Value of this 'Science' Channel as quick intro

[D.S.Beyer]

TL;DR

Is this youtube channel offering solid information : ScienceClic English

I found, what appears to be, a good channel on General Relativity and other science topics.



I'm dubious because... the internet.

I'd love a second opinion on whether this channels first few videos on The Maths of General Relativity are doing it justice.
I'm a dad with a day job and I can't take a physics class right now, so little videos like this are awesome for me... but not if they are leading me down the wrong path. I want to learn the math, so I want to know if this is an okay place to start.

The only reason I even considered posting this here is because in video 3 he starts explaining Christoffel symbols, and at that point I thought, "Maybe this is the real deal. Better double check with the team."

Also, any other suggestions of similar videos, or books, that I can digest after chasing a toddler around are appreciated.

 

[PAllen]

I looked at the video you posted, and it looked pretty good, except for the somewhat controversial notion of speed through spacetime.

It appears the author is a grad student in physics with an interest in general relativity.

As for other possible videos, I would recommend Leonard Susskind’s. He is a top physicist with many years experience teaching GR. Just google “susskind general relativity” to find his YouTube lectures.

[add: I looked a little at the second video and saw he proceeds further with the notion of speed through spacetime. I won’t quite say this notion is wrong, but many of us here find it leads to misunderstandings, and is wholly inessential. You will not find it in any of the major textbooks on GR, or, for that matter, mentioned anywhere by Einstein. For those reasons, I would suggest other videos, e.g. Susskind’s.]

 

[vanhees71]

What's "speed through spacetime"? I've never heard this expression, and I've not the time to watch videos (I'm a bit oversaturated with talks given via Zoom conferences anyway; it's better than not having the talk but it's no substitute for real-world live talks...).

 

[martinbn]

What's "speed through spacetime"? I've never heard this expression, and I've not the time to watch videos (I'm a bit oversaturated with talks given via Zoom conferences anyway; it's better than not having the talk but it's no substitute for real-world live talks...).

I think it comes from geometry. If you have a curve in a (pseudo)Riemannian manifold, the tangent vector is often called the velocity, and the length the speed, even in pure geometric questions with no machanics in sight. When you have a world-line in space-time you get expresions as "the speed in space-time". And with the usual parametrisation for time-like curves you get "in space-time everithing travels at the speed of light". All this is just my guess, I didn't watch the video.

 

[vanhees71]

Argh, yes. I've seen this in some popular-science book. I think it's rather confusing than helpful.

So it's the "proper four-velocity", $U^{\mu} =c u^{\mu}$ with $u_{\mu} u^{\mu}=1$, of a massive particle. It's $U^{\mu}=\mathrm{d}_{\tau} x^{\mu}$ with $\tau$ the proper time of a massive particle, $\mathrm{d} \tau^2=g_{\mu \nu} \mathrm{d} x^{\mu} \mathrm{d} x^{\nu}/c^2$.

 

[robphy]

Argh, yes. I've seen this in some popular-science book. I think it's rather confusing than helpful.

So it's the "proper four-velocity", $U^{\mu} =c u^{\mu}$ with $u_{\mu} u^{\mu}=1$, of a massive particle. It's $U^{\mu}=\mathrm{d}_{\tau} x^{\mu}$ with $\tau$ the proper time of a massive particle, $\mathrm{d} \tau^2=g_{\mu \nu} \mathrm{d} x^{\mu} \mathrm{d} x^{\nu}/c^2$.

With this formulation (which I agree with... *),
the corresponding quantity appears in a Galilean Spacetime diagram [a.k.a. The ordinary position-vs-time diagram with the implicit and underappreciated Galilean degenerate temporal metric with signature (+,0,0,0).]. In that case, the “c” is just a convenient unit of velocity—-not an upper bound of speeds.

So, although it seems to introduce something new kinematically to distinguish Special relativity from Galilean relativity...
this particular feature of “speed through spacetime” really doesn’t distinguish special relativity...
...other than elevating the important finite speed in special relativity...and suggesting that Galilean relativity should be reformulated with similar affine-geometrical structures.
update:
This however does introduce a new misconception or unnecessary confusion with the fact that
the spatial-velocity of light (essentially the slope of light's 4-momentum) is c
and
that massive particles can have their 4-velocities (unit tangent vectors) normalized to c.*I’d prefer “dimensionful velocity” since I have heard the term “proper velocity”, which is associated with “celerity” (the spatial component of the 4-velocity”). I was not aware of “proper 4-velocity”.

update:
[Some might reserve "metric" to be Riemannian ( vs pseudo-Riemannian) or to be invertible (vs possibly-degenerate). Degeneracy implies that additional structures are needed to approach the features of the nondegenerate case... but it's not all bad. [Euclidean geometry is degenerate from a projective-geometric viewpoint.] ]

 

[vanhees71]

In fact, I don't know whether this quantity has a commonly used name at all. It's of course momentum divided by $m c$ (with $m$ the invariant mass of the particle).

 

[robphy]

Also, any other suggestions of similar videos, or books, that I can digest after chasing a toddler around are appreciated.

Although he doesn't have fancy animated graphics,
https://www.youtube.com/user/eigenchris/playlists
( https://www.youtube.com/user/eigenchris/videos )
is pretty good.

 

[robphy]

I looked at the video you posted, and it looked pretty good, except for the somewhat controversial notion of speed through spacetime.

...snip...

[add: I looked a little at the second video and saw he proceeds further with the notion of speed through spacetime. I won’t quite say this notion is wrong, but many of us here find it leads to misunderstandings, and is wholly inessential. You will not find it in any of the major textbooks on GR, or, for that matter, mentioned anywhere by Einstein. For those reasons, I would suggest other videos, e.g. Susskind’s.]

Ugh... this is from an older video called "We all move at the Speed of Light".

The description of light in this video's diagram suggests that at &t=7m19s
the diagram shown is not a spacetime diagram...
but a velocity dial of some kind.
The "time axis" is probably some kind of "proper-time axis"... definitely not a spacetime diagram.

Light travels along the light-cone, which is at 45 degrees on a spacetime diagram.



Maybe the more recent videos have improved...

 

[D.S.Beyer]

Ugh... this is from an older video called "We all move at the Speed of Light".

The description of light in this video's diagram suggests that at &t=7m19s
the diagram shown is not a spacetime diagram...
but a velocity dial of some kind.
The "time axis" is probably some kind of "proper-time axis"... definitely not a spacetime diagram.

Light travels along the light-cone, which is at 45 degrees on a spacetime diagram.



Maybe the more recent videos have improved...

Right.
He's got other videos that are even more dubious, and deserve entire threads unto themselves to unpack the problems. Such as this one

I would love to talk about that video specifically, in depth, but first I wanted to brush up on the math before I started calling out proper-length 2d+1 problems etc. Hence, first starting with the critique of these 'math' videos.

Thanks for all your attention to this. This community really helps me get a deeper understanding of things.
I'm really trying to slow down with my questioning and take things step by step these days.

 

[PeterDonis]

What's "speed through spacetime"? I've never heard this expression

Lucky you. I would strongly suggest not reading any further in this thread, in order not to contaminate your mind.

 

[A.T.]

Ugh... this is from an older video called "We all move at the Speed of Light".

The description of light in this video's diagram suggests that at &t=7m19s
the diagram shown is not a spacetime diagram...
but a velocity dial of some kind.
The "time axis" is probably some kind of "proper-time axis"... definitely not a spacetime diagram.

Light travels along the light-cone, which is at 45 degrees on a spacetime diagram.

Yes this looks like a space-propertime diagram, where the path length is the coordiante-time. So when parameterized by coordiante-time, everything advances in space-propertime at the same rate (to avoid the "speed in spacetime" terminology).

 

[PeterDonis]

this looks like a space-propertime diagram

Which breaks down, along with the whole "speed through spacetime" thing, as soon as you consider cases like the "twin paradox" scenario, where you have two different objects that return to the same point in space with different proper times. (For an especially fun version of this, consider the even simpler case of a light ray bouncing off a mirror and returning to its starting point.)

 

[A.T.]

Which breaks down, along with the whole "speed through spacetime" thing, as soon as you consider cases like the "twin paradox" scenario, where you have two different objects that return to the same point in space with different proper times.

For the "twin paradox" the space-propertime diagram actually shows the age difference visually, unlike the usual space-coodinatetime diagram.

(For an especially fun version of this, consider the even simpler case of a light ray bouncing off a mirror and returning to its starting point.)

Yes, for this special case a static space-propertime diagram is not useful. However, we are discussing animations here.

Both types of space-time diagrams have their pros and cons.

 

[robphy]

And what is often left out of the
"we (massive particles) all move with the speed of light [through spacetime]" notion
because the 4-momentum of a massive particle can be normalized to a unit 4-velocity
is that
"light signals move with the ZERO speed [through spacetime]"
because the 4-momentum of a light-signal is zero.

What we already knew...
"light signals move with the speed of light [through SPACE]"
and
"we (massive particles) all move with the speed LESS THAN THAT of light [through SPACE]".Leaving out some important keywords in the comparisons
suggests a symmetry where there is none... hence a source of needless misconceptions.

 

[robphy]

Yes, for this special case a static space-propertime diagram is not useful. However, we are discussing animations here.

Both types of space-time diagrams have their pros and cons.

But the "space-propertime diagram" IS NOT EVEN a spacetime diagram.
At least a Loedel diagram is a spacetime diagram... but this is not.

 

[robphy]

For the "twin paradox" the space-propertime diagram actually shows the age difference visually, unlike the usual space-coodinatetime diagram.

The usual Minkowski spacetime diagram,
when supplemented with the spacetime paths of light signals in a light-clock,
shows the differences visually... and quantitatively.

 

[PeterDonis]

For the "twin paradox" the space-propertime diagram actually shows the age difference visually

It "shows" this by having the two twins end up at different points on the diagram, even though they are at the same point in spacetime. That's what I mean by "breaks down".

we are discussing animations here.

I don't see how an "animation" fixes anything.

 

[PAllen]

In a space proper time diagram of an arbitrary system of particles, any point on the diagram may correspond to any number of different events; further, any single event may be represented by any number different points on the diagram.

 

[A.T.]

The usual Minkowski spacetime diagram,
when supplemented with the spacetime paths of light signals in a light-clock,
shows the differences visually... and quantitatively.

View attachment 274050
View attachment 274051

Yes, I am aware of this method and I like it too. But to see the age difference here is not as direct, as simply reading of the propertime coordinate in a space-propertime diagram. It requires a lot of additional content (the light clock signals)

I'm all for using multiple methods to visualize something.

 

[A.T.]

It "shows" this by having the two twins end up at different points on the diagram, even though they are at the same point in spacetime. That's what I mean by "breaks down".

Calling this a "breakdown" makes no sense. Every type of diagram shows different aspects and has a different interpretation. This is no different that using different types of diagrams in classical mechanics: position-time, velocity-time, velocity-position etc.

I don't see how an "animation" fixes anything.

When you animate current location of the bouncing light signal, the overlaid paths are less confusing. But I would not say that a space-propertime diagram is useful in this case. It's better suited for time-like worldlines.

 

[A.T.]

Is this youtube channel offering solid information : ScienceClic English

I found, what appears to be, a good channel on General Relativity and other science topics.

I have only watched a bit of the videos on this channel. My first impression is that it tackles many aspects, only for a few seconds each. So it is okay as an intro or overview only.

I wish there were more videos on relativity in the style of the 3Blue1Brown channel, which does a great job on actually visualizing the relationship between the formulas and the graphs:
https://www.youtube.com/c/3blue1brown/videos

 

[PeterDonis]

I'm all for using multiple methods to visualize something.

But the point is that for a "twin paradox" scenario, the space-propertime diagram is giving a wrong visualization. It's telling you that the two twins don't meet up again at the end.

Every type of diagram shows different aspects and has a different interpretation.

But correct diagrams of different types are not inconsistent with each other. The space-propertime diagram tells you things that are inconsistent with other diagrams.

This is no different that using different types of diagrams in classical mechanics: position-time, velocity-time, velocity-position etc.

All of those diagrams tell you things that are consistent with each other, so they're not the same as the space-propertime diagram vs. other types of diagrams in SR.

When you animate current location of the bouncing light signal, the overlaid paths are less confusing.

The diagram is still telling you something wrong: it's telling you that the light signal doesn't meet up again with the source object at its starting point.

 

[A.T.]

But the point is that for a "twin paradox" scenario, the space-propertime diagram is giving a wrong visualization. It's telling you that the two twins don't meet up again at the end.

No, it doesn't tell you that. Different types of diagrams have to be interpreted differently. In a space-propertime diagrams a meeting is not a crossing of the paths, but the arrival at the same space coordinates after traveling along the same path length (cooridante time).

The space-propertime diagram tells you things that are inconsistent with other diagrams.

There is nothing inconsistent with other diagrams in terms of physics. It looks different and is interpreted differently, because it is a different type of diagram.

 

[PeterDonis]

a meeting

What do you mean by "meeting"? You can't mean "the paths of two different objects crossing on the diagram", because "meetings" like that have no physical meaning at all on this diagram.

 

[A.T.]

What do you mean by "meeting"?

The meeting of the twins.

 

[PeterDonis]

Both types of space-time diagrams have their pros and cons.

Can you give an example, in the literature, of a space-proper time diagram actually being used to make predictions?

 

[A.T.]

Can you give an example, in the literature, of a space-proper time diagram actually being used to make predictions?

Diagrams are a tool to visualize data. For predictions calculations are used.

 

[PAllen]

Diagrams are a tool to visualize data. For predictions calculations are used.

Both spacetime diagrams and @robphy ’s tilted graph paper diagrams make exact predictions. Especially in the latter, predictions are read directly from the diagram.

 

[A.T.]

Both spacetime diagrams and @robphy ’s tilted graph paper diagrams make exact predictions. Especially in the latter, predictions are read directly from the diagram.

@PeterDonis is asking about use for predictions in professional research literature, if I understand him correctly.