HN Theater @HNTheaterMonth

PBS Space Time has done a couple of episodes on Stationary Action and Noether's Theorem that are approachable by those not yet already exposed to Langrangians:

https://www.youtube.com/watch?v=Q_CQDSlmboA

https://www.youtube.com/watch?v=04ERSb06dOg

Sabine Hossenfelder also has a good episode on it:

https://www.youtube.com/watch?v=A0da8TEeaeE

I'd recommend the two episodes released right before the one about the black hole information paradox too. They set up for what is covered in the information paradox episode.

"Why Quantum Information is Never Destroyed" - https://www.youtube.com/watch?v=HF-9Dy6iB_4

"What Survives Inside A Black Hole?" - https://www.youtube.com/watch?v=GscfuQWZFAo

Maybe the episode before those two also. I vaguely recall that something from the information paradox episode used something from that (and if I'm misremembering, it was still a neat episode):

"Noether's Theorem and The Symmetries of Reality" - https://www.youtube.com/watch?v=04ERSb06dOg

I have a question about the episodes you cited. They cover how beyond the event horizon space becomes time and time becomes space. They go over how that means that inside you can't go backwards in space for the same reason that out here in the normal universe you can't go backwards in time. You are doomed to only go forward, which inside means toward the singularity.

(Much better than the ridiculous analogy often given that you can't get out of a black hole because the escape velocity equals or exceeds the speed of light. That's a ridiculous analogy because it only explains why you can't get out ballistically).

But all their explanations used a simplified black hole in a spacetime with just 1 space dimension and 1 time dimension. We've actually got 3 space dimension. Does that mean that in a real block hole past the event horizon, you end up in a spacetime with 3 time dimensions and 1 space dimension?

If so, does anything interesting happen due to having more than one time dimension?

⬐ neom

I think that's the million dollar question. :)

This episode touches on that a bit (but not really), and we're getting into holographic universe theory - https://www.youtube.com/watch?v=klpDHn8viX8

Things are conserved when there's a corresponding symmetry; this is Noether's Theorem.[1] I won't pretend to understand half that article, but here's a video[2] on it.

[1]: https://en.wikipedia.org/wiki/Noether%27s_theorem

[2]: https://www.youtube.com/watch?v=04ERSb06dOg

The Map is Not the Territory!

https://wiki.lesswrong.com/wiki/The_map_is_not_the_territory

Another piece of widespread ignorance I've seen here on HN, is the treatment of conservation laws as if they're baked into the fabric of reality. This results in programmers making philosophical/cosmological arguments in ignorance. As far as we know, conservation laws are not baked into reality. Instead, they are very useful analysis tools which can take advantage of symmetries. (Or near-symmetries.) Any given conservation law can disappear if a given symmetry doesn't apply, but Noether's Theorem still remains.

https://www.youtube.com/watch?v=04ERSb06dOg

If you want to see an example of how social media "bubbles" can impede the dissemination of knowledge, note that I've actually been flagged on HN for trying to explain this, apparently because someone misread this as advocacy for perpetual motion machines. It is not! (Also, because I used <facepalm> -- but when you're wrong, you're wrong, and when you're wrong and you think it's clever, it feels worse.)

(That title, "The Map is Not the Territory" acts as a pointer to a series of literary references. https://en.wikipedia.org/wiki/The_Map_and_the_Territory )

⬐ tzs

Sean Carroll has an interesting article on this: "Energy Is Not Conserved": http://www.preposterousuniverse.com/blog/2010/02/22/energy-i...

⬐ manyoso

Completely unrelated to the original article which is just more multiverse bullocks of the stringy landscape variety. These scientists will die off and with it these articles.

⬐ tobmlt

I went to exactly the same post on Carroll's blog in response to the parent comment as well! Quite relevant I thought, given the comments about conservation laws and the especially the mention of dark energy that followed. -I elected not to post up there as I am studying GR - and not so confident with it! Thanks for dropping it in.

⬐ s-shellfish

The map is the territory for belief about belief though, sometimes, if people choose to agree.

You can believe things about how people think and this can affect how people think. Sometimes precisely, such as in the case of a mental illness diagnosis a person may have been indoctrinated into believing is their identity, sometimes generally, chaotically, without direct transmission perfectly.

I'd compare Machiavellian motivations here, belief about belief with the intent to control comes from the desire to control and rule through thinking, but the domination of thought/behavior of individuals through one's thoughts alone... people eventually become aware of intents, if there's always that imbalance. The problem often stems from assuming one has earned the right to dominate and another must do X,Y,Z to earn respect. Quite frankly, humans from birth to death and every point in between are equivalently autonomous and worthy of being able to think the way they want to, without having to do anything to have earned such a right. Thinking otherwise is a good example of being wrong and clever in a way that can be quite haunting.

I think these kinds of validations get conflated with hard data. Often, it is a lot easier to just listen to people and let them believe what they want to. Gotta trust people to come to their own conclusions independently.

In the age of machine learning, behavior shaping, I think a lot of this is quite topical.

⬐ stcredzero

The map is the territory for belief about belief though, sometimes, if people choose to agree.

Let's say I build a theme park in the form of a giant map of the world. I could then print a map to my theme park.

Quite frankly, humans from birth to death and every point in between are equivalently autonomous and worthy of being able to think the way they want to, without having to do anything to have earned such a right.

You can think any way you want to, and I will respect your right to think that way. I can respect that you think, but that doesn't mean I have to respect what you think.

⬐ s-shellfish

> You can think any way you want to, and I will respect your right to think that way. I can respect that you think, but that doesn't mean I have to respect what you think.

That's totally fine, just in my personal experience, stuff like that has a funny way of coming back in thought.

I find that no matter what words come out in reality, transmission through language, it never really tells you very much about how a person actually thinks. Kind of hard to know how another person thinks, because, that kind of seems like believing in telepathy.

Let's say that the mere act of me saying what I 'think' causes my thinking to change, instantly, perfectly flipping to a perfectly opposite perspective. What's there to respect at that point?

⬐ stcredzero

What's there to respect at that point?

You were thinking. I respect that. Hell, if you were sincerely trying to think, then had a total brain-fart, I'd still respect the attempt.

⬐ s-shellfish

I suppose at this point I would ask the question, what does it mean to think? What is 'thinking'? What's the goal?

⬐ stcredzero

I tell you what, you think about that and get back to me about it.

⬐ s-shellfish

I've thought about it a lot. It just seems to loop, to find a way that allows me to believe I have done enough work such that I am allowed to have the thoughts I wanted to have from the beginning. There are all sorts of ways I seem to invent to do this. Doing differently, every single time, every new way of working through 'thought', what's the original point?

What do you think? Let's compare notes.

⬐ stcredzero

I've thought about it a lot.

I think your experience of thought is worth a lot more than anything I could tell you about it. (Yes, I planned that out.)

Doing differently, every single time, every new way of working through 'thought', what's the original point?

Is it fun? If it's not fun, then don't do that. Also, as far as a "point" goes, that is up to you. Let me testify to you, as an atheist, that you can find meaning in life by living it "meaningfully." Do that enough, and you will find it. Physical and aesthetic activities with others help a lot. Sharing food and experiences with true friends is key.

What do you think? Let's compare notes.

See the thread above.

⬐ s-shellfish

The concept of 'baked in'.

I sort of find doing stuff with words fun, sometimes. It's a creative endeavor, but also fairly rigorous.

Otherwise, stare off into space, and wonder if the terrible things I don't want to happen have happened yet.

Food, experiences, aesthetics, pleasure, hedonism. I study Zen quite a bit. I don't find it fun. It's just a way to reveal truths to others because,they can't be revealed directly and accepted at face value, for some.

Words are memes. Ideas are baked in. Connections dance in patterns. Math and logic form the foundation. Mind tests for correctness. Self, universe, theory. Universe is infinite, self knowledge - finite (or is it?). Theory unites with self, universe serves as reality check. Theory united with self, is this equivalent to the universe?

What is mind? The experience of everything you've ever experienced, collapsing in on itself.

https://youtu.be/1PT90dAA49Q

What happens after that? That, I find interesting. Post modernism, maybe. Where are the new words, new theories, new patterns? Dance on top of all that exists.

⬐ stcredzero

The experience of everything you've ever experienced, collapsing in on itself.

I usually experience paroxysms of guilt from the embarrassment of everything stupid I've ever done.

https://proxy.duckduckgo.com/iur/?f=1&image_host=http%3A%2F%...

What happens after that? That, I find interesting. Post modernism, maybe.

Well, if there is a new wave of reason, then a backlash of unreason is not unexpected.

https://www.youtube.com/watch?v=qwZ651i5vls

⬐ None

None

⬐ s-shellfish

I used to be like that, but, life is too short to allow embarrassment to paralyze you. If you go through it often enough, you develop a sort of numbness to it. I'm sure I can still embarrass myself, but I try not to dwell in that micro blackhole. PTSD has taught me that if you are constantly focused on those patterns, you will see them in everything. So you might wind up feeling like you are embarrassing yourself constantly even though external reality has no validation mechanic to prove this. Are people saying you are embarrassing? And should you care, if they do think this? That judgement is their own burden.

You can keep wondering, but to me that's the same as thinking everything is traumatic because the reality of the present is 'connected' to the memory of the past. All those links, you can keep stepping back into them until you feel like, "I am reliving this again", but, that happens frequently enough and I dunno.

Labeling things stupid just means you have less tools to work with when a stupid thing might actually be the more smart thing to work with. Doesn't mean you won't make mistakes. As far as intelligence is concerned, I'm not sure any human is intelligent enough to be it while knowing what it is.

⬐ thanatropism

It's hard to make time symmetry (and thus conservation of energy) "disappear", though.

⬐ stcredzero

Physicists have already shown that Time symmetry isn't absolute.

https://www.youtube.com/watch?v=yArprk0q9eE

We already know that conservation of energy isn't absolute. It is, however, a very powerful analysis tool, just as Euclidian geometry is a very powerful powerful analysis tool. It's very accurate on certain scales, however, that's not how the universe works if you look closely enough.

⬐ myWindoonn

There probably isn't a plain time symmetry, but maybe there is CPT symmetry. Lucky 10000: https://en.wikipedia.org/wiki/CPT_symmetry

⬐ wnoise

He's talking about time-translation symmetry, not time-reversal symmetry, which is the T in CPT.

⬐ tobmlt

A quick check makes me think that one has fallen quite recently(?): https://arxiv.org/pdf/1202.2539v2.pdf

https://en.wikipedia.org/wiki/Time_translation_symmetry https://en.wikipedia.org/wiki/Time_crystal

Edit: Also: https://www.reddit.com/r/askscience/comments/52has4/what_is_...

https://arxiv.org/pdf/1603.08001v4.pdf

Periodic, discrete symmetry holds, continuous is toast. Interesting.. Maybe there should be a rule of thumb (XKCD?) that says for any intuition one may hold, some researcher somewhere is, at ``this'' moment (in some measuring system) constructing a contrived situation that will break it via some contrivance that is strange in inverse proportion to the homeliness of the intuition? ....And some talky-site-poster (me in this case) is preparing to make it yak about it?

⬐ wnoise

These don't break fundamental time translation symmetry, anymore than regular crystals break fundamental space translation symmetry (which is equivalent to conservation of momentum). The fundamental versions of these symmetries are that the laws of physics are unchanged under such changes.

These are merely systems such that the system itself lacks such a symmetry. This will indeed allow a change in the "effective" laws of physics (like electrons having different effective mass in metals or semiconductors than in free space, and quantized momenta), and give something interacting with the system the illusion that energy or momentum is not conserved. But this is only an illusion: momentum and energy of something interacting with the system are exchanged with the system.

This shouldn't be mysterious though -- a time changing potential already didn't preserve the energy of what it's interacting with, and a crystal can absorb momentum as a whole without any local disturbances that could be seen by a particle in it (e.g. Mossbauer effect). But the upshot is that what counts as a symmetry depends on what's fixed under your analysis vs what's part of the state space.

⬐ tobmlt

Thanks for the details and big picture. Very nicely put.

⬐ stcredzero

Good point!

⬐ danbruc

Energy is not conserved in general relativity in the general case due to the expansion of the universe.

⬐ alexbeloi

There may as well be no territory, the only thing relevant is the map and how it reacts to probing.

⬐ stcredzero

the only thing relevant is the map and how it reacts to probing

Sounds like Postmodernism to me. If you think it's not, then let me point out that you can just substitute "text" for "map" and you're pretty much there.

There must be something underlying the maps, because so many of those maps have turned out to be wildly wrong, completely barking up the wrong tree. It's not even that they didn't answer the questions correctly -- they were so wrong, they were asking nonsense questions in the first place.

There is a nice little allegory by Raymond Smullyan, where some ancient philosophers are debating what keeps the world from "falling down." I think it's in "5000 BC," and is the story by that name.

https://www.amazon.ca/5000-B-C-Other-Philosophical-Fantasies...

⬐ kolpa

Scientific maps are wrong when they are shown to be inconsistent or incomplete. Of course people can make mistakes.

⬐ stcredzero

I was responding to, "There may as well be no territory, the only thing relevant is the map and how it reacts to probing."

If there are only maps, then when map A is wrong, I can just make my own map B for which map A is a good map. In that case, no map is falsifiable, and all maps are equally valid. It's Postmodernism!

⬐ AnimalMuppet

> As far as we know, conservation laws are not baked into reality.

I think that's going too far. As far as we know, the symmetries could be baked into reality. And, via Noether's Theorem, so therefore are the conservation laws.

⬐ stcredzero

> I think that's going too far. As far as we know, the symmetries could be baked into reality.

Are you aware that the symmetries have been falling and that physicists been retreating? First, parity symmetry fell in 1956, resulting in a retreat to CP symmetry, which also fell. Now we're to CPT symmetry, which implies that there is no time symmetry, which in turn has been verified by physicists.

https://www.youtube.com/watch?v=yArprk0q9eE

⬐ ymolodtsov

Those are different symmetries.

⬐ AnimalMuppet

Well, it implies that charge symmetry, parity symmetry, and time-reversal symmetry are different aspects of the same thing. I'm not sure that's quite "falling", though.

⬐ stcredzero

You just admitted that charge symmetry, parity symmetry, and time-reversal symmetry are incomplete. I'm quite sure that the old mental models which held those to be absolute did "fall."

⬐ AnimalMuppet

You seem to want to play "gotcha" games with my wording. I admitted far less than you seem to want to make my words say. And if you're going to try to manipulate what I said to make it fit the axe you're trying to grind, then I'm done talking to you.

⬐ stcredzero

You seem to want to play "gotcha" games with my wording.

It's not a game. You ironically committed the Map/Territory error, in a Map/Terriotry discussion. A condition of underlying reality where a given symmetry exists, or only appears to exist, can't fall. It either is or isn't. But the mental model -- the Map -- using symmetry can indeed be shown to be false and fall.

And if you're going to try to manipulate what I said to make it fit the axe you're trying to grind, then I'm done talking to you.

I did no such manipulation. I bet you can't substantiate that with reasoning and quotes. In any case, I am well satisfied to let 3rd parties read and decide for themselves.

(Ironic in the Alanis Morrisette sense, not the hipster sense.)

⬐ kolpa

It is falling. The old theory was that these were 3 fundamental facts in the universe. The modern theory is that there is 1 fundamental "triangular" fact, not derivable from simpler facts. That makes the Universe more fundamentally complicated than previously thought.

And furthermore, it's not simply that any given random kind of particle is either "Yes or "No" on each of the 3 corners, while constrained to be "Yes" on the combination. There is a strong bias toward Yes in all three points -- which is even more asymmetry than was previously thought possible. (A fact that samples at 100% true or 50% true is far more symmetric than sampling at 98% true -- the bias needs a deeper explanation, or more fundamental parameters of the universe)

⬐ kolpa

What does "baked into reality" mean? We can never know more about reality than what we observe, and furthermore conservation laws are axiomatic -- conservation simply means that we are able to account for (almost) everything we observe, in a consistent way. When conservation is broken, we name a new form of energy, and (so far), we find that it can by accounted in a consistent, predictable way. (Dark matter is an unsolved problem. Knowledge is incomplete. That doesn't mean conservation is false.)

When it comes to fundamental science, a consistent map is the territory. "Map is not the territory" applies to simplifications that omit detail.

I don't see people trying to be "clever".

⬐ stcredzero

What does "baked into reality" mean? We can never know more about reality than what we observe, and furthermore conservation laws are axiomatic -- conservation simply means that we are able to account for (almost) everything we observe, in a consistent way.

You said it right there. "Almost." We keep on prying and doing experiments, and we can't find any exception. If we've tried hard enough for long enough, we can start to conclude that we're probably getting close to reality. If we pry and we find it's "almost" then we know it's not baked into reality.

When conservation is broken, we name a new form of energy, and (so far), we find that it can by accounted in a consistent, predictable way. (Dark matter is an unsolved problem.

[Citation Needed] Yes, we still don't know what Dark Matter is, but do you understand that dark energy is not dark matter, and the current model for dark energy involves space expanding and more dark energy appearing due to the space expanding? Citing dark energy is tantamount to admitting that conservation of energy isn't universal.

When it comes to fundamental science, a consistent map is the territory.

Arrgh. You're getting your pointers mixed up here. A context where science is the territory would be the study of Science, as in the philosophy of science. When it comes to fundamental reality, Science is the map and fundamental reality is the territory.

⬐ kolpa

Sorry, I should have said we don't understand dark energy yet.

In what sense does "fundamental reality" exist?

⬐ goatlover

That which gives rise to experimental results and perception. If you don't think there's a real world responsible for those, then how do you explain what we sense and the results from experiments? What makes the technology work? God?

⬐ throwaway37585

> God?

What do you mean by this?

⬐ goatlover

I mean that if reality (nature, the world) isn't responsible for our experiences of a world, including scientific experiments, then what is? Does the empirical just a appear for no reason with nothing behind it?

⬐ gowld

I surely don't know. That's metaphysics, not science.

⬐ stcredzero

I surely don't know. That's metaphysics, not science.

But you can clearly do science on the technology. People do this with high degrees of success, developing theoretical models with high predictive ability. It's called "reverse engineering." If you're going to retreat into metaphysical mumbo-jumbo, that's up to you. The doing and the results will speak for themselves, and no one will pay attention to the metaphysical mumbo-jumbo obscurantists.

⬐ stcredzero

We're working on it. We'll get back to you on that. (Maybe we need a bigger particle accelerator?)

⬐ pkghost

kudos to stcredzero for a humorous and tactful exit... I'll be the killjoy and explain his joke, which I think was a last-ditch attempt illustrate the point he's been trying (and failing) to get across all thread, which is that

> When it comes to fundamental science, a consistent map is the territory

isn't the case.

Science/empiricism merely produce predictive models; over the last few hundred years, these models have improved dramatically, but they are nonetheless only maps of a territory ("reality"), and it's still fundamentally uncertain that the underlying assumptions (that laws of nature exist/that reality is mappable) are reliable.

> "Map is not the territory" applies to simplifications that omit detail.

Even if we had a perfect model, which we don't (and it's not clear that such a model is obtainable) that could predict everything, it would still be separate from the territory. You might think this is a pedantic distinction, and in your ideal world where we have a unified field theory, it certainly would be, but like I said above, it's not clear that such a thing is obtainable, so it's important to hold onto the distinction lest we forget the fact that we're still sitting on an incredibly young and uncertain foundation.

⬐ None

None

⬐ goatlover

> When it comes to fundamental science, a consistent map is the territory. "Map is not the territory" applies to simplifications that omit detail.

But physics does leave out detail. It's an abstraction over many particular instances. Nature isn't a physics equation. An equation doesn't generate a field of force, nor does it have any causal powers.

> We can never know more about reality than what we observe

If that were true, then theoretical physics wouldn't exist. Much of scientific theory involves unobservables, or processes way too long for us to observe. Most of evolutionary history is unobservable. We have to fill in the gaps with a theory explaining the fossil record, genetics, and the organisms around us.

We don't have time machines, nor billion year old cameras.

Yes the actual laws of physics can't be broken

Conservation laws should be considered more as powerful analysis tools than as foundations of reality. So more Newtonian gravity than Relativity. In fact, you can regard Newtonian orbital mechanics as elaborations on conservation of energy and momentum. Conservation laws themselves have an underlying principle:

https://www.youtube.com/watch?v=04ERSb06dOg

Another analogy: Conservation laws are like Euclidian geometry. On the scale of building a cabinet or an office building, Euclidian geometry rules! On intergalactic scales, it simply fails. So too, with the conservation of energy. If someone tries to sell you a perpetual motion or over unity machine, it is pretty rock solid. But if you're going to try to make some kind of cosmological argument using conservation of energy, that's just plain facepalm territory there. (Some HNer actually reported me for using <facepalm> in response to conservation of energy in a cosmological argument.)

⬐ Florin_Andrei

> Conservation laws themselves have an underlying principle:

(before checking the link - "I bet it's Noether's theorem")

(checks link - yep)

I've always thought Noether's formulation and the conservation laws are more like equivalent shapes of the same features of reality.

⬐ stcredzero

Except that any particular conservation law might fly out the window, but so long as there was some sort of symmetry, Noether's theorem would still be there.

> if you're saying conservation of momentum can be violated, or conservation of energy can be violated, then basically all of modern physics would have to be wrong.

Conservation is not a fundamental law, but an emergent property of a deeper principle called Noether's Theorem:

https://en.wikipedia.org/wiki/Noether%27s_theorem

https://www.youtube.com/watch?v=04ERSb06dOg&t=594s

And it is constantly violated.

⬐ smaddox

Can you give an example of how it is "constantly violated"? One not involving a "perpetual motion machine"?

⬐ geon

The linked video mentions the expansion of the universe, and relativity.

⬐ raattgift

Just to follow-up on my longer reply above: the solar system is not expanding. So within the solar system, there should be exact conservation of energy. (And we do test this in many ways, and it holds up).

The metric expansion only operates on scales much larger than that of the solar system (and even larger than that of the Milky Way and its collection of nearby neighbours).

(One can take a theory other than General Relativity and finely-tune the expansion of the solar system to match the null results on measures of it, and this is done in some quintessence and other models, but this won't help one do away with exact conservation of energy at scales of EmDrives; or give much room to have more energy moving into (or out of) a boundary drawn outside the solar system and the wider universe).

⬐ raattgift

> Noether's Theorem

Right, and we have determined the exact local symmetry with which we can use Noether's Theorem to show a set of exact conservation laws, and expect it to apply everywhere in the universe (and we test against that assiduously).

Concretely, we have ample direct experimental evidence that everywhere accessible in the solar system, to extremely high precision, at length scales of microseconds (and light-microseconds), spacetime has an exact local symmetry group SO(1,3), which is the Poincaré group. The exact symmetries of the Poincaré group include invariance of systems under rotations and translations. Colloquially, it doesn't matter whether your laboratory is laid out east-west vs north-south if you're testing Poincaré invariance wholly within the laboratory, i.e., you're not deliberately testing something much larger, like the Earth's magnetic field, or solar neutrinos, and it doesn't matter if you run your tests in northern hemisphere spring or northern hemisphere winter (notably the planet is at a very different point compared to other solar system bodies at both times, so this is a full spacetime translation).

That is, the results of locally-determinable non-gravitational experiments do not depend on position in spacetime, or orientation with respect to some distant object.

The rotational invariance, via Noether, gives us conservation of angular momentum.

The translation invariance, via Noether, gives us conservation of energy-monentum. With any reasonable splitting of 4-spacetime into three spatial and one timelike dimension, we take the resulting spatial translation invariance and get conservation of linear momentum, and the resulting time translation invariance and get conservation of energy.

In General Relativity, we are guaranteed a patch of flat spacetime around every point in the manifold. Far from massive objects, that patch can cover a fairly large region of spacetime (>> microseconds or light-microseconds). The metric of flat spacetime directly maps to the Poincaré group; more formally, the Poincaré group is the local group theory of Minkowski space, and the Lorentzian metric on the whole spacetime guarantees Minkowski space in small regions.

So even though we must bring in the equivalence principle when doing so, we fully preserve Poincaré invariance at laboratory scales even when on the surface of the various massive bodies in our solar system. This has already been tested experimentally to high precision against several different planetary objects other than the Earth, and several objects which aren't in approximate hydrostatic equilibrium (and thus not planets).

Everywhere we observe (on Earth, elsewhere in the solar system, and with astronomical observations) we see evidence for local Poincaré invariance (up to strong gravity, which is hidden behind event horizons anyway) from emissions and absorptions spectra, and various other observables.

Note, though, that while everywhere-flat spacetime -- the setting of Special Relativity, and in fact what makes the theory Special -- has global Poincaré symmetry, that is not true for spacetime which is not everywhere flat. The global symmetries of the FLRW model of the standard cosmology, for instance, are not time-translation invariant. Therefore there is no correspondence via Noether to a conservation of energy. However, the "swiss-cheese" approach lets us replace a comoving speck of the standard cosmology's expanding dust with a smaller-than-Megaparsec scale region of flat spacetime (corresponding to a region of spacetime far outside any galaxy clusters) or a smaller-than-Megaparsec scale region of Schwarzschild(-like) spacetime (corresponding to a region of spacetime in which there is some collapsing mass, like a galaxy cluster). This is a "sewing" or "stitching-in" process which is described in various places like Misner-Thorne-Wheeler's section on the Israel junction conditions. The standard cosmology gives us a slicing into spatial and timelike dimensions. Thus within in the two examples of "stitched-in" regions, we would the local symmetries in each such spacetime to apply, with appropriately conserved quantities per Noether's Theorem.

Indeed, we test to see whether building up the solar system by sewing together small patches of Schwarzschild(-like) and Minkowski spacetimes accords with the previously mentioned observational tests of General Relativity, at the level of numerical relativity. They do.

So, there is no escaping conservation-of-energy within the solar system theoretically. Tests of the fundamental pieces of this (which are ultimately tests of the equivalence principle under some very light assumptions, and tests of the Standard Model of Particle Physics, which incorporates the Poincaré group directly into it's formalism) support this to many decimal places.

Thus,

> it is constantly violated

is not true anywhere within the solar system, nor anywhere within the local group of galaxies back to when it first started forming stars. That is a rather large volume of spacetime.

However, after one moves sufficiently far away from that region, spacetime is no longer well modelled by a Schwarzschild-like solution, but is instead well-modelled by a Robertson-Walker metric (conversely, within the Milky way, nowhere is space well-modelled by a Robertson-Walker metric). In faraway regions of the universe which matches the observables of Robertson-Walker, one should expect a failure of the global symmetries of Schwarzschild(-like) spacetime.

Finally, even with an expanding Friedmann-Lemaître-Robertson-Walker (FLRW) model, and without "swiss cheese-ing" it, there is still at every point a small patch of spacetime in which the local symmetries are experimentally indistinguishable from Poincaré. Thus, to observe a violation of conservation of momentum (or energy) in our standard expanding spacetime with the observed value for the cosmological constant, you need a separation of millions of lightyears. This is why we see a cosmological redshift from distant galaxies but no cosmological redshift from nearby ones.

⬐ igravious

The section of the video dealing with Noether's Theorem and The Symmetries of Reality actually ends at t=594s :/ so just the main link is needed: https://www.youtube.com/watch?v=04ERSb06dOg

If one or another of these so-called fundamental laws is being apparently broken by the EmDrive then that would make it a very very unusual object. Consequently there would need to be repeatable verifiable evidence that it does so and at least the beginnings of a theory as to how in fact this breakage is occurring–Noether's theorem notwithstanding.

seems that pbs has a new one on Noethers theorem: https://www.youtube.com/watch?v=04ERSb06dOg