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

quantamagazine.org

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

#101

Post by codethief »

oldandtired wrote: post #78
x3n0ph3n3 wrote: post #46

Earlier quoted context omitted.

If it were true that the speed of light is different in different directions, the CMB would look completely different than it does. This was a major oversight in Veritasium's video.

Not at all. You are applying an assumption for which you cannot actually determine is true or false. That assumption is that we could measure the differences because we would see a "linear" flow (using the word linear is the sense that it is anything that is not radially determined). What it boils down to is that it is not a measurable quantity (the one way speed of light).

I'm not following and, so far, strongly agree with the parent here (the fact that Veritasium didn't mention the CMB a single time really surprised me when I watched the video for the first time).

Why wouldn't we be able to measure the differences in the CMB, depending on the direction?

What do you mean by "linear flow"?

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

#102

Post by ijidak »

nextaccountic wrote: post #92
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)

Wow. Thank you so much for sharing these. These videos do make it clearer!!

It finally clicks!

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

#103

Post by [deleted] »

blueplanet200 wrote: post #60
tagrun wrote: post #57

Earlier quoted context omitted.

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…

Ex-physicist here. This is not true. See https://www.youtube.com/watch?v=pTn6Ewhb27k for an explanation. You can have a spatially asymmetric speed of light and be perfectly in line with every experiment to date. The speed of light appearing constant in every inertial reference frame is experimentally verified and measured. But it's an axiom that the speed of light has no spatial preference. Each measurement of the sp…

[deleted]

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

#104

Post by tagrun »

blueplanet200 wrote: post #60
tagrun wrote: post #57

Earlier quoted context omitted.

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…

Ex-physicist here. This is not true. See https://www.youtube.com/watch?v=pTn6Ewhb27k for an explanation. You can have a spatially asymmetric speed of light and be perfectly in line with every experiment to date. The speed of light appearing constant in every inertial reference frame is experimentally verified and measured. But it's an axiom that the speed of light has no spatial preference. Each measurement of the sp…

What is not true? You can't have reference frame independent (which is a term that also includes orientations) Maxwell equations and anisotropic speed of light at the same time.

If Maxwell equations are correct (which was already well-tested by then), speed is already the same for forward and backward propagating electromagnetic waves (=light), and there is no other spatial anisotropy either.

Differing one-way speed of light is an amusing "loophole" in the experiments measuring the speed of light (which requires one particular magical angular distribution of c to slip through a Michelson-Morley interferometer) but never existed in the theory that directly predicted it to begin with, so if you insist on it, one needs to ask how would that even work with the rest of physics? c doesn't have a spatial/direction preference in electrodynamics or quantum electrodynamics, vacuum permeability and permittivity (\mu_0 and \epsilon_0) don't have any observed spatial dependence. (Such a thing happens in condensed matter systems, effective mass, vacuum permittivity, g-factor, etc etc are in general anistroptic due to the medium, and is easily detectable, and their spatial derivatives do show up and need to be taken into account to match the observations as in the case of the kinetic term -\hbar^2(d/dx)(1/2m(x))(d/dx). Coulomb force doesn't get stronger or weaker when you rotate the table you perform your experiments on, current carrying wires don't produce stronger magnetic fields as you change their orientation (at least not within any observed precision). Similar goes for any field theory in the standard model.

I should add that in terms of experimental precision, quantum electrodynamics is the most accurate theory that we have, and can put very strong limits on possible anisotropic deviations if any.

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

#105

Post by pdonis »

codethief wrote: post #99
pdonis wrote: post #38

Earlier quoted context omitted.

> 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 o…

> We are not talking about coordinate speed here, we are talking about the light cone looking different, depending on which direction you go.

Before you could even test for this, you would need to come up with a consistent mathematical model of it and show how it's different from the mathematical models in standard GR. Otherwise you won't even know what to test for.

Note that in standard GR, models that do not have isotropy of space also do not necessarily have the "isotropy of light cones" that you describe, at least not once you go beyond a single local patch of spacetime that is small enough for curvature to be ignored.

I'm not aware of any such mathematical model that is different from standard GR.

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

#106

Post by aliraheem »

leephillips wrote: post #44
aliraheem wrote: post #31

Earlier quoted context omitted.

Here it is https://science.howstuffworks.com/gyroscope.htm#pt2 I've never thought much of it.

The misleading and faulty explanation in this link talks about the “desire” of a point on the wheel to move in a certain direction. Now that’s some magical thinking.

I agree.

I don't see how this is not magical thinking but the rules of arithmetic are.

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

#107

Post by drdeca »

mrow84 wrote: post #93
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…

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…

Angular momentum would still be conserved when you cut the wire though?

Also, couldn’t you just as well frame all the linear momentum in terms of angular momentum?

... hm, I guess one question is, how would we describe a world where one is conserved but not the other, and visa versa, So e.g. a physics invariant under rotation around each point but not under translations, or visa versa...

Well, it seems like being invariant under rotation around any point, should maybe imply invariance under translations as well..

But, if we are talking about just rotations around a particular point, then a good example is a model of an atom where we consider the nucleus to be the fixed origin, and with the electrons to just be in a rotationally symmetric potential well, and in that model angular momentum is quite important, while linear momentum isn’t quite so important?

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

#108

Post by db48x »

CamperBob2 wrote: post #83
db48x wrote: post #16

Earlier quoted context omitted.

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.

Nope. A ring–laser gyro sends two light waves in opposite directions around a loop. Some of the light from both beams is let out at one point on the perimeter and the interference between them is measured. It can be any shape you like, as long as the beams trace out the perimeter of some area. When the gyro is rotating, one of the beams has to travel around the perimeter plus some extra distance due to the rotation, while the other beam has to travel the perimeter less that same distance. This causes the interference pattern to shift. The amount of the shift is proportional to the area inside the perimeter, the amount of rotation, the speed of light, and the frequency of the light that you are using.

When the speed of light is anisotropic, we have to replace the constant c with some horrible integral which makes the math a lot worse. However, it is important to recognize that the overall time to go around the perimeter clockwise and counterclockwise is the same: both beams go the same distance to the left as they go to the right. As long as the leftwards speed of light and the rightward speed of light average out to the usual value, then the result will work out to be the same as when the speed of light is a constant with the usual value in all directions.

Any time you send a pulse of light out and back, the time to travel the distance d will be αcd+βcd=2cd, where α and β show the relationship between the speeds of light in those two directions. We generally assume that α=β=1.0, but as long as α+β=2.0, then everything we can measure will work out to be exactly the same.

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

#109

Post by pdonis »

adelarsq wrote: post #97
pdonis wrote: post #72

Earlier quoted context omitted.

> 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?

> if the matter on the big bang was limited

It wasn't, according to our best current model. In that model the universe is spatially infinite and always has been, so it contains an infinite quantity of matter.

> wouldn't a limit on the universe size based on how much matter exists

There are mathematical models in which the universe has a finite size and contains a finite amount of matter. (These models are not completely ruled out by our current data, but they are considered very unlikely as compared to the ones in which the universe is spatially infinite.)

However, even in those models, the universe has no boundary: it is spatially a 3-sphere, which has a finite volume and no boundary similar to the way the surface of the Earth, a 2-sphere (at least approximately) has a finite area and no boundary.

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

#110

Post by pdonis »

oldandtired wrote: post #79
pdonis wrote: post #36

Earlier quoted context omitted.

> If there is an expanstion then there must be a shape and then there must be a center However intuitively plausible this seems to you, it's still false. The fact that our intuitive visualization capabilities cannot directly visualize the mathematical entities involved does not change that.

Mathematics is a simplification methodology and doesn't necessarily match what actually exists. So to say that the original comment is "false" means that you have to "prove" that it is false in the sense of the logical and mathematical axioms you use. If those axioms are changed, you get a different logical and mathematical outcome.

> to say that the original comment is "false" means that you have to "prove" that it is false in the sense of the logical and mathematical axioms you use.

The comment I responded to was making a categorical statement. A single counterexample is sufficient to falsify it. The entire family of FRW models used in cosmology, in all of which the statement I responded to is false, are counterexamples.

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