Struggles with the geometrical analogy

[PeterDonis]

It not what I typically do but is a thought exercise that I have done.

And that's my point. There is nothing "special" about the frame in which you are at rest. You don't have to use it, and in cases like this one, nobody actually does. You only think about it as "a thought exercise", not when you're actually trying to go somewhere.

the definitions that I have come across for proper length is the length of an object measured by an observer which is at rest relative to it.

Yes, and "observer which is at rest relative to it" is a physical condition that picks out a particular spacetime interval to represent the "proper length" of the object. So the proper length is invariant because spacetime intervals are invariant; it doesn't mean you need to calculate the proper length in the frame of the observer at rest relative to the object whose proper length you want to know.

Proper time is more involved but, as I understand it, a particular application is that if two events happen at the same location using an inertial frame then the spacetime separation between the events is completely timelike and the proper time. Is that correct?

If we are restricting to inertial observers, yes. (Things get more complicated if you allow non-inertial, accelerated observers, but it seems like you are thinking about inertial observers here.) But notice that there is still a frame-independent spacetime interval involved: the timelike interval between the two events. You can calculate the length of that interval using any coordinates you like; there is no requirement that you have to use the coordinates in which the two events both happen at the same spatial location. The proper time is the length of the interval, which is invariant, the same in all frames.

The point is that you need some kind of transformation.

To do what? That's where I'm not sure about what you are trying to say.

if each uses a different measuring device then I do not know what you are trying to say unless there is a relationship between the measurements of each device.

Of course there is a relationship between the measurements of each device, if they're all measuring properties of the same object. For example, if two observers in relative motion both try to measure the length in their rest frames of an object, they will get different answers, but their answers must be related by the length contraction formula.

If the different measuring devices are measuring different, unrelated objects, then of course there doesn't have to be a relationship between their measurements, but that's because they're measuring different, unrelated objects. But I didn't think that case was being discussed here.

 

[Dale]

Actually, I forgot to point out a key property that frames in the first sense have (coordinate charts) that frames in the second sense do not have:

One other key property that coordinate charts have that frame fields do not have is simultaneity. I am not sure if that is relevant to the discussion here though

 

[pervect]

I am sorry you feel that way.

That is not my intent.

That simultaneity is relative is something that I think I appreciate.

Your rap over my knuckles is acknowledged. However, it seems that an observer may chose a frame of reference to deem whether events are simultaneous and I dare to ask whether that is correct? I ask because if I measure two bolts of lightning in different locations to be simultaneous it seems that my experience of measuring simultaneity can be arbitrarily disregarded (and in a sense of using transformations to use a different frame of reference it can but to disregard my experience seems to involve its own convoluted rationale).

I think a lot of this ongoing argu - discussion, is due to semantic issues, possibly mixed with philosophy.

Suppose we have an observer with a camera, a watch, and a lab notebook. The observer can observe when the flash of light from the bolt of lightining arrives at their camera, he can note the time on his watch, he can take a photograph of the flash, and he can write down the time he saw and photographed the flash in his logbook. He could also set it up so that the camera can record automatically when the flash of light lights occurs, the watch could be illuminated by the flash, and only visible in the photograph at the instant the flash occurred, for instance.

I would call this (the camera, the notebook, the watch) what the observer experiences.

If one lightining bolt is 1 kilometer away, and another lightning bolt is 2 kilometers away, the observer will experience , photograph, and log in their lab notebook two different light flashes that arrive at different times. These flashes will be a 3 microsecond apart.

A frame of reference is a way of organizing these raw experiences. But I would not call this organizational process an experience. One does not directly "experience" distant events. It's a mental model, or a perception.

Normally it doesn't mater much, the speed of light is so fast that one can usually ignore the travel time of light. But in relativity, we are dealing with situations that are more taxing and require more precision of thought and measurement. We cannot just ignore the fact that light has a finite speed.

I think you may have some different notion of what an "experience" is than what I suggest, but I'm not sure what your notion is. I would argue that you are calling things that you create in your mind , what I call "mental models" or "perceptions" by a different word, "experiences", but they are not the raw experiences I am talking about.

While I like my definitions better, what's important is that we share a common understanding of what we mean by the words. And the word "experience" here seems to be the problem in communication. If you want to use different words to describe the philosophical categories that I call "raw events" and "percpetions" be my guest. But you'll have to explain what they are. And you'll need two different words, the two categories are not identical. It may be that you are combining them into one concept in your mind, but that combining process (I would call it conflating) is causing communication difficulties.

Not having studied philosophy, I can't say that my usage of words is standard in any philosohical sense. I'm also not quite sure what the current status of philsophical discussions on Physics Forums is - at one time, they were not allowed, I think that's changed recently to just being discouraged, but tolerated if it's necessary.

The relativity of simultaneity then simply says that "simultaneity" is a mental model. Because it's a mental model, different observers can and do interpret the simultaneity of different events differently. This is not possible for "raw events" - everyone will agree on what the photograph of the light flash shows, what time the watch reads when the flash lights up the watch. But it is possible that the perceptual process of different observers will define events as to be simultaneous, or not, depending on the details of the choice "the observer" makes for "the frame of reference". I would argue that in fact, this is what the "relativity of simultaneity" means.