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.
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.
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.
Correct, cl+cr = 2cu is the best you can measure. But it doesn’t follow that cl = cr! Assume a linear transformation like αcl+βcr = 2cu, where α and β tell you how the speed of light varies in between left and right. We simply assume that α = β = 1.0, but what if α=½ and β=³⁄₂? Or α=2 and β=0? A long as α + β = 2.0, then everything will look exactly the same.
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.
No disagreement on what you write, but the CMB spectrum is about as useless as radiocarbon dating for deciding which of two Hydrogen maser clocks on opposite sides of a university laboratory is wrong when they differ by ten nanoseconds.
However, we can generalize your point and say that real configurations of matter let us make those decisions reasonably and with good accuracy. (The BIPM UTC Circular-T contributors seem to manage fine, as do the various GNSS operators).
If the video had taken care to set their experiment in vacuum flat spacetime (perturbed only by the experiment), as the shown Einstein 1905 work <https://www.fourmilab.ch/etexts/einstein/specrel/> (top of p. 3) did, it would be better. That's because that setting offers no convenient-to-agree way to slice spacetime into space and time. The CMB does, but we suffer from practical limits on measuring the CMB's blackbody temperature.
> Veritasium has a nice video about it on YouTube.
He is often wrong in subtle and not—subtle ways, though. In this case, regardless of the issue of one-way measurements of c, his sources do not really support an anisotropy in the speed of light.
His video was mentioned already 5 or 6 times here. Isn’t here anything better at all?
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.
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.
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.
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.
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.
This does not imply that the speed of light could depend on direction, though. If that were the case, we could see it by rotating a simple Michelson interferometer.
That would imply an axiom that forces/light/whatever are on a gradient we operate against and does not change based on reference point.
I think the heart of the what the GP is getting at is no matter how you define it, you can measure things smaller than your measuring equipment can detect.
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).
> 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.
You can change other things to get the same result.
You can build a consistent theory of aether by asserting that everything (including you) doppler shifts just so and there is a 0 speed through the aether. You get a complicated theory that is not experimentally distinguishable and is incredibly difficult to use and noone would have any idea how to extend to QM or gravity because it's so cumbersome, but it's consistent and mechanics works.
You could easily reframe the frame of reference in such a theory where the lab is moving at 0.999c absolute (which exists in this theory despite being immeasurable) as light moving very slowly in one direction and near instantly in the other.
> Also, their light would have traveled a much longer distance (due to the ongoing expansion of space) and so would be redshifted much more.
I need to correct myself: If light traveled instantaneously, the expansion of space wouldn't matter because in the very instant in which light would be traveling space wouldn't be expanding. -> No redshift at all.
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.
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.
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).
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")?
The problem is probably insoluble in Special Relativity alone*, because of the available clock-synchronization schemes in a universe populated only by the self-contained experimental apparatus (sender + local clock, receiver + local clock), experimental pulse of light, and flashing-light morse code or whatever to compare timestamps. If we are allowed to add more matter of our choosing, we can probably measure the one-way delay with good precision.
The absence of gravitational sources is an aspect of the flat spacetime of Special Relativity, but if we are cheating by adding in (and declaring gravitationally negligible) the experimental apparatus, why can't we cheat by adding in a non-gravitationally evolving bit of matter which can serve as a clock? A low-mass, sparse, spherical, uniform cloud of of hot dust expanding adiabatically can serve as a clock by measuring its and temperature if the one-way-transmitter and one-way-receiver are freely falling within it and moving slowly compared to light. This is essentially a demotion of the sparse cosmic microwave background gas/dust of massless photons -> sparse gas/dust of neutral low-mass molecules. The CMB expands and cools, while we're within it. Our non-relativistic molecular gas expands and cools, while our one-way test equipment is within it.
Of course, what is too much of a cheat in Special Relativity and what is not is debatable. In all the cases above we are ignoring the Raychaudhuri equation with the only justifications being that the timescales are too long to tell if we're focusing, and we aren't obviously engaging post-Newtonian (PN) corrections. (What gets us into trouble with PN formalisms in GR can get us into trouble in gravitation-free SR though: ultraboost one side of the experiment, rather than "... moving the clock slowly with respect to the stationary one". You guessed correctly that boosts and accelerations could be a problem in (2)&(3). However, contra your (3) acceleration is perfectly permissible in "pure" SR and the result is only equivalent to being in a uniform gravitational field (rather than with a potential gradient), and only somewhat briefly (you can rest your clock on an enormous rocky planet for much longer than you can accelerate your clock at ~ 10 g). The time dilation in (3) is Minkowski / Born / von Laue / Einstein 1905-1911 Special Relativistic and not post-1915 General Relativitistic. Your (1) is done for you for free in "pure" SR, since there is no gravitation there.)
General relativity is hardly a panacea: if we have a strongly expanding vacuum our one way pulse might never reach the detector. In a dynamical curved spacetime we can break the symmetry between legs of a reflection 2-way test in any number of ways.
It's really the breaking of the vacuum condition that lets us set up a "global" or at least wide-enough-area clock. When we're allowed to introduce half-life decays or thinning background matter or radiation, or distant millisecond pulsars, we are more likely to be able to use a synchronization scheme sufficiently different from Einstein's method and successfully compare timestamps at the sender and receiver of a one-way flash.
- --
* If we assume Special Relativity then we already have global Poincaré invariance, so we have already have symmetrical legs of a reflection test. If we have a setting which is maybe Minkowski spacetime, or maybe something other than Minkowski space that breaks the symmetry of the legs in a reflection test, then we probably can't do it with a one-way test along the lines you're thinking.
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.
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.
> 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.
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.
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.
What I was commenting on was your categorical claim that the selected portion of the original comment was false and you have not provided that mathematical "proof".
As for a single counter example, you need to demonstrate that the counter example is applicable. I don't think you have. At least not to the degree that would support your categorical claim.
In regards to both of your views, I am making no statement as to validity or otherwise of those statements. This is simply a matter of asking for you and him to provide supporting evidence for your respective positions.
This would then allow further discussion on the views and their evidence.
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.
The classical 'visualisation' of this is 'cake expansion'.
If you think about what's happening inside a cake when you put it in an oven, it expands in all directions, and the center has only a meaning there because the cake is finite.
For a 2D model, consider only the surface of a balloon. As the balloon expands, each point on the surface increases in distance from every other point, but there is no center of the surface.
Be sure to consider only the surface, not the 3D embedding your (flawed) intuition wants to inject.
You can do the same thing in 1D with a circle.
This works in any dimension, including the 3+1 spacetime manifold.
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.
> 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.
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.
> 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.
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.
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?
The CMB is assumed to be what it is stated to be. If you look at the various theoretical predictions for the CMB, you will see that the theoretical predictions have been quite inaccurate. In absolute magnitude, the temperature that would be expected is quite small. However, the error in those predictions relative to each other is quite high (way too high, if I recall correctly this error is on the order of +/- 50%). I have done laboratory experiments which had similar errors and it was considered a failed experiment. The predicted value from theory was supposed to be less than a couple of percent to give some credence that the theory was actually applicable.
Based on the evidence so far provided, I have some concerns that what the CMB is supposed to represent is not actually what it represents.
Once you have experimental or observational anomalies that conflict with theory, one has to look at that theory as either being wrong or incomplete. After 40 years of watching these things, I conclude that we are still very ignorant of the nature of our universe.
Unfortunately, there are inherent infrastructure problems in scientific investigation and we often see politics and dogma interfering. This works to limit our understanding. I see this as a repeat of what was happening in the late 19th century. We didn't learn from our mistakes then and so we are doomed to repeat those mistakes now.
From an observational POV, we can see light coming to us from all directions radially towards us. We treat the speed as an essentially constant value, even though we know this is false in reality. It is a useful approximation that we use to simplify our models and calculations.
The calculated speed of light through a medium is related to both the permittivity and the permeability of the medium through which the light is passing. When you get to the situation where any kind of changes occur in these values over the path you then see other thing happening related to the frequencies involved.
These things make for all sorts of changes in the path and the speed over which light travels.
An analogy might help here (might). Take a particle of any kind and have it move along a path with potential assistance in its travel in one direction and then return that particle along the same path in the opposite direction. Ask the question, what is the one way speed of that particle if all you have is the total time for two path traversal and you are assuming that the particle is the one that traverses the path at a constant speed. What can you tell me about its instantaneous velocity over the path? You do not know what assistance, if any, that particle has received.
We make certain assumptions for which we cannot determine if they are true or not. To simplify our models, we take the view that our assumptions are NOT unreasonable, but we cannot test them. This is a normal state of affairs with relation to much of our scientific investigation. When we do find additional information that indicates that one or more of these assumption is potentially or actually false, we make modifications to our models and theories or we replace them entirely.
We make much ado about GR and curved space-time and that "gravity" bends light. There is an assumption here that medium changes and hence permittivity/permeability changes are not applicable or consequential in the observed path changes. The thing here is that we cannot measure those permittivity and permeability changes and assume that the light is traveling is traveling through a perfect vacuum, which we also know is false. But it "simplifies" the model and calculations.
We no longer use a geocentric model of the universe (this is effectively using Fourier Series) and we have moved over to a Heliocentric model because it is "simpler" to use. Yet, the heliocentric model is also wrong because it cannot take onto account the gravitational effects of all orbiting bodies. This gives rise to using perturbation theory. This makes the modelling much more complex and yet it too is not at all complete for it has not taken into account the motion of the sun and the orbiting bodies on the path through the galaxy. Again this gives rise to further complexity that must be taken into account.
For simplistic models, we use the heliocentric model and for short term situations, we just ignore perturbation effects of these other things. We do no less in analog circuit analysis or digital circuit analysis, orbital satellite mapping, weather forecasting, river flows, and the list goes on and on.
We use simpler models because they are "good enough" for what we are trying to do. But they will all fail once you get outside of the simplifying assumptions that underlay them. I return you to the aphorism popularised by George Box "All models are wrong, some are useful."
I'm still not following. If the speed of light in one direction was infinite, there would not be any redshift nor any microwave background coming from that direction[0] to begin with. The photons from recombination time would have long passed us.
Of course, this assumes that the universe is isotropic and what not. But again[1], the alternative would be a fine-tuning conspiracy of cosmological scale.
I know that classical rotational symmetry leads to conservation of angular momentum by Noether's theorem.
I suspect if you break the rotational symmetry of the speed of light that you wind up breaking something like conservation of quantum spin angular momentum and the universe rapidly becomes nonsensical.
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 was correct, and the Maxwell equations (which also define the speed of light) were only valid in the special reference frame of the aether.
Special relativity assumes Maxwell equations are always correct in all reference frames and orientations, which was already an experimentally observed fact (albeit puzzling, back then), rather than an axiom, which implied that it is Galilean relativity that is broken and needs to be refined.
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 speed of light sneaks in this axiom in subtle ways.
I think you misinterpreted the parent's point. They weren't saying c being a constant in all reference frames is an axiom. Rather, they were saying that it's convention that c doesn't have a spatial, directional, preference. It's a different claim.
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.
You should watch the video. There is no experiment that has been done that shows the speed of light does not have a preference because every measurement sneaks in the assumption it's symmetric.
See also: https://en.wikipedia.org/wiki/One-way_speed_of_light . From the article: "Experiments that attempt to directly probe the one-way speed of light independent of synchronization have been proposed, but none have succeeded in doing so.[3] Those experiments directly establish that synchronization with slow clock-transport is equivalent to Einstein synchronization, which is an important feature of special relativity. However, those experiments cannot directly establish the isotropy of the one-way speed of light since it has been shown that slow clock-transport, the laws of motion, and the way inertial reference frames are defined already involve the assumption of isotropic one-way speeds and thus, are equally conventional.[4] In general, it was shown that these experiments are consistent with anisotropic one-way light speed as long as the two-way light speed is isotropic.[1][5]
"
I get what you're saying and I'm well aware that Maxwell's equations are rotation invariant. I'm saying it's more subtle and complicated than you think. For instance, time dilation will have an asymmetry under these assumptions.
tl;dr: coincident-events first, then labels (coordinates). [Einstein 1916, p.117 [2] although I remembered to look there only after writing all of the below]. One-way speed of light arguments are in danger of being coordinates-first, and thus insufficiently general for physics.[3]
The key word in your comment is
> directly
But why do we care? We have an abundance of indirect evidence, premised on direct tests of coordinate-independent features of our best most-fundamental theory. The two important features of (general) relativity are pointwise local Lorentz covariance -- where c is the only free parameter of the Lorentz group -- and the minimal coupling. Special relativity's Minkowski space is in this view a special static time-orientable spacetime in which we have global Poincaré invariance (c again is the only free parameter of the Poincaré group; the Lorentz group is a subgroup of the Poincaré group -- the latter includes all the spacetime translations, and in the Minkowski case the space-translation and time-translation symmetries all commute). When we go blithely parallel-transporting null vectors, this is what matters.
It is far from silly to write down a theory where c varies in spacetime. It is the foundation of several alternative-to-cosmic-inflation decaying-bimetric theories of the very early universe, where c eventually stabilizes to its value in our local spacetime having been a different (typically much much much -- ~30 orders of magnitude -- higher) value during the formation of primordial matter density variations. The faster speed of light allows for distant reaches of the early universe to reach the same temperature with uniformity up to the small fluctuations in the cosmic microwave background.
Of course we run into the same point you've been working in this thread: it's hard to discover the exact function on c in the early universe. We have to rely on indirect evidence, and strong gravitational lensing is useful there. SVOM <https://svom.cnes.fr/en/SVOM/GP_mission.htm> is looking for Lorentz-invariance-violation (LIV)-induced modifications to the photon dispersion relation in vacuum, and is a particularly good platform for test of a Taylor-series expansion like E^2=p^2 c^2 ( 1 +- \sum_{n=1}^{\infty} a_n ), since GRBs at least somewhat escape the problem that the lowest order terms dominate at small energies, and they are distributed across the sky and at different redshifts. We are also now better equipped to study light echos (oh for a galactic supernova!) and detailed strong galactic lensing studies. Spoiler: the constraints on a spacetime-translational vari...
For a (physical) relativist, the speed of light is really simple. c = 1, everywhere and everywhen. <https://en.wikipedia.org/wiki/Geometrized_unit_system> This is because we have excellent evidence for the utility of <https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold#App...>, and the further astrophysically-driven demands of global hyperbolicity or at least reasonably strong causality conditions, no isometric embeddings, geodesic incompleteness, asymptotic flatness around sources, junctions in sufficiently flat space, and energy conditions. Those further demands are the basis for continuing to rely on Special Relativity in laboratory settings.
[1] quoting your wikipedia link, "... inertial frames and coordinates are defined from the outset so that space and time coordinates as well as slow clock-transport are described isotropically". Well, yes. Establish points first then assign coordinate labels is the relativist's procedure, surely?
On this point, Earth laboratories are in general not in inertial frames, thanks to gravitation. No laboratory is in general in an inertial frame, thanks to the metric expansion of space. We can in principle extract a preferred foliation (e.g. the scale factor a, or some function on lunisolar tides) and use that as the basis for time coordinates instead. In effect this is what we do for high-redshift objects and many lunar laser ranging experiments <https://ssd.jpl.nasa.gov/ftp/eph/planets/ioms/>[a] <https://arxiv.org/abs/1606.08376> §3,§4. <https://link.springer.com/article/10.1007/s10569-010-9303-5> discusses aspects of how to choose a preferred foliation (in the context of gauge freedom) in the solar system, and in the context of grinding out a results-prediction for some future LLR experiment. The goal is to be able to show that the locations of the three instruments were accurately predicted, and Lorentz-invariance is thoroughly baked in (the calculations are so exceptionally sensitive to the introduction of tiny breaking parameters in the style of SME <https://arxiv.org/abs/0801.0287> that it has led to the discovery and/or better understanding of several of the features listed as parameters at [[a] LLR_Model_2020_DR.pdf §4]).
You can call in convention as many times as you want, but unfortunately, it just is not a convention. It is called theory of electrodynamics which is a well established, experimentally verified branch of physics.
What exactly is more subtle and complicated in the context of Maxwell equations? If speed of light has the anisotropy that you are describing, Maxwell equations must be incorrect. In what electromagnetic experiment has such anistropy of magnetic or electric constants have been ever observed?
You're basically saying "you haven't measured the one-way speed of light directly, so you haven't ruled it out the possibility of my exotic theory", but it is actually been ruled out by Maxwell equations a long time ago. Unless you have some experimental proof that Maxwell equations need to be modified to accommodate that elusive version of your aether, you can't claim the existence of such an anisotropy.
Physics is well connected in that you can't change one part of it (in your case, c in the context of special relatively) just because you found something that wasn't experimentally ruled out, and hope the rest of the physics (basically all massless field theories and relevant experimental results in this case) won't break.
> the notion that space has no preferential direction is an axiom in the theory.
This was the case in special relativity, with a flat space-time. In general relativity, space-time is curved and there are locally special directions. The laws of Physics still do not define special directions a priori. It is quite fundamental actually, and so far everything behaves as expected, at least in this respect. It is not as much an axiom as a consequence of Maxwell’s equations, from which we can deduce that light has a well-defined velocity in vacuum, irrespective of location or direction.
> 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.
There is something I don’t get here. If we shine a light on a detector, we can measure the time the light takes to reach the detector. Are you saying that the light hits the detector instantly, and then goes back to the source, or that the detector is the source and the light comes back to it after hitting the source instantly?
In practice, the speed of light does not depend on direction, as far as we can measure.
If you shine a light on a detector, you measure the time it takes to travel both legs. What is being said is that all we can know is the average time from when it leaves us to when it gets back to us (i.e. the sensor results).
It could well be the same magnitude each direction or it could be instantaneous one way and 1/2 c back the other or any other combination of values as long as the average of the two way measurement is c.
Final note: the value that we put as c is only true in a very specific environment. It depends on the characteristics of the medium through which light is traveling as to what we will measure as the average two way speed. This is a consequence of the permeability and the permittivity of the medium through which the light is traveling. This is standard electrical engineering fare.
>> If we shine a light on a detector, we can measure the time the light takes to reach the detector. Are you saying that the light hits the detector instantly, and then goes back to the source, or that the detector is the source and the light comes back to it after hitting the source instantly?
> If you shine a light on a detector, you measure the time it takes to travel both legs.
reflector, surely, rather than detector? Your director can record a timestamp locally while you and your flashlight are across the room. You don't need two legs.
The main objection upthread is that while your flashlight's "on" switch can also record a timestamp within the flashlight, synchronizing the flashlight's time to the detector's time so that one can compare the timestamps after the experiment is done (or days later, or weeks later, again and again) is not feasible within the framework of Special Relativity. Therefore if one has confidence in one's local timestamps, one can compare them when measuring the round trip of the flashlight beam reflected off a mirror across the room back onto a detector mounted right beside the flashlight's bulb, inside the flashlight.
However, nature provides several gravitationally-driven systems which can provide a "preferred foliation", or a naturally-produced easily-compared timestamp. Examples include fancy sundials (including observations of millisecond pulsars), lunisolar tides, and the cosmological scale factor. These can be recovered independently in a (probably pretty large) flashlight and the detector looking for the light from the flashlight. Timestamps can then be compared with greater precision than available via Special Relativity synchronization methods.
Indeed, this is something that has been worked on in lunar-ranging experiments over the past decades. Can we use detailed knowledge of the solar system to predict a signal aimed Earthward by a 21st century space probe on or very near the moon as well as a signal launched from Earth to a reflector on the moon that is picked up by a detector on Earth? It turns out we can, to good precision!
> Final note
"c" is the free parameter of the Lorentz group, which is the fundamental isometry group of Special Relativity (and quantum electrodynamics and the Standard Model of particle physics). "c" is also a constant in the Einstein Field Equations of General Relativity, and there is a mathematical connection between that and Special Relativity.
In both theories, unless interfered with by interaction with matter, massless objects are constrained to move, obligatorily, from one spacetime point to another point from a restricted set of neighbours. These points are on the surface of a null cone.
Light is experimentally massless, so null curves are often called lightlike curves, null cones are usually called light cones, and so on. However, electromagnetic radiation is not the only massless species in the cosmos.
> very specific environment
An excellent approximation of vacuum (very long mean free paths for electromagnetic radiation at all frequencies) dominates the observable universe, so the permeability and permittivity of free space is a good choice except in very specific environments (planet-bound electrical engineering laboratories and copper wires are out-volumed by intergalactic, or even interplanetary, space by a lot). In those matter-rich environments, the mean free path of light is low. The constant c remains the same in such matter-rich environments, but electromagnetic radiation passing through them does not propagate at c.
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.
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.
You might want to read “The Intentional Stance” by Daniel Dennett, a philosophical treatise basically on how we usefully ascribe desire or intention to inanimate objects and phenomena as a mental model (for example, saying that “The thermostat tries to keep the temperature between 20 and 30”).
(This is not a comment on the precession video itself, which haven’t clicked on)
I’m well aware of this manner of speaking. Everyone is. If you did look at what I was commenting on (not a video) you might agree that its use in that case doesn’t help, at all. Or not.
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?
> how is that applied when the force is gravity, applied to every point of the object at every time?
It's about the point of suspension resisting gravity. The axis is "held" at a point, applying an "upward" force (resisting gravity). With gravity as you say evenly acting, the point opposite that through the centre of gravity will have a downward vector. The natural result of these opposing vectors might be rotation through the centre of gravity, but when those rotational forces are applied to moving targets you get suspension from the product.
Here's an insight that helped me: gyroscopic precession is the rotational analog of a circular orbit.
A circular orbit is when a linear force is applied orthogonal to linear velocity. The direction changes, but not magnitude (speed).
Gyroscopic precession is when a rotational force (torque) is applied orthogonal to rotational velocity. The axis of rotation changes but not magnitude (rotational speed).
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.
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 singular thing but really a bunch of particles bouncing against each other, but can still be described by ideal gas laws as if it were a singular object.
That seems like it would violate the conservation of energy. If all the momentum was linear, than changing the direction of those individual particles would require a force.
Lay person’s attempt at an explanation: Centripetal force, but no work is done because the motion of the spinning object is perpendicular to the force continually changing the linear motion to follow the circular course?
There are forces holding atoms together, such that the conglomerate constitutes a solid object whose geometry is stable in time. Those forces are strong, and are often sufficient to keep a solid object in the same shape even if rotating at high speeds. Sometimes they are not, in which case the solid object is deformed as the individual atoms are "flung outward" by the (ultimately linear) momentum, which overcomes the attractive force that binds atoms into molecules/lattices/whatever.
Thought experiment: if you have an elastic band floating in space, and you nudge it repeatedly to get it rotating faster and faster, will it stretch out (the way a timing belt would if run too fast) or will it stay slack? In its own reference frame, is the band being put under tension — and so experiencing elastic deformation — from the momentum of the particles within it?
Changing linear momentum does require a force (but not necessarily work), as does changing angular momentum. In orbits it's gravity, in particle interactions it's the electromagnetic force.
Well, if it completes a full rotation, the applied force over the time of the full rotation is zero (hence, work is zero). So yes, the momentum is linear, but it all pencils out by the direction, right?
That's my understanding of this, but I'm far from a physics expert.
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 someone could change the time/position/orientation/etc of the region in which you did your experiment and you would get the same results as long as you stayed in the lab they moved).
Angular momentum is the conserved quantity from rotational symmetry and is just as primary as energy-momentum or charge.
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.
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.
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."
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.
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 difference between this and what happens at the atomic scale.
The not layman’s answer is Noether’s theorem: the invariance of the laws of physics after a rotation of the frame of reference implies conservation of angular momentum.
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.
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?
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.
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.
In support of your idea, engineers routinely use FEA simulation software that models dynamic systems without any explicit representation of angular momentum or rotational inertia. Only linear displacement/velocity/acceleration, "translational" mass, and elasticity. Such software can still model rotating systems and all the complex effects that come with rotation. So at least classically, I don't think angular momentum is a fundamentally essential concept.
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.
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.
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[ 131 ms ] story [ 4164 ms ] threadThere'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.
Directional speed of light would be very weird, I think it'd show up everywhere in experiments if it weren't true.
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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.
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.
However, we can generalize your point and say that real configurations of matter let us make those decisions reasonably and with good accuracy. (The BIPM UTC Circular-T contributors seem to manage fine, as do the various GNSS operators).
If the video had taken care to set their experiment in vacuum flat spacetime (perturbed only by the experiment), as the shown Einstein 1905 work <https://www.fourmilab.ch/etexts/einstein/specrel/> (top of p. 3) did, it would be better. That's because that setting offers no convenient-to-agree way to slice spacetime into space and time. The CMB does, but we suffer from practical limits on measuring the CMB's blackbody temperature.
He is often wrong in subtle and not—subtle ways, though. In this case, regardless of the issue of one-way measurements of c, his sources do not really support an anisotropy in the speed of light.
His video was mentioned already 5 or 6 times here. Isn’t here anything better at all?
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.
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.
I think the heart of the what the GP is getting at is no matter how you define it, you can measure things smaller than your measuring equipment can detect.
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).
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)
You can build a consistent theory of aether by asserting that everything (including you) doppler shifts just so and there is a 0 speed through the aether. You get a complicated theory that is not experimentally distinguishable and is incredibly difficult to use and noone would have any idea how to extend to QM or gravity because it's so cumbersome, but it's consistent and mechanics works.
You could easily reframe the frame of reference in such a theory where the lab is moving at 0.999c absolute (which exists in this theory despite being immeasurable) as light moving very slowly in one direction and near instantly in the other.
I need to correct myself: If light traveled instantaneously, the expansion of space wouldn't matter because in the very instant in which light would be traveling space wouldn't be expanding. -> No redshift at all.
Edit: What I was missing was time dilation. Physically transporting the clocks would mean that they are no longer synchronized.
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")?
The absence of gravitational sources is an aspect of the flat spacetime of Special Relativity, but if we are cheating by adding in (and declaring gravitationally negligible) the experimental apparatus, why can't we cheat by adding in a non-gravitationally evolving bit of matter which can serve as a clock? A low-mass, sparse, spherical, uniform cloud of of hot dust expanding adiabatically can serve as a clock by measuring its and temperature if the one-way-transmitter and one-way-receiver are freely falling within it and moving slowly compared to light. This is essentially a demotion of the sparse cosmic microwave background gas/dust of massless photons -> sparse gas/dust of neutral low-mass molecules. The CMB expands and cools, while we're within it. Our non-relativistic molecular gas expands and cools, while our one-way test equipment is within it.
Of course, what is too much of a cheat in Special Relativity and what is not is debatable. In all the cases above we are ignoring the Raychaudhuri equation with the only justifications being that the timescales are too long to tell if we're focusing, and we aren't obviously engaging post-Newtonian (PN) corrections. (What gets us into trouble with PN formalisms in GR can get us into trouble in gravitation-free SR though: ultraboost one side of the experiment, rather than "... moving the clock slowly with respect to the stationary one". You guessed correctly that boosts and accelerations could be a problem in (2)&(3). However, contra your (3) acceleration is perfectly permissible in "pure" SR and the result is only equivalent to being in a uniform gravitational field (rather than with a potential gradient), and only somewhat briefly (you can rest your clock on an enormous rocky planet for much longer than you can accelerate your clock at ~ 10 g). The time dilation in (3) is Minkowski / Born / von Laue / Einstein 1905-1911 Special Relativistic and not post-1915 General Relativitistic. Your (1) is done for you for free in "pure" SR, since there is no gravitation there.)
General relativity is hardly a panacea: if we have a strongly expanding vacuum our one way pulse might never reach the detector. In a dynamical curved spacetime we can break the symmetry between legs of a reflection 2-way test in any number of ways.
It's really the breaking of the vacuum condition that lets us set up a "global" or at least wide-enough-area clock. When we're allowed to introduce half-life decays or thinning background matter or radiation, or distant millisecond pulsars, we are more likely to be able to use a synchronization scheme sufficiently different from Einstein's method and successfully compare timestamps at the sender and receiver of a one-way flash.
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* If we assume Special Relativity then we already have global Poincaré invariance, so we have already have symmetrical legs of a reflection test. If we have a setting which is maybe Minkowski spacetime, or maybe something other than Minkowski space that breaks the symmetry of the legs in a reflection test, then we probably can't do it with a one-way test along the lines you're thinking.
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.
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.
There is no "border" to our universe. The fact that you have trouble visualizing such models does not mean they don't exist.
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.
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.
If those axioms are changed, you get a different logical and mathematical outcome.
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.
As for a single counter example, you need to demonstrate that the counter example is applicable. I don't think you have. At least not to the degree that would support your categorical claim.
In regards to both of your views, I am making no statement as to validity or otherwise of those statements. This is simply a matter of asking for you and him to provide supporting evidence for your respective positions.
This would then allow further discussion on the views and their evidence.
If you think about what's happening inside a cake when you put it in an oven, it expands in all directions, and the center has only a meaning there because the cake is finite.
For a 2D model, consider only the surface of a balloon. As the balloon expands, each point on the surface increases in distance from every other point, but there is no center of the surface.
Be sure to consider only the surface, not the 3D embedding your (flawed) intuition wants to inject.
You can do the same thing in 1D with a circle.
This works in any dimension, including the 3+1 spacetime manifold.
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.
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.
> 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.
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.
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.
Vertasium video on the subject - https://www.youtube.com/watch?v=pTn6Ewhb27k
Why wouldn't we be able to measure the differences in the CMB, depending on the direction?
What do you mean by "linear flow"?
Based on the evidence so far provided, I have some concerns that what the CMB is supposed to represent is not actually what it represents.
Once you have experimental or observational anomalies that conflict with theory, one has to look at that theory as either being wrong or incomplete. After 40 years of watching these things, I conclude that we are still very ignorant of the nature of our universe.
Unfortunately, there are inherent infrastructure problems in scientific investigation and we often see politics and dogma interfering. This works to limit our understanding. I see this as a repeat of what was happening in the late 19th century. We didn't learn from our mistakes then and so we are doomed to repeat those mistakes now.
From an observational POV, we can see light coming to us from all directions radially towards us. We treat the speed as an essentially constant value, even though we know this is false in reality. It is a useful approximation that we use to simplify our models and calculations.
The calculated speed of light through a medium is related to both the permittivity and the permeability of the medium through which the light is passing. When you get to the situation where any kind of changes occur in these values over the path you then see other thing happening related to the frequencies involved.
These things make for all sorts of changes in the path and the speed over which light travels.
An analogy might help here (might). Take a particle of any kind and have it move along a path with potential assistance in its travel in one direction and then return that particle along the same path in the opposite direction. Ask the question, what is the one way speed of that particle if all you have is the total time for two path traversal and you are assuming that the particle is the one that traverses the path at a constant speed. What can you tell me about its instantaneous velocity over the path? You do not know what assistance, if any, that particle has received.
We make certain assumptions for which we cannot determine if they are true or not. To simplify our models, we take the view that our assumptions are NOT unreasonable, but we cannot test them. This is a normal state of affairs with relation to much of our scientific investigation. When we do find additional information that indicates that one or more of these assumption is potentially or actually false, we make modifications to our models and theories or we replace them entirely.
We make much ado about GR and curved space-time and that "gravity" bends light. There is an assumption here that medium changes and hence permittivity/permeability changes are not applicable or consequential in the observed path changes. The thing here is that we cannot measure those permittivity and permeability changes and assume that the light is traveling is traveling through a perfect vacuum, which we also know is false. But it "simplifies" the model and calculations.
We no longer use a geocentric model of the universe (this is effectively using Fourier Series) and we have moved over to a Heliocentric model because it is "simpler" to use. Yet, the heliocentric model is also wrong because it cannot take onto account the gravitational effects of all orbiting bodies. This gives rise to using perturbation theory. This makes the modelling much more complex and yet it too is not at all complete for it has not taken into account the motion of the sun and the orbiting bodies on the path through the galaxy. Again this gives rise to further complexity that must be taken into account.
For simplistic models, we use the heliocentric model and for short term situations, we just ignore perturbation effects of these other things. We do no less in analog circuit analysis or digital circuit analysis, orbital satellite mapping, weather forecasting, river flows, and the list goes on and on.
We use simpler models because they are "good enough" for what we are trying to do. But they will all fail once you get outside of the simplifying assumptions that underlay them. I return you to the aphorism popularised by George Box "All models are wrong, some are useful."
Of course, this assumes that the universe is isotropic and what not. But again[1], the alternative would be a fine-tuning conspiracy of cosmological scale.
[0]: More precisely, from the opposite direction.
[1]: https://news.ycombinator.com/item?id=32111588
I suspect if you break the rotational symmetry of the speed of light that you wind up breaking something like conservation of quantum spin angular momentum and the universe rapidly becomes nonsensical.
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 was correct, and the Maxwell equations (which also define the speed of light) were only valid in the special reference frame of the aether.
Special relativity assumes Maxwell equations are always correct in all reference frames and orientations, which was already an experimentally observed fact (albeit puzzling, back then), rather than an axiom, which implied that it is Galilean relativity that is broken and needs to be refined.
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 speed of light sneaks in this axiom in subtle ways.
I think you misinterpreted the parent's point. They weren't saying c being a constant in all reference frames is an axiom. Rather, they were saying that it's convention that c doesn't have a spatial, directional, preference. It's a different claim.
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.
This is a convention. It's called the Einstein synchronization convention. https://en.wikipedia.org/wiki/Einstein_synchronisation
See also: https://en.wikipedia.org/wiki/One-way_speed_of_light . From the article: "Experiments that attempt to directly probe the one-way speed of light independent of synchronization have been proposed, but none have succeeded in doing so.[3] Those experiments directly establish that synchronization with slow clock-transport is equivalent to Einstein synchronization, which is an important feature of special relativity. However, those experiments cannot directly establish the isotropy of the one-way speed of light since it has been shown that slow clock-transport, the laws of motion, and the way inertial reference frames are defined already involve the assumption of isotropic one-way speeds and thus, are equally conventional.[4] In general, it was shown that these experiments are consistent with anisotropic one-way light speed as long as the two-way light speed is isotropic.[1][5] "
I get what you're saying and I'm well aware that Maxwell's equations are rotation invariant. I'm saying it's more subtle and complicated than you think. For instance, time dilation will have an asymmetry under these assumptions.
tl;dr: coincident-events first, then labels (coordinates). [Einstein 1916, p.117 [2] although I remembered to look there only after writing all of the below]. One-way speed of light arguments are in danger of being coordinates-first, and thus insufficiently general for physics.[3]
The key word in your comment is
> directly
But why do we care? We have an abundance of indirect evidence, premised on direct tests of coordinate-independent features of our best most-fundamental theory. The two important features of (general) relativity are pointwise local Lorentz covariance -- where c is the only free parameter of the Lorentz group -- and the minimal coupling. Special relativity's Minkowski space is in this view a special static time-orientable spacetime in which we have global Poincaré invariance (c again is the only free parameter of the Poincaré group; the Lorentz group is a subgroup of the Poincaré group -- the latter includes all the spacetime translations, and in the Minkowski case the space-translation and time-translation symmetries all commute). When we go blithely parallel-transporting null vectors, this is what matters.
We can certainly write down an f(c) theory. Dicke did this in in his superb 1957 "Gravitation without a Principle of Equivalence" >https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.29....? and so have several others (See Ellis or Magueijo for a review <https://link.springer.com/article/10.1007/s10714-007-0396-4> corresponding with <https://arxiv.org/abs/astro-ph/0703751> resp. <https://iopscience.iop.org/article/10.1088/0034-4885/66/11/R...> open access, but corresponds with <https://arxiv.org/abs/astro-ph/0305457>).
It is far from silly to write down a theory where c varies in spacetime. It is the foundation of several alternative-to-cosmic-inflation decaying-bimetric theories of the very early universe, where c eventually stabilizes to its value in our local spacetime having been a different (typically much much much -- ~30 orders of magnitude -- higher) value during the formation of primordial matter density variations. The faster speed of light allows for distant reaches of the early universe to reach the same temperature with uniformity up to the small fluctuations in the cosmic microwave background.
Of course we run into the same point you've been working in this thread: it's hard to discover the exact function on c in the early universe. We have to rely on indirect evidence, and strong gravitational lensing is useful there. SVOM <https://svom.cnes.fr/en/SVOM/GP_mission.htm> is looking for Lorentz-invariance-violation (LIV)-induced modifications to the photon dispersion relation in vacuum, and is a particularly good platform for test of a Taylor-series expansion like E^2=p^2 c^2 ( 1 +- \sum_{n=1}^{\infty} a_n ), since GRBs at least somewhat escape the problem that the lowest order terms dominate at small energies, and they are distributed across the sky and at different redshifts. We are also now better equipped to study light echos (oh for a galactic supernova!) and detailed strong galactic lensing studies. Spoiler: the constraints on a spacetime-translational vari...
For a (physical) relativist, the speed of light is really simple. c = 1, everywhere and everywhen. <https://en.wikipedia.org/wiki/Geometrized_unit_system> This is because we have excellent evidence for the utility of <https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold#App...>, and the further astrophysically-driven demands of global hyperbolicity or at least reasonably strong causality conditions, no isometric embeddings, geodesic incompleteness, asymptotic flatness around sources, junctions in sufficiently flat space, and energy conditions. Those further demands are the basis for continuing to rely on Special Relativity in laboratory settings.
For a theoretical relativist, well, the best metric signature is probably +,+,+,...,+ (89,0). (cf. Egan's (4,0) "Riemannian General Relativity", <https://www.gregegan.net/ORTHOGONAL/06/GRExtra.html>)
- --
[1] quoting your wikipedia link, "... inertial frames and coordinates are defined from the outset so that space and time coordinates as well as slow clock-transport are described isotropically". Well, yes. Establish points first then assign coordinate labels is the relativist's procedure, surely?
On this point, Earth laboratories are in general not in inertial frames, thanks to gravitation. No laboratory is in general in an inertial frame, thanks to the metric expansion of space. We can in principle extract a preferred foliation (e.g. the scale factor a, or some function on lunisolar tides) and use that as the basis for time coordinates instead. In effect this is what we do for high-redshift objects and many lunar laser ranging experiments <https://ssd.jpl.nasa.gov/ftp/eph/planets/ioms/>[a] <https://arxiv.org/abs/1606.08376> §3,§4. <https://link.springer.com/article/10.1007/s10569-010-9303-5> discusses aspects of how to choose a preferred foliation (in the context of gauge freedom) in the solar system, and in the context of grinding out a results-prediction for some future LLR experiment. The goal is to be able to show that the locations of the three instruments were accurately predicted, and Lorentz-invariance is thoroughly baked in (the calculations are so exceptionally sensitive to the introduction of tiny breaking parameters in the style of SME <https://arxiv.org/abs/0801.0287> that it has led to the discovery and/or better understanding of several of the features listed as parameters at [[a] LLR_Model_2020_DR.pdf §4]).
[2] <https://archive.org/details/principleofrelat00eins/page/n189...>. Einstein 1916 is adapted into the arguably handier <https://en.wikisource.org/wiki/The_Founda...
What exactly is more subtle and complicated in the context of Maxwell equations? If speed of light has the anisotropy that you are describing, Maxwell equations must be incorrect. In what electromagnetic experiment has such anistropy of magnetic or electric constants have been ever observed?
You're basically saying "you haven't measured the one-way speed of light directly, so you haven't ruled it out the possibility of my exotic theory", but it is actually been ruled out by Maxwell equations a long time ago. Unless you have some experimental proof that Maxwell equations need to be modified to accommodate that elusive version of your aether, you can't claim the existence of such an anisotropy.
Physics is well connected in that you can't change one part of it (in your case, c in the context of special relatively) just because you found something that wasn't experimentally ruled out, and hope the rest of the physics (basically all massless field theories and relevant experimental results in this case) won't break.
This was the case in special relativity, with a flat space-time. In general relativity, space-time is curved and there are locally special directions. The laws of Physics still do not define special directions a priori. It is quite fundamental actually, and so far everything behaves as expected, at least in this respect. It is not as much an axiom as a consequence of Maxwell’s equations, from which we can deduce that light has a well-defined velocity in vacuum, irrespective of location or direction.
> 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.
There is something I don’t get here. If we shine a light on a detector, we can measure the time the light takes to reach the detector. Are you saying that the light hits the detector instantly, and then goes back to the source, or that the detector is the source and the light comes back to it after hitting the source instantly?
In practice, the speed of light does not depend on direction, as far as we can measure.
It could well be the same magnitude each direction or it could be instantaneous one way and 1/2 c back the other or any other combination of values as long as the average of the two way measurement is c.
Final note: the value that we put as c is only true in a very specific environment. It depends on the characteristics of the medium through which light is traveling as to what we will measure as the average two way speed. This is a consequence of the permeability and the permittivity of the medium through which the light is traveling. This is standard electrical engineering fare.
> If you shine a light on a detector, you measure the time it takes to travel both legs.
reflector, surely, rather than detector? Your director can record a timestamp locally while you and your flashlight are across the room. You don't need two legs.
The main objection upthread is that while your flashlight's "on" switch can also record a timestamp within the flashlight, synchronizing the flashlight's time to the detector's time so that one can compare the timestamps after the experiment is done (or days later, or weeks later, again and again) is not feasible within the framework of Special Relativity. Therefore if one has confidence in one's local timestamps, one can compare them when measuring the round trip of the flashlight beam reflected off a mirror across the room back onto a detector mounted right beside the flashlight's bulb, inside the flashlight.
However, nature provides several gravitationally-driven systems which can provide a "preferred foliation", or a naturally-produced easily-compared timestamp. Examples include fancy sundials (including observations of millisecond pulsars), lunisolar tides, and the cosmological scale factor. These can be recovered independently in a (probably pretty large) flashlight and the detector looking for the light from the flashlight. Timestamps can then be compared with greater precision than available via Special Relativity synchronization methods.
Indeed, this is something that has been worked on in lunar-ranging experiments over the past decades. Can we use detailed knowledge of the solar system to predict a signal aimed Earthward by a 21st century space probe on or very near the moon as well as a signal launched from Earth to a reflector on the moon that is picked up by a detector on Earth? It turns out we can, to good precision!
> Final note
"c" is the free parameter of the Lorentz group, which is the fundamental isometry group of Special Relativity (and quantum electrodynamics and the Standard Model of particle physics). "c" is also a constant in the Einstein Field Equations of General Relativity, and there is a mathematical connection between that and Special Relativity.
In both theories, unless interfered with by interaction with matter, massless objects are constrained to move, obligatorily, from one spacetime point to another point from a restricted set of neighbours. These points are on the surface of a null cone.
Light is experimentally massless, so null curves are often called lightlike curves, null cones are usually called light cones, and so on. However, electromagnetic radiation is not the only massless species in the cosmos.
> very specific environment
An excellent approximation of vacuum (very long mean free paths for electromagnetic radiation at all frequencies) dominates the observable universe, so the permeability and permittivity of free space is a good choice except in very specific environments (planet-bound electrical engineering laboratories and copper wires are out-volumed by intergalactic, or even interplanetary, space by a lot). In those matter-rich environments, the mean free path of light is low. The constant c remains the same in such matter-rich environments, but electromagnetic radiation passing through them does not propagate at c.
> the value that we put as c
is exactly 1. <https://en.wikipedia.org/wiki/Geometrized_unit_system>
I've never thought much of it.
(This is not a comment on the precession video itself, which haven’t clicked on)
I’ll look up the Dennett article, thanks.
I don't see how this is not magical thinking but the rules of arithmetic are.
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?
It's about the point of suspension resisting gravity. The axis is "held" at a point, applying an "upward" force (resisting gravity). With gravity as you say evenly acting, the point opposite that through the centre of gravity will have a downward vector. The natural result of these opposing vectors might be rotation through the centre of gravity, but when those rotational forces are applied to moving targets you get suspension from the product.
A circular orbit is when a linear force is applied orthogonal to linear velocity. The direction changes, but not magnitude (speed).
Gyroscopic precession is when a rotational force (torque) is applied orthogonal to rotational velocity. The axis of rotation changes but not magnitude (rotational speed).
What is the flaw in my thinking?
That's my understanding of this, but I'm far from a physics expert.
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 someone could change the time/position/orientation/etc of the region in which you did your experiment and you would get the same results as long as you stayed in the lab they moved).
Angular momentum is the conserved quantity from rotational symmetry and is just as primary as energy-momentum or charge.
> 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.
In what sense is it the same? If we called them completely different names, what would be different or more complex?
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.
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?
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.
The not layman’s answer is Noether’s theorem: the invariance of the laws of physics after a rotation of the frame of reference implies conservation of angular momentum.
edit: I accept that the non-layman’s answer may hold, I just find the intuition a bit off.
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?
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.
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?
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)
It finally clicks!