Mass and angular momentum, left ambiguous by Einstein, get defined • Hacker News Board

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

#81

Post by andreareina » Sat, Jul 16, 2022, 3:08 AM UTC

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…

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

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

#82

Post by andreareina » Sat, Jul 16, 2022, 3:16 AM UTC

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…

This isn't explanatory, but should at least demonstrate that it is separate: electrons are point-like particles and thus have no internal substructure to rotate, yet they behave as though they have angular momentum. This "intrinsic angular momentum" is the electron's spin.

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

#83

Post by CamperBob2 » Sat, Jul 16, 2022, 3:41 AM UTC

db48x wrote: post #16

CamperBob2 wrote: post #15

Earlier quoted context omitted.

M-M compared the speed in one direction to the speed at right angles. That's not quite the same thing as a one-way measurement, but it's also not the same thing as a two-way measurement along the same path.

Right, but the way that they measured the speed in any direction was by making a two-way measurement. They sent a pulse of light out to be reflected and timed how long it took for it to return.

I imagine that a ring-laser gyro would return some pretty strange results in a universe where c was anisotropic.

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

#84

Post by xhrpost » Sat, Jul 16, 2022, 4:28 AM UTC

hinkley wrote: post #7

Maybe a year ago, possibly here, I finally saw gyroscopic precession demonstrated in a way that didn’t invoke magic thinking. The person simply pointed out that the mistake is in thinking of the rotating mass as a stationary object, when in fact you are applying the lateral force to a different spot on the object at each time interval, leading to very strange vectors.

Hmm, can this explanation work in reverse? I've always found the conservation of momentum to be very confusing. Why does a spinning body cause an orthogonal rotation upon itself and thus any rigid body it's attached to? I know there's math to explain it, but it just doesn't seem intuitive to understand.

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

#85

Post by alecst » Sat, Jul 16, 2022, 4:40 AM UTC

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…

Ok so you want the flaw in your reasoning.

Imagine a hula hoop. It’s spinning, but otherwise not moving. Mentally divide it up into lots of little chunks.

Each chunk has a little bit of linear momentum.

1. Is each chunk’s linear momentum constant in time? No, because its direction of motion is changing. Hm, that’s unfortunate.

2. What about if you do R x p, the radius of the loop crossed with the momentum of that little chunk. That gives you a quantity for each chunk that’s unchanging. That’s called the angular momentum of that chunk.

If you add the angular momentum for all the chunks, you get the total angular momentum.

So you see that angular momentum works just like linear momentum. You take a conserved quantity for a single chunk and add up over all the chunks.

You’re free to think of all the little particles and their linear momentum, but that isn’t so useful, since summing the linear momenta gives you zero, whereas summing R x p gives you something to reason about.

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

#86

Post by Schroedingersat » Sat, Jul 16, 2022, 5:30 AM UTC

kadoban wrote: post #74

Schroedingersat wrote: post #63

Earlier quoted context omitted.

It's very decidedly not an abstraction on linear momentum. It's a conserved quantity just like any other. Light has angular momentum even when travelling in a straight line. Anything with spin does even when stopped. In physics there is a concept known as symmetry. Any way you can swap around your variables without influencing the answers corresponds to a way in which the laws of physics are symmetric (or a way someo…

Is that the _same_ angular momentum, or just the same term used for something different? My understanding is that "spin" isn't really anything necessarily spinning and it's more just an analogy for a property of subatomic particles that doesn't exactly correspond to a concept at the macro level.

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 conserved in things that are spinning.

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

#87

Post by kadoban » Sat, Jul 16, 2022, 5:52 AM UTC

Schroedingersat wrote: post #86

kadoban wrote: post #74

Earlier quoted context omitted.

Is that the _same_ angular momentum, or just the same term used for something different? My understanding is that "spin" isn't really anything necessarily spinning and it's more just an analogy for a property of subatomic particles that doesn't exactly correspond to a concept at the macro level.

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?

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

#88

Post by [deleted] » Sat, Jul 16, 2022, 6:01 AM UTC

tagrun wrote: post #57

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…

Physicist here. It's not an axiom, historically, it follows from Michelson-Morley experiments, which precede special relativity, and whose purpose was to detect such an isotropy. They repeated the experiment during different times of the day and different seasons, since the velocity of the Earth (and the lab) relative to the hypothetical aether would be different. The working assumption was that Galilean relativity w…

[deleted]

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

#89

Post by ijidak » Sat, Jul 16, 2022, 6:50 AM UTC

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 resistance forever... As if space-time is incapable of exerting any force of its own.

Why does spacetime only exert force when curved?

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

#90

Post by Schroedingersat » Sat, Jul 16, 2022, 6:52 AM UTC

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?

To flip the spin of a particle from eg. +1/2 to -1/2 it must exchange some angular momentum with its environment, usually in the form of a spin 1 photon. Each unit of spin corresponds to a fundamental amount of angular momentum, and if you add up all of the angular momentum in a closed system the total does not change.

Spin falls out of qm equations as the quantized number associated with the angular momentum quantity that falls out of classical equations.

Much like you get energy-momentum from translating in time and space, and this falls out in a constrained quantum system where energy-momentum is quantized as an integer we call wave number.