# What does this spacetime diagram mean?

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fee_de
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I don't understand a spacetime diagram about relativty and simultaneity that I found in a book and its explaination by the author
I'm reading a book called "Reality is not what it seems: the journey to quantum gravity" by Carlo Rovelli and I'm struggling to understand this diagram that is part of the chapter about special relativity.

https://i.stack.imgur.com/JgBDJ.jpg

Before this image Rovelli writes:

"It's not possible to have a satisfying conversation from Earth to Mars. If I'm on Mars and you are here, I ask you a question, you answer as soon as you hear what I told you and I receive your answer 15 minutes after I asked you the question. This quarter of an hour of mine is time that is neither past nor future as compared to the moment when you answered. This implies that you can't say that an event on Mars is happening "now" because "now" does not exist".

I understand this concept, but then the author adds a footnote:

"The astute reader will object that the moment in the middle of my quarter of an hour can be considered simultaneus to your answer. The reader who studied physics may recognize that this is the "Einstein convention" to define simultaneity. However, this definition depends on the way I move, so it doesn't define simultaneity directly between two events, but only a simultaneity that is relative to the motion of specific bodies. In picture 3.3 (the diagram I attached), a dot is halfway between a and b, the points where I exit the past of the observer and I enter his future. the other dot is halfway between c and d, the points where I exit the past of the observer and I enter his future if I follow a different path. Both the dots are simultaneous to the reader, following this definition of simultaneity; however, they happen one after the other. The two dots are both simultaneous to the reader, but relatively to two different motions."

(I'm reading this book in Italian so I had to translate the paragraph, I'm sorry if it's not faultless).

First of all I don't understand what it means that "the moment in the middle of my quarter of an hour can be considered simultaneus to your answer". I tried to draw diagrams, I'm really struggling but I can't grab the concept. Talking about the diagram, why can we say that the observer perceives the two dots as simultaneous? They don't exit his past and enter his future at the same time, do they? In these diagrams souldn't we find simultaneous events on the same horizontal line?

I'm completely stuck, I would be very grateful if you could help me.

[Mentor Note -- Image attached to post from the OP's link]

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Delta2 and PeroK

First of all I don't understand what it means that "the moment in the middle of my quarter of an hour can be considered simultaneus to your answer".
This just states that, in our everyday experience, if we know something takes a given time to go to some destination and back again, then it must have arrived at the destination after half this time.
Think of something more tangible than a beam of light - like a train. I write a letter on day 1, give it to the conductor, and wait for your answer. The conductor says the train will be back in two weeks, so I can conclude that you will receive the letter and write your answer after one week. If I'm writing a week before your birthday, I could put a 'happy birthday' in the letter, and be certain that you'll read it on that day.
I.e. I can assume that the moment of your answer will happen after half the round trip time.

It's same here. A beam of light is the equivalent of the letter traveling on the train. You take the half-way moment between emission and reception to conclude when the answer was composed and sent.
It takes 15 mins for a round trip between Mars and Earth in this example, so it should take half of that until you get to answer, right?

Talking about the diagram, why can we say that the observer perceives the two dots as simultaneous? They don't exit his past and enter his future at the same time, do they? In these diagrams souldn't we find simultaneous events on the same horizontal line?
The observer ('the reader') has no way of knowing whether any distant events happen on the horizontal line or not. He has to exchange signals and try to use some convention for deducing when that thing happened. On Earth, pretty much everything is relatively stationary (any arrow drawn on the diagram would be vertical), which let's us use the convention described above - every event half-way between reception and emission does happen on the same horizontal line as the reader's position.
The argument here is that if we tried using the same convention when the communicating objects are not nailed to the ground, we'd arrive at different answers depending on how the objects move. Which makes the aforementioned convention pretty useless.

Just to clarify what's on the diagram:
The sender ('Me') is traveling along one of the two arrows relative to 'the reader' (from a to b in one case, and from c to d in the other case), while the reader is considered stationary. The movement is shown in space-time, so in spatial-only terms the sender is moving away from the reader in one case (a-b), with some speed, and towards the reader (c-d) with a different speed.
The long lines show the path of the signal from emission (points a and c) to the reader, who responds and sends the signal back to sender to be received where and when the line intersects the arrow again.

In the first case the sender sends the signal at point (in space-time it's called an 'event') a. In the second case, it's at event c.
The signal travels to the reader along the line shown. It is reflected back to the sender, and is received by him at event b or d, respectively.
The key is, the differently angled arrows intersect with the path of the signal in such a way, that the half-way point between emission and reception (the middle of the a-b and the c-d lines) is in different places. These are those dots marked on the arrows - in particular, as you notice, they're not on the same horizontal line (not the same time coordinate).
So if you were to try and apply the same convention for assuming when the answer was composed as was tried before, by halving the signal travel time, you'll arrive at different answers depending on the relative motions between the sender and the reader.

PeroK and fee_de
fee_de
This just states that, in our everyday experience, if we know something takes a given time to go to some destination and back again, then it must have arrived at the destination after half this time.
Think of something more tangible than a beam of light - like a train. I write a letter on day 1, give it to the conductor, and wait for your answer. The conductor says the train will be back in two weeks, so I can conclude that you will receive the letter and write your answer after one week. If I'm writing a week before your birthday, I could put a 'happy birthday' in the letter, and be certain that you'll read it on that day.
I.e. I can assume that the moment of your answer will happen after half the round trip time.

It's same here. A beam of light is the equivalent of the letter traveling on the train. You take the half-way moment between emission and reception to conclude when the answer was composed and sent.
It takes 15 mins for a round trip between Mars and Earth in this example, so it should take half of that until you get to answer, right?

The observer ('the reader') has no way of knowing whether any distant events happen on the horizontal line or not. He has to exchange signals and try to use some convention for deducing when that thing happened. On Earth, pretty much everything is relatively stationary (any arrow drawn on the diagram would be vertical), which let's us use the convention described above - every event half-way between reception and emission does happen on the same horizontal line as the reader's position.
The argument here is that if we tried using the same convention when the communicating objects are not nailed to the ground, we'd arrive at different answers depending on how the objects move. Which makes the aforementioned convention pretty useless.

Just to clarify what's on the diagram:
The sender ('Me') is traveling along one of the two arrows relative to 'the reader' (from a to b in one case, and from c to d in the other case), while the reader is considered stationary. The movement is shown in space-time, so in spatial-only terms the sender is moving away from the reader in one case (a-b), with some speed, and towards the reader (c-d) with a different speed.
The long lines show the path of the signal from emission (points a and c) to the reader, who responds and sends the signal back to sender to be received where and when the line intersects the arrow again.

In the first case the sender sends the signal at point (in space-time it's called an 'event') a. In the second case, it's at event c.
The signal travels to the reader along the line shown. It is reflected back to the sender, and is received by him at event b or d, respectively.
The key is, the differently angled arrows intersect with the path of the signal in such a way, that the half-way point between emission and reception (the middle of the a-b and the c-d lines) is in different places. These are those dots marked on the arrows - in particular, as you notice, they're not on the same horizontal line (not the same time coordinate).
So if you were to try and apply the same convention for assuming when the answer was composed as was tried before, by halving the signal travel time, you'll arrive at different answers depending on the relative motions between the sender and the reader.
Thank you for your explanation, it was really clear!

Homework Helper
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Summary:: I don't understand a spacetime diagram about relativity and simultaneity that I found in a book and its explanation by the author

I'm reading a book called "Reality is not what it seems: the journey to quantum gravity" by Carlo Rovelli and I'm struggling to understand this diagram that is part of the chapter about special relativity.

https://i.stack.imgur.com/JgBDJ.jpg

Before this image Rovelli writes:

"It's not possible to have a satisfying conversation from Earth to Mars. If I'm on Mars and you are here, I ask you a question, you answer as soon as you hear what I told you and I receive your answer 15 minutes after I asked you the question. This quarter of an hour of mine is time that is neither past nor future as compared to the moment when you answered. This implies that you can't say that an event on Mars is happening "now" because "now" does not exist".

I understand this concept, but then the author adds a footnote:

"The astute reader will object that the moment in the middle of my quarter of an hour can be considered simultaneus to your answer. The reader who studied physics may recognize that this is the "Einstein convention" to define simultaneity. However, this definition depends on the way I move, so it doesn't define simultaneity directly between two events, but only a simultaneity that is relative to the motion of specific bodies. In picture 3.3 (the diagram I attached), a dot is halfway between a and b, the points where I exit the past of the observer and I enter his future. the other dot is halfway between c and d, the points where I exit the past of the observer and I enter his future if I follow a different path. Both the dots are simultaneous to the reader, following this definition of simultaneity; however, they happen one after the other. The two dots are both simultaneous to the reader, but relatively to two different motions."

(I'm reading this book in Italian so I had to translate the paragraph, I'm sorry if it's not faultless).

First of all I don't understand what it means that "the moment in the middle of my quarter of an hour can be considered simultaneus to your answer". I tried to draw diagrams, I'm really struggling but I can't grab the concept. Talking about the diagram, why can we say that the observer perceives the two dots as simultaneous? They don't exit his past and enter his future at the same time, do they? In these diagrams souldn't we find simultaneous events on the same horizontal line?

I'm completely stuck, I would be very grateful if you could help me.
That all seems very confusing to me (and I'm not sure it's caused by poor translation). I don't like complicated wordy descriptions like, as I find them hard to follow.

It may be that Rovelli wants to say more than just that simultaneity is relative, but I've seen much simpler presentations of the basic idea.

fee_de and vanhees71
Gold Member
2022 Award
Also a real Minowski diagram may be much clearer. Looking at Rovelli's picture alone, I don't understand it too.

fee_de
That all seems very confusing to me (and I'm not sure it's caused by poor translation). I don't like complicated wordy descriptions like, as I find them hard to follow.

It may be that Rovelli wants to say more than just that simultaneity is relative, but I've seen much simpler presentations of the basic idea.
Honeslty I think you are right. I generally like him as a science writer but in this book he made general relativity easier to understand than special relativity ^^"

vanhees71 and PeroK