A Geometrical View of Time Dilation and the Twin Paradox - Comments

[PeterDonis]

I think that there is unrecognized value in seeing that an outbound (non-returning) observer sees Earth clock running slow, later synchronizes his "ahead" clock with an inbound clock, then watches the inbound clock go from being ahead to being behind Earth do to the greater inbound vs. outbound relative velocity.

But the single traveling twin doesn't do this. He just goes out, comes back, and never adjusts his clock at all during the whole trip--yet when he comes back, his clock has less elapsed time than his stay-at-home twin. So it seems to me that your "explanation" is introducing extraneous factors that aren't there in the original scenario. That seems more likely to confuse than to enlighten a person who is struggling to understand the scenario.

Doing this in all three observer rest frames and getting the same clock skew I think is compelling to a beginner, and the concept of proper time was not even needed or required.

Have you ever actually tried this? Has it worked?

 

[the_emi_guy]

But the single traveling twin doesn't do this. He just goes out, comes back, and never adjusts his clock at all during the whole trip--yet when he comes back, his clock has less elapsed time than his stay-at-home twin. So it seems to me that your "explanation" is introducing extraneous factors that aren't there in the original scenario. That seems more likely to confuse than to enlighten a person who is struggling to understand the scenario.

Sure, the two observer problem statement is simpler (2 < 3), but the explanation seems to be a stumbling block for many (thus the existence of this very thread). And even if they learn how to draw the diagrams, they may not have an intuitive feel for what is going on. Again, I am sharing that there is a way to introduce the clock skew phenomena in a way that does not require proper time, Minkowsky diagrams, etc. As soon as a student gets time dilation he/she can discover and understand clock skew behavior with three observers.

Have you ever actually tried this? Has it worked?

You have never heard of this approach? I thought it was fairly well known.
Section 4 of the attached journal is one reference and begins:

"In this section we will demonstrate a method that can be used in the “clock paradox” problem without the need to consider the effects of various accelerations and decelerations, at least in principle. Such a method was first proposed by Lord Halsbury in 1957 [17], as a “triplet” or a “three clocks” problem, and can be briefly stated as follows..."

 

[PeterDonis]

but the explanation seems to be a stumbling block for many (thus the existence of this very thread)

This thread is about Orodruin's post describing the geometric method, which, as he says, he uses to teach the subject.

You have never heard of this approach? I thought it was fairly well known.

I don't mean solving the problem yourself; of course that can be done. I mean using it to teach someone else. That's what you're claiming: that your approach will work better for teaching. Have you tried that? Has it worked?

 

[Dale]

On the other hand, the "traveling" twin is undergoing acceleration bringing him into a different inertial frame. This is outside the scope of SR unless we assume a non-physical observer

I disagree with both of these sentences.

In the first, no object goes into or out of any frame. All objects or observers are in every frame at all points of the journey. An object may be at rest in one frame and moving in another, but it is in both frames.

In the second, SR applies as long as gravity is negligible (spacetime is flat). An accelerating observer is certainly within the scope of SR.

 

[Orodruin]

Again, I am sharing that there is a way to introduce the clock skew phenomena in a way that does not require proper time, Minkowsky diagrams, etc.

This to me is counter productive for the real understanding of SR, which should be the actual goal. You will still require the use of the Lorentz transformations, the application of the relativity of simultaneity, etc. This completely defeats the pedagogical purpose as it is essentially just giving the formulas and letting the student figure out their meaning. It is like giving a student the formula for the coordinate change due to a rotation and expect them to figure out the rest.

Proper time and Minkowski diagrams are fundamental tools in understanding SR. You should teach them, not try to sweep them under the carpet.

 

[greswd]

But exactly here lies the problem. I am not arguing that the coordinates are abad idea, I just question the pedagogical value to people who are just learning relativity. I do not see the point of introducing non-inertial coordinate systems on top of the struggles they already have.

That's true. But the moment they understand time dilation, they will demand to know things from the traveling twin's perspective.