Uncover Traps in Spacetime Diagrams: Bob & Alice's Cases

[Freixas]

Which category a particular scenario falls into depends on whether there are events of interest that do not all lie along a single spatial direction. That's basically the upshot of this thread's discussion.

Well, that's your upshot, not mine. Yes, I've come to the conclusion that all of the things that I asked for will be variations of things that require the y and z coordinates. But I was hoping for some additional items to add to my list of three.

In other words, you had in mind a case where person A and person B are the same person. How is the problem I described above, of person A getting misled because person B left out some relevant information when telling person A about the scenario, even possible if person A and person B are the same person?

Example:

Person A is learning about spacetime diagrams, sets up a Bob/Alice problem and diagrams it. Then person A adds an arbitrary event M and studies the diagram to find the (x, t) and (x', t') coordinates for the event. Person A has now extended the problem by adding to the diagram and has correctly extracted information from the diagram.

Person A adds event N and does the same thing. Then person A looks at angle of the line segment from M to N. Seeing that it is less than 45 degrees, person A concludes that this is a "space-like" interval. But person A starts to feel uneasy about it being this simple. Person A returns to the formula for determining if two events are space-like and realizes that the information on the diagram is insufficient; to use the angle in this way requires adding new information to the problem: that events M and N share the same (y, z) coordinates.

Another example:

Back in #7, I included a Bob/Alice diagram with event M. Looking at the diagram, person A might ask the question: "when does Alice see event A?" Person A might then get the bright idea then drawing the light worldline will answer the question. After some reflection, person A decides that this technique won't work unless the problem statement is extended to state that Alice and M share the same (y, z) coordinates.

These scenarios are quite possible (speaking from experience), but probably not if person A is Peter Donis.

The answers I'm getting (including from you) are along the lines of "your problem statement is wrong" or "you are using the wrong diagram." Well, duh! The OP was about enumerating cases that might seem reasonable but require that the problem statement be revised or that a different diagram be used.

 

[PeterDonis]

I was hoping for some additional items to add to my list of three.

You already have the general rule. What's the point of enumerating more and more special cases?

Then person A adds an arbitrary event M

Doesn't person A know what the y and z coordinates of event M are when they add it?

Person A adds event N

Same question as above.

Person A returns to the formula for determining if two events are space-like and realizes that the information on the diagram is insufficient

Why didn't he realize that back when he specified the y and z coordinates of events M and N and looked to see whether they were the same?

Back in #7, I included a Bob/Alice diagram with event M. Looking at the diagram, person A might ask the question: "when does Alice see event A?"

Here person A is not you, which means it's not the case you said you were thinking of. Which case do you want to discuss?

These scenarios are quite possible (speaking from experience)

I can understand how the scenario where person A and person B are different is possible, sure. I've already said so. But I also quoted a statement from you that said you were thinking of the case where person A and person B are the same person. I still am unable to understand how such a scenario as you described is possible if person A and person B are the same person. See my questions above.

 

[Freixas]

You already have the general rule. What's the point of enumerating more and more special cases?

Because t's not always obvious that a special case falls under the general rule--that was why I asked it.

Doesn't person A know what the y and z coordinates of event M are when they add it?

No. Person A just puts a dot on a diagram.

Same question as above.

Same answer as above.

Why didn't he realize that back when he specified the y and z coordinates of events M and N and looked to see whether they were the same?

Because person A is not Peter Donis (or equivalent).

Here person A is not you, which means it's not the case you said you were thinking of. Which case do you want to discuss?

Bob is my name for the rest frame. Alice is my name for the moving frame. Person A is the only real person in all this.

I can understand how the scenario where person A and person B are different is possible, sure. I've already said so.

You are confused--there is only one person involved in my last post. I've used the Bob/Alice terminology in several posts in this thread, including #7, but I can understand why you might have missed this.

The scenario is possible in the absolute sense that it I experienced it. Your inability to understand how the scenario is possible makes you a poor candidate for answering the question I asked.

 

[PeterDonis]

Person A just puts a dot on a diagram.

Then how is it even known what the y and z coordinates are? Person A is the one making up the scenario. He can't just punt and say someone else defined what the y and z coordinates are. There is no someone else. He's the only person involved. Either he defines the y and z coordinates, or the y and z coordinates don't exist and hence can't possibly be relevant to the problem.

The scenario is possible in the absolute sense that it I experienced it.

So if you experienced it, surely you must have some answer to the questions I keep asking. When you defined event M, what y and z coordinates did you give it? Same question for event N. If your answers are "I didn't think of y and z coordinates at all", then how were you able to discover that the y and z coordinates of events M and N were even different? You can't say someone else told you, because you're the only person involved.

In short, while you can claim all you want that you experienced something, the way you are describing what you experienced doesn't make any sense with the information you've given so far. So either you're leaving information out, or you're simply not describing what actually happened correctly.

Your inability to understand how the scenario is possible makes you a poor candidate for answering the question I asked.

I don't see how you can expect anyone to answer questions about a scenario that doesn't even make sense.