[HN Gopher] Mass and angular momentum, left ambiguous by Einstei...
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Mass and angular momentum, left ambiguous by Einstein, get defined
Author : andsoitis
Score : 105 points
Date : 2022-07-15 15:06 UTC (7 hours ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| ncmncm wrote:
| I really appreciate articles that don't just say what a new thing
| reveals, but puts it in a context of what we still don't know.
| mmmmpancakes wrote:
| hinkley wrote:
| 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.
| leephillips wrote:
| Does this have something to do with the article?
|
| I don't recall any "magic thinking" in the explanation of
| precession in my introductory undergraduate physics text. Just
| Newton's laws and vector cross-products.
|
| "you are applying the lateral force to a different spot on the
| object at each time interval" : how is that applied when the
| force is gravity, applied to every point of the object at every
| time?
| polishdude20 wrote:
| Is there a link to a resource on this or was it just in person?
| I'd love to hear the intuition you describe!
| aliraheem wrote:
| Here it is
| https://science.howstuffworks.com/gyroscope.htm#pt2
|
| I've never thought much of it.
| leephillips wrote:
| 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.
| [deleted]
| shadowgovt wrote:
| 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
| require information to re-converge at the original site of the
| experiment's beginning.
|
| It's a pretty good axiom, because we also have no reason to
| believe there's a preferred direction in space... But it's an
| axiom.
| qubex wrote:
| That's not an axiom, it's an assumption. Anyway, it's the
| assumption of isotropy.
| [deleted]
| naasking wrote:
| An axiom is an assumption:
| https://en.wikipedia.org/wiki/Axiom
| qubex wrote:
| 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 mxn=mxn (which is true for scalars,
| but not true in general for matrices).
| naasking wrote:
| 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.
| defined wrote:
| Did you mean mxn=nxm?
| HWR_14 wrote:
| Both are axioms. a = a (and by extension mxn = mxn) is
| another axiom.
| nine_k wrote:
| If there is an experiment that could detect the discrepancy,
| it's no longer an axiom, and can be falsified.
|
| If there's no such experiment, it just means that for all
| intents and purposes, light travels at the "same speed" in any
| direction for an observer _inside our Universe_ , because the
| speed of light is how we measure time in the first place. If an
| outside observer could notice that our spacetime is non-
| uniform, it's a fun thing to contemplate, but it does not
| change anything for us inside.
| [deleted]
| pdonis wrote:
| _> 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.
| qsdf38100 wrote:
| Veritasium has a nice video about it on YouTube. We can only
| measure the average back and forth speed of light.
| x3n0ph3n3 wrote:
| That video was pretty bad, though. It completely ignores
| everything we know about the CMB. If it were true that the
| speed of light was different in different directions, the CMB
| would look very different.
| gnramires wrote:
| I'm not sure that claim is true. Take this experiment, where
| A sends B a message following two paths:
| /-->--B (/ and \ are mirrors) | | | |
| \--<--A
|
| 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 not isotropic. To see that's always
| possible, A and B can simply bounce back path 2, so B
| receives pulses every 2cu (and hence can measure and compare
| to other time intervals).
|
| Directional speed of light would be very weird, I think it'd
| show up everywhere in experiments if it weren't true.
|
| ---
|
| Also, I think there's a notable distinction in physics: they
| are usually called postulates to distinguish from axioms. A
| postulate is an assumption about a physical theory (usually
| something simple and "beautiful" -- mathematically neat and
| satisfying Occam's razor); if a theory doesn't match reality,
| one of its postulates is incorrect. An axiom in mathematics
| of course can't be proven wrong. Because axioms are the basis
| for your mathematical theory describing reality, they can't
| be incorrect (as long as they form a mathematically
| consistent theory); the most could happen is they're
| insufficient to describe reality (you need other axioms and
| another mathematical theory), but they're not (somewhat)
| falsifiable in the sense of physical postulates.
| kortilla wrote:
| Your experiment doesn't verify that cr = cl nor does it
| verify cu = cd.
| qsdf38100 wrote:
| 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.
| [deleted]
| 323 wrote:
| 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.
| snarfy wrote:
| We've never actually measured the speed of light in one
| direction. It's impossible.
|
| Vertasium video on the subject -
| https://www.youtube.com/watch?v=pTn6Ewhb27k
| x3n0ph3n3 wrote:
| 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.
| codethief wrote:
| > But it's an axiom.
|
| I don't agree. If light traveled instantaneously in one
| direction, then if we looked in the opposite direction (where
| such light originates from) we would be seeing stars and
| galaxies at much more recent time (now). Also, their light
| would have traveled a much longer distance (due to the ongoing
| expansion of space) and so would be redshifted much more. All
| in all what we see on the sky would look very differently in
| terms of redshifts, matter distribution and so on - unless of
| course there's no isotropy, i.e. unless there's some cosmos-
| sized conspiration that fine-tuned matter distribution,
| distances etc. in such a way that the universe looked isotropic
| to us even though it is not.
| tasty_freeze wrote:
| I get what you are saying, it suggests there is no preferred
| direction, but it is just an inference. The point is one
| cannot create an experiment to _measure_ the speed of light
| other than a round trip average speed.
| CamperBob2 wrote:
| Wasn't that the whole idea behind Michelson-Morley ( https:
| //en.wikipedia.org/wiki/Michelson%E2%80%93Morley_exper...)?
| db48x wrote:
| Yes, that is an example of a measurement of the two-way
| speed of light. What is impossible, however, is a
| measurement of the one-way speed of light.
| gumby wrote:
| I don't remember that experiment measuring the speed, but
| merely showing (via lack of a beat pattern) that there
| was no difference in the speed, whatever it was, in two
| paths at right angles to each other.
| CamperBob2 wrote:
| 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.
| db48x wrote:
| 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.
| kolinko wrote:
| Red shift would be different in various directions then. We
| would also see fewer young galaxies / stars in the
| direction in which light flies faster.
| throwk8s wrote:
| > if we looked in the opposite direction (where such light
| originates from) we would be seeing stars and galaxies at
| much more recent time (now)
|
| If the preferred/non-preferred directions were "toward you"
| and "away from you", then rotating yourself to look in the
| "opposite direction" wouldn't make a difference.
|
| (Note: not a physicist)
| Beldin wrote:
| Good point! Simplified (trying to explain to myself), if
| light travelled slower in one direction than others, some
| objects would be less far away from us and each other and
| thus their gravitational effects would be different.
|
| Basically, our cosmological horizon would be significantly
| closer in one direction than others - and all objects (=
| mass) in that direction would be as well.
|
| There might be a very specific way in which matter could be
| distributed so that this is actually true but
| indistinguishable from uniform light speed in all directions,
| from our specific point of view. But I'd expect the effects
| to be noticeably different even within a fairly limited time
| range (decades, perhaps centuries).
| sytelus wrote:
| 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.
| pdonis wrote:
| _> 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.
| adelarsq wrote:
| 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.
| pdonis wrote:
| _> Take a line between the two sides from the theoretical
| border_
|
| There is no "border" to our universe. The fact that you
| have trouble visualizing such models does not mean they
| don't exist.
| xavxav wrote:
| The visualization that works for me is to imagine the surface
| of a balloon as a 2D universe. As you inflate the balloon it
| stretches out despite the skin having no "center" to speak
| of.
| alex_smart wrote:
| 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.
| bee_rider wrote:
| Like 75% of my intro to modern physics class was "Couldn't
| you just <thing that results in further relativistic
| weirdness>." Not sure it lead to the most well-founded
| understanding of relativity, but I was an engineering major
| -- if engineers have to correct for relativity, probably the
| device is operating very out of spec (ignoring very specific,
| well understood cases).
| AnimalMuppet wrote:
| 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")?
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