B MinutePhysics Special Relativity Series

[ZapperZ]

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.

 

[jedishrfu]

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

 

[Herman Trivilino]

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!

 

[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.

 

[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.

 

[robphy]

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.

I'm especially intrigued by that machine that appears to be a hyperbola tracer. Geometry!

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.

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 .

 

[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.

 

[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 ;-)).

 

[robphy]

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...

Some comments

• 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" ].

 

[ZapperZ]

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.

 

[ZapperZ]

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



Zz.

 

[robphy]

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

Zz.

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

 

[ZapperZ]

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.

 

[Sorcerer]

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



Zz.

Where is chapter 3? >:(

 

[Ibix]

Where is chapter 3? >:(

Time dilated.

 

[Orodruin]

Time dilated.

You are saying it is quickly moving towards us?

 

[Ibix]

You are saying it is quickly moving towards us?

Or stuck close to a black hole.

 

[Orodruin]

Or stuck close to a black hole.

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

 

[Orodruin]

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

(I know, I am nitpicking ... )

 

[Sorcerer]

Perhaps not the snapshot you would expect from a video on SR.
View attachment 222442
(I know, I am nitpicking ... )

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

 

[Sorcerer]

Time dilated.

Post of year ^^

 

[Orodruin]

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

Oh no doubt. I just found it curious.

 

[Sorcerer]

Oh no doubt. I just found it curious.

The decision to do it that way will probably confuse people. But I suppose if he presents it right and they really pay attention it might work. I think he should have specified he was working in the rules of Euclidean geometry. Maybe. Then again maybe that would cause confusion, too.

 

[ZapperZ]

Here's Chapter 3 of the series. This is where he used that thing-ma-jiggy.



Zz.

 

[nitsuj]

I liked their in depth description of a spacetime diagram...an animation would maybe run smoother lol

He calls it a "spacetime globe", globe is a shape and it's not square; I'm sure the rest is accurate though

 

[Orodruin]

He calls it a "spacetime globe", globe is a shape and it's not square; I'm sure the rest is accurate though

”Space-time map” might have worked better. It can illustrate rotations just as well and, like Minkowski space, it is flat. The globe could be saved for GR.

 

[OmCheeto]

The discussions below the video at Youtube inspired me to start learning linear algebra.
This thread in particular:

Holobrine
22 hours ago (edited)

Major sudden realization: The speed of light is the eigenvector of the Lorentz transformation!​

.
.
.
Paulo Bardes
22 hours ago

This is a great sign that this video is a good learning tool. Maybe Henry could do a collab with Grant (from 3blue1brown) to share your realization with those who couldn't see it, or those who don't even know what eigenvectors are exactly. ​

I would fall into the "those who have no idea what an eigenvector is" category.

I wonder if this is why Henry waits so long between video releases? To let all of us slow people catch up?

ps. I'm studying Linear Algebra at the Khan Academy. 142 videos. I think it will take me at least a week. I can't find where they list the time to finish a course, and the 3 hours of videos I watched last night varied between 5 and 25 minutes, so that's just a wild guess.

 

[ZapperZ]

I posted earlier that Fermilab's Don Lincoln did a video explaining the apparent twin paradox, and it had nothing to do with acceleration/deceleration. Turns out a lot of people requested the same explanation, but without using math (if that was possible). So he decided to revisit the explanation, and made another video explaining the twin paradox, but without using any math!



Not sure if this is a clearer or more convincing argument, but I guess it depends on how much you are able to understand what is being shown.

Zz.

 

[Orodruin]

Major sudden realization: The speed of light is the eigenvector of the Lorentz transformation!

Too bad that sudden realisation is wrong. The speed of light is not a vector and the 4-frequency is only an eigenvector of the Lorentz transformation for a pure boost in the direction that the light travels. The eigenvalue is then the Doppler factor.

 

[OmCheeto]

Too bad that sudden realisation is wrong. The speed of light is not a vector and the 4-frequency is only an eigenvector of the Lorentz transformation for a pure boost in the direction that the light travels. The eigenvalue is then the Doppler factor.

In that case, should I stop studying "Linear Algebra"?
It doesn't seem to have many applications down at my level of everyday problem solving, so I've avoided it up until yesterday.
I figure I have about 10 years left before my brain completely gives out, and don't like the idea of wasting what little time I have left.

 

[Orodruin]

In that case, should I stop studying "Linear Algebra"?

Of course not, that was not my point. The conclusion can be correct even if the argument is not. You cannot do physics without linear algebra.

 

[kith]

Does anybody know of a computer simulation which does something similar to minutephysics' time globe?

 

[Orodruin]

Does anybody know of a computer simulation which does something similar to minutephysics' time globe?

Have a look at the Interactive Minkowski Diagrams that @Ibix made at some point: http://ibises.org.uk/Minkowski.html

 

[robphy]

Does anybody know of a computer simulation which does something similar to minutephysics' time globe?

Have a look at my GeoGebra visualization https://www.geogebra.org/m/bFxv6tja
that I used in my Insight https://www.physicsforums.com/insights/relativity-variables-velocity-doppler-bondi-k-rapidity/
(which underlies the methods described in my other Insight https://www.physicsforums.com/insights/relativity-rotated-graph-paper/ ,
which could be described as a pencil-and-paper version of the "spacetime globe" )

 

[ZapperZ]

It is fascinating that as MinutePhysics is embarking on its SR project, Don Lincoln is coincidentally delving into many aspects of SR at almost the same time. So here is another video by him. This time, he's tackling the concept of "length contraction".



Zz.

 

[SiennaTheGr8]

Speaking of which:

 

[ZapperZ]

Still waiting for the next chapter for the MinutePhysics series. In the meantime, Don Lincoln continues with his own series on Special Relativity, and his new video appeared today. This time, he tackles velocity addition.



Zz.

 

[SiennaTheGr8]

As soon as I saw the subtitle of the video I knew he'd make the error he makes at 6:11, when he talks about observers traveling toward each other at the speed of light. The "1 + 1 = 1" business is just wrong. It's really "$1 \pm \, v = 1$," with $0 \leq v<1$:

$\dfrac{1 + v}{1 + (1)(v)} = 1$

and

$\dfrac{1 - v}{1 - (1)(v)} = 1$,

where the latter equation explicitly rules out $v = 1$.

 

[ZapperZ]

This is Chapter 5 of the MinutePhysics SR series.



Zz.

 

[ZapperZ]

Here's Chapter 6 of MinutePhysics's Special Relativity lessons. This time, they are tackling something that we get asked about on here ad nauseum - relativistic velocity addition.



Zz.

 

[ZapperZ]

Chapter 7 of MinutePhysics's Special Relativity lesson. This time, it tackles on what is meant by spacetime intervals.



Zz.

 

[David Lewis]

Don Lincoln is coincidentally delving into many aspects of SR at almost the same time. So here is another video by him. This time, he's tackling the concept of "length contraction".

Don said: "If you start with a basketball, and accelerate it at high speed, it'll look like a pancake."

It will be shaped like a pancake but unless you're very close to it, the basketball will look spherical, and rotated way from you.

 

[Nugatory]

Don said: "If you start with a basketball, and accelerate it at high speed, it'll look like a pancake."

It will be shaped like a pancake but unless you're very close to it, the basketball will look spherical, and rotated way from you.

Everyone watching/reading this thread has to be aware that in this context the word "look" has to be taken literally - it's what you'll actually see based on light traveling to your eye along paths of different lengths from different points on the object.

 

[ZapperZ]

Chapter 8 of MinutePhysics's Special Relativity lesson. This time it is on the Twin Paradox, and he uses the thingmajiggy to illustrate the concept.



You may supplement this video with the one done by Don Lincoln a while back that tackled the same topic and using the same explanation.



Zz.