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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

#31

Post by aliraheem »

polishdude20 wrote: post #24
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.

Is there a link to a resource on this or was it just in person? I'd love to hear the intuition you describe!

Here it is https://science.howstuffworks.com/gyroscope.htm#pt2

I've never thought much of it.

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

#32

Post by HWR_14 »

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?

Both are axioms. a = a (and by extension mxn = mxn) is another axiom.

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

#33

Post by sytelus »

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 axiom to be true. If you think in these terms, this axiom seems very problematic.

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

#34

Post by AnimalMuppet »

alex_smart wrote: post #19
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…

Could you not, at least theoretically, create two synchronized clocks and physically transport one of them to another location and then throw a beam of light from the location of the first clock and measure the time of arrival at the second clock? Am I missing something? Edit: What I was missing was time dilation. Physically transporting the clocks would mean that they are no longer synchronized.

But can't you still do it? It just takes a long time to set up.

That is: I synchronize two clocks at a particular point. I then move one clock to the other end of the apparatus (which could be multiple kilometers away). Now, there are three "time dilations" that I have to worry about:

1. Gravitational red shift. I can avoid this by having both ends of the experiment, and the path the clock takes to move from one to the other, all be at the same gravitational potential.

2. Special relativity time dilation. I can minimize (not totally avoid) this one by moving the clock slowly with respect to the stationary one.

3. General relativity time dilation. I can minimize (again, not totally avoid) this one by accelerating the moving clock slowly.

By taking enough time to set up the experiment, can't I minimize all three of those far enough that I can tell that the speed of light is the same in both directions (to some error margin, still, but better than "I can't tell if it's instantaneous in one direction")?

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

#35

Post by qsdf38100 »

gnramires wrote: post #14
qsdf38100 wrote: post #4

Earlier quoted context omitted.

Veritasium has a nice video about it on YouTube. We can only measure the average back and forth speed of light.

I'm not sure that claim is true. Take this experiment, where A sends B a message following two paths: /-->--B (/ and \ are mirrors) | | | | \-- with speeds: (assume lengths are all 1m) /--cr--B | | cu cu | | \--cl--A The time it takes for path 1 (left,up,right) is cl+cu+cr. The time it takes for path 2 is cu. B can measure the difference cl+cu+cr-cu = cl+cr. A can compare cl+cr to cu: if cl+cr != 2cu the velocity is…

I think you assume one can measure the time between two events at different locations. I believe Einstein proved you can’t because there’s no way to truly synchronize clocks at different locations.

Another way to say it is that there’s no instantaneous "now" that all observers can agree on. In special relativity, "now" is meaningless. Or rather, "now" depends on the observer’s inertial frame of reference. There’s a nice diagram one can plot, with 1 dimension of space and 1 dimension of time, that shows lines of simultaneous events based on the velocity of a moving observer in another frame of reference.

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

#36

Post by pdonis »

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…

> 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.

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

#37

Post by naasking »

qubex wrote: post #21
naasking wrote: post #17

Earlier quoted context omitted.

An axiom is an assumption: https://en.wikipedia.org/wiki/Axiom

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).

It's a distinction without a real difference. Calling an "assumption local to a theory" an axiom is fine. We have axiomatizations of both general relativity and quantum mechanics, for instance.

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

#38

Post by pdonis »

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 of solutions that describe black holes.)

> 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.

You're confusing two different concepts here. The concept of spatial isotropy, which is what "space has no preferential direction" refers to, is different from the concept that the one-way speed of light could vary by direction.

The first concept, spatial isotropy, is an invariant concept: it's a geometric property that either is or is not possessed by particular solutions of the Einstein Field Equation.

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. Or you can take a spacetime that is not spatially isotropic, and choose coordinates on it that make it seem like the one-way speed of light does not vary by direction. So the one-way speed of light is simply the wrong thing to think about.

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

#39

Post by adelarsq »

pdonis wrote: post #36
sytelus wrote: post #33

Earlier quoted context omitted.

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…

> 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.

At same time that a center does not exists it exists. Take a line between the two sides from the theoretical border, divide in the middle and will be a center. But isn't a center.

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

#40

Post by 323 »

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…

Why is it a requirement for the experiment information to get back to the originating point right away?

We do all the time experiments where the information is re-converged much later, even months later like at the LHC.

We tested many times the speed of light on earth, and we know that so far no directional speed difference was detected over earthly distances, which you say it's an impossible statement to make.

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