How to resolve the contradiction in twin clocks?

[nitsuj]

Ah, okay

 

[ghwellsjr]

I've seen this discussion before, and to me it always comes down to people (myself included) not being completely clear about the distinction between coordinate time along the worldline of an observer at rest at the spatial origin of a coordinate system and proper time along the same worldline.

I'm surprised that you express confusion (or at least not being completely clear) about the distinction between Coordinate Time and Proper Time after you gave such an excellent explanation of them both in post #45:

- Proper time, which is invariant and what the position of the clock's hands (or the progress of any physical process: fraction of a radioactive sample that has decayed between two observations, number of oscillations of a cesium atom between two observations, number of my hairs which have turned gray between two observations) measures.
- Coordinate time, which is different for different observers using different coordinate systems (also known as "frames of reference"). The Lorentz transformations describe how to convert one observer's coordinates, including coordinate time, to another observer's coordinates in a way that preserves the laws of physics and especially ensures that the relationship between the position of the hands of the clock and each observers' coordinate time is consistent with the physical process moving the hands of the clock.

What am I missing?

Also, I should have included you in the list of experts who state that Proper Time is what a clock measures.

 

[ghwellsjr]

Thanks for the corrections. I'll have to admit I haven't quite come to terms with the twin paradox yet

The Twin Paradox is easy--just pick an Inertial Reference Frame (IRF) to specify the scenario, then the Proper Time for each twin is a function of their speed in the IRF, the faster they travel, the slower their clock ticks. Therefore, if only one moves, he will accumulate less time than the other one who remains stationary. Since they must start out together and end up together, that means the one who moves must accelerate (at least change direction).

- I've read Feynman who simply dismissed me as a cocktail party phillosopher saying symmetry breaks down at acceleration and only inertial frames are relative.

I think he must mean that only IRF's can be transformed into other IRF's using the Lorentz Transformation process. IRF's are the standard frames in SR. If you want to veer off into non-inertial frames, then you have to establish your own convention or state which of several conventions other people have promoted you wish to use. My favorite is the convention established by using Radar Methods. In fact, I don't use any others.

How does the acceleration affect the time isn't mentioned in his lecture. (I issued the lectures from library after returning that ancient book of intro to "modern" physics.)

Acceleration doesn't have to affect the time, it only has to affect the direction of the traveling twin. It's the speed according to the IRF that affects the time.

So you are essentially saying that proper time can be measured even in non inertial frames?

I think what you are meaning to ask about is non inertial observers (twins). One of the twins is non inertial because he accelerates. I don't think anyone ever sets up a Twin Paradox scenario by specifying the coordinates of the stay-at-home twin in the non inertial coordinate system of the traveling twin. I have always seen the traveling twin specified in the IRF of the stay-at-home twin. For example, one twin travels away from the stationary twin at some speed for some period of Coordinate Time or Proper Time or for some distance and then turns around and returns at the same speed. That makes it very easy to determine the aging difference. But then the question is asked about other frames (which cannot change the answer). If the other frame is also an IRF, then you can use the Lorentz Transformation. If the other frame is non inertial, then much more work must be done but it is possible.

I am going to look a bit into that for now that and twin paradox.
And I am kicking myself for that line about 2u.
(Also as a clarification I started reading SR from 9th grade
from children's biographies of einstein, documentries and such like. It's only last weekend I read an official text on SR for the first time. Am in btech 1st yr now.)
Regards
P.S. Calculations of Janus are somewhere in the beginning of the post. Sorry about the confusion.

 

[ghwellsjr]

The more traditional way and very proper way of doing things is to define an "ideal clock" as a device that reads proper time.
...
An example for SR would be a non-ideal clock like a wristwatch that's been run over by a truck.

The comment that I asked justin about was:

A ruler in comparative motion is not a "proper" ruler, same goes for the clock.

Now I assumed that his comment would be in contrast to this comment:

"A ruler in comparative rest is a "proper" ruler, same goes for the clock."

EDIT: It turns out I don't have to assume a contrasting statement, justiin provided it in post #69:

A ruler at rest with you is a proper length. Same goes for the clock, I am unsure how else to word it.

I didn't think his comment had anything to do with a broken ruler or a wristwatch run over by a truck. I assumed that he was saying that a ruler at rest measures proper length but a ruler in motion does not and that a clock at rest measures proper time but a clock in motion does not. That's what I asked him for clarification about.

 

[ghwellsjr]

The observation is not part of the physics being observed. So musing over what the clock that has length dependent displays reads while in comparative motion isn't going to yield anything regarding the physical processes of the clock itself. The clock isn't different because it has been observed

The observation is very much a part of the physics being observed. It is fundamental to the Principle of Relativity. If you discount the observations of clocks in motion, then you cannot have a complete Principle of Relativity. It's precisely because two clocks in relative motion both see the other ones clock ticking symmetrically at a different rate compared to their own that we have the Principle of Relativity. And it's the Principle of Relativity applied even to light that leads to the Lorentz Transformation which completely overhauled physics from Newtonian-based to Einsteinian-based.

Of course the clock isn't different because it has been observed, but our physics is different and therefore our understanding of the physical processes of the clock is different because scientists have made careful measurements of clocks in motion (I'm using "clock" in the broadest sense of the term).

A ruler at rest with you is a proper length. Same goes for the clock, I am unsure how else to word it. It is such a blatant point, but was raised to make the distinction between these measuring devices in motion are not the same as when at rest.

True, but a ruler that has been accelerated so that it has a different length (according to its original rest IRF), still has a Proper Length and can be used to correctly measure the length of any object that is comoving with it. A clock that has been accelerated so that it has a different tick rate (according to its original rest IRF), still has a Proper Time and can be used to measure the passage of time of anything comoving with it.

I referred to the original rest IRF in both these situations but keep in mind that if you're talking about a ruler or a clock that start out at rest in an IRF and then are accelerated to a constant speed in the same IRF, it is always possible to pick another IRF in which the objects are at the same speed before and after the acceleration and so there is no change in the Proper Length of the ruler or the Proper Time of the clock.

or the quoted part remember clocks are not perfect. I'm gunna assume you agree that a clock doesn't "read" proper time at all, it displays it. The variance between the two could be idealized away, even my mechanical watch that loses minutes over days is accurate enough for my scheduling . Sometimes extremely accurate measures of proper time are needed(CERN Neutrino mearement, probably gravity wave detection ect), sometimes it's just a fun distinction to make.

No, I don't agree. I don't even know what you're talking about or why you're talking about this. It has nothing to do with the subject you and I have been discussing.

 

[nitsuj]

The observation is very much a part of the physics being observed. It is fundamental to the Principle of Relativity. If you discount the observations of clocks in motion, then you cannot have a complete Principle of Relativity. It's precisely because two clocks in relative motion both see the other ones clock ticking symmetrically at a different rate compared to their own that we have the Principle of Relativity. And it's the Principle of Relativity applied even to light that leads to the Lorentz Transformation which completely overhauled physics from Newtonian-based to Einsteinian-based.

It over hauled Newton physics because Newton physics is wrong. My point is inline with your retort to "The observation is not part of the physics being observed." Who cares about symmetry? That only has purpose for creating the metric. Nothing in your post explained how an observation of a physical process is part of that physical process.

Of course the clock isn't different because it has been observed, but our physics is different and therefore our understanding of the physical processes of the clock is different because scientists have made careful measurements of clocks in motion (I'm using "clock" in the broadest sense of the term).

What do you mean by "But our physics is different." To your point regarding relative motion there is nothing "different" heck it's symmetrical.

True, but a ruler that has been accelerated so that it has a different length (according to its original rest IRF), still has a Proper Length and can be used to correctly measure the length of any object that is comoving with it. A clock that has been accelerated so that it has a different tick rate (according to its original rest IRF), still has a Proper Time and can be used to measure the passage of time of anything comoving with it.

Yuppers, and goes without saying. What typically doesn't go without saying, is this distinction between the very very well known proper length and that the concept is often carried over to length contraction incorrectly. The point is that a moving ruler is not a "traditional" measuring stick. as simple as that. There is no need to bring up the point that motion is relative. That's should be implicit if discussing relativistic effects.

I referred to the original rest IRF in both these situations but keep in mind that if you're talking about a ruler or a clock that start out at rest in an IRF and then are accelerated to a constant speed in the same IRF, it is always possible to pick another IRF in which the objects are at the same speed before and after the acceleration and so there is no change in the Proper Length of the ruler or the Proper Time of the clock.

Yup again motion is relative, and again is implicit here.

No, I don't agree. I don't even know what you're talking about or why you're talking about this. It has nothing to do with the subject you and I have been discussing.

It was with respect to the quoted part in that post. Clocks are imperfect, nuff said. So while a clock or anything for that matter experiences proper time as we define it, getting a clock to accurately display this as an incremental reading is complicated...it's all just so fast and keeping up with the constancy of c with a display is pretty tricky I am sure.

Sorry for quoting & replying to your post in a complicated way/

 

[phyti]

What do you mean by that? The literal readings on an actual clock need not correspond to the proper time along the worldline of the clock. (Actual clocks run fast or slow.) Do you just mean that an ideal clock, i.e., a device constructed in such a way as to read the proper time along its worldline, will read the proper time along its worldline? True enough, but circular. Or do you mean that the temporal state of a clock will progress in proportion to proper time, even though this may not correspond to the literal readings on the clock? If so, then it doesn't need to be a "clock", you could just as well refer to any physical system, and then you would need to say what is meant by "temporal state", which you can't define with reference to elapsed proper time or it is circular.

Telling people that "every clock measures proper time" is not good, because it could only be literally true if we simply defined 'proper time' to be whatever any clock reads, which of course would be utterly incoherent. That's what beginners tend to think you must mean, which totally sends them down the wrong track.

There is a non-circular way of correctly saying what you are probably trying to say, but it's quite a bit more subtle and complicated than just saying "every clock reads proper time".

I agree.
"every clock reads proper time" (for the observer moving with the clock). (requires context)
Einstein said the time of the event is simultaneous with a clock event (position of the hand) located at the event. The poor word choice 'proper' relates more to etiquette or social behavior.
It's about location, so why not define it as local time, in keeping with his additional statements regarding A time (local) and B time (distant).

 

[Dale]

The poor word choice 'proper' relates more to etiquette or social behavior.
It's about location, so why not define it as local time, in keeping with his additional statements regarding A time (local) and B time (distant).

The term "proper time" is standard terminology. The term "local time" was used by LET to denote coordinate time in the non-aether frames, so I think that a different term is preferable. However, it is a purely semantic preference with no physical content whatsoever.

 

[Dale]

The observation is not part of the physics being observed.

I disagree with this statement. Observations are always made by some physical process. You do try to minimize the impace that the observation has on the system being observed, but I don't think that you can say that they are completely separated.

 

[nitsuj]

I disagree with this statement. Observations are always made by some physical process. You do try to minimize the impace that the observation has on the system being observed, but I don't think that you can say that they are completely separated.

You're absolutely right, the observation itself is a physical process connected to the whatever was being observed, all else is "elsewhere".

It's clear enough when in context; your point border lines hyperbole.

My observation of time dilation doesn't mean that clock is "broken" or otherwise any different physically then if I hadn't observed it at all.

 

[ghwellsjr]

It over hauled Newton physics because Newton physics is wrong. My point is inline with your retort to "The observation is not part of the physics being observed." Who cares about symmetry? That only has purpose for creating the metric. Nothing in your post explained how an observation of a physical process is part of that physical process.

What do you mean by "But our physics is different." To your point regarding relative motion there is nothing "different" heck it's symmetrical.

I just meant that our understanding of physics since Einstein is different than before because he applied the Principle of Relativity to all of physics and not just part of it.

 

[Dale]

It's clear enough when in context; your point border lines hyperbole.

Fair enough. I admit, I had not been following the conversation between you and ghwellsjr carefully, so I read it somewhat out of context.

 

[phyti]

The term "proper time" is standard terminology. The term "local time" was used by LET to denote coordinate time in the non-aether frames, so I think that a different term is preferable. However, it is a purely semantic preference with no physical content whatsoever.

"Bald eagle" is standard/common terminology, but the eagle isn't bald!

I'll stick with local time, which implies a clock with the observer, and not remotely located.
The ether is ignored today, and it's use in the 1900's does not prohibit the use of 'local' in a different context now.

 

[ghwellsjr]

"Bald eagle" is standard/common terminology, but the eagle isn't bald!

I'll stick with local time, which implies a clock with the observer, and not remotely located.
The ether is ignored today, and it's use in the 1900's does not prohibit the use of 'local' in a different context now.

And what is your preferred term for the eagle?

 

[WannabeNewton]

I just wanted to add this to the other two references I gave (this one is taken from Malament's text): http://postimg.org/image/hig2mjgyr/

 

[nitsuj]

I just meant that our understanding of physics since Einstein is different than before because he applied the Principle of Relativity to all of physics and not just part of it.

I don't know enough about the entire subject of physics to say with authority, but I see PoR as emergent from the geometry of spacetime, remember regardless of comparative motion physics is the same. I'd agree in that sense PoR, specifically spacetime, is "applied" to all physics, maybe better said as all physics happens within spacetime; but that seems like a silly thing to say.

Isn't PoR merely the geometric symmetry of the physics being observed ?

 

[ghwellsjr]

I don't know enough about the entire subject of physics to say with authority, but I see PoR as emergent from the geometry of spacetime, remember regardless of comparative motion physics is the same. I'd agree in that sense PoR, specifically spacetime, is "applied" to all physics, maybe better said as all physics happens within spacetime; but that seems like a silly thing to say.

Isn't PoR merely the geometric symmetry of the physics being observed ?

No, the geometric symmetry of spacetime emerges from Einstein's first postulate, the PoR, and his second postulate, the propagation of light at c independent of its source.

 

[Dale]

"Bald eagle" is standard/common terminology, but the eagle isn't bald!

I'll stick with local time, which implies a clock with the observer, and not remotely located.

As long as you realize that you are deliberately inviting miscommunication by this approach.

 

[atyy]

I don't know enough about the entire subject of physics to say with authority, but I see PoR as emergent from the geometry of spacetime, remember regardless of comparative motion physics is the same. I'd agree in that sense PoR, specifically spacetime, is "applied" to all physics, maybe better said as all physics happens within spacetime; but that seems like a silly thing to say.

Isn't PoR merely the geometric symmetry of the physics being observed ?

Essentially yes. One can say that the principle of relativity emerges from the Poincare symmetry of the physical laws, where the Poincare symmetry is the isometry group of the Minkowski spacetime geometry.

The historical route went in the other direction - the Poincare symmetry was inferred from the PoR and the invariance of the speed of light. If one uses only PoR without requiring a speed limit, then Newtonian physics is allowed. Exactly how to infer Poincare symmetry from the PoR and a universal speed limit has subtleties which Fredrick once discussed in a very long thread, and whose details I can't remember.

 

[atyy]

I just wanted to add this to the other two references I gave (this one is taken from Malament's text): http://postimg.org/image/hig2mjgyr/

Yes, it's a problem in Newtonian physics too. I like Stephani's definition: time is what makes the laws of physics true.

 

[WannabeNewton]

I like Stephani's definition: time is what makes the laws of physics true.

Hehe.

 

[nitsuj]

No, the geometric symmetry of spacetime emerges from Einstein's first postulate, the PoR, and his second postulate, the propagation of light at c independent of its source.

wasn't spacetime there before it was modeled?

 

[ghwellsjr]

wasn't spacetime there before it was modeled?

No, spacetime is a model and it had no existence prior to Einstein's two postulates. There are other models just as viable that have existed.

 

[nitsuj]

No what? Everything after the comma agrees. anyways George this is silly...like I said earlier #86.

If you want to continue pm, let's not let me tarnish pf quality with you as my lead.

 

[Dale]

There are other models just as viable that have existed.

What do you mean by this?

 

[ghwellsjr]

What do you mean by this?

The same thing I presume you were referring to in post #78:

The term "proper time" is standard terminology. The term "local time" was used by LET to denote coordinate time in the non-aether frames, so I think that a different term is preferable. However, it is a purely semantic preference with no physical content whatsoever.

Namely LET which did not have relative space and relative time or spacetime but rather absolute space and time since it did not affirm Einstein's second postulate that light propagates at c in all IRF's but only in the rest IRF of the ether.

 

[Dale]

Oh, right. I forgot about LET.

 

[JM]

SR clocks

You don't understand--I am a beginner and most of what I've learned is from experts like these:
So I think you will have to agree, I'm not just sending beginners down the wrong track, I've been sent down there with them.

George: I think that the literature of SR is not clear, as I gather you do. With respect to Einsteins 1905 SR, these ideas make sense to me:
1 All clocks are ideal, in that they step off time in equal steps, i.e. the interval between 'ticks' is the same as time moves ahead.
2 Clocks that are at rest wrt each other are synched so that when one clock reads t = 10 e.g. all clocks read 10.
3 Clocks of two inertial frames in relative inertial motion start at zero and advance at the same rate. See Feynman's light clock analysis in Not so easy Pieces.
4 The Lorentz Transforms define the relation between the coordinates of the two frames, but leave room for many different ways to use the LTs.
5 Starting with x' = 0 and viewing the ticks of this clock as the events of interest, leads to the slow clock formula t' = t √( 1-v²/c². Since this clock is present at all the events ( the ticks ) it can be regarded as a proper clock reading proper time.
Note that this formula demands that t and t' be measured in the same units, and if there are clocks measuting the time , they must proceed at the same rate.
6 But there are other events that can be chosen; the relation x = f(t) can be chosen so that t' is zero, equal to t, or larger than t. And since the clocks are in synch all the clocks of K' read the same value, including the one at x' = 0. Its possible that none of the clocks are proper.
7 So a given clock can be proper or not proper depending on the particular events chosen for study.
Regards, JM

 

[ghwellsjr]

George: I think that the literature of SR is not clear, as I gather you do. With respect to Einsteins 1905 SR, these ideas make sense to me:
1 All clocks are ideal, in that they step off time in equal steps, i.e. the interval between 'ticks' is the same as time moves ahead.
2 Clocks that are at rest wrt each other are synched so that when one clock reads t = 10 e.g. all clocks read 10.
3 Clocks of two inertial frames in relative inertial motion start at zero and advance at the same rate. See Feynman's light clock analysis in Not so easy Pieces.
4 The Lorentz Transforms define the relation between the coordinates of the two frames, but leave room for many different ways to use the LTs.
5 Starting with x' = 0 and viewing the ticks of this clock as the events of interest, leads to the slow clock formula t' = t √( 1-v²/c². Since this clock is present at all the events ( the ticks ) it can be regarded as a proper clock reading proper time.
Note that this formula demands that t and t' be measured in the same units, and if there are clocks measuting the time , they must proceed at the same rate.
6 But there are other events that can be chosen; the relation x = f(t) can be chosen so that t' is zero, equal to t, or larger than t. And since the clocks are in synch all the clocks of K' read the same value, including the one at x' = 0. Its possible that none of the clocks are proper.
7 So a given clock can be proper or not proper depending on the particular events chosen for study.
Regards, JM

Since Einstein never used the term "proper clock" in his 1905 SR paper, I'm not sure why you referenced his paper with regard to your comments. And I'm sure most people don't know what the term "proper clock" means. This subject came up in your thread entitled Special Relativity Clocks at post #104 where the definition is of an inertial clock that passes through two events and so measures a time-like spacetime interval. So if you're still following that definition in your comments, a clock can only be proper if it is inertial during the interval under consideration so if a clock is inertial for some period of time and non-inertial during other periods, then, yes, "a given clock can be proper or not proper depending on the particular events chosen for study."

But this has nothing to do with the issue linked to in your quote of mine where the discussion was about Proper Time, not Proper Clocks. All clocks measure Proper Time all the time, even when they are non-inertial and can't be regarded as Proper Clocks.

 

[yuiop]

I am pretty confused in the following situation:

Two identical clocks moving at a constant speed v from each other in x-direction. If each clock is made up of a ball moving at a constant speed of 1 on a ruler in y-direction, then the position of the ball of a clock is the time of the clock. According to special relativity, y' = y no matter at what speed the two inertial reference frames move away from each other. Thus, the two clocks will always have the same time in both reference frames if they start from the same time at the same position, which contradicts the time conversion formula in the Lorentz Transformation.

Can anybody give me an explanation how to resolve the contradiction?

This thread is very long and I apologise if what I have to say has already been said and I missed it. Basically the situation described in the OP is almost identical to the classic light clock except we replace the balls with photons. If the classic light clock moves in the x direction, the photon bounces up and down along the y' axis, and the time recorded by the light clock is proportional to its accumulated distance up and down the y' axis. If we have two light clocks, A and B, with A at rest in irf S, and B moving relative to irf S. (Clock B is at rest in irf S'.) To observers at rest in S, when the photon in light clock A reaches the top where the mirror is, the photon in clock B is only part of the way up to its mirror. The speed of photons in the y direction is not the same for both clocks in either inertial reference frame S or S'. Note that to observers at rest with respect to irf S', the photon of clock B reaches its top mirror before the photon in clock A reaches its top mirror.

 

[JM]

But this has nothing to do with the issue linked to in your quote of mine where the discussion was about Proper Time, not Proper Clocks. All clocks measure Proper Time all the time, even when they are non-inertial and can't be regarded as Proper Clocks.

George- What definition of proper time and proper clock are you using? Moore says 'the time between two events measured by any clock present at both events is called a proper time between those events.' According to Taylor and Wheeler 'the special clock that records the proper time directly has the name proper clock for this pair of events.'
Do you use other definitions?
JM

 

[ghwellsjr]

George- What definition of proper time and proper clock are you using? Moore says 'the time between two events measured by any clock present at both events is called a proper time between those events.' According to Taylor and Wheeler 'the special clock that records the proper time directly has the name proper clock for this pair of events.'
Do you use other definitions?
JM

Those are both incomplete quotes and if you read the entire definitions in context, you will see why they are different, the first being general and the second being "special".

I don't have access to Moore's definition but the part you quoted is very similar to the first sentence for the definition of Proper Time from wikipedia:

In relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events. The proper time depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a smaller elapsed time between two events than that measured by a non-accelerated (inertial) clock between the same two events. The twin paradox is an example of this effect.

Doesn't Moore also have further explanation to point out that the Proper Time between two events depends on the motion of the clock?

Taylor and Wheeler's "special clock" is one that has a constant velocity as it travels between the two events. Look further up page 10 where you quoted and you will see:

We carry our wristwatch at constant velocity from one event to the other one.

So a Proper Clock (according to Taylor and Wheeler) is an inertial clock (one whose velocity is constant, in other words, non-accelerating) that passes between the two events in question. The point that Taylor and Wheeler are making is that a Proper Clock directly measures the invariant Spacetime Interval between two events.

In contrast, a clock that accelerates (changes it's velocity--that is, changes either its speed or its direction or both) on its way between the two events in question will measure a different time interval than a Proper Clock will (or another clock that accelerates differently).

So, no, I don't use other definitions except that to make it easier to understand for novices, I just say, "Proper Time is what any clock measures".

 

[JM]

So, no, I don't use other definitions except that to make it easier to understand for novices, I just say, "Proper Time is what any clock measures".

George- Thanks, that clarifies the definitions. So, now consider:
Given: Einsteins 1905 theory, and the Lorentz transforms.
Two events, (y,z = 00, v/c =0.8) first occurs at x,ct = 0,0 and the second at x = 5, ct = 10. The LT shows that ct' = 10. Since this time applies to all clocks of K', the time also applies to the clock at x' = 0. This clock is inertial, but not proper,because it is not present at both events, so its time is not a proper time.
But if ct = 10 and x = 8 then x' = 0 and this clock is present at both events so it is a proper clock and it reads proper time. Even if Einstein didn't use those terms.
So a given clock, such as the one at x' = 0, can be proper or not proper depending on the particular events chosen.
This suggests that there are significant differences between '1905' and the theory that you are using, wouldn't you say?
JM

 

[ghwellsjr]

So, no, I don't use other definitions except that to make it easier to understand for novices, I just say, "Proper Time is what any clock measures".

George- Thanks, that clarifies the definitions. So, now consider:
Given: Einsteins 1905 theory, and the Lorentz transforms.
Two events, (y,z = 00, v/c =0.8) first occurs at x,ct = 0,0 and the second at x = 5, ct = 10. The LT shows that ct' = 10. Since this time applies to all clocks of K', the time also applies to the clock at x' = 0. This clock is inertial, but not proper,because it is not present at both events,

True.

so its time is not a proper time.

Not true. You just quoted me as saying that "Proper Time is what any clock measures" so why would you say the time for this clock is not a proper time?

But if ct = 10 and x = 8 then x' = 0 and this clock is present at both events so it is a proper clock and it reads proper time. Even if Einstein didn't use those terms.

True.

So a given clock, such as the one at x' = 0, can be proper or not proper depending on the particular events chosen.

True.

This suggests that there are significant differences between '1905' and the theory that you are using, wouldn't you say?
JM

Do you still think there is any difference besides the insignificant terminology difference using the word "Proper" after fixing your earlier mistake?

 

[Dale]

This suggests that there are significant differences between '1905' and the theory that you are using, wouldn't you say?

No, it doesn't. Why would it?