A delightful quirk of relativity theory • Hacker News Board

Re: A delightful quirk of relativity theory

#21

Post by irthomasthomas » Tue, Jan 18, 2022, 11:54 AM UTC

This would be more fun in a blog post. Twitter is a fucking horrible format for a complex analysis of special relativity.

That aside, my favourite quirk from relativity is this:

  "The more you move in space, the less you move in time."

Like relativity in general, it sounds simple enough, but it's consequences are profoundly shocking. (That is, if you take the time to understand it, and don't leap to the conclusion that you know relativity better than Einstein or Penrose ;)

Take the case of two people on Earth, one stationary and one travelling past in a car. They each have a different reference frame, and a different set events which make up their present. Now imagine that there is an alien government in Andromeda debating a possible invasion of Earth. In the reference frame of the person on Earth who is moving, the debate is still going on. But, in the reference frame of the stationary person, it is a day or so later in Andromeda, and the invasion fleet is already on it's way! In nature there is no absolute reference frame we can call base reality, and both observers reference frames are equally valid. Then the outcome of the invasion debate is a foregone conclusion. How can there be any room for free will in the deliberations of the alien government? This is the crux of the Andromeda Paradox and the Reitdijk-Putnam-Penrose argument.

BTW:

  "Notice that neither observer can actually "see" what is happening in Andromeda, because light from Andromeda (and the hypothetical alien fleet) will take 2.5 million years to reach Earth. The argument is not about what can be "seen"; it is purely about what events different observers consider to occur in the present moment."

https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argume...

More info https://en.m.wikipedia.org/wiki/Relativity_of_simultaneity

Edit: If you know of any serious alternatives to the 4D spacetime/ block universe theory then I would love to read it. Rescuing free-will from the jaws of spacetime would be cool!

Re: A delightful quirk of relativity theory

#22

Post by 300bps » Tue, Jan 18, 2022, 11:58 AM UTC

enriquto wrote: post #18

soneca wrote: post #12

Earlier quoted context omitted.

Twitter threads don’t bother me. The brain quickly adapts to skipping the irrelevant parts (username, like buttons, etc) and to expecting the cadency of tweets. I believe it is harder to write (due to the character limit of each text block), but, far from “unreadable”, I can read it fairly easily.

Oh, I don't bother by the stupidly repeated usernames and dates. I just want to read the damn thing. But it is literally unreadable to me. I couldn't finish reading the thread and had to find an alternative way out of twitter. Fist trial, using my android phone with fennec fox. There is a modal that hides the content asking me to "log in"; if I close the modal I go back to the twitter homepage. Thus unreadable becaus…

For what it’s worth, I clicked on the HN link on my iPhone and it opened in the Twitter app (that I never use) and it was extremely readable. Literally no problems reading it at all.

Re: A delightful quirk of relativity theory

#23

Post by Ma8ee » Tue, Jan 18, 2022, 12:00 PM UTC

irthomasthomas wrote: post #21

This would be more fun in a blog post. Twitter is a fucking horrible format for a complex analysis of special relativity. That aside, my favourite quirk from relativity is this: "The more you move in space, the less you move in time." Like relativity in general, it sounds simple enough, but it's consequences are profoundly shocking. (That is, if you take the time to understand it, and don't leap to the conclusion tha…

Isn't the whole point that talking about "the present moment" about something very far away isn't particularly meaningful when simultaneity for spatially separated events depends on the observer?

Re: A delightful quirk of relativity theory

#24

Post by stared » Tue, Jan 18, 2022, 12:00 PM UTC

In the topic of special relativity, I wholeheartedly recommend recently published "Unusually Special Relativity| by Andrzej Dragan (https://www.amazon.com/Unusually-Special-Relativity-Andrzej-...). It starts from basic high-school mathematics but covers many paradoxes and puzzles. Some might challenge ordinary students, who know the formula but didn't stretch their minds on "what if" questions. It includes cases where velocity is higher than the speed of light - as there are a few caveats on "nothing can travel faster than light".

Also, this "velocity addition for vI read its draft almost 20 years ago (back then, it was a collection of notes in Polish) and didn't find anything remotely close to it in English. Later, I had the pleasure of attending his course.

Also, Andrzej Dragan is a notorious individual, primarily known in photography (https://andrzejdragan.com/). To the point that there are posts on "how to Draganize a picture".

Re: A delightful quirk of relativity theory

#25

Post by alfiedotwtf » Tue, Jan 18, 2022, 12:02 PM UTC

acadapter wrote: post #10

enriquto wrote: post #4

I love the name of the scientist Al Unapietra. The thing is very well explained, but it's very sad to see it as a twitter thread, which is a mostly unreadable format.

Twitter threads are in general a very sad successor of the blogosphere.

Sure, but you can't knock it for the speed at which cool info like this thread spread

Re: A delightful quirk of relativity theory

#26

Post by alfiedotwtf » Tue, Jan 18, 2022, 12:06 PM UTC

MattPalmer1086 wrote: post #8

Lovely explanation. Builds up from simple angles and suddenly makes what seemed weird in relativity actually kind of obvious. I particularly like how the model you choose to describe things can make the same phenomenon easy or hard to understand.

My favourite example of this is planet epicycles vs ellipses around the Sun :)

Re: A delightful quirk of relativity theory

#27

Post by elcomet » Tue, Jan 18, 2022, 12:08 PM UTC

irthomasthomas wrote: post #21

This would be more fun in a blog post. Twitter is a fucking horrible format for a complex analysis of special relativity. That aside, my favourite quirk from relativity is this: "The more you move in space, the less you move in time." Like relativity in general, it sounds simple enough, but it's consequences are profoundly shocking. (That is, if you take the time to understand it, and don't leap to the conclusion tha…

You can check https://unrollthread.com/t/1482811504424542211/ to view it as a blog post

Re: A delightful quirk of relativity theory

#28

Post by d-d » Tue, Jan 18, 2022, 12:08 PM UTC

doctoboggan wrote: post #15

I like this, but it doesn't completely remove the "unintuitivenes" of relativity. For example, why do we measure in fractions of light speed? What happens when we are already rotated all the way to light speed and then fire another bullet? I guess there are other ways to reason about this, but it still doesn't feel intuitive to me.

No post body was provided.

Re: A delightful quirk of relativity theory

#29

Post by messe » Tue, Jan 18, 2022, 12:11 PM UTC

An interesting quirk of this, is that the description of the path of a particle under constant proper acceleration in special relativity is mathematically very close to that of a simple harmonic oscillator.

Now, just as you can use rotation in the complex plane (i^2 = -1) to describe a simple harmonic oscillator in 2D space,

    x + iy = e^(it)

It's possible to use a rotation in the split-complex plane[1] (j^2 = 1) to describe the motion of a particle undergoing constant proper acceleration,

    x + jt = e^(ajτ)/a - 1           [2]

This is because multiplying by e^(jτ) preserves the split-complex modulus (|x+jt|^2 = (x + jt)(x - jt) = x^2 - t^2), which is equivalent to the Minkowski norm. Expanding the above gets you,

    x = cosh(aτ)/a - 1
    t = sinh(aτ)/a

which are the more traditional expressions you would typically see.

[1]: https://en.wikipedia.org/wiki/Split-complex_number

[2]: There's a line of reasoning that allows you to write this down almost immediately, or in maths-speak makes it trivial, but I can't remember it at the moment. I spent a good deal of time thinking about this for a university assignment years ago in order to avoid spending 2 minutes doing an integral.

Re: A delightful quirk of relativity theory

#30

Post by thesz » Tue, Jan 18, 2022, 12:12 PM UTC

formerly_proven wrote: post #17

thesz wrote: post #14

I cannot help but add a reference to a conformal geometric algebra here: https://en.wikipedia.org/wiki/Conformal_geometric_algebra Why? Because it describes movement as rotation from the infinitely far away point (a special basis vector there). And "coordinates" there are somewhat self-normalizing, because there is a special basis vector that keeps coordinates' squares. And, of course, it is investigated as a tool to…

> Because it describes movement as rotation from the infinitely far away point Doesn't this also work in normal geometry as the length of a translation goes to zero and the distance to the rotation's origin goes to infinity... because a big circle looks like a straight line up close?

Exactly. CGA has special point e_{inf} which is infinitely far away from any other regular point (with regular euclidian coordinates) and linear movements are rotations around that point.