Andrzej Dragan's "Course on Relativity" Videos | YouTube Playlists

[robphy]

Andrzej Dragan ( https://www.fuw.edu.pl/~dragan/ )
has a "Course on relativity" on YouTube.

https://www.youtube.com/c/relaTVty/playlists


I'm not familiar with Dragan... but the videos display some flair and personality.
( https://www.vice.com/en/article/nz4nyx/meet-the-filmmaker-exploring-physics-with-haunting-vfx )
( https://www.wired.co.uk/article/quantum-theory-speed-light-dragan
( https://andrzejdragan.com/ , his artistic side )

I'm not sure of the effectiveness of his pedagogical approach
... but he certainly is working toward his research viewpoint.
I have some healthy skepticism. ... so I don't think I'd recommend it for beginners. (I labeled this thread "I" (not "B").)

There's a blend of pop-sci and some detailed calculations on a tablet... but you'll have to go elsewhere for more details and rigor.
I like the deep-fake talking heads.

Apparently he has new book, Unusually Special Relativity ,
https://www.amazon.com/dp/1800610807/?tag=pfamazon01-20
( there is a course by the same name http://informatorects.uw.edu.pl/en/courses/view?prz_kod=1100-2`NSTW
which has a broken link to lecture notes.
However, http://web.archive.org/ reveals a versions of notes in Polish with 101 pages (2004), 109 pages, and 206 pages. )

The videos are interesting enough for me to watch...
but with some healthy skepticism, as I said earlier.
I need to see more details.
I would be curious to the see the new book... (no time to try to Google-translate the parts of the lecture notes).

My $0.02.

 

[vanhees71]

Just looking on the first pages on Amazon, I'd not recommend the book, because to use the $\mathrm{i} c t$ convention is hopelessly outdated nowadays. You have to unlearn this nuissance anyway again sooner or later (at the latest when you want to learn general relativity).

 

[robphy]

He started with the ict in the beginning of the video (insert record-scratch sound),
probably to motivate "rotation" using the ordinary circular trigonometric functions,
then moved to real-variables with hyperbolic trigonometry. (whew!)
I presume this happens in the book as well... but I haven't looked.

 

[weirdoguy]

because to use the convention is hopelessly outdated nowadays.

He is not using it in general during his lectures. I didn't attend his SR lectures but he did teach my relativistic quantum mechanics class and I have quite good memories

However, http://web.archive.org/ reveals a versions of notes in Polish with 101 pages (2004), 109 pages, and 206 pages. )

I've read those notes back in 2010 and I would recommend them, it's quite an alternative way of teaching SR. His lectures were really popular.

 

[Sagittarius A-Star]

Andrzej Dragan is a Polish physicist and photographer.
Source (in German):
https://de.wikipedia.org/wiki/Andrzej_Dragan

He derives a Lorentz-transformation that allows superluminal speed in his video Why do we need FASTER-THAN-LIGHT observers. Here is a related publication:

Why devil plays dice?

Andrzej Dragan

Institute of Theoretical Physics, University of Warsaw, Hoza 69, 00-681 Warsaw, Poland

Principle of Relativity involving all, not only subluminal, inertial frames leads to the disturbance
of causal laws in a way known from the fundamental postulates of Quantum Theory. We show
how quantum indeterminacy based on complex probability amplitudes with superposition principle
emerges from Special Relativity.

Source:
https://archive.org/details/arxiv-0806.4875/mode/2up

 

[vanhees71]

The link to the real arXiv shows that this preprint seems not to be published:
https://arxiv.org/abs/0806.4875

 

[Sagittarius A-Star]

In the video I linked, the following paper is mentioned:

Quantum principle of relativity

Andrzej Dragan, Artur Ekert

Abstract
Quantum mechanics is an incredibly successful theory and yet the statistical nature of its predictions is
hard to accept and has been the subject of numerous debates. The notion of inherent randomness,
something that happens without any cause, goes against our rational understanding of reality. To add
to the puzzle, randomness that appears in non-relativistic quantum theory tacitly respects relativity,
for example, it makes instantaneous signaling impossible. Here, we argue that this is because the
special theory of relativity can itself account for such a random behavior. We show that the full
mathematical structure of the Lorentz transformation, the one which includes the superluminal part,
implies the emergence of non-deterministic dynamics, together with complex probability amplitudes
and multiple trajectories. This indicates that the connections between the two seemingly different
theories are deeper and more subtle than previously thought.

Source:
https://iopscience.iop.org/article/10.1088/1367-2630/ab76f7/meta

 

[Sagittarius A-Star]

He started with the ict in the beginning of the video (insert record-scratch sound),
probably to motivate "rotation" using the ordinary circular trigonometric functions,
then moved to real-variables with hyperbolic trigonometry. (whew!)
I presume this happens in the book as well... but I haven't looked.

Yes. According to the preview in Google books, this happens in the book as well.

$\tau \equiv ict$

$$\Delta \tau^2 + \Delta x^2 + \Delta y^2 + \Delta z^2 = \Delta \tau'^2 + \Delta x'^2 + \Delta y'^2 + \Delta z'^2$$
... If we assume that at $t = t' = 0$ the origins of both reference frames coincided, then the rotation must take the following form:
$$(1.5) \begin {cases}
\tau' = \tau \cos \Theta + x \sin \Theta = \frac{\tau}{\sqrt{1+\tan^2 \Theta}} + \frac{x \tan \Theta}{\sqrt{1+\tan^2 \Theta}} \\
x' = x \cos \Theta - \tau \sin \Theta = \frac{x}{\sqrt{1+\tan^2 \Theta}} - \frac{\tau \tan \Theta}{\sqrt{1+\tan^2 \Theta}}
\end {cases}$$
... From the cop's perspective that point is moving away with the velocoty $V$ along the $x$ axis according to the formula $x = V t$. Plugging that into the second equation (1.5) we obtain
$$x'= 0 \Rightarrow \frac{x}{\tau} = \frac{x}{ict} = \frac{V}{ic} = \tan \Theta$$
... After replacing $\tau$ with $ict$ we get
$$(1.7) \begin {cases}
t' = \frac{t - Vx/c^2}{\sqrt{1- V^2/c^2}} \\
x' = \frac{x - Vt}{\sqrt{1- V^2/c^2}}
\end {cases}$$

Source (with Chrome browser):
https://books.google.de/books?id=BI...=gbs_selected_pages&cad=2#v=onepage&q&f=false

Then he moves (via $\sin \Theta = -i \sinh i\Theta$, $\cos \Theta = \cosh i\Theta$ and substituting $\delta = i \Theta$) to hyperbolic trigonometry and derives the construction of the Minkowski diagram.

For didactic reasons, I like this approach. The normal rotation is more intuitive than the hyperbolic rotation. I find this even more intuitive than the fastest derivation of the Lorentz transformation.

 

[vanhees71]

I find it very unintuitive to introduce imaginary numbers in a real vector space. It's making everything more complicated, and it has to be "unlearned" as soon as you like to go on with general relativity. One should emphasize that Minkowski space is utterly different from a Euclidean affine manifold rather than hiding it with some trick.

 

[Sagittarius A-Star]

It's making everything more complicated, and it has to be "unlearned" as soon as you like to go on with general relativity.

He is doing the "unlearning" directly afterwards, in the 2^nd sub-chapter "1.2 Motion as a Hyperbolic Rotation of Spacetime". To see both, helps also to understand the analogies and differences between normal rotation and hyperbolic rotation.

He does not propose to change the physical unit system to an imaginary ratio between "1 meter" and "1 second", as H. Minkowski did at the end of his chapter IV.

 

[robphy]

Indeed… the subject is not intuitive.
In any new topic, we have to “unlearn” certain aspects of what we learned and refine them.

I think Dragan uses that approach because “rotation” is an important concept to him and his research. I think his opening statements suggested that.

Others might use a different point of emphasis and craft a storyline around that. (For example, I would lean more on causality, operational definitions, and geometry. Others prefer to lean on “transformations”. Others look at relativity as “corrections” to everyday common sense.)

 

[robphy]

From the Cayley-Klein(projective geometry) view and the use of complex numbers (and its hypercomplex analogues), Euclidean geometry uses complex numbers and so-called dual-numbers (https://en.m.wikipedia.org/wiki/Dual_number).

For Euclidean geometry, the complex numbers are associated with the signature and the dual numbers are associated with the affine structure.

But, yes, it is not intuitive (partly because of how our intuitions are developed).

 

[Sagittarius A-Star]

I think Dragan uses that approach because “rotation” is an important concept to him and his research. I think his opening statements suggested that.

I find this "rotation" approach for deriving the Lorentz transformation from the Minkowski metric more elegant than how it is done in the book Spacetime Physics (Taylor & Wheeler), regardless, which mathematical notation is used (complex numbers and normal trigonometric functions vs. real numbers and hyperbolic trigonometric functions).

In Taylor & Wheeler, they use as an intermediate step the time dilation formula (L-3) and "This leads to the rather cumbersome result" (before L-7).