B Struggles with the geometrical analogy

[Dale]

Your have claimed it but I do not think you have shown it.

Sure I did. In 66 I showed that experience does not relate to the reference frame for what you called raw experience. Then in 71 I showed that for your calculated experience it applies to all reference frames equally.

How does experience relate to frames of reference?

As I showed above, raw experience relates to the past light cone rather than your reference frame, and your calculated experience relates equally to any frame of reference.

It is all very to say the any chosen frame is valid but so is the question and to write the question off because of the way it is handled by geometry and analogues with space alone (which seems to me what you are effectively doing) might be presumptuous.

The question was not written off, it was answered. You just didn’t like the answer.

Frankly, it is somewhat irritating to me to provide a substantive answer to your question, have you not respond to the substance of the answer, and then
1) claim that I hadn’t shown what anyone can read and see that I did show
2) say that I “wrote off” a question which I in fact had answered
3) call me presumptuous for the non-existent write off

Really, do you think that is acceptable? If you don’t like or don’t agree with the answer that is one thing, but to claim that you were dismissed or not answered is clearly untrue. Perhaps you were overwhelmed with the volume of responses and could not make a substantive response to mine. That is fine and understandable, but it is also the exact opposite of writing the question off.

one has had more experience, so to speak, than the other, if time is a measure of experience.

Ok, so now you have introduced a third meaning of experience. The time that would be related to someone’s experience is called proper time. Proper time is invariant so all frames agree on it. It does not single out any frame as special.

So now we have three meanings of “experience”. Raw experience depends on the past light cone. Calculated experience could equally apply to any frame. Proper time experience is frame invariant. So none of the three meanings of experience uniquely implies the observer’s rest frame.

the experience of time is the same for that person and the rate of ticks of perfect clocks in a persons pocket is does not vary for that person; as I see it

That is correct. This quantity is called proper time and it is invariant. All reference frames agree on it. Proper time is the Minkowski invariant geometric quantity that is analogous to the Euclidean invariant geometric quantity of length. Your “as I see it” comment actually indicates that you are not too far away from the geometric analogy. You just need to make the connection between your comment above and the analogy.

 

[whatif]

It seems to me that comparing 2 frames in which the objects of interest are represented as stationary, in their respective frames, represents the comparative difference of how all things are experienced in reality. That is, it is not just a different interpretation of reality, it is a different real experience. If not, then I would like to know why not?

With respect to special relativity and inertial frames:

1. The laws of physics apply to all frames. All frames are valid. The laws of physics have no preference for any particular frame.
2. It seems to me that frames in which objects are stationary are special with respect to the object of interest, especially when the object is a person.

I see no conflict between 1 and 2. However, 2 seems to be frowned upon because of 1, even though frames in which objects are at rest are typically chosen for analysis; so far as I have seen. I would like to understand why.

Is this explained anywhere?

 

[PeterDonis]

It seems to me that comparing 2 frames in which the objects of interest are represented as stationary, in their respective frames, represents the comparative difference of how all things are experienced in reality. That is, it is not just a different interpretation of reality, it is a different real experience.

The word "frame" unfortunately has multiple meanings which imply different answers to this.

First, a word change: the word "experience" is not a good one to use here. I will use "measurements" instead, because we are not (or should not be) talking about subjective opinions of people, but about objective measured quantities that everyone can agree on.

The more common usage is to use "frame" to mean "coordinate chart". (This is more or less the usage in the other open thread you have on this general topic.) A coordinate chart is not (more precisely, does not have to be) a description of anyone's measurements. It is just a mathematical convenience: we assign four numbers to each event in spacetime, with certain requirements on continuity, differentiability, etc. (for example, the numbers describing events that are near each other in spacetime should not differ by much). The numbers do not even have to describe "space" and "time" the way the usual coordinates used for pedagogy in special relativity (global inertial coordinates) do. They can be any numbers whatever that meet the mathematical requirements.

However, there is another, less common usage of "frame", to mean what is more correctly called a "frame field". This is an assignment of four unit vectors, one timelike and three spacelike, to every event in spacetime (again with requirements about continuity, etc.). These vectors represent, heuristically, a clock and three mutually perpendicular rulers that are used by an observer at a given event in spacetime to make measurements. So different frames in this sense represent different physical measuring devices, and therefore different measurement results, i.e., something actually physically different, with the difference being observable.

It's easy to cause confusion in relativity discussions by confusing the above two meanings of "frame".

(Note, btw, that "inertial frame" has meaning in both senses; in the first sense, it means an inertial coordinate chart, i.e., a chart in which objects moving in free fall have worldlines that are straight lines; and in the second sense, it means an assignment of unit vectors at every event such that they are also the basis vectors of some inertial coordinate chart at that event, i.e., they "point" in the four coordinate grid directions at that event.)

The laws of physics apply to all frames. All frames are valid. The laws of physics have no preference for any particular frame.

This is correct, for both senses of "frame" above.

It seems to me that frames in which objects are stationary are special with respect to the object of interest, especially when the object is a person.

Only in the sense that it is often convenient for a person to choose a frame in which they are at rest in order to describe measurements. But that is a matter of convenience, and is not even always true. For example, when you go to the grocery store, do you adopt a frame in which you are at rest? If you do, that means you think of your footsteps on the ground, or the wheels of your car, as moving the Earth and everything on it while you stand still. Is that how you think of it?

I see no conflict between 1 and 2.

There isn't if 2. is interpreted as I did above. But many people (including, I think, you in your other open thread) try to interpret 2. to mean more than I said it did above. The correct response is to not do that.

 

[whatif]

Thank you. I do not fully understand, and I won’t labour these points further to making these comments.

There must a connection with reality to apply the physics.

The more common usage of frames, as described, seems to be a purely abstract exercise. I cannot envisage the practical application. That is, for a practical application the numbers must measurable in some way, no? I do not need to know what it is but that it is true.

So different frames in this sense represent different physical measuring devices, and therefore different measurement results, i.e., something actually physically different, with the difference being observable.

I am wondering about the translation. For example, if 2 circumstances are measured with the same device and then again with a different device then the use of either device will detect a physical difference. Otherwise a transformation is required between the measurements to relate them to a common base.

First, a word change: the word "experience" is not a good one to use here. I will use "measurements" instead, because we are not (or should not be) talking about subjective opinions of people, but about objective measured quantities that everyone can agree on.

I understand but the subjective experience must contain a fixed physical influence, in terms of the values of the measurements. So experience can be restricted to the values of the measurements for the purpose, no?

If you do, that means you think of your footsteps on the ground, or the wheels of your car, as moving the Earth and everything on it while you stand still. Is that how you think of it?

I can and have but that situation still involves a comparison between 2 frames in which the objects are considered at rest in their respective frames. It does not describe a different scenario.

Only in the sense that it is often convenient for a person to choose a frame in which they are at rest in order to describe measurements.

Also in the sense of proper length and proper time, no?

 

[PeterDonis]

There must a connection with reality to apply the physics.

The connection with reality is the measurable numbers. That's why the first postulate is so important: what it amounts to is that you can calculate the measurable numbers any way you like, because all ways will give the same results. If you're not comfortable with one way, you can just use another, with confidence that you will still be getting the same answers.

The more common usage of frames, as described, seems to be a purely abstract exercise. I cannot envisage the practical application.

Quite possibly not, since you appear to have only a "B" level knowledge of the subject. But note carefully that I pointed out that, for the special case of inertial frames in special relativity, the two usages are basically the same: there is a one-to-one correspondence between frames in the first sense (global inertial coordinate charts) and frames in the second sense (sets of four unit vectors at each event). This sort of correspondence is what Einstein, for example, was referring to when he talked about "frames" as being sets of measuring rods and clocks. Seeing practical applications of such constructions is the purpose of most of the homework problems presented in a textbook such as Taylor & Wheeler's Spacetime Physics.

At more advanced levels, the practical applications of coordinate charts are probably easier to see. For example, in General Relativity, where spacetime can be curved, there are no global inertial coordinate charts, and no global inertial frames in the second sense corresponding to them. And it is often easier to see things like the causal structure of a curved spacetime by coming up with well chosen coordinate charts, even if it is impossible (or at least very difficult) to construct a frame in the second sense that "matches up" with the chart.

if 2 circumstances are measured with the same device and then again with a different device then the use of either device will detect a physical difference.

If the circumstances are physically different, yes. Your description is too general to know. A specific concrete example would help.

Otherwise a transformation is required between the measurements to relate them to a common base.

Transformations are for enforcing the first postulate, that the measurable numbers are the same regardless of which frame you choose. So if you and I both want to calculate the same measurable number (say, the reading on the clock in the tower of Big Ben in London at the instant that the doors of Parliament open on a particular day), and we are using different frames, the frame-dependent quantities in our different frames must be related by certain transformations in order for our answers for the measurable number to both come out the same.

This may be what you are trying to say here; I'm not sure.

the subjective experience must contain a fixed physical influence, in terms of the values of the measurements.

If "fixed physical influence" means objectively measurable quantities, then the effect those quantities have on anyone's subjective experience is outside the domain of physics; it's in the domain of psychology or neuroscience or cognitive science or something like that. Trying to fit it into your understanding of physics is only going to cause problems for you.

So experience can be restricted to the values of the measurements for the purpose, no?

If you want to use the word "experience" this way, I suppose I can't stop you, but I think it is just going to cause problems because you won't be able to resist the temptation to think of it as something subjective. I would recommend avoiding the word completely when you are discussing physics, at least until you have a much better understanding.

I can and have

Really? When you go to the grocery store, you think of yourself as staying still and the Earth and everything else as moving?

Also in the sense of proper length and proper time, no?

You don't need to use a frame in which you are at rest in order to calculate your proper length and proper time. You still are missing the point of the first postulate: you can use any frame you like to calculate any measurable quantity.

 

[PeterDonis]

The more common usage of frames, as described, seems to be a purely abstract exercise. I cannot envisage the practical application.

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: using a particular coordinate chart doesn't commit you to modeling a particular set of measuring devices, whereas choosing a frame field does. So, for example, if you and I are using different coordinate charts, we can still use them to calculate the same measurable number: our calculations will have different intermediate numbers in them (the frame-dependent quantities), but they will give the same final answer. But if you pick one frame field and I pick another, strictly speaking, we are picking two different measuring devices to model, so we are not going to be able to calculate the same measurable numbers. There are ways around this, but they are much less straightforward than the machinery of coordinate charts. That's why coordinate charts are so much more commonly used and why the standard usage of "frame" refers to coordinate charts.

 

[Ibix]

A frame, in its usual usage, is a map of spacetime (or, at least, a decision on how to draw one). As with any map, it's usually easiest to interpret if you arrange it so that it somehow reflects your present circumstances (the direction you are facing is up the page, your rest frame), but it's certainly not obligatory to do so. And in any case, the map will never look like what you see. A sufficiently detailed map will allow you to deduce what any given observer would see (that's what Google Street View does) but the map doesn't show that.

 

[whatif]

Really? When you go to the grocery store, you think of yourself as staying still and the Earth and everything else as moving?

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

You don't need to use a frame in which you are at rest in order to calculate your proper length and proper time.

Calculate, yes. However, 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.
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?

 

[whatif]

This may be what you are trying to say here; I'm not sure.

I believe so. The point is that you need some kind of transformation. Also, 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.

 

[Dale]

It seems to me that frames in which objects are stationary are special with respect to the object of interest, especially when the object is a person

This is such a weak claim that it can easily be made to be true. All you have to do is define “special” such that it is true.

That is, it is not just a different interpretation of reality, it is a different real experience. If not, then I would like to know why not?

First you need to fix your definition of experience. So far there have been three, and none of them single out the rest frame. You keep moving the goalposts, which is not acceptable. Choose your definition clearly and let’s discuss.

My personal preference is to use the word “measurements” instead as a means of eliminating the subjective aspect. @PeterDonis recommend that and I think it is a good idea too.

 

[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.