reference frame where his clocks are synchronized.
Right?

 

[Dale]

I am not ignoring your explanations, in fact I am paying attention to them. I am still approaching relativity, so I have a lot of difficulty understanding it.

Yes, this is a difficult subject. That is why it is so important to directly engage with the specific answers that you have received.

I think I understand now

I hope that is true, but you still have not made any specific replies about the answer. So it is impossible for me to tell either way.

If you have difficulty understanding the answers, then please ask questions about the answer itself.

 

[Hak]

Yes, this is a difficult subject. That is why it is so important to directly engage with the specific answers that you have received.

Very difficult, but I'm getting so passionate about it, even though I'm always saying junk and platitudes. It happens. I will try to improve as much as I can. I learned a lot, thank you. It is for this reason that I will now open another thread on another question on special relativity, this time I will try to be much more cooperative and to pick up your possible advice as much as possible. Thank you again.

I hope that is true, but you still have not made any specific replies about the answer. So it is impossible for me to tell either way.

Yes, I understand. I did not respond to any of the answers because I would not know how to comment. I just learn and try to assimilate, understanding the reasoning.

If you have difficulty understanding the answers, then please ask questions about the answer itself.

Yes, certainly, thank you. I already did: I had asked why the relativity of simultaneity is intuitive (I await confirmatory response to my justifications of the intuitive character). However, I spoke with a professor, according to him it is not so intuitive. That is why I had stated that it was counter-intuitive. He is probably wrong. Thank you again.

 

[Dale]

I had asked why the relativity of simultaneity is intuitive

It is not intuitive. It is the single most counter-intuitive concept in relativity. That is precisely why it is the biggest conceptual hurdle for students and the biggest source of “paradoxes” in SR.

 

[Hak]

It is not intuitive. It is the single most counter-intuitive concept in relativity. That is precisely why it is the biggest conceptual hurdle for students and the biggest source of “paradoxes” in SR.

Sorry, how is this possible? @FactChecker has repeatedly said that it is intuitive... Look at the previous posts, how can this be reconciled?

 

[PeterDonis]

I am making counter-arguments precisely to try to understand the main theory

You can't expect to make counter-arguments to a theory you don't understand. So making counter-arguments can't possibly be a good way to achieve understanding.

 

[FactChecker]

Close, but the details are a little tricky to keep track of. Honestly, I have trouble keeping the details straight. But in any case, it makes it clear that the clocks of different IRFs must be set differently.

This difference in arrival time implies that the clocks at the ends of the train are not synchronized according to the observer on the ground. In fact, he will see that the clock at the front of the train is ahead of the clock at the back of the train by a certain amount that depends on how fast the train is moving:

I think it's the opposite. The ground observer thinks that the beam hits the front of the train later, yet the clock on the train says it is at the same time. So the train clock at the front is reading earlier than it should be (according to the ground observer).

this would be time dilation, which means that moving clocks run slower than stationary clocks.

This does get tricky. Ground observers are seeing a moving train clock as it moves forward to a different ground location and different ground observers.
Keeping the details straight is where Minkowski spacetime diagrams become really useful tools.

The observer on the train, however, will not notice any time dilation, because he is in his own inertial reference frame where his clocks are synchronized.
Right?

Right.

 

[Sagittarius A-Star]

Sorry, how is this possible? @FactChecker has repeatedly said that it is intuitive... Look at the previous posts, how can this be reconciled?

It may become intuitive for you, after you have trained your intuition.

 

[Hak]

Close, but the details are a little tricky to keep track of. Honestly, I have trouble keeping the details straight. But in any case, it makes it clear that the clocks of different IRFs must be set differently.

I think it's the opposite. The ground observer thinks that the beam hits the front of the train later, yet the clock on the train says it is at the same time. So the train clock at the front is reading earlier than it should be (according to the ground observer).

This does get tricky. Ground observers are seeing a moving train clock as it moves forward to a different ground location and different ground observers.
Keeping the details straight is where Minkowski spacetime diagrams become really useful tools.

Right.

I thank you. Can't you add anything to my explanation to make the relativity of simultaneity even more correctly defined?

 

[Nugatory]

Sorry, how is this possible? @FactChecker has repeatedly said that it is intuitive... Look at the previous posts, how can this be reconciled?

It’s one of those things that becomes crystal-clear and intuitive once you understand it - but is counterintuitive until you’ve gotten there.

 

[Dale]

Sorry, how is this possible? @FactChecker has repeatedly said that it is intuitive... Look at the previous posts, how can this be reconciled?

The reconciliation is easy: whether something is “intuitive” or not is an opinion. Things are not objectively “intuitive” or not. Since it is an opinion, it can differ from person to person. My opinion is different from @FactChecker. He and I are allowed to have different opinions.

 

[Hak]

The reconciliation is easy: whether something is “intuitive” or not is an opinion. Things are not objectively “intuitive” or not. Since it is an opinion, it can differ from person to person. My opinion is different from @FactChecker

Now everything is clear. Thank you.

 

[FactChecker]

The reconciliation is easy: whether something is “intuitive” or not is an opinion. Things are not objectively “intuitive” or not. Since it is an opinion, it can differ from person to person. My opinion is different from @FactChecker

Yes, I should have been more clear. The fact that light beams going forward and backward in a relatively moving IRF are measured at the same speed leads me intuitively to accept that the clocks are set differently in that IRF. So the basic conclusion that simultaneity is relative seems intuitive. More than that is not "intuitive" to me.

 

[PeroK]

The reconciliation is easy: whether something is “intuitive” or not is an opinion. Things are not objectively “intuitive” or not. Since it is an opinion, it can differ from person to person. My opinion is different from @FactChecker. He and I are allowed to have different opinions.

That's called the relativity of intuition.