1. Einsteins definition:

The events a and b are simultaneous if and only if lightrays from a and b arrives simultaneously at the midpoint of the segment ab.

Somebody else said:
Simultaneity is the question as to whether two events separated by space occur at the same time, or not.

Consider: three points in space A,M,B. AM = MB, M is physically midway between A & B.

Add two events, E1 and E2: Flashes light propagated at A and B, the light from these events arrive at M simultaneously.

E1 and E2 are therefore simultaneous.
It seems to me this bewildered layman that we should use some OTHER concept than "simultaneously"
in understanding the concept "simultaneous". Otherwise we seem to define a concept with itself.

When we determine that two things happens simultaneously,
arent we really deciding that they are simultaneous?

Why then did Einstein need to introduce the definition?

Cant we be satisfied with the concept "at the same time",
or is that concept in need of explanation as well?

Perhaps its not really a definition!
Only a description of the method for measuring?

But if so then: Measuring what? Depending on what?
How do we prove there are not TWO different concepts here?
The first (Nevermore to be used?) defining the second?

2.

3. Why then did Einstein need to introduce the definition?

Cant we be satisfied with the concept "at the same time",
He introduced it because in relativity different observers measure time differently, and thus the term "at the same time" no longer makes any sense. This is different from the situation in classical mechanics, where a universal time coordinate is used.

4. Originally Posted by sigurdV
Einsteins definition:

The events a and b are simultaneous if and only if lightrays from a and b arrives simultaneously at the midpoint of the segment ab.

Somebody else said:
Simultaneity is the question as to whether two events separated by space occur at the same time, or not.

Consider: three points in space A,M,B. AM = MB, M is physically midway between A & B.

Add two events, E1 and E2: Flashes light propagated at A and B, the light from these events arrive at M simultaneously.

E1 and E2 are therefore simultaneous.
It seems to me this bewildered layman that we should use some OTHER concept than "simultaneously"
in understanding the concept "simultaneous". Otherwise we seem to define a concept with itself.
Yes, that sounds like a good idea to me, too.

Originally Posted by sigurdV
When we determine that two things happens simultaneously,
arent we really deciding that they are simultaneous?
Yes, and we need a basis upon which to decide this.

Originally Posted by sigurdV
Why then did Einstein need to introduce the definition?

Cant we be satisfied with the concept "at the same time",
or is that concept in need of explanation as well?
Yes, that concept is in need of an explanation itself, especially if the events we are talking about aren't happening in the same place as you are - i.e. if they happened at a distance from you.

The reason for this is that light takes time to travel to you, from an event. So the event did not happen when you saw it to happen, it happened some time in the past and then the light from that event took time to reach you.

So, Einstein defined those events as being simultaneous if the light from those events reaches a place halfway in between those events, at the same time. This means the time it took the light to travel from both events is the same, and as the distance to the events is also the same those events must have happened at the same time in the past.

If you are standing halfway between two events (let's use lightning strikes!), and the light from those events reaches you at the same time, then you can confidently decide that those events happened at the same time in the past - they are simultaneous events, in relation to your position.

But does that mean events can only be simultaneous for an observer standing halfway between them? Surely they must also be simultaneous for other observers in different places? Well, we can imagine another observer, standing halfway between yourself and one of the lightning strikes, if we like. That observer is three times the distance from one of the events as he is from the other. The light from those events will reach him at different times, so how should he decide whether they were simultaneous or not?

If that second observer knows how fast light covers the distance involved, he can calculate whether those events were simultaneous or not, even though he saw the light from those events at different times.

Let's say, just for argument, that the distance between the events was the distance light covers in 4 seconds. You are standing halfway between the events, and the light from them reaches you at the same time. You would conclude that the events were simultaneous, and that they happened 2 seconds before you saw them, 2 seconds in the past. That other observer is 1 light second away from one of the events and 3 light seconds away from the other. The light from those events would reach him 2 seconds apart, 1 second after the closest event and 3 seconds after the more distant event. Knowing the distances involved, he would also conclude they were simultaneous, and happened 1 second before he saw the light from the closest event.

To anyone standing anywhere in relation to those events, those events were simultaneous.

But what if a third observer is in motion in relation to you and that second observer?

What if the third observer was flying past you, 2 seconds before you saw the events to occur simultaneously? What if that observer reached the place the second observer was when the light reached him from the closest event?

To you, he was halfway between the events when they occurred simultaneously, but is now closer to one of the events as the light from it reaches him. To you, he is moving in relation to the light from those events, moving away from the place where one event happened and towards the place the other happened. The light from those events doesn't reach him at the same time, even though he was in the same place as you were when they occurred. So the question is, how can he decide whether those events were simultaneous, or not?

He satisfies the requirement of being halfway between the events when they occurred, but he doesn't satisfy the requirement of seeing the light from those events at the same time.

At this point we should look at one of the basic postulates of Special Relativity, namely that light is always measured to travel at the same speed regardless of the motion of the observer who is doing the measuring. In a nutshell, this means that everyone measures the speed of light to be ~300,000 km/s faster than themselves, regardless of who is moving and who is stationary!

The upshot of this is that the other observer will measure the speed of the light reaching him from those events to be different from the speed you measure the light to be travelling, in relation to him. To you, he is moving away from the light from one event and towards the light from the other, so the light from those events is closing in on him at different speeds. But to him, the light all comes towards him at the same speed from both directions!

We already know, for sure, that the light from those events doesn't reach him at the same time, as he was in the same place as that other observer earlier on - 3 light-seconds from one event and 1 light-second from the other, when the light reaches him. (take note of this, space at the centre)

So, we have to conclude from this that he will calculate himself to have been the same distance from both events, as we know that from his point of view the light propagates at the same speed towards him from both events, and that he can thus consider himself to be at rest in relation to those events (even if he not at rest in relation to the frame in which they occurred), and yet the light reaches him at different times. So, we can only conclude that those events were not simultaneous to the moving observer.

Now have a look at those animations for the train and embankment once again:

From the embankment: simultaneous

From the train: NOT simultaneous

Same events, different observers, but with both observers measuring the speed of light to be ~300,000 km/s in relation to themselves, and both being equidistant between the events.

This weirdness (the relativity of simultaneity) is all due to the constancy of the speed of light to all observers. Whatever your motion in relation to any other observer, you will always measure light to propagate at ~300,000 km/s in relation to yourself. So, you can always consider yourself to be at rest in relation to light, whatever else is moving in relation to you. If an object passes you and flashes a lightbulb, the light from that bulb propagates from a place at rest in relation to you, whilst the object moves on through the propagating light, whilst from the point of view of the object itself, the light simply propagates from the bulb. This is the strangeness that led Einstein to conclude that time, distance and thus simultaneity are relative, rather than absolute.

5. What stopped me from answering immediately is the bloody train experiment...
Its difficult to grasp! I feel like postponing deciding on it...

Originally Posted by SpeedFreek
Originally Posted by sigurdV
Einsteins definition:

The events a and b are simultaneous if and only if lightrays from a and b arrives simultaneously at the midpoint of the segment ab.

Somebody else said:
Simultaneity is the question as to whether two events separated by space occur at the same time, or not.

Consider: three points in space A,M,B. AM = MB, M is physically midway between A & B.

Add two events, E1 and E2: Flashes light propagated at A and B, the light from these events arrive at M simultaneously.

E1 and E2 are therefore simultaneous.
It seems to me this bewildered layman that we should use some OTHER concept than "simultaneously"
in understanding the concept "simultaneous". Otherwise we seem to define a concept with itself.
Yes, that sounds like a good idea to me, too.

Originally Posted by sigurdV
When we determine that two things happens simultaneously,
arent we really deciding that they are simultaneous?
Yes, and we need a basis upon which to decide this.

Originally Posted by sigurdV
Why then did Einstein need to introduce the definition?

Cant we be satisfied with the concept "at the same time",
or is that concept in need of explanation as well?
Yes, that concept is in need of an explanation itself, especially if the events we are talking about aren't happening in the same place as you are - i.e. if they happened at a distance from you.

The reason for this is that light takes time to travel to you, from an event. So the event did not happen when you saw it to happen, it happened some time in the past and then the light from that event took time to reach you.

So, Einstein defined those events as being simultaneous if the light from those events reaches a place halfway in between those events, at the same time. This means the time it took the light to travel from both events is the same, and as the distance to the events is also the same those events must have happened at the same time in the past.

If you are standing halfway between two events (let's use lightning strikes!), and the light from those events reaches you at the same time, then you can confidently decide that those events happened at the same time in the past - they are simultaneous events, in relation to your position.

But does that mean events can only be simultaneous for an observer standing halfway between them? Surely they must also be simultaneous for other observers in different places? Well, we can imagine another observer, standing halfway between yourself and one of the lightning strikes, if we like. That observer is three times the distance from one of the events as he is from the other. The light from those events will reach him at different times, so how should he decide whether they were simultaneous or not?

If that second observer knows how fast light covers the distance involved, he can calculate whether those events were simultaneous or not, even though he saw the light from those events at different times.

Let's say, just for argument, that the distance between the events was the distance light covers in 4 seconds. You are standing halfway between the events, and the light from them reaches you at the same time. You would conclude that the events were simultaneous, and that they happened 2 seconds before you saw them, 2 seconds in the past. That other observer is 1 light second away from one of the events and 3 light seconds away from the other. The light from those events would reach him 2 seconds apart, 1 second after the closest event and 3 seconds after the more distant event. Knowing the distances involved, he would also conclude they were simultaneous, and happened 1 second before he saw the light from the closest event.

To anyone standing anywhere in relation to those events, those events were simultaneous.

But what if a third observer is in motion in relation to you and that second observer?

What if the third observer was flying past you, 2 seconds before you saw the events to occur simultaneously? What if that observer reached the place the second observer was when the light reached him from the closest event?

To you, he was halfway between the events when they occurred simultaneously, but is now closer to one of the events as the light from it reaches him. To you, he is moving in relation to the light from those events, moving away from the place where one event happened and towards the place the other happened. The light from those events doesn't reach him at the same time, even though he was in the same place as you were when they occurred. So the question is, how can he decide whether those events were simultaneous, or not?

He satisfies the requirement of being halfway between the events when they occurred, but he doesn't satisfy the requirement of seeing the light from those events at the same time.

At this point we should look at one of the basic postulates of Special Relativity, namely that light is always measured to travel at the same speed regardless of the motion of the observer who is doing the measuring. In a nutshell, this means that everyone measures the speed of light to be ~300,000 km/s faster than themselves, regardless of who is moving and who is stationary!

The upshot of this is that the other observer will measure the speed of the light reaching him from those events to be different from the speed you measure the light to be travelling, in relation to him. To you, he is moving away from the light from one event and towards the light from the other, so the light from those events is closing in on him at different speeds. But to him, the light all comes towards him at the same speed from both directions!

We already know, for sure, that the light from those events doesn't reach him at the same time, as he was in the same place as that other observer earlier on - 3 light-seconds from one event and 1 light-second from the other, when the light reaches him. (take note of this, space at the centre)

So, we have to conclude from this that he will calculate himself to have been the same distance from both events, as we know that from his point of view the light propagates at the same speed towards him from both events, and that he can thus consider himself to be at rest in relation to those events (even if he not at rest in relation to the frame in which they occurred), and yet the light reaches him at different times. So, we can only conclude that those events were not simultaneous to the moving observer..
But on what you said above I wonder: Cant the moving observer figure out his situation? Shouldnt he realise that if the events are simultaneous then they shouldnt seem simultaneous to him? Isnt he aware of all necessary facts? What stops him from figuring out in what order the light should reach him for the events to be simultaneous? Should not his knowledge of the theory of relativity anyway prevent him from jumping to too hasty conclusions?

This part of the theory is hard for laymen to understand and you will go on to describe the thought experiment of the train. And your conclusion will be that simultaneity is relative. And I will disappoint you! All I can agree to is that we cant always by only using the theory of relativity tell whether any two events are simultaneous! Whether they are, or are not, cant be decided by our data, but that does not constitute proof that they are NOT simultaneous in an absolute sense!

There is a similar situation in Quantum Mechanics. We cant both discover the position and momentum of elementary particles but that does not prove they do not have both momentum and position.

Modern Science tells us that not everything can be known...we have to live with that until we find a way around it.

6. Originally Posted by sigurdV
But on what you said above I wonder: Cant the moving observer figure out his situation? Shouldnt he realise that if the events are simultaneous then they shouldnt seem simultaneous to him? Isnt he aware of all necessary facts? What stops him from figuring out in what order the light should reach him for the events to be simultaneous? Should not his knowledge of the theory of relativity anyway prevent him from jumping to too hasty conclusions?
Good questions!

Let me start with a quick word or two about the postulates of Special Relativity - the principle of relativity and the constancy of c to all inertial frames.

Postulate 1. The laws of physics are the same in all inertial frames of reference.
Postulate 2. The speed of light is always measured to be c, relative to any inertial frame of reference.

The whole of special relativity is based on those two postulates alone. Everything else we talk about in SR (time-dilation, length contraction, relativity of simultaneity) is a direct result of those two postulates.

Postulate 1 means the observer is figuring out his situation, as you stated. He calculates that the two events were not simultaneous in his frame of reference, using his knowledge of relativity. But using that same knowledge, he can calculate that the two event were simultaneous from the frame of reference of the embankment. The question we have to ask here is if the frame of reference of the embankment is any more representative of reality than the frame of the train?

You might decide that it makes sense to choose the embankment as a preferred frame, because the train is only moving in relation to the embankment due to the train having accelerated. But ask yourself this:

What if the train is moving at the same speed as the Earth rotates, but in the opposite direction? Then, from the view of, say, the Sun, it is the train that is not moving, whilst the Earth moves beneath it! Here, it is the moving frame in which the events are simultaneous, whilst in the frame at rest those events were not simultaneous.

Originally Posted by sigurdV
This part of the theory is hard for laymen to understand and you will go on to describe the thought experiment of the train. And your conclusion will be that simultaneity is relative. And I will disappoint you! All I can agree to is that we cant always by only using the theory of relativity tell whether any two events are simultaneous! Whether they are, or are not, cant be decided by our data, but that does not constitute proof that they are NOT simultaneous in an absolute sense!
This is where the theory actually disagrees with you. Whether the events are simultaneous, or not, can be decided by the data, from any frame of reference.

The fact that we know time-dilation is real (as has been shown in many experiments) means that time itself cannot be absolute, so the relativity of simultaneity simply falls out of the same theory that correctly predicts time-dilation. To deny the relativity of simultaneity, and thus to deny there is no such thing as absolute simultaneity, is to deny Special Relativity itself. This is why I have been saying you are arguing against SR.

Originally Posted by sigurdV
There is a similar situation in Quantum Mechanics. We cant both discover the position and momentum of elementary particles but that does not prove they do not have both momentum and position.
The situation is different with Special Relativity. We can prove simultaneity is not absolute - because all experiments that show time-dilation are actually proving simultaneity is not absolute, if you think about it hard enough!

7. Originally Posted by SpeedFreek
Originally Posted by sigurdV
But on what you said above I wonder: Cant the moving observer figure out his situation? Shouldnt he realise that if the events are simultaneous then they shouldnt seem simultaneous to him? Isnt he aware of all necessary facts? What stops him from figuring out in what order the light should reach him for the events to be simultaneous? Should not his knowledge of the theory of relativity anyway prevent him from jumping to too hasty conclusions?
Good questions!

Let me start with a quick word or two about the postulates of Special Relativity - the principle of relativity and the constancy of c to all inertial frames.

Postulate 1. The laws of physics are the same in all inertial frames of reference.
Postulate 2. The speed of light is always measured to be c, relative to any inertial frame of reference.

The whole of special relativity is based on those two postulates alone. Everything else we talk about in SR (time-dilation, length contraction, relativity of simultaneity) is a direct result of those two postulates.

Postulate 1 means the observer is figuring out his situation, as you stated. He calculates that the two events were not simultaneous in his frame of reference, using his knowledge of relativity. But using that same knowledge, he can calculate that the two event were simultaneous from the frame of reference of the embankment. The question we have to ask here is if the frame of reference of the embankment is any more representative of reality than the frame of the train?

You might decide that it makes sense to choose the embankment as a preferred frame, because the train is only moving in relation to the embankment due to the train having accelerated. But ask yourself this:

What if the train is moving at the same speed as the Earth rotates, but in the opposite direction? Then, from the view of, say, the Sun, it is the train that is not moving, whilst the Earth moves beneath it! Here, it is the moving frame in which the events are simultaneous, whilst in the frame at rest those events were not simultaneous.?
Why prefer any frame? We have a framerelated concept of simultaneity...its better than nothing Id say. But it seems not to be a natural concept of simultaneity ...I suppose you are so used to it so you dont find it...ahem...er...somewhat artificial? This reminds me of a situation in logic...the distinction of object language and metalanguage: The concept of truth is defined in the metalanguage and applies only on sentences in the object language if one asks about the truth of the metalinguistic sentences one must got to a metalanguage of the metalanguage to define a truth concept for what is now the nearest objectlanguage for the new metalanguage...in this way you get a series of truth concepts and a natural objection is that we have one truth concept only! Not an infinite series of truth concepts with varying applicability! But formal logicians tend to think no price is too expensive to escape paradoxes. (The irony of it is that escaping paradox is actually free.)
Well then. This means all frames are related, doesnt it? What is the cause of that?Is there a natural order to frames?
Originally Posted by SpeedFreek
Originally Posted by sigurdV
This part of the theory is hard for laymen to understand and you will go on to describe the thought experiment of the train. And your conclusion will be that simultaneity is relative. And I will disappoint you! All I can agree to is that we cant always by only using the theory of relativity tell whether any two events are simultaneous! Whether they are, or are not, cant be decided by our data, but that does not constitute proof that they are NOT simultaneous in an absolute sense!
This is where the theory actually disagrees with you. Whether the events are simultaneous, or not, can be decided by the data, from any frame of reference.
Oh!? Perhaps we need to get things straight here: Do you claim that simultaneous events in one frame are not simultneous in at least one other frame?And vice versa that theres always another frame where non simultaneous events are simultaneous? Say...today and tomorrow.
Originally Posted by SpeedFreek
The fact that we know time-dilation is real (as has been shown in many experiments) means that time itself cannot be absolute,
It dont see why that is so. It should be the other way around. There should be some not dilated frame to compare all the dilated frames with.
Originally Posted by SpeedFreek
so the relativity of simultaneity simply falls out of the same theory that correctly predicts time-dilation.
Again I dont see that. Wouldnt the speed against a universal frame also correctly predict time dilation?
Originally Posted by SpeedFreek
To deny the relativity of simultaneity, and thus to deny there is no such thing as absolute simultaneity, is to deny Special Relativity itself. This is why I have been saying you are arguing against SR.,
What is absolute simultaneity? Do you mean two lightrays meeting in a point somewhere?
Originally Posted by SpeedFreek
[
Originally Posted by sigurdV
There is a similar situation in Quantum Mechanics. We cant both discover the position and momentum of elementary particles but that does not prove they do not have both momentum and position.
The situation is different with Special Relativity. We can prove simultaneity is not absolute - because all experiments that show time-dilation are actually proving simultaneity is not absolute, if you think about it hard enough!
Sorry but if its not obvious and one must think hard... then it probably is because it takes time to convince oneself to believe in something thats not true.

8. Originally Posted by sigurdV
Why prefer any frame? We have a framerelated concept of simultaneity...its better than nothing Id say. But it seems not to be a natural concept of simultaneity ...I suppose you are so used to it so you dont find it...ahem...er...somewhat artificial?
We don't prefer any particular frame and that is the whole point - no frame of reference can claim the duration between two events (which are separated by space) to be any more a truth, or a presentation of true reality, than any other. That is the essence of relativity in a nutshell.

The problem we have to deal with here is that science has to be able to quantify things, to measure things, in order to come up with an explanation for these things - a description of how things work. So, when dealing with things like size, or distance, we need to use some form of measuring device and when dealing with durations we have to use some form of clock. We can only trust our own measurements. A frame of reference means you are using your own ruler and clock to measure reality in relation to yourself.

Now, when we do that, we find that the results of any experiment performed to quantify physical processes in our own frame always match up with other peoples results for experiments performed in their own frame. Everyone agrees that, by their own measurement, all atoms act the same way, all chemical processes act the same way, all radiation acts the same way, everything we can measure or quantify acts the same way. The laws of physics apply equally in every frame of reference.

That is the most natural setting for performing science.

Now, if we look at an experiment from a distance, and that experiment is at rest in relation to us, the same applies. We can use our own ruler and clock on that distant experiment (measurement of atoms, chemicals, radiation, physical processes etc) and we find the same result as when we measured it right in front of us. (That is, until we get far enough that the expansion of the universe is a factor!)

So, if two frames are at rest in relation to each other, then they can be considered to be the same frame of reference.

Way back in days of yore, Galileo was thinking about this. He was on a boat sailing on a very calm sea or lake (I can't remember exactly), sitting in a closed cabin, and he noticed that he couldn't tell if he was moving or not. He could only tell by going to look at the shoreline, or distant landmarks. So the question arises as to whether motion affects the laws of physics for the moving observer.

It turns out that the laws of physics are all exactly the same, if you cannot feel you are moving. Galileo described relativity, using an example of a ship on a lake where the experiment is performed in a cabin with no windows. This is why, when you are on a train moving at constant speed and you throw a ball up and down, it acts exactly the same way as it would if you were standing on the platform.

This seems natural, as nothing should be affected by movement if you cannot even feel that you are moving. If you cannot perform a physical experiment in a closed cabin that can determine you are moving, simply using the laws of physics (measurements of clocks, atoms, a pendulum etc) without reference to the outside world, then why should your movement be a factor? Surely the laws of physics should be the same, wherever you are and whatever you are doing.

So, what about if we measure an experiment performed in a different frame of reference (i.e. one that is moving in relation to us), using our own ruler and clock?

Well, we find that a strange thing happens. Whilst we know that the observer in the moving frame measures atoms to act exactly as we do, and the same applies to all other physical process, what we find using our own ruler and clock is that there is a difference in our results for that other frame, in relation to our own. We find atoms vibrate slower, chemical processes take longer, and even the other observers clock is running slow in relation to our own.

So, if we assume the other observer isn't lying to us about the results he obtained in his own frame, and yet we measure that his experiment took longer to complete than he claims it did, what are we to do?

What Einstein did was retain the concept of Galilean relativity, and drop the Newtonian assumption that time is absolute between all frames of reference. If no experiment in your own frame can discern any difference in your own frame, then time must be relative, rather than absolute.

Originally Posted by sigurdV
This reminds me of a situation in logic...the distinction of object language and metalanguage: The concept of truth is defined in the metalanguage and applies only on sentences in the object language if one asks about the truth of the metalinguistic sentences one must got to a metalanguage of the metalanguage to define a truth concept for what is now the nearest objectlanguage for the new metalanguage...in this way you get a series of truth concepts and a natural objection is that we have one truth concept only! Not an infinite series of truth concepts with varying applicability! But formal logicians tend to think no price is too expensive to escape paradoxes. (The irony of it is that escaping paradox is actually free.)
Well then. This means all frames are related, doesnt it? What is the cause of that?Is there a natural order to frames?
The infinite series of truth concepts do not have varying applicability, they all have exactly equal applicability.

Frames are related only by space and time. Which are relative.

Originally Posted by sigurdV
Do you claim that simultaneous events in one frame are not simultneous in at least one other frame?
Yes. The lightning strikes that are simultaneous in the frame of the embankment are not simultaneous in the frame of the train. They are also not simultaneous for a helicopter flying above following the track at twice the speed of the train. So in at least one other frame, they are not simultaneous.

Originally Posted by sigurdV
And vice versa that theres always another frame where non simultaneous events are simultaneous? Say...today and tomorrow.
No, that doesn't always follow. If you can have the same observer at both events, and they are separated by space, then they cannot happen at the same time, for anyone. Nobody can pass through two events separated by space, at the same time!

But if you start with two events that someone can determine to be simultaneous, there will be others who do not.

Originally Posted by sigurdV
Originally Posted by SpeedFreek
The fact that we know time-dilation is real (as has been shown in many experiments) means that time itself cannot be absolute,
It dont see why that is so. It should be the other way around. There should be some not dilated frame to compare all the dilated frames with.
Ahh! Nice work there! You raise a valid point.

Now try to think of a way to find that frame, using the laws of physics.

Lorentz ether theory - Wikipedia, the free encyclopedia (please, read the whole thing, it is all relevant to this discussion)

Originally Posted by sigurdV
Originally Posted by SpeedFreek
so the relativity of simultaneity simply falls out of the same theory that correctly predicts time-dilation.
Again I dont see that. Wouldnt the speed against a universal frame also correctly predict time dilation?
Yes it would, but if there is no way to determine that frame, what use is it? Nobody can know what the preferred frame is, as it is completely hidden from any form of measurement. You might want to arbitrarily consider the rest frame of the CMB as a surrogate for that frame, but to the laws of physics it would be completely arbitrary to do so. It would just complicate everything for no return.

It wouldn't change the fact that the train measures and calculates the lightning strikes to be not simultaneous, it would just mean observers on the train would have to transform their results to an "truly" unknown, but arbitrarily chosen surrogate "universal" frame in order to say that, to that frame the events were simultaneous.

If you choose the rest frame of the CMB as a surrogate, then the Earth is moving at 600 km/s in relation to it, so the embankment would no longer be able to say the events were simultaneous either, even though they measured them to be so!

Originally Posted by sigurdV
Originally Posted by SpeedFreek
To deny the relativity of simultaneity, and thus to deny there is no such thing as absolute simultaneity, is to deny Special Relativity itself. This is why I have been saying you are arguing against SR.,
What is absolute simultaneity? Do you mean two lightrays meeting in a point somewhere?
Absolute simultaneity is everyone determining two events separated by space to be simultaneous, using their own measurements of those events and subtracting the time it took the light to travel from those events to themselves, knowing their own distance to the events.

Originally Posted by sigurdV
Originally Posted by SpeedFreek
The situation is different with Special Relativity. We can prove simultaneity is not absolute - because all experiments that show time-dilation are actually proving simultaneity is not absolute, if you think about it hard enough!
Sorry but if its not obvious and one must think hard... then it probably is because it takes time to convince oneself to believe in something thats not true.

9. Thank you for really trying to enter my thoughts. But I think I should inform you that theres no popularisation thoughts on relativity im not familiar with... whats lacking in my education is mathemathics...not any popular conceptions. But I think you made a good job in describing relativity outside of the technical details.

I felt tired and rested for a couple of days. And I dont really have the same impetus for the moment. And theres lots of details I could start writing about...say...reminding you that theres no truth concept in the chain that defines truth for itself. As a truth concept conforming to the "natural" concept does. Also no two chain concepts has the same area of applicability...so youre out sailing when you claim they have equal applicability...It seems youre not aware of the difference between object and meta language. Thats not important for our discussion however. ... I WOULD like to improve my knowledge of Lorentz Ether Theory...but I am not sure that can be done very quickly... Its better if I succeed in improving the view from where I look.

On simultaneity...I will only remark at the moment that Einsteins definition is not the only possible (or intelligible) one...I think the age of our universe is more similar to what we ordinarily use: If the age of the universe is the same at two events then they are swimultaneous... note that everything within a fourdimensional point is simultaneous using that definition...and that the exact age is not necessary to calculate.

It would be interesting to check a proof that there can be two events where the universe has the same age but, as seen from some frame, the two events are not simultaneous according to Einsteins definition. (Since the theory is used in acquiring both measurements (I believe) something might be amiss.)

At the moment Im more interested in the ships meeting with constant speed in intergalactic space. (The train experiment will have to wait!) Can we discuss the ships in here or should a new thread be opened? (Bah!) It is said that there is no way to decide if one of the ships is at rest or not...Isnt it? If so Im not yet convinced:

Space is not empty. In interstellar space doubling the speed raises friction fivefold! (I was once told)
I suppose intergalactic space is not equally resistant to acceleration but still there should be friction when the ships travel.

So the ship experiencing the lowest friction is moving slower than the other ship,
and if there is no friction at all then the ship is at rest. And the other ship is doing all the movement.

10. ... whats lacking in my education is mathemathics...
It's never too late to change that. It is very fortunate that we live in the Internet age, so there are some excellent resources for self-study out there, all it takes is determination and patience.
I feel if you could develop your maths skills a little, it would open up an entirely new level of understanding for you.

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