# B MinutePhysics Special Relativity Series

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1. Feb 2, 2018

### ZapperZ

Staff Emeritus
MinutePhysics is attempting to produce a series of video lessons on Special Relativity, using an approach, according to the video, that will be different and "simpler" than the traditional method that SR has been taught in schools.

Since we often get questions on here about this topic, especially on the consequences of SR postulates such as time-dilation and length-contraction, I thought maybe it is appropriate to present these videos in a thread in this forum. If this material is effective and useful, it can be used to point to new members who often want to learn about SR, but were too afraid to go look for them! :)

The series has just started, so only the intro to the series (Chapter 1) appearing so far. I'll update and post the videos in the series as they appear, or you can subscribe to the Minute Physics channel on YouTube.

Chapter 1

Not sure if you need build that contraption that was shown at the end of the video. It'll be interesting to see how that will be used to illustrate the time-dilation/length-contraction effects.

Zz.

2. Feb 2, 2018

### Staff: Mentor

You should add it to the media library also (before I do)...

3. Feb 2, 2018

### Mister T

Looks promising. Not overly flashy like some of the videos that promise an explanation you'll be able to grasp without understanding the math. The problem is that math forms the foundation so attempts at achieving an understanding by skipping the math are doomed to fail. But that's just the curmudgeon in me talking. Stuff like this has value because it can be used as an aid in understanding the theory, provided you do it along with a proper study of the math. I don't believe the math is an impediment to understanding, rather it's an aid.

I look forward to seeing the whole series of videos, I'm especially intrigued by that machine that appears to be a hyperbola tracer. Geometry!

4. Feb 3, 2018

### vanhees71

I've a very vague idea what this contraption might be, but I've no clue how he wants to use it to explain the affine Minkowski manifold ((1+1) D only of course, but you can explain a lot of SR using only 1+1 spacetime dimensions), but it looks very promising indeed.

Of course the claim that you can do without the "complicated square-root formulae" is much less convincing than introducing some hands-on gadget to illustrate Minkowski spacetime. In my opinion it's didactically wrong to present math as something ugly you have to deal with as with the necessity to swallow some bitter medicine to get well again when you are sick. Math should be presented as fun, helping to solve puzzles! I loved the slogan of the Mathematikum in Giessen, Germany, which is a very successful math museum, founded by a professor of mathematics and math didactics. It's "Mathe macht glücklich", i.e., "Math makes you happy" :-))). It's great to see the big advertisement poster of the museum at the exit of the train station :-))).

Let's see, what comes out of these SR-without-confusing-square-roots videos.

5. Feb 3, 2018

### PeroK

I could probably write an essay about what I don't like about that video. Casting mathematics in the role of the bad guy is especially hard to take. If you're going to turn and run every time you see a square root sign, there's not much future for you in physics or engineering.

My biggest issue is that, although SR is not that hard a subject, it is not that easy either. Teaching methods can help and many modern texts already take the best from a hundred years of academic experience. But, fundamentally, for anyone to learn SR, they are going to have to spend quality time seriously learning the subject matter. It is bound to be a struggle: getting things wrong, getting frustrated, going back to square one and, hopefully, finally getting it.

I would turn his mountaineering analogy round. You could be helicoptered onto the summit of the Eiger, say, but that doesn't make you a mountaineer. You learn nothing about mountaineering from that. There are definitely easier ways up the SR mountain than the one Einstein found, but they all still involve mental mountaineering. With SR, like the Eiger, there is no gentle path to the summit.

6. Feb 3, 2018

### robphy

From timestamp 03:37, the hyperbola tracer looks like a mechanical representation of
the Light-Clock Diamond from my PF insight ( https://www.physicsforums.com/insights/relativity-rotated-graph-paper/ ).
The hyperbolas enforce the preservation of the area of the light-clock diamond (since the determinant of the boost is 1), as well as keep the edges of the diamond lightlike (parallel to the asymptotes of the hyperbola).

In my approach, you never have to write down $\frac{1}{\sqrt{1-\beta^2}}$... unless trying to make contact with standard formulas. But for doing routine relativity problems, you might have to take the square root of an integer that you counted. At the worst, the most complicated square-root you might see is the Doppler formula, involving $k=\sqrt{\frac{1+\beta}{1-\beta}}$... but that's why I write it as $k^2=\frac{1+\beta}{1-\beta}=\frac{\rm{width\ } u}{\rm{height\ } v}$.

Note he uses a rotated grid in the view he shows.
Since he uses a 6x6 grid, he'll probably be able to count diamonds like I do on rotated graph paper.
The 6x6 grid allows simpler calculations since the 36 subunits can be reshaped from 6x6 to 9x4, 12x3, 18x2, 36x1 corresponding to Doppler factors of 1, 3/2, 2, 3, and 6 (speeds of 0, 5/13, 3/5, 4/5, 35/37) which lead to pythagorean triples and, thus, calculations easily done with fractions.

It would be interesting to see if he uses something similar to my diagram for length contraction (comparing the separation between the mirror-worldlines in [say] Alice's frame) and time dilation (comparing the time-component of OF and OT according to Alice).
(It would be more interesting to see if he uses something very different!)

For my diagram (using Light-Clock Diamonds on rotated graph paper) for the Clock Effect/Twin Paradox,
see https://www.physicsforums.com/insights/spacetime-diagrams-light-clocks/ ,
“Relativity on rotated graph paper,” Am. J. Phys. 84, 344-359 (2016); http://dx.doi.org/10.1119/1.4943251 ,
and https://arxiv.org/abs/1111.7254 .

Last edited: Feb 3, 2018
7. Feb 3, 2018

### SiennaTheGr8

Yeah, when I saw that I thought it looked suspiciously similar to @robphy's diamond business. I do wonder if it was the inspiration.

8. Feb 4, 2018

### vanhees71

Very good, so I guess we understand the idea of the contraption now, but (don't get me wrong @robphy, I like your rotated-graph paper approach too) is it a bug or a feature of a didactical approach to SR, if "you never have to write down $\gamma=(1-\beta^2)^{-1/2}$, which is among the most important expressions in GR. As I said earlier, I regard any didactics which diminishes the importance of mastering the adequate math to understand a physical model. In SR, it's really not very much to call for: All the kinematics is, as in Newtonian mechanics, completely explainable with what's taught in the first semester of Linear Algebra at universities, and it's even possible at a level usually also taught at high schools (at least when I went to high school, which I left already in 1990; it may well be that the anti-mathematical opinion of many didactic "experts" got the level down as much that you can't even expect this to be taught at high schools, which would be a clear betrayal of the young generation to have a chance to understand the modern technology based life ;-)).

9. Feb 4, 2018

### robphy

• The use of $\gamma=1/\sqrt{1-v^2}$ arises because of our choice to use the velocity parameter $v$ (which we physicists regard as important).
If instead we used rapidity parameter $\theta$, then $v=\tanh\theta$ and $\gamma=\cosh\theta$... which invites one to import intuition from ordinary trigonometry (although this approach is claimed to be “too advanced”).
(By analogy, if we choose to describe rotations using the slope parameter $m$, we would write expressions like $1/\sqrt{1+m^2}$ and $m/\sqrt{1+m^2}$... but thankfully, we don't)
• The light-clock diamond [the way I use it (and possibly the clever MinutePhysics contraption, as well)] secretly uses light-cone coordinates $u$ and $v$, which uses the eigenbasis of the Lorentz boosts. (By analogy, when studying a set of coupled oscillators, it's useful to study the normal modes of the system.) From a relativity standpoint, the light-clock diamonds emphasize: the invariance of the speed of light (via the edges), the square-interval (via the area), and the causal structure [using the more general notion of a "causal diamond"]. In the velocity-based approach, these have to be features have to be derived. (Radar methods and the Bondi k-calculus implicitly use light-cone coordinates.)
• By the way, in Galilean spacetime geometry with rapidity parameter $\theta_g$ (arc-length along the Galilean-unit-circle),
one has $v=(\rm{GalileanTangent\ of\ }\theta_g )=(\theta_g )$, which says the Galilean-velocities are additive. If we had this realization early on [and felt comfortable enough], we could have followed the route that emphasized angle instead of slope or velocity... leading to trig functions rather than expressions like $\gamma=1/\sqrt{1-v^2}$ in typical presentations of relativity. But, as I often argue [and the MinutePhysics video argues], the introductory presentations of relativity follow Einstein's presentation and notation, rather than say the geometric-spacetime presentation of Minkowski [who is "just a mathematician" ].

Last edited: Feb 4, 2018
10. Feb 27, 2018

### ZapperZ

Staff Emeritus
We are still waiting for MinutePhysics to produce new videos on their Relativity series. But in the meantime, Fermilab's Don Lincoln has produced a video on the things people get wrong with SR's time dilation.

If you have missed it, he has produced at least a couple of other videos related to SR that you should check out.

So c'mon, MinutePhysics! Where are the videos that you promised?!

Zz.

11. Feb 28, 2018

### ZapperZ

Staff Emeritus
Hey, they must have heard my complain (not!), because here's Chap. 2 of this series. :)

Zz.

12. Feb 28, 2018

### robphy

Now awaiting your next complaint to get Chap 3.. (don't wait so long ).

13. Mar 13, 2018

### ZapperZ

Staff Emeritus
Obviously, MinutePhysics is not known for speed in producing their videos, which is kinda ironic considering that they call themselves MINUTE physics!

In any case, Fermilab's Don Lincoln has produced another interesting video. This time, he is arguing that he is giving the REAL explanation that removes the Twin Paradox in Special Relativity, and it doesn't involve any acceleration/deceleration of one twin either!

The math only involves algebra, but you will need to pay attention to assigning who's moving to where, and the sign of the velocity.

Zz.

14. Mar 20, 2018

### Sorcerer

Where is chapter 3? >:(

15. Mar 20, 2018

### Ibix

Time dilated.

16. Mar 21, 2018

### Orodruin

Staff Emeritus
You are saying it is quickly moving towards us?

17. Mar 21, 2018

### Ibix

Or stuck close to a black hole.

18. Mar 21, 2018

### Orodruin

Staff Emeritus
Now don't be silly, the series is on special relativity.

19. Mar 21, 2018

### Orodruin

Staff Emeritus
Perhaps not the snapshot you would expect from a video on SR.

(I know, I am nitpicking ... )

20. Mar 21, 2018

### Sorcerer

My guess is in the next video he is going ro replace “distance” with “spacetime interval.”