Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Mass and angular momentum, left ambiguous by Einstein, get defined

quantamagazine.org

Post reply on HN
Print view View original

91–100 of 125 posts

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#91

Post by kergonath »

andreareina wrote: post #81
kergonath wrote: post #70

Earlier quoted context omitted.

From a layman’s perspective, if something spins, you need to apply a force to it to stop spinning, otherwise it will just keep spinning. Hence, conservation of angular momentum. If you change the mass distribution, it will spin faster or slower, just like ice skaters (this is probably the most striking example), but the angular momentum is still conserved, regardless their linear momentum. There is no fundamental dif…

Which implies that it's separate from linear momentum (the conservation of which is implied by invariance after linear translations).

Indeed!

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#92

Post by nextaccountic »

ijidak wrote: post #89

This might be an easy question, but it's always bothered me... If gravity is caused by curvature of space-time (like I'm a train on a curved rail), doesn't that mean that space-time itself exerts forces? But if that's the case, why doesn't space exert a retarding force against all moving objects, like a form of friction or wind resistance? In a total vacuum, an object would move through space-time with zero resistanc…

But under this point of view there's no force at all. Gravity doesn't exert a force on you, the movement under gravity is purely inertial. I know this is bonkers.

Here's the video that made me finally understand it https://www.youtube.com/watch?v=wrwgIjBUYVc (https://www.youtube.com/watch?v=twPaOtfpneo is another good video from the same author)

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#93

Post by mrow84 »

kergonath wrote: post #70
colordrops wrote: post #52

From a layman's perspevtive I've never understood the existence of angular momentum as anything other than a mental model or abstraction. My intuition tells me that all momentum is only linear (except maybe at the fundamental particle level), and perceived rotation is really just a huge amount of linear interactions by individual particles that make up a larger object. This is similar to how a gas is not really a sin…

From a layman’s perspective, if something spins, you need to apply a force to it to stop spinning, otherwise it will just keep spinning. Hence, conservation of angular momentum. If you change the mass distribution, it will spin faster or slower, just like ice skaters (this is probably the most striking example), but the angular momentum is still conserved, regardless their linear momentum. There is no fundamental dif…

Your layman’s answer still doesn’t quite do it for me - if you had two masses in space, joined together by a wire, and you span them around their combined centre of mass, angular momentum would remain conserved even if we wound the wire in or payed it out. If I cut the wire, though, wouldn’t the masses immediately shoot off (roughly) in whatever direction they were travelling at the time? That is my interpretation of the “everything seems linear” perspective colordrops offered - it seems like you only get the apparent rotation because of all the other forces holding things together.

edit: I accept that the non-layman’s answer may hold, I just find the intuition a bit off.

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#94

Post by qubex »

defined wrote: post #29
qubex wrote: post #21

Earlier quoted context omitted.

It’s a matter of scope. Axioms are assumptions that undergird the formal edifice (those or mathematics or arithmetic) whereas assumptions are local to the theory. ‘Assumptions’ is a synonym of ‘postulates’. Axioms are foundational, such as m×n=m×n (which is true for scalars, but not true in general for matrices).

Did you mean m×n=n×m?

Yes. Oops.

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#95

Post by hakuseki »

kadoban wrote: post #87
Schroedingersat wrote: post #86

Earlier quoted context omitted.

It has almost the same relationship to angular momentum (and tangentially magnetic fields) as charge on an electron has to charge in a capacitor or an electric fields. > My understanding is that "spin" isn't really anything necessarily spinning Yeah, this is kind of the point. A bunch of non-spinning things like particles, or more abstractly an EM field can have angular momentum. This is the same quantity that is con…

> This is the same quantity that is conserved in things that are spinning. In what sense is it the same? If we called them completely different names, what would be different or more complex?

IANAP, but it seems to me that right now we are able to make the statement: "Angular momentum is conserved."

If we were to give different names to different types of angular momentum, we could no longer say that. Instead we would have to say something like: "The sum of Type 1 Angular Momentum and Type 2 Angular Momentum is conserved."

Does that qualify as more complex?

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#96

Post by Schroedingersat »

hakuseki wrote: post #95
kadoban wrote: post #87

Earlier quoted context omitted.

> This is the same quantity that is conserved in things that are spinning. In what sense is it the same? If we called them completely different names, what would be different or more complex?

IANAP, but it seems to me that right now we are able to make the statement: "Angular momentum is conserved." If we were to give different names to different types of angular momentum, we could no longer say that. Instead we would have to say something like: "The sum of Type 1 Angular Momentum and Type 2 Angular Momentum is conserved." Does that qualify as more complex?

Yes to your statement. I'm not quite sure what you're asking with the question, but will try.

I mean you're increasing the complexity of your explanation I guess, and if you don't draw the distinction quite right you might be doing so for no explanatory benefit and a net reduction in communication effectiveness. But there are other reasons quantized spin is important and relevant compared to, say, the net angular momentum you have around Detroit at the current time.

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#97

Post by adelarsq »

pdonis wrote: post #72
tick_tock_tick wrote: post #51

Earlier quoted context omitted.

There is an "effective" border because of speed of light limits. Technically we are "at the center" of our intractable universe.

> Technically we are "at the center" of our intractable universe. We are at the center of our observable universe, yes, but that fact does not support any of the claims I have been responding to in this thread.

But if the matter on the big bang was limited wouldn't a limit on the universe size based on how much matter exists?

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#98

Post by Schroedingersat »

sytelus wrote: post #33
shadowgovt wrote: post #2

The most eye-opening thing I've learned about relativity in the past few years is that the notion that space has no preferential direction is an axiom in the theory. There's nothing about the way we measure the speed of light that would disambiguate if light traveled instantaneously in one direction and at half the measured speed of light in the other. We just don't have a way to know, because time measurements requi…

It's a great axiom until it isn't. One thing I still cannot visualize is exapanding universe. If there is an expanstion then there must be a shape and then there must be a center and then must be one direction that is not exactly same as another because expansion rates are different. I read that universe expands same everywhere and there is no "center" which is very hard to visualize but it is a requirement for this…

Put some ink dots on a balloon and blow it up.

The surface is expanding fairly well uniformly, and the dots are getting further apart. Now if you did the same with a uniform spherical balloon that's inflating somehow, there's no center and no shape to the 2d surface.

Similarly you could be inside a giant cake as it's cooking. Any two raisins will be moving apart and this happens the same way near the middle or halfway to the edge (excluding temperature/pressure unevenness). Now if you make the cake bigger until you can no longer reach the edges it all works the same everyhwere in the cake.

If you take out the non-raisin parts, and the bit where you consider that there might be edges, and that the cake started already big rather than tiny, you get the universe.

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#99

Post by codethief »

pdonis wrote: post #38
shadowgovt wrote: post #2

The most eye-opening thing I've learned about relativity in the past few years is that the notion that space has no preferential direction is an axiom in the theory. There's nothing about the way we measure the speed of light that would disambiguate if light traveled instantaneously in one direction and at half the measured speed of light in the other. We just don't have a way to know, because time measurements requi…

> The most eye-opening thing I've learned about relativity in the past few years is that the notion that space has no preferential direction is an axiom in the theory. No, it's not. It's a geometric property of particular solutions in the theory. Those solutions include the ones we use to describe the universe as a whole. But there are plenty of other solutions that don't have this property. (For example, the family…

The distincion you're making between isotropy of space and isotropy of the speed of light is important but I don't think the following is true:

> The second concept, anisotropy of the one-way speed of light, is not an invariant concept or a geometric property: it's an artifact of your choice of coordinates. You can take a spacetime that is spatially isotropic, and choose coordinates on it that make it seem like the one-way speed of light varies by direction.

We are not talking about coordinate speed here, we are talking about the light cone looking different, depending on which direction you go. This is (or would be) a geometric / invariant property.

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#100

Post by hakuseki »

Schroedingersat wrote: post #96
hakuseki wrote: post #95

Earlier quoted context omitted.

IANAP, but it seems to me that right now we are able to make the statement: "Angular momentum is conserved." If we were to give different names to different types of angular momentum, we could no longer say that. Instead we would have to say something like: "The sum of Type 1 Angular Momentum and Type 2 Angular Momentum is conserved." Does that qualify as more complex?

Yes to your statement. I'm not quite sure what you're asking with the question, but will try. I mean you're increasing the complexity of your explanation I guess, and if you don't draw the distinction quite right you might be doing so for no explanatory benefit and a net reduction in communication effectiveness. But there are other reasons quantized spin is important and relevant compared to, say, the net angular mom…

To clarify, my question was basically asking whether the author of the parent comment is satisfied by my comment.
Post reply on HN