But all I said is compatible with saying that “Galilean invariance” is a technical term that in QM includes the phase thing and so it has a slightly different meaning (which is probably what matters to your question in any case!). This might be reflected in the group cohomologies but I am not sure

I think invariance up to this phase thing is a bit of a trick and it is not real Galilean invariance (yes, this is controversial!). It is different in the case of the lagrangian since invariance up to a total derivative is a natural idea (it is inv of the action) and leads to conserv quantities

I was thinking of papers like this one: Greenberger, D. M. (2001). Inadequacy of the Usual Galilean Transformation in Quantum Mechanics. Physical Review Letters, 87 (10), 100405.

I don’t know the answer, but the Sch equation is not invariant under (standard) Galilean transformations so to me it would seem strange if one could derive it that way.

On this topic, I really enjoy showing my students that some texts of “natural magic” read like modern physics, that Newton wrote considerably more about theology and alchemy than physics, and that Galileo never accepted elliptical orbits for roughly the same reasons as the ancients.

For example, here is a fun continuos symmetry of the classic harmonic oscillator: x goes to x+cos(t). It changes the acceleration and amplitude of a spring! People often says that symmetries “preserve the physics” or “capture redundancy” but that is not universally true as this simple case shows

@johncarlosbaez.bsky.social has some good notes on this topic in his blog, which I actually used some years ago to better understand the LPR vector. I like the animations in that link, though! Dynamical symmetries are often counter intuitive because they live in a more abstract space (eg jet space)

I see! Yeah, I just think that if I were to genuinely believe this, I wouldn’t be able to think of myself or the world in the same way.

At the very least, I would be very anxious and confused… I wouldn’t even know how to think of my identity over time nor of my decisions and my plans for the future. I also would probably worry about the well-being of my “copies” quite a bit, perhaps as much or more than a very close relative, etc

To me that sounds a bit closer to many worlds (defenders of it don’t act as if they really believed that there are multiple copies of themselves after any measurement).

The Principia is a very hard book for sure. I think this commentary is conceptually very good and makes a great effort at presenting the main arguments in their original geometrical formulation with no calculus: www.greenlion.com/books/Newton...

He also says that the proofs of Cor V and Cor VI are based on the 2nd law. Newton does say that they are (hence “corollary”), but scholars of Newton usually think they don’t follow and that’s a mistake on Newton part.

Thanks for the reference! I did a quick search and I was surprised all he said about it was that “this shows that Newton’s laws hold even in some accelerated frames”. Perhaps it was obvious to him the connection to Einstein’s equivalence principle and didn’t feel the need to elaborate.

Sorry for the Typos: “… as if they were not acted on by those forces.” In short, we have an important element of General relativity already in Newton :) But Einstein (and many others) never cited this corollary, so probably it was unknown to him.

Newton used this corollary to apply his laws of motion to Jupiter’s moons. After all, the force of gravity on Jupiter and the moons produced roughly the same acceleration on both, and so one can then neglect the Sun’s influence and pretend the Jupiter-moon system is isolated!

It reads “ if bodies are moving in any way whatsoever with respect to one another, and are urged by equal accelerative forces along parallel lines, they will all continue to move with respect to one another in the same way as they would if they were not active home by those forces.”

My favorite example is Newton’s corollary 6 to the laws in the Principia. He essentially states Einstein’s equivalence principle more than 200 years before Einstein! This is very rarely noted in physics, and even in the history of physics tends to be neglected. 1/

Thanks. what I meant to ask is if some of the axiomatic approaches you listed seems to be making more progress, in your view, towards the interacting 4d case (by “struggles” I meant there is no known construction in AQFT that gives raise to interactions or “realistic physics” if that makes sense).

Thanks for clarifying. I know algebraic QFT really struggles with interactions. In your view, which of those other options has done a better job of recovering interactions and getting “closer” to the qft of physics classes?

My “mathematician QFT” do you mean algebraic QFT or a different thing ? I confess I never heard of “constructive QFT”!

In fact, some simple classical systems are not even Galilean covariant! The symmetries for the differential equation of a simple classical wave such as a string attached to two fixed points are Lorentz’, not Galileo’s (fixing the tension and the density is formally just like a light wave).

On the history and philosophy behind some of these discussions, I recommend several papers by Rynasiewicz including this one: ‘Absolute vs. Relational Spacetime: An Outmoded Debate?’, Journal of Phi-
losophy

These things are related to the question of what exactly the relativity principle says (it is less clear than what many seem to think). I talk about its history and some philosophical aspects of it here (curious to hear your thoughts!) onlinelibrary.wiley.com/share/APRFMK...

Working with Us Call for Applications: Postdoctoral Fellowship The University of Geneva offers a 2-year fully funded postdoctoral fellowship within Baptiste Le Bihan’s SNSF Starting Grant project Space, Time and C…

Deadline for applying to a postdoc position on my projet in less than a month. Looking for candidates with a PhD in metaphysics or philosophy of physics.
spaceqg.com/visit-us/

A fantastic kickoff tonight of the Boston Network for History & Philosophy of Physics, organized by @miguelohn.bsky.social & featuring talk by Peter Galison on his work with the Black Hole Initiative. #HPS ⚛️

There is a mistake regarding the title of my paper with Nic Teh (the paper listed there is not ours). Thanks :)

I am very sorry Helen. Thanks for all the wonderful things you have done for philosophy, academia and the world more widely.

I am very happy to share this popular piece about relative motion, from Galileo to Einstein! It is roughly based on my recent research on the topic! I am thankful to @iai.tv and Dan Walker for reaching out, and for their great editorial work !

Galileo, Einstein, and the unexpected origins of relativity | Sebastián Murgueitio Ramírez

How Galileo cracked the problem of relative motion. | iai.tv/articles/gal...

@murgue.bsky.social argues that distinguishing between "internal" and "external" versions of the principle highlights Galileo's forward-thinking.

#philsky ⚛️ 🧪

And fighting Squirrel!