# Problem with relativity of simultaneity original example

• baivulcho
In summary, the concept of relativity of simultaneity is explained through the example of a train moving at a constant speed relative to an embankment. The observer on the embankment sees two simultaneous lightning strikes at the midpoint, while the observer on the train sees them as occurring at different times due to the movement of the train. This confusion is resolved when points on the train are synchronized with the points on the embankment, and the perspective of both the embankment and train passengers are taken into consideration. However, it is important to note that this argument only holds if the train passengers assume that the lightning strikes occurred simultaneously in their own frame, which is not necessarily the case.
baivulcho
In special relativity the relativity of simultaneity is explained with the following example.
We have one frame of reference - a train moving from left to right with constant speed v relatively to the embankment, and second frame of reference - the embankment itself. On the embankment there are points A and B and their midpoint M. On the train there is the point M'. When M and M' meet each other, two lightnings strike both A and B. The observer on the embankment sees that the two flashes of light meet at the midpoint M. But since the train is moving and the point M' with it, M' moves towards B and therefore the observer on the train will see that the beam from B will arrive first at point M' and after that will arrive the beam from A. And so simultaneity is relative - for one observer the two events are simultaneous, but for the other they are not.

But let's imagine for a moment that when the points M and M' coincide we put points A' and B' on the train which coincide respectively with A and B. So it is the same whether we say the beams start at A and B or at A' and B' - at the moment of the lightning strikes, those points coincide with each other.

Lets imagine the people on the embankment and those on the train are aware of the experiment that is taking place. What is the point of view for the people on the embankment? They know that the speed of light is constant c in every direction, and therefore when the point M and M' meet they begin to wait for the two flashes of light and expect the light beams to meed at their midpoint M - the light needs equal time to travel the equal distances AM and BM. So they are right for themselves.

Now let's consider the point of view of the train passengers. They know about the principle of relativity and so too expect the speed of light to be constant c in every direction. At the moment when point M and M' meet, the people start to wait for the flashes too. They know that point A' and B' are equally distant from the point M', because when M and M' coincide(and the flashes occur) - A and A', and B and B' coincide too(whether we take length contraction into account or not shouldn't matter because the important thing here is that the length A'M' is equal to B'M' according to the train passengers - according to them A and B are equally distant from M, and M' and M coincide at that moment with or without length contraction). So knowing that A'M'=B'M' and expecting the speed of light to be the same both from A' to B' and from B' to A', they would expect the light to cover the distances A'M' and B'M' for the same time, and therefore meet at point M'.

What prevents the passengers from making such conclusions, and not be surprised when the two flashes don't meet at their midpoint M'? What is the difference between the train and the embankment - surely we can say that the train is stationary and the embankment is moving relatively to it with velocity v, so when the flashes occur at points A' and B', the point M will be moving towards A' and the people on the train will expect that for the people on the embankment the flashes won't be simultaneous. So is this difference in the way the two beams arrive at points M and M' real - for the people on the train the beams will meet at some other point? Or it is only a matter of relative conclusion - the observer on the embankment will expect the beams will meet only on his midpoint, and the observer on the train will expect the same thing?

baivulcho said:
Now let's consider the point of view of the train passengers. They know about the principle of relativity and so too expect the speed of light to be constant c in every direction. At the moment when point M and M' meet, the people start to wait for the flashes too. They know that point A' and B' are equally distant from the point M', because when M and M' coincide(and the flashes occur) - A and A', and B and B' coincide too(whether we take length contraction into account or not shouldn't matter because the important thing here is that the length A'M' is equal to B'M' according to the train passengers - according to them A and B are equally distant from M, and M' and M coincide at that moment with or without length contraction). So knowing that A'M'=B'M' and expecting the speed of light to be the same both from A' to B' and from B' to A', they would expect the light to cover the distances A'M' and B'M' for the same time, and therefore meet at point M'.
But this argument only makes sense if the train observers for some reason assume both strikes happened simultaneously in their own frame--why should they do that, a priori? Einstein wasn't proposing that the embankment observers would just assume a priori that the strikes happened simultaneously in the embankment frame, he was including that as a fact unique to this particular physical scenario. There's nothing odd about the notion that two lightning strikes at equal distances from a given observer (in this case the train observer) might happen at different times in the observer's frame, in which case that observer will see the light from them at different times. If I'm sitting in my house for a week, and on Monday I see the light from a strike 1 mile to my North, and on Friday I see the light from a strike 1 mile to my South, I'm obviously not going to think that both strikes happened simultaneously and therefore be puzzled by the "paradox" that I saw the light from them at different times, I'll just conclude that one strike happened Monday and the other happened on Friday.

Of course you could imagine a different physical scenario than the one Einstein proposed, one where the strikes do happen simultaneously in the train frame, but this would mean they happen non-simultaneously in the embankment frame so the observer at M doesn't see the light from each one at the same time. In any specific physical scenario, there's going to be some specific fact about which frame the strikes were simultaneous in and which they weren't.

JesseM said:
But this argument only makes sense if the train observers for some reason assume both strikes happened simultaneously in their own frame--why should they do that, a priori?
That is exactly what I want you to imagine - that they are aware of the experiment. Because the flashes of lightning occur just when points M and M' coincide, therefore both observers can experience that moment equally well, and will know that two beans of light are traveling(from point A and B for the embankment and from A' and B' for the train) towards their middle points, and can begin to wait for the beams of light to arrive. Isn't it only natural for both of them to expect the beams to cover the equal distances from the front to the middle and from the back to the middle for the same time?

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baivulcho said:
So then let's imagine this experiment:
In the moment when the six points A, A' M, M', B and B' coincide respectively, at points A, A', B and B' strike lightnings.
What do you mean by "in the moment" though? In the train frame, the distance between A and B is shorter than the length of the train (i.e the distance between A' and B') because of length contraction, so the moment that A and A' coincide happens earlier than the moment that B and B' coincide.
baivulcho said:
So then the flashes from A' and B' will meet at M', and those from A and B meet at M, right?
No, in both frames the light beams meet each other at the position of M--all frames must agree about local facts confined to a single location in space and time, like when two objects meet one another. Of course in the train frame M is moving, and at the time the two light beams meet M is closer to the back of the train (B') than to the front (A').
baivulcho said:
If you are in the middle of the train and two lightnings strike the front and the rear end, then the light from them should meet at the middle
Not if the strikes happen at different moments! Suppose the distance from the end of a train to the middle is 5 light-seconds, and one strike hits the front end at t=30 seconds, and then another strike hits the back at t=32 seconds. In that case, if each beam travels at c so it takes 5 seconds to move 5 light-seconds, naturally the light from the front strike will reach the center at t=35 seconds, and the light from the back strike will reach the center at t=37 seconds.
baivulcho said:
If so wouldn't it be odd for the observer on the embankment to see that the flashes in his frame meet in one point and those from the other meet at other point
That can't happen, as I said all frames must agree about local events. For example, suppose there was a bomb at the center of the train with light-sensors on both sides, programmed to explode if it detects flashes of lights on each side at the same moment--if different frames could disagree about whether the bomb explodes that would obviously be a pretty serious problem!
baivulcho said:
Probably I am just asking the same question, but it seems to me that for both observers the flashes have to cover equal distances(A'M' and B'M' for the train and AM and BM for the embankment), but for one observer they meet at the middle and for the other they don't. This seems to me contradicts with the idea that the light propagate with constant velocity for every observer in every direction. It looks like the train observer will conclude that the beam from B' has traveled faster, which is totally wrong.
Again, why do you think there's a problem with the train observer just saying the lightning strikes themselves happened at different moments, so that's why the light from each one reached him at different moments?

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So you mean that in the original Einstein's example when it is said "Just when the flashes of lightning occur, the point M' coincides with the point M...", it is meant that when the points coincide the flashes occur but only for the observer on the embankment - so the whole example is described from the embankment observer's stand point. For the observer on the train first occurs the flash at B then the points M and M' meet each other and after that the strike at A occurs - and what the passenger describes(first flash from B and then that from A) is logical consequence of the the sequence of the events. So my confusion came from the way the example is described from like a third(distant) point of view. The conclusion is that when we describe something in the theory of relativity we describe it either from one frame of reference or from another - never from some murky outside third view point.

baivulcho said:
So you mean that in the original Einstein's example when it is said "Just when the flashes of lightning occur, the point M' coincides with the point M...", it is meant that when the points coincide the flashes occur but only for the observer on the embankment - so the whole example is described from the embankment observer's stand point.
Yes, any statement about simultaneity (which includes any statement about one event happening 'when' another event is happening at a different location) is meant to be from the embankment frame's view. Of course local events, like the fact that the lightning strikes the front at the same position and time that A and A' coincide, are true in both frames.
baivulcho said:
For the observer on the train first occurs the flash at B then the points M and M' meet each other and after that the strike at A occurs
I thought A was the front of the train and B was the back? Either way, in the train frame first the front of the train coincides with the front point on on the track (which I was calling A), then later M and M' coincide, then later the back of the train coincides with the back point on the track (which I was calling B).
baivulcho said:
The conclusion is that when we describe something in the theory of relativity we describe it either from one frame of reference or from another - never from some murky outside third view point.
Yes, that's right, any description involving frame-dependent facts such as simultaneity or length can only be from the perspective of a particular frame.

I never liked this example (although I think that it was formulated by Einstein himself). I think it is confusing and hard to understand. To understand the relativity of simultaneity, it is much easier to imagine a light being turned on in the middle of the train. The light reaches the front and the back of the train simultaneously, according to an observer on the train. But according to an observer on the embankment, the light will reach the back of the train before it reaches the front of the train, because according to such an observer, the light that reaches the back of the train will have traveled a shorter distance than the light that reaches the front of the train, since train is moving, according to this observer.

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JesseM said:
But this argument only makes sense if the train observers for some reason assume both strikes happened simultaneously in their own frame--why should they do that, a priori? Einstein wasn't proposing that the embankment observers would just assume a priori that the strikes happened simultaneously in the embankment frame, he was including that as a fact unique to this particular physical scenario. There's nothing odd about the notion that two lightning strikes at equal distances from a given observer (in this case the train observer) might happen at different times in the observer's frame, in which case that observer will see the light from them at different times. If I'm sitting in my house for a week, and on Monday I see the light from a strike 1 mile to my North, and on Friday I see the light from a strike 1 mile to my South, I'm obviously not going to think that both strikes happened simultaneously and therefore be puzzled by the "paradox" that I saw the light from them at different times, I'll just conclude that one strike happened Monday and the other happened on Friday.

Of course you could imagine a different physical scenario than the one Einstein proposed, one where the strikes do happen simultaneously in the train frame, but this would mean they happen non-simultaneously in the embankment frame so the observer at M doesn't see the light from each one at the same time. In any specific physical scenario, there's going to be some specific fact about which frame the strikes were simultaneous in and which they weren't.

Yeah, personally I find it easier to inverse the scenario and give the example of a light bulb in the middle of the train. That avoids such unlikely pure chance events.
Edit: I now see that I'm not the only one with that preference! :-)

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Erland said:
I never liked this example (although I think that it was formulated by Einstein himself). I think it is confusing and hard to understand. To understand the relativity of simultaneity, it is much easier to imagine a light being turned on in the middle of the train. The light reaches the front and the back of the train simultaneously, according to an observer on the train. But according to an observer on the embankment, the light will reach the back of the train before it reaches the front of the train, because according to such an observer, the light that reaches the back of the train will have traveled a shorter distance than the light that reaches the front of the train, since train is moving, according to this observer.

At the time, it would have been a very intuitive explanation (I think it still is) given the prevalence of commuter rail, and the often unique experience associated (Which train is moving)? I can see why the mind would drift in that direction, and I think it's unfair to dismiss it because it's not instantly grasped by all.

That said, time has passed so maybe tradition needs to give way to accessiblity about a century later. :)

Suppose we have two light sources, one moving in the middle of the moving train and one stationary in the middle of the station platform and they both flash when they are co-located, will the light on the train reach the ends of the train simultaneously according to an observer on the train and will the light on the platform reach the ends of the platform simultaneously according to an observer on the platform?

Of course the answer is yes.

Now repeat the experiment with one of the light sources failing to flash. Is anything different?

Of course the answer is no.

To me, this is a much more interesting scenario to analyze.

ghwellsjr said:
Suppose we have two light sources, one moving in the middle of the moving train and one stationary in the middle of the station platform and they both flash when they are co-located, will the light on the train reach the ends of the train simultaneously according to an observer on the train and will the light on the platform reach the ends of the platform simultaneously according to an observer on the platform?

Of course the answer is yes.

Now repeat the experiment with one of the light sources failing to flash. Is anything different?

Of course the answer is no.

To me, this is a much more interesting scenario to analyze.
Are you suggesting that there is a problem here?

No, just a more interesting (to me) scenario to consider, since we are considering different scenarios from the OP.

ghwellsjr's example makes sense to me, and I've already been clear that I like Einstein's version.

Ok now suppose that there are 2 extra-observers put at B and A ends of the train. They are instructed to send light signals once their detectors are stroke by the lightening. Then the light signals from both ends go to a mirror in the middle of the train ( where the middle observer is there) and reflected back to B and A where they can register them and record the times of arrival. In that particular case, the recorded times of final arrival of the signal will be equal for both B and A simply because the light from B takes shorter time to reach the middle mirror but compensates that by taking longer time after reflection relative to A. So both B and A observer will agree that both lightning events happen at the same time same like the conclusion of the embankment observer. However, there will be a definite disagreement with the middle observer M who still insists that B happens ahead of A
So the final conclusion for all the observers in the train is that the train is moving in the direction of B. This can simply solve the puzzle. However, as we learned from Mickelson experiment, that no such way to know that the inertial FOR is moving because the laws of physics and c remain invariant. This makes new paradox. It also undermines the weakness of Einsteins hypothesis that the simultaneity is a relative thing because:
1) it assumed that the whole calculation is made from the embankment observer point of view
2) it does not give clear definition of what does detecting an event means relative to different observers apart from using just light signal to detect the events

Ok now suppose that there are 2 extra-observers put at B and A ends of the train. They are instructed to send light signals once their detectors are stroke by the lightening. Then the light signals from both ends go to a mirror in the middle of the train ( where the middle observer is there) and reflected back to B and A where they can register them and record the times of arrival. In that particular case, the recorded times of final arrival of the signal will be equal for both B and A simply because the light from B takes shorter time to reach the middle mirror but compensates that by taking longer time after reflection relative to A. So both B and A observer will agree that both lightning events happen at the same time same like the conclusion of the embankment observer.
No. Recall that the lightning strikes are simultaneous only in the embankment frame, but not in the train frame. The observers on the ends of the train will detect the lightning strikes at different times (per their clocks) and thus send their light signals out at different times.
However, there will be a definite disagreement with the middle observer M who still insists that B happens ahead of A
Sure, but that's because your assumption that A' and B' detect the lightning strikes at the same time is incorrect.

The assumption I made that A and B are simultaneous is based on a though experiment I proposed when a reflecting mirror put in the middle of the train. Remember that Einsteinone was also a thought experiment. The strikes of lightning seen on A and B happen at the same time for the stationary observer but the calculation based on detecting them relative to M is also based on the stationary observers point of view. And for my model with 2 observers located at the 2 ends of the train, their observation should coincide after receiving the reflecting signals. I did not propose that A and B are simultaneous or not, I just flow with the experiment. There is no preference to assume that the simultaneity should be observed according to M while it could be recorded using 2 observers A and B and then they can use a conventional communication channels to share their results regarding the time of recording the signals !

The assumption I made that A and B are simultaneous is based on a though experiment I proposed when a reflecting mirror put in the middle of the train. Remember that Einsteinone was also a thought experiment. The strikes of lightning seen on A and B happen at the same time for the stationary observer but the calculation based on detecting them relative to M is also based on the stationary observers point of view. And for my model with 2 observers located at the 2 ends of the train, their observation should coincide after receiving the reflecting signals. I did not propose that A and B are simultaneous or not, I just flow with the experiment. There is no preference to assume that the simultaneity should be observed according to M while it could be recorded using 2 observers A and B and then they can use a conventional communication channels to share their results regarding the time of recording the signals !
I don't see your point. If train observers A' and B' detect the arrival of the reflected light at the same time (according to their clocks) then there's no way that observer train observer M' (at the middle of the train) could have seen light from A' and B' arrive at different times. Note that we are merely discussing observations made from a single frame--that of the train--so relativity hasn't even entered the picture yet.

(Note that this is a different scenario than that used by Einstein.)

We are discussing the interpretation of observation made in train FOR based on the consideration of the stationary observer according to the laws of optics and light transmission. Remember that the whole process started when lightning strikes the 2 ends of train at the same time as seen by the external observer. The problem is that when you regard the ordering of events is due to interpretation of M, the 2 ends-observers will disagree with M either after recording their observation from the reflected light from M-mirror or after communication by conventional channels for instance,,, There is one way out for that,,,,,, is to accept the fact that the train is moving in direction of B ( which contradicts the relativity principle)

We are discussing the interpretation of observation made in train FOR based on the consideration of the stationary observer according to the laws of optics and light transmission. Remember that the whole process started when lightning strikes the 2 ends of train at the same time as seen by the external observer.
OK, so now you're back to Einstein's example: The lightning strikes at the ends of the train are simultaneous according to the platform observers. Good.
The problem is that when you regard the ordering of events is due to interpretation of M, the 2 ends-observers will disagree with M either after recording their observation from the reflected light from M-mirror or after communication by conventional channels for instance,,,
No, none of the train observers disagree. All their observations are consistent with the lightning striking the ends of the train at different times (per their clocks). For some reason, you think that observers A' and B' will detect the lightning at the same time; not so.
There is one way out for that,,,,,, is to accept the fact that the train is moving in direction of B ( which contradicts the relativity principle)
Of course the train is moving. Why do you think that contradicts the relativity principle?

Doc Al said:
No, none of the train observers disagree. All their observations are consistent with the lightning striking the ends of the train at different times (per their clocks). For some reason, you think that observers A' and B' will detect the lightning at the same time; not so.

If you flow with the thought experiment that observers A and B registration of events depends on the time of arrival of signals after reflection from M-mirror, yes of course there will be an expected disagreement according to external observer consideration of light transmission. But in the reality, no such disagreement. So, the conclusion is the temporal ordering of events according to M-observer alone is Wrong
This could be also seen when trying to answer the following question: Why interpretation of events should rely on M-observer and not on A & B according to the external observer point of view?

Of course the train is moving. Why do you think that contradicts the relativity principle?

Because for train observers, no such way to know that they are moving or not based on any experiment deploying light transmission ( equivalent to the negative result of Mickelson)

Because for train observers, no such way to know that they are moving or not based on any experiment deploying light transmission ( equivalent to the negative result of Mickelson)
You are perhaps thinking that the measurements made on the train by observers A', B', and M', will allow them to tell that they are moving in some absolute sense. No. All the measurements allow them to conclude is that the lightning struck the ends of the train at different times. Which is true (in the train's frame of reference).

Now if the train observers communicate with the platform observers and compare notes, sure they will be able to tell that they are in relative motion. No surprise there.

try to answer the following question: Why interpretation of events should rely on M-observer and not on A & B according to the external observer point of view?

try to answer the following question: Why interpretation of events should rely on M-observer and not on A & B according to the external observer point of view?
I'm not sure what you are trying to say. All you need are A' and B' looking at their local clocks when the lightning strikes. They record the time and later compare notes. But all three train observers agree! The lightning struck A' and B' at different times and thus the light from those strikes reached M' at different times. What's the problem?

Why do you assume that lightning struck A and B at different times? What kind of light transmission arrangement justifies this assumption?

Why do you assume that lightning struck A and B at different times? What kind of light transmission arrangement justifies this assumption?
If you're using Einstein's scenario, the lightning strikes simultaneously with respect to the platform observers. Einstein shows that the train observers will see the strikes happen at different times.

If you would like to discuss a different scenario, you'd better define it.

Why do you assume that lightning struck A and B at different times?
Why do you assume that lightning struck A and B at the same time? As I understand it, in this thread it has already been specified that the strikes were at the same time relative to the platform observers, so you can't just assume they are at the same time relative to anyone else.

On the other hand, if you want to explore a different scenario where the strikes are simultaneous relative to the train, you can do so, but this is a different experiment so none of the previous results apply.

What I am trying to say clearly is:
1) The M observer has no such preference over the end-observers to interpret the results according to the external observer point of view
2) You assume that A and B have different timing, while if you make them use the reflected signal from M-mirror, they will coincide their measurements ( simply because the all events have started from the moment of striking the train ends at the same time according to the external observer point of view regarding the light transmission)
3) The Train thought experiment is mainly used to show that difference is only when interpreted from external observer MIND

You claim that A and B are different based on what? On the interpretation of M? Ok,,, so why M sees events in different time? because M moves in the direction of B-signal faster than than Aone,,, so why that happens? because you consider that from the embankment point of view,,, Pronto
But if you see the experiment whwn A and B are involved ( also according to the embankment point of view),,, the matter changes clearly,,, pronto

What I am trying to say clearly is:
1) The M observer has no such preference over the end-observers to interpret the results according to the external observer point of view
I don't understand this statement.
2) You assume that A and B have different timing, while if you make them use the reflected signal from M-mirror, they will coincide their measurements ( simply because the all events have started from the moment of striking the train ends at the same time according to the external observer point of view regarding the light transmission)
Here you assume that somehow using a mirror at M' will show the reflected light arriving at A' and B' simultaneously. Why do you assume that? In Einstein's scenario, he shows that the light from the strikes arrives at M' at different times. Nothing is merely 'assumed'.
3) The Train thought experiment is mainly used to show that difference is only when interpreted from external observer MIND
I don't understand this statement. The train thought experiment is used to show that things that are simultaneous in one frame are not necessarily simultaneous in another.

You claim that A and B are different based on what? On the interpretation of M? Ok,,, so why M sees events in different time? because M moves in the direction of B-signal faster than than Aone,,, so why that happens? because you consider that from the embankment point of view,,, Pronto
The only data we are given is from the embankment point of view. Of course we'll use it!

In the Einstein scenario you are told that the lightning strikes are simultaneous in the embankment frame. That's the only information you are given. But that's enough to show that the train observers will see the lightning striking at different times. (It is shown, not 'assumed'.)
But if you see the experiment whwn A and B are involved ( also according to the embankment point of view),,, the matter changes clearly,,, pronto
I don't understand this statement. All frames agree that the light strikes M' at different times!

i also agree about different timing at M but not for A and B,,, let's say that M wants to share his data with A and B,,, then he sends light signals once he received ( equivalent to using M-mirror),,, if M sees B before A then according to the train FOR, B should also receive the reflected signal before A. But as seen from the external observer, no such thing happens, why? because this time, the light has to travel a bit longer distance to reaches B than A and finally they will be coincide their measurments

i also agree about different timing at M but not for A and B,,, let's say that M wants to share his data with A and B,,, then he sends light signals once he received ( equivalent to using M-mirror),,, if M sees B before A then according to the train FOR, B should also receive the reflected signal before A.
He does! According to the train clocks, B' receives the signal before A'.
But as seen from the external observer, no such thing happens, why? because this time, the light has to travel a bit longer distance to reaches B than A and finally they will be coincide their measurments
It's certainly true that according to embankment clocks the light strikes the observers at the ends of the train at the same time. But not according the train clocks. That's the entire point of the thought experiment--to illustrate the relativity of simultaneity.

But what happens actually is because A and B coincide their measurements after receiving the reflection from M,,, they should do so both for the ground observer and for the train ( for the ground it is easy to imagine that and for the train this should be done after having a communication with each other). There is no point when you say that M should be have different timing for both frames of references and on the other hand, A and B should not. As long as, the All matter is judged from the external observer point of view :)

But what happens actually is because A and B coincide their measurements after receiving the reflection from M,,, they should do so both for the ground observer and for the train ( for the ground it is easy to imagine that and for the train this should be done after having a communication with each other).
The folks on the train measure distance and time using their own clocks, of course. Everyone uses their own clocks! What you want to do is compare what the train clocks would say to what the embankment clocks would say. There's nothing special about the embankment clocks. That's one of the key aspects of relativity.
There is no point when you say that M should be have different timing for both frames of references and on the other hand, A and B should not.
The difference between them is that arrival of the light at M' happens at the same location on the train, but A' and B' are at different ends of the train. That makes a big difference! If two things happen at the same time at the same place (to M', for example), then everybody in every frame agrees that they happen at the same time. (And using their own clocks, of course.) But if two things happen at the same time but at different locations in one frame, they will be seen to happen at different times in another frame.
As long as, the All matter is judged from the external observer point of view :)
Uh, no.

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