Yes? It means the Lorentz invariance is automatic from the form of the expression, does it not?
Yes. But when "Lorentz invariance isn't automatic from the form of the expression" it does NOT follow that you don't have Lorentz invariance.
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ekjhgkejhgk commented on String theory inspires a brilliant, baffling new math proof quantamagazine.org/string... · Posted by u/ArmageddonIt
ekjhgkejhgk commented on String theory inspires a brilliant, baffling new math proof quantamagazine.org/string... · Posted by u/ArmageddonIt
Ok, so I looked into it a bit, and here’s my understanding:
The Polyakov action is kinda by default manifestly Lorentz invariant, but in order to quantize it, one generally first picks the light cone gauge, where this gauge choice treats some of the coordinates differently, losing the manifest Lorentz invariance. The reason for making this gauge choice is in order to make unitarity clear (/sorta automatic).
An alternative route keeps manifest Lorentz invariance, but proceeding this way, unitarity is not clear.
And then, in the critical dimensions (26 or 10, as appropriate; We have fermions, so, presumably 10) it can be shown that a certain issue (chiral anomaly, I think it was) gets cancelled out, and therefore the two approaches agree.
But, I guess, if one imposes the light cone gauge, if not in a space of dimensionality the critical dimension, the issue doesn’t cancel out and Lorentz invariance is violated? (Previously I was under the impression that when the dimensionality is wrong, things just diverged, and I’m not particularly confident about the “actually it implies violations of Lorentz invariance” thing I just read.)
> losing the manifest Lorentz invariance.
You understand that this have nothing to do with actual Lorentz invariance, yes? It sounds like you don't really understand the meaning of those terms you're using.
Do you understand what "manifest Lorentz invariance" means?
ekjhgkejhgk commented on Tesla US sales drop to nearly 4-year low in November reuters.com/business/auto... · Posted by u/doener
When I watched a very short clip juxtaposed next to a clip of a nazi salute, then it looked like one to me.
But when I watched it in context, it looked like a man putting a hand on his heart and then proffering his thanks to the audience.
My belief is that it was most likely not a nazi salute and is not relevant evidence in the important task of assessing Musk's political stances.
Looked like a man putting a hand on his heart and then saluting the fuhrer.
ekjhgkejhgk commented on Tesla US sales drop to nearly 4-year low in November reuters.com/business/auto... · Posted by u/doener
Every time I see a CyberTruck out in the wild, I feel like reality is broken.
The level of disaster of that rollout, combined with D.O.G.E. and "Mechahitler" Grok, has forever tarnished the Tesla brand. I suspect there is a sizable group of people who will never buy a product by that brand ever again (or at least as long as Musk is at the helm).
I notice you skipped mentioning the CEO doing nazi salutes.
ekjhgkejhgk commented on String theory inspires a brilliant, baffling new math proof quantamagazine.org/string... · Posted by u/ArmageddonIt
> But there are such experiments. String theory says that the result of such experiment is: Lorentz invariance not violated.
This is not a new prediction... String theory makes no new predictions, I hear. I don't understand why you need to be told this.
To your point, there exist various reformulations of physics theories, like Lagrangian mechanics and Hamiltonian mechanics, which are both reformulations of Newtonian mechanics. But these don't make new predictions. They're just better for calculating or understanding certain things. That's quite different from proposing special relativity for the first time, or thermodynamics for the first time, which do make novel predictions compared to Newton.
> there exist various reformulations of physics theories, like Lagrangian mechanics and Hamiltonian mechanics, which are both reformulations of Newtonian mechanics
You have no clue what you're talking about. Did you hear this in some youtube video and have been looking to try it on someone?
ekjhgkejhgk commented on String theory inspires a brilliant, baffling new math proof quantamagazine.org/string... · Posted by u/ArmageddonIt
Pardon, but, huh? I very much thought that Lorentz invariance was built into the assumptions of string theory.
Concluding from “A AND B” that “A”, while it does reach a conclusion that is distinct from the assumption, is not impressive.
If string theory does not bake SR into its assumptions, wouldn’t that make the way it is formulated, not manifestly Lorentz invariant? Don’t physicists typically prefer that their theories be, not just Lorentz invariant, but ideally formulated in a way that is manifestly Lorentz invariant?
Of course, not that it is a critical requirement, but it is very much something I thought string theory satisfied. Why wouldn’t it be?
Like, just don’t combine coordinates in ways that aren’t automatically compatible with Lorentz invariance, right?
If you formulate a theory in a way that is manifestly Lorentz invariant, claiming to have derived Lorentz invariance from it, seems to me a bit like saying you derived “A” from “A AND B”.
If string theory isn’t manifestly Lorentz invariant, then, I have to ask: why not??
Lorentz invariance is built into some descriptions of some stringy theories. For example chapter 1 of the Polchinski, you have the 26-dimensional bosonic string which is constructed to be Lorentz invariance. Obviously in this case it's not a "prediction", but then again, it's just a toy-model. Our Universe doesn't have 26 dimensions and doesn't have only bosons.
You know, when I see GNU, I don't necessarily think it's the best software in all dimensions, but it's almost the best in terms of respecting its users.
Ironically, it's the FSF which discourages the use of "commercial" to mean "non-free":
https://www.gnu.org/philosophy/words-to-avoid.en.html#Commer...
Obviosuly discourages because they're not equivalent and creates confusion. Stallman himself was selling copies of Emacs while releasing it under a Free license.
The truth is that pedagogy and instruction is just a lazy way of providing childcare. So who cares what they do with their time.
This is why I, despite my deep appreciation for the pursuit of knowledge and having spent a significant chunk of my life in the academia after graduating, want my kids to spend as little time as strictly necessary in primary or secondary schools. And the need comes from the fact that I need some of that childcare, not that I need someone else to teach my children anything.