Which Train Explodes First in the Time Dilation Paradox?

[harrylin]

Thank you very much. This is convincing, but is SR really that simple?

Regretfully not, that is classical Doppler. Classical physics already takes the speed of light in consideration in measurements at a distance. And it is extremely useful to have a good understanding of classical physics before trying to understand SR.

Classical Doppler: http://en.wikipedia.org/wiki/Doppler_effect

Relativistic Doppler: http://mathpages.com/rr/s2-04/2-04.htm

As a matter of fact, the first positive determination of the "time dilation" factor was done on that effect.

 

[bgq]

Hi,

Thank you all for your helpful replies.

I did some math, and try to study the whole situation from the point of view of train A. I really found that the both trains will explode (when the light signal reaches B, the signal from B has been already sent), anyway I reach the result the both explodes, but according to my calculations they will not explode simultaneously (B will explode before), but I think this is natural, there is also relativity of simultaneity. I use that the timer sends signal at 2 seconds (not 2 minutes in order to escape from unit conversions) and the speed of the trains relative to each other is 0.6c.

Again thank you all for your replies, they are very helpful, I like this forum, may be I ask other questions later.

 

[altergnostic]

Hi,

Thank you all for your helpful replies.

I did some math, and try to study the whole situation from the point of view of train A. I really found that the both trains will explode (when the light signal reaches B, the signal from B has been already sent), anyway I reach the result the both explodes, but according to my calculations they will not explode simultaneously (B will explode before), but I think this is natural, there is also relativity of simultaneity. I use that the timer sends signal at 2 seconds (not 2 minutes in order to escape from unit conversions) and the speed of the trains relative to each other is 0.6c.

Again thank you all for your replies, they are very helpful, I like this forum, may be I ask other questions later.

That's great!
One observation, though. You said that they don't happen simultaneously, but you have to take care: they don't happen simultaneously as seen from the train A. Remember that from the central point, there is an observed simultaneity. Remember that in SR everything is relative, you can't make absolute statements. Ever. Everything must be considered as the point of view from the frame you are doing measurements.

Good luck with your studies!

 

[bgq]

Good luck with your studies!

Thank you very much.

 

[ghwellsjr]

Remember that in SR everything is relative, you can't make absolute statements. Ever. Everything must be considered as the point of view from the frame you are doing measurements.

None of these statements are true.

As I pointed out in post #21, the Doppler analysis shows us what each observer actually sees, observes and measures and does not depend on which frame you use to do the analysis and, in fact, doesn't even require a frame to do the analysis. Different frames don't change what observers see, observe or measure. All they do is change how the calculations are made to determine what they see, observe and measure but the end result is the same. I have pointed this out multiple times in this thread. It's one of the issues the OP needs to understand because he has been expressing the idea that different frames not only change what observers see, they also change the outcome of what happens.

 

[altergnostic]

None of these statements are true.

As I pointed out in post #21, the Doppler analysis shows us what each observer actually sees, observes and measures and does not depend on which frame you use to do the analysis and, in fact, doesn't even require a frame to do the analysis. Different frames don't change what observers see, observe or measure. All they do is change how the calculations are made to determine what they see, observe and measure but the end result is the same. I have pointed this out multiple times in this thread. It's one of the issues the OP needs to understand because he has been expressing the idea that different frames not only change what observers see, they also change the outcome of what happens.

I think i may have been unclear with what i meant say. I wasn't implying that different frames will reach different conclusions, only that whenever you do relativity, you are in only one frame and there's no absolute frame. Two observers in different frames may disagree on direct observarions, such as the time some event takes place compared to his own watch, but by applying sr equations both will reach agreeing conclusions.

I was only trying to point out that statements such as "simultaneous" need to be reached from only one reference frame of choice, from where you make your measurements. The final results will be in agreement with any other frame you choose to do your calcularions from.

 

[PAllen]

Two observers in different frames may disagree on direct observarions, such as the time some event takes place compared to his own watch, but by applying sr equations both will reach agreeing conclusions.

Actually, no, and that was ghwellsjr's point. There will never be disagreement between frames on direct observations. A direct observation is, e.g. time on 'A's watch when they detect event X.

I was only trying to point out that statements such as "simultaneous" need to be reached from only one reference frame of choice, from where you make your measurements. The final results will be in agreement with any other frame you choose to do your calcularions from.

Frames will disagree on simultaneity precisely because it is not an observation; it is a convention or calculation. An observation is e.g. light from X and Y reach A at the same time. 'A' might interpret this as X and Y are simultaneous. B might have different interpretation. Neither will disagree on the observable: that light form X and Y reach A at the same time.

 

[bgq]

Actually, no, and that was ghwellsjr's point. There will never be disagreement between frames on direct observations.

Each of the observers in the train "observes" that the clock of the other is slower. Observer in train A observes that clock of B is slower than clock of A, but observer in train B observes that clock of A is slower than that of B. There is a clear disagreement about what each observes.

 

[harrylin]

Each of the observers in the train "observes" that the clock of the other is slower. Observer in train A observes that clock of B is slower than clock of A, but observer in train B observes that clock of A is slower than that of B. There is a clear disagreement about what each observes.

They don't really observe but calculate that. With "direct observations", we mean that everyone agrees about what everyone observes on his/her clock when a signal arrives at the location where that clock is. Those are called "events" in SR jargon:

A direct observation is, e.g. time on 'A's watch when they detect event X.

 

[bgq]

They don't really observe but calculate that.

According to my understanding of physics and sciences, we do calculations to know what could be observed even if observations are not exist. If calculations do not reveal what could be observed (or at least what being true), then there is no point to do any calculations, and all formulas of physics has nothing to do with the real world!

 

[harrylin]

According to my understanding of physics and sciences, we do calculations to know what could be observed even if observations are not exist. If calculations do not reveal what could be observed (or at least what being true), then there is no point to do any calculations, and all formulas of physics has nothing to do with the real world!

Right. Once more: everyone agrees about what everyone observes on his/her clock when a signal arrives at the location where that clock is. Also everyone can calculate what someone else would calculate, based on certain assumptions. That is the point of doing calculations. However, they may use contrary assumptions. In particular, the calculated rate of a moving clock depends on one's assumption about simultaneity (you know this if you know how to derive the time dilation factor, as shown in good textbooks; but if you don't know, ask!).

To give a more graphic example: a laser hits an analogue watch and melts it so that the dial is stuck in place. Everyone must agree what time that watch indicated when it was melted by the laser pulse. What people do not have to agree on, was what time it "really" was when that happened.

BTW, also relativity of simultaneity is explained in the two references that I provided at your request (#30, #33).

 

[altergnostic]

Actually, no, and that was ghwellsjr's point. There will never be disagreement between frames on direct observations. A direct observation is, e.g. time on 'A's watch when they detect event X.


Frames will disagree on simultaneity precisely because it is not an observation; it is a convention or calculation. An observation is e.g. light from X and Y reach A at the same time. 'A' might interpret this as X and Y are simultaneous. B might have different interpretation. Neither will disagree on the observable: that light form X and Y reach A at the same time.

I meant to say that ANY two frames may disagree on observatios, not the two specified in this particular problem. I was generalising, i guess this wasnt clear. If you have three frames with different relative velocites to each other they will not agree on the time of their observatios on events occurring on all three of them. If light from a source takes longer to reach an observer than another, they will not agree. They will agree on observations when the situation is symmetrical.

 

[altergnostic]

Each of the observers in the train "observes" that the clock of the other is slower. Observer in train A observes that clock of B is slower than clock of A, but observer in train B observes that clock of A is slower than that of B. There is a clear disagreement about what each observes.

That's a calculation, not an observation. The observation is "light signal at t seconds on my watch" and from there you calculate the difference between clocks. Remember, observations are local events, light has to reach you, be inside your own frame, you can't see light at a distance. Everything that happens on another frame at a considerable distance and/or relative velocity has to be calculated.

 

[ghwellsjr]

They don't really observe but calculate that. With "direct observations", we mean that everyone agrees about what everyone observes on his/her clock when a signal arrives at the location where that clock is. Those are called "events" in SR jargon:

I think this could be misleading. "Events" in SR jargon have a wider meaning than merely when something significant "happens" in a scenario. The term "event" refers specifically to the four coordinates of a location in space at a particular time as defined by a particular frame, whether or not anything is present at that location and at that time and the value of those four coordinates are different in different reference frames. So while all frames will agree on what any observer sees on their own clocks and the signals they receive from other clocks, they will not agree on the values of the coordinates that they assign to those events. It's these four coordinates that we use the Lorentz Transformation process to see how any arbitrary event in one inertial frame takes on different values in a different inertial frame moving with respect to the first one. The values of the coordinates of these events provide no relation to what, if anything, is actually "happening" at those events.

 

[ghwellsjr]

Each of the observers in the train "observes" that the clock of the other is slower. Observer in train A observes that clock of B is slower than clock of A, but observer in train B observes that clock of A is slower than that of B. There is a clear disagreement about what each observes.

There is never any disagreement about what any observers actually see, measure or observe.

According to my understanding of physics and sciences, we do calculations to know what could be observed even if observations are not exist. If calculations do not reveal what could be observed (or at least what being true), then there is no point to do any calculations, and all formulas of physics has nothing to do with the real world!

This quote seems at odds with the first quote. First you said there is disagreement about observations and now you say that observations should reflect the truth about what is going on in the real world. What you need to understand is that there are different ways to calculate what observers will see, measure and observe but those calculations can have completely different numbers until you get to the final result. You also need to understand that time dilation is not one of those things that observers can see. Don't confuse the observed slowing down of a moving clock with time dilation.

Consider a new situation where two observers are approaching each other from a great distance apart. They will each observe the other ones clock as running faster than their own and then after they pass each other, they will each observe the other ones clock running slower than their own. These are just normal relativistic Doppler effects, correct?

Yet, if you apply the rules of Special Relativity and select any arbitrary inertial frame to analyze the situation, the time dilation of each clock remains the same while they approach, pass, and depart from each other. Do you understand that? The time dilation doesn't change while they each see the others clock first running faster than their own and then slower.

So, for example, if we analyze this new situation from a frame in which both observers are traveling at the same speed toward each other, we will calculate that they both have the same time dilation, even though they both first see each others clock running faster than their own and then running slower than their own after they pass.

Then if we use a second frame in which one of the observers is at rest, we will calculate that his clock has no time dilation while the other clock has an even greater time dilation than in the first frame and yet they still both see each others clock running faster then slower.

And if we use a third frame in which the other observer is at rest, we will exchange all the calculations between the two observers from the second frame.

And we can pick other frames in which both travelers are moving but at different speeds and then we will calculate they each have different time dilations.

So in each of these different frames, the time dilations of the two observers is a constant during the scenario for each observer and yet they still both see the other ones clock first running faster and then running slower than their own by exactly the same ratios.

The time dilation is a calculation based on the speed of the clock in the arbitrarily selected frame and is not something that anyone can ever see or measure or observe.

 

[harrylin]

I think this could be misleading. "Events" in SR jargon have a wider meaning than merely when something significant "happens" in a scenario. [..]whether or not anything is present at that location and at that time [..]

Such extreme jargon would loose all connection to the true meaning of the word.
IMHO the following summarizes "event" rather well:
http:http://en.wikipedia.org/wiki/Event_(relativity)

 

[ghwellsjr]

I meant to say that ANY two frames may disagree on observatios, not the two specified in this particular problem. I was generalising, i guess this wasnt clear. If you have three frames with different relative velocites to each other they will not agree on the time of their observatios on events occurring on all three of them.

I'm not sure you have a clear understanding here, but even if you do, you are not expressing it clearly. Any two frames will always agree on "observations" if by that we mean what observers will observe. What they will not agree on is their assignment of the coordinate values of events. There is clear terminology to express what you seem to be saying, why not use it? Instead of saying:

If you have three frames with different relative velocites to each other they will not agree on the time of their observatios on events occurring on all three of them.

Why not say:

If you have three frames with different relative velocities to each other they will not agree on the coordinate times of the events occurring on all three of them.

If light from a source takes longer to reach an observer than another, they will not agree. They will agree on observations when the situation is symmetrical.

It's statement like this that makes me wonder if you really understand SR. What is it that you are saying they don't agree on or do agree on? Observations? If you are saying that two distant observers will see the same thing at the same time if they are the same distance from the source of the observation, then that really begs the question. How do you know that they are the same distance and that their observations are taken at the same time? That's an issue that requires a frame to settle, not observations.

Or are you saying that they will agree on the coordinate location and time of a remote event? Well this will be true if they are both using the same frame and they are both discussing the same event.

Look, in this scenario, when we are talking about the symmetry of observations, we are not talking about either of these things. We are saying that each observer sees the other ones clock ticking slower than his own by the same ratio and this is independent of any frame and it is not an observation of time dilation. Note that the observers are not observing the same events, the first observer is observing the second observer's clock in relation to his own and the second observer is observing the first observer's clock in relation to his own.

Each of the observers in the train "observes" that the clock of the other is slower. Observer in train A observes that clock of B is slower than clock of A, but observer in train B observes that clock of A is slower than that of B. There is a clear disagreement about what each observes.

That's a calculation, not an observation. The observation is "light signal at t seconds on my watch" and from there you calculate the difference between clocks. Remember, observations are local events, light has to reach you, be inside your own frame, you can't see light at a distance. Everything that happens on another frame at a considerable distance and/or relative velocity has to be calculated.

Again, even if you understand SR correctly, you're not expressing it correctly. You seem to be incorporating more than one frame to explain what is happening. Stick with one frame at a time. And I'm not sure when you say that bgq's statement is regarding a calculation rather than an observation is correct. His statement about their observations is correct. His statement that there is disagreement is not correct. I don't know what you mean by:

The observation is "light signal at t seconds on my watch" and from there you calculate the difference between clocks.

What calculation in the difference between the clocks are you talking about?

You are correct that observations are local events because light has to reach you, but why do you say "inside your own frame" and why do you say "on another frame at a considerable distance"? In SR, all inertial frames cover all distances. It's not like I'm in one frame local in extent to me and the other observer, who is at a considerable distance away from me (whether or not he is moving with respect to me) is in another frame local in extent to him. If you want to consider my rest frame, then it also includes that distant other observer. Or if you want to consider his rest frame, then it also includes me. In my rest frame, my clock ticks at the same rate as the coordinate time and his moving clock ticks at a slower rate. In his rest frame, his clock ticks at the same rate as the coordinate time and my clock ticks slower. In a frame in which we are both traveling at the same speed, both our clocks tick slower, by the same amount, than the coordinate time.

 

[ghwellsjr]

Such extreme jargon would loose all connection to the true meaning of the word.
IMHO the following summarizes "event" rather well:
http:http://en.wikipedia.org/wiki/Event_(relativity)

There are multiple "true meanings" of the word "event". The wikipedia article is pointing out that "a glass breaking on the floor" is not the idealized event that we use in SR which does not have an extent either in space or in time. To call the idealized meaning of the word "event" when applied to the Lorentz Transformation process as extreme jargon is to discredit an understanding what I was trying to point out. "Event" has a very specific meaning in Special Relativity that many people are confused about specifically because they want to link it to a happening such as a concert which is also called an event.

 

[harrylin]

[..] To call the idealized meaning of the word "event" when applied to the Lorentz Transformation process as extreme jargon is to discredit an understanding what I was trying to point out.[..]

I find the idealized meaning of the word "event" as currently described in Wikipedia acceptable jargon, in contrast with your description which I called extreme jargon. Thus we don't appreciate each other's explanations of this; and that is no problem, as everyone can verify the references and make up his/her own mind while taking the best of both.

 

[bgq]

Consider a new situation where two observers are approaching each other from a great distance apart. They will each observe the other ones clock as running faster than their own
.

Actually, I don't understand why each observes the other clock faster, the time dilation formula does say nothing about the direction of motion, can you clarify this to me?

 

[ghwellsjr]

I find the idealized meaning of the word "event" as currently described in Wikipedia acceptable jargon, in contrast with your description which I called extreme jargon. Thus we don't appreciate each other's explanations of this; and that is no problem, as everyone can verify the references and make up his/her own mind while taking the best of both.

Then are you saying that if I specify a set of coordinates in a particular frame, say at t=3 seconds, x=4, y=5 and z=6 (all in light-seconds) but there is nothing but empty space at that location at that time, then it is not an event?

 

[ghwellsjr]

Actually, I don't understand why each observes the other clock faster, the time dilation formula does say nothing about the direction of motion, can you clarify this to me?

I've been trying to say that you can't observe time dilation, it's a calculation based on the speed in an arbitrarily selected inertial frame of reference. If you could observe it, it would be a bunch of different values depending on which frame someone chooses. An observation is what you actually see with your eyes or with an instrument like a telescope or a radio or a television. These all depend on the changing light travel time which makes things appear faster when approaching or slower when receding. Doppler is what you observe, time dilation is what you calculate.

 

[bgq]

I've been trying to say that you can't observe time dilation, it's a calculation based on the speed in an arbitrarily selected inertial frame of reference. If you could observe it, it would be a bunch of different values depending on which frame someone chooses. An observation is what you actually see with your eyes or with an instrument like a telescope or a radio or a television. These all depend on the changing light travel time which makes things appear faster when approaching or slower when receding. Doppler is what you observe, time dilation is what you calculate.

Well, I think I had a problem with the exact meaning of "observation" which lead to some confusion; anyway I think I now get it.
Thanks.

 

[PAllen]

I'll add what I hope is the simplest possible separation of measurement versus assignment (of coordinates or labels).

Bob and Alice, each with a wristwatch, have relative motion and pass each other. We don't care about anything except the event they go right past each other.

There are two measurements here: Bob reads his watch at passage and see 2 PM. Alice read her watch and sees 3 PM. Each can see the other's watch, so Bob agrees that Alice measured 3 PM. Alice agrees that Bob measured 2 PM. Everyone in universe who can gain information about these measurements agrees on the result of each of these two measurements.

What differs by frame or observer is the time assigned to the passing event. Bob assigns 2 PM to the event. Alice assigns 3 PM to the event. Other observers will assign different time to this same 'passing' event.

 

[bgq]

I'll add what I hope is the simplest possible separation of measurement versus assignment (of coordinates or labels).

Bob and Alice, each with a wristwatch, have relative motion and pass each other. We don't care about anything except the event they go right past each other.

There are two measurements here: Bob reads his watch at passage and see 2 PM. Alice read her watch and sees 3 PM. Each can see the other's watch, so Bob agrees that Alice measured 3 PM. Alice agrees that Bob measured 2 PM. Everyone in universe who can gain information about these measurements agrees on the result of each of these two measurements.

What differs by frame or observer is the time assigned to the passing event. Bob assigns 2 PM to the event. Alice assigns 3 PM to the event. Other observers will assign different time to this same 'passing' event.

OK, that's clear.

 

[ghwellsjr]

I'll add what I hope is the simplest possible separation of measurement versus assignment (of coordinates or labels).

Bob and Alice, each with a wristwatch, have relative motion and pass each other. We don't care about anything except the event they go right past each other.

There are two measurements here: Bob reads his watch at passage and see 2 PM. Alice read her watch and sees 3 PM. Each can see the other's watch, so Bob agrees that Alice measured 3 PM. Alice agrees that Bob measured 2 PM. Everyone in universe who can gain information about these measurements agrees on the result of each of these two measurements.

What differs by frame or observer is the time assigned to the passing event. Bob assigns 2 PM to the event. Alice assigns 3 PM to the event. Other observers will assign different time to this same 'passing' event.

This can even be confusing because you are implying that just because Bob and Alice have their own watches (which always keep Proper Time) that they will automatically use that for the coordinate time of their own rest frames which is not a requirement specifically if they are not inertial. Furthermore, it is convenient to use the Standard Configuration for assigning Coordinate times and locations, otherwise, you cannot use the simple version of the Lorentz Transform to convert coordinates from one frame to another. When you do that, it would be most convenient to assign the origins of their two rest frames to the event of their passing and then calculate their Proper Times as an offset from those (along with whatever time dilation is required). The way you are doing it requires an awful lot of complicated computation to convert events from one frame to the other. Why can't we capitalize on the conventional easy way of doing and expressing these things, especially to novices? Once they grasp the simple way to understand Special Relativity, they can go off into all the other complicated ways that don't add one single thing to the understanding of SR.

 

[PAllen]

This can even be confusing because you are implying that just because Bob and Alice have their own watches (which always keep Proper Time) that they will automatically use that for the coordinate time of their own rest frames which is not a requirement specifically if they are not inertial. Furthermore, it is convenient to use the Standard Configuration for assigning Coordinate times and locations, otherwise, you cannot use the simple version of the Lorentz Transform to convert coordinates from one frame to another. When you do that, it would be most convenient to assign the origins of their two rest frames to the event of their passing and then calculate their Proper Times as an offset from those (along with whatever time dilation is required). The way you are doing it requires an awful lot of complicated computation to convert events from one frame to the other. Why can't we capitalize on the conventional easy way of doing and expressing these things, especially to novices? Once they grasp the simple way to understand Special Relativity, they can go off into all the other complicated ways that don't add one single thing to the understanding of SR.

I wanted to bypass the issues of setting up a complete coordinate system, and transforming between them, to focus exclusively, in isolation, on the distinction between measurement and assigning a single coordinate label in one obvious way. I feel reducing to this simplest case is helpful. Sorry if you don't.

 

[ghwellsjr]

I wanted to bypass the issues of setting up a complete coordinate system, and transforming between them, to focus exclusively, in isolation, on the distinction between measurement and assigning a single coordinate label in one obvious way. I feel reducing to this simplest case is helpful. Sorry if you don't.

But how does your example show the distinction between the measurement of Proper Time on a watch and the assigning of Coordinate Time when they are the same for each observer?

You say other observers will assign different times to this same 'passing' event but wouldn't they also have to be present at the same 'passing' event if your simplest case is how they assign Coordinate Time based on the arbitrary Proper Time displayed on their watches?

 

[PAllen]

But how does your example show the distinction between the measurement of Proper Time on a watch and the assigning of Coordinate Time when they are the same for each observer?

You say other observers will assign different times to this same 'passing' event but wouldn't they also have to be present at the same 'passing' event if your simplest case is how they assign Coordinate Time based on the arbitrary Proper Time displayed on their watches?

I am not bothering to make such distinctions, or get into details of how other observers might assign a time (just that they could, and wouldn't generally pick the same values), or that Bob and Alice have other choices besides the obvious one. I am focusing purely on the distinction between measurements and the act of choosing a coordinate value.

I believe there was confusion on this specific point, and I wanted to focus on it in isolation. I believe it was helpful.

I do not want to belabor this anymore.

 

[harrylin]

Then are you saying that if I specify a set of coordinates in a particular frame, say at t=3 seconds, x=4, y=5 and z=6 (all in light-seconds) but there is nothing but empty space at that location at that time, then it is not an event?

For me that's just a space-time coordinate. Regretfully the Wikipedia article only paraphrases the referenced textbooks, so here's a citation of how Alonso and Finn (Fundamental University Physics) define "event" in their chapter on the Lorentz transformation:

"An event is a specific occurrence that happens at a particular point in space and at a particular time".

I won't comment further on this except if it's an issue for bgq.

 

[altergnostic]

I'm not sure you have a clear understanding here, but even if you do, you are not expressing it clearly. Any two frames will always agree on "observations" if by that we mean what observers will observe. What they will not agree on is their assignment of the coordinate values of events. There is clear terminology to express what you seem to be saying, why not use it?
It's statement like this that makes me wonder if you really understand SR. What is it that you are saying they don't agree on or do agree on? Observations?

Yes, i meant the coordinates in space and time, not what they see. I didn't speak of coordinates of events since it was clear, i think, we were always talking about coordinates, not if one sees an explosion and the other sees jerry seinfeld, but ok, there's better terminology indeed.

What calculation in the difference between the clocks are you talking about?

When you compare the rate of two clocks you are already calculating. You are computing the difference between the time in your clock and the observed time on a clock located in the primed frame, that's all. You will se a prevously sync'd clock going slower.

You are correct that observations are local events because light has to reach you, but why do you say "inside your own frame" and why do you say "on another frame at a considerable distance"? In SR, all inertial frames cover all distances. It's not like I'm in one frame local in extent to me and the other observer, who is at a considerable distance away from me (whether or not he is moving with respect to me) is in another frame local in extent to him. If you want to consider my rest frame, then it also includes that distant other observer. Or if you want to consider his rest frame, then it also includes me. In my rest frame, my clock ticks at the same rate as the coordinate time and his moving clock ticks at a slower rate. In his rest frame, his clock ticks at the same rate as the coordinate time and my clock ticks slower. In a frame in which we are both traveling at the same speed, both our clocks tick slower, by the same amount, than the coordinate time.

I say that it is in your own frame because seeing light is always a local event, you can't speak of light in another frame. I mean that regardless of the position and motion of another frame, light is either in your own frame right in your eyes, or you are not aware of it at all. And i said "considerable distance" because at small distances / velocities we don't really need to consider special relativity. And another frame is the primed frame, not a frame that is no longer inside your own frame, just a frame that would locally measure its own coordinates to be in disagreement with your observations. If i see my clock at 2s and yours at 1s, you would see your own at 2s and mine at 1s. Yours at 1 and yours at 2 are different measurements, that's what "separetes" frames.
Now, when you talk of a frame in which we are both traveling at the same speed you are talking about a third frame, right? If so, i agree with all you have said.

 

[Dale]

I say that it is in your own frame because seeing light is always a local event

Seeing light is local, but frames are not local. So this is a reason to not use your terminology.

 

[altergnostic]

Seeing light is local, but frames are not local. So this is a reason to not use your terminology.

But seeing light is always done in your own frame, i don't see any problem with it other than being redundant.

 

[Dale]

But seeing light is always done in your own frame

No, this is incorrect. If I see the light in one frame then I see it in all frames. Changing coordinate systems does not make me blind as you suggest. I do not need to use any particular coordinate system in order to see.

 

[Nugatory]

But seeing light is always done in your own frame, i don't see any problem with it other than being redundant.

"Your frame" is another of those dangerous phrases that can lead to misunderstanding. It is a convenient shorthand for "the frame in which you just coincidentally happen to have zero instantaneous velocity" - and if you try substituting that for the bolded text you may see the problem with saying that you do anything (including seeing) "in a frame".

Events, such as light hitting your retina, don't happen in frames. They just happen; and different frames are just different sets of rules for assigning them space and time coordinates.