Relativity on Rotated Graph Paper - Comments

[robphy]

robphy submitted a new PF Insights post

Relativity on Rotated Graph Paper

Continue reading the Original PF Insights Post.

 

[Dale]

Do you know if anyone has used this approach in an introductory relativity class?

 

[robphy]

As far as I know, I am the only one who has tried it in a relativity class or in an intro class (calc-based and algebra-based) discussing the topic of relativity. I have used the clock diamonds... But not the fancier causal diamond methods (yet).

 

[Dale]

How well did you feel that it worked? Did it help the students gain an intuition for SR?

 

[robphy]

While I haven't done any detailed surveys or pre-/post-exams...,

I feel that this method does a better job of motivating and explaining relativity
over approaches that rely heavily on the Lorentz transformation formulas and other formulas (time-dilation, length-contraction,...).
(In a formulaic approach, the problem [for the students] seems to boil down to determining which quantities are primed and which are unprimed.)

In my opinion, constructing the diagram emphasizes the operational interpretation of relativistic quantities... with minimal mathematical requirements for the end user.
I like to think of it as a "physics first, [Lorentz Transformation] formulas later".
Then, having a completed diagram encodes many "tangeable" features that could be used for further discussion and elaboration [reinterpreted with standard formulas, if desired].

Hopefully, this helps make it easier to draw and interpret spacetime diagrams.

 

[pervect]

I've noticed many PF posters seem to have difficulties in drawing space-time diagrams (or perhaps it's just reluctance?). I'm not sure how to interpret this. I often suggest drawing time lines of events as a warm up exercise, hopefully that is a familiar exercise that will get across the abstract notion that one not only can draw a diagram that represents time, one has probably already done so in the past. I'm not sure if anyone has ever taken me up on my suggestion though, or if it's helped any.

It doesn't seem like much of a leap to go from drawing time-lines to drawing space-time diagrams, but I suspect the later seems harder than the former.

The end goal (as I see it) is to lead the reader to the realization that every event in space-time, aka "reality", is represented by one point on the space-time diagram, and that this is true no matter whose perspective the diagram is drawn from. This doesn't seem too outlandish, or hard, but it does involve the notion of one-one correspondences between infinite sets. Maybe it's the lingering (and perhaps somwhat justified) fear that there are non-intuitive aspects to infinite sets that causes the difficulties? I really don't know for sure, I suppose that it's something that would take a lot of 1:1 private converstations to get an appreciation of the issues - it's just too difficult to get anyone to talk about what they don't understand in a public forum.

 

[robphy]

It seems that students generally don't draw useful diagrams: position-vs-time graphs or free body diagrams. Rather they try to reason with words, with possibly flawed intuition (especially on non-intuitive situations), and with formulas awaiting input. If a diagram is drawn, it's usually more of a cartoon rather than a diagram approximating the geometry of the situation.

For Relativity, I think not knowing where the tickmarks adds an additional obstacle. This is what motivated my approach.

 

[Greg Bernhardt]

Great Insight @robphy!

 

[hamideh]

your approach is very beautiful and motivates me to think of using it for other areas
thanks

 

[vanhees71]

I've noticed many PF posters seem to have difficulties in drawing space-time diagrams (or perhaps it's just reluctance?). I'm not sure how to interpret this. I often suggest drawing time lines of events as a warm up exercise, hopefully that is a familiar exercise that will get across the abstract notion that one not only can draw a diagram that represents time, one has probably already done so in the past. I'm not sure if anyone has ever taken me up on my suggestion though, or if it's helped any.

I can draw Minkowski diagrams, but I never found them very helpful compared to just using the formulae, based on the covariant Minkowski-space formalism. My main trouble with Minkowski diagrams is that I have to forget the intuition we are used to from elementary school on interpreting the "paper plane" as a Euclidean plane.

 

[robphy]

I can draw Minkowski diagrams, but I never found them very helpful compared to just using the formulae, based on the covariant Minkowski-space formalism. My main trouble with Minkowski diagrams is that I have to forget the intuition we are used to from elementary school on interpreting the "paper plane" as a Euclidean plane.

In my opinion, one has to refine (or relax) one's intuition since
some features (e.g. incidence, parallelism, and scaling) are common to Euclidean and Minkowski geometries...
and some features (e.g., "circles", tangency to "circles" as "perpendicular" to radii, "angle"="arclength"/"radius") are analogous
and some features (e.g., sum of the angles in a triangle = 180 degrees) have to be discarded.

Do you find it useful to draw position-vs-time graphs (Galiliean space-time diagrams) when doing PHY 101 kinematics problems?

 

[vanhees71]

It's useful to draw such graphs. Also Minkowski diagrams can be useful to visualize the results of algebraic calculations, but indeed as you say, you have to get used to them.

 

[houlahound]

thank you for the great insight.

is the article;

Am. J. Phys. 84, 344-359 (2016); http://dx.doi.org/10.1119/1.4943251

Reference https://www.physicsforums.com/insights/relativity-rotated-graph-paper/

the same article posted here?

it is a pay per view as far as I can tell. I would like to download it in a more readable format ie printable.

 

[robphy]

Thanks.
That Insight and the earlier one describe key features of my AJP paper. Details are in the paper. There is an earlier draft at
http://arxiv.org/abs/1111.7254

The post below describes the major changes since that draft version.

https://www.physicsforums.com/threa...of-light-clocks-comments.875884/#post-5502068

 

[houlahound]

thanks, i think i will to open an account at the site and buy the full paper.

 

[robphy]

I recently gave a talk at the 2016 MAA MathFest.
My slides have been posted here (at the session organizer's website)
https://www.framingham.edu/faculty/smabrouk/Maa/mathfest2016/tcps9/
and the GeoGebra files I created for the presentation are available here
https://www.geogebra.org/m/HYD7hB9v#

The last GeoGebra file features a tool to draw clock diamonds along segments
so that one can more easily visualize the proper-time along timelike piecewise-inertial segments.