On Saturday, June 7, 2025 at 5:04:33 AM UTC-6 John Clark wrote:
On Sat, Jun 7, 2025 at 1:52 AM Alan Grayson <[email protected]> wrote: *>> The conservation of energy is not a statement about pure mathematics or logic, it is a statement about the physical world, so it's not surprising that historically its derivation has come from observation and experimentation. Nobody has ever been able to derive the conservation of energy from logic alone, and I very much doubt anybody ever will. In fact nobody has ever been able to derive ANY physical law from mathematics alone, unless you want to say that it's a physical law that 2 rocks plus another 2 rocks is equal to 4 rocks. * *> You're mistaken. Try this, by Feynman, https://ocw.mit.edu/courses/8-01sc-classical-mechanics-fall-2016/mit8_01scs22_chapter14.pdf <https://ocw.mit.edu/courses/8-01sc-classical-mechanics-fall-2016/mit8_01scs22_chapter14.pdf>* *If you look, you'll see that Feynman shows that in classical mechanics, energy is conserved on a closed loop. He proves many other things about energy conservation in that link.* *NO! Feynman proved IF you assume that a system obeys the Principle Of Least Action AND you assume that the system has Time-translation invariance THEN, because of Noether's theorem, the system must obey the law of Conservation Of Energy. But both the Principle Of Least Action and Time-Translation Invariance are observations, NOT logical necessities. I can imagine a universe with different physics in which neither the Principle Of Least Action nor Time Translation Invariance are true, but I can't imagine a universe that contained a largest prime number. * *John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* Where in Feynman's argument does he assume the Principle of Least Action and Time-translation invariance to conclude Conservation of Energy around a closed loop? AG -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/f21e0a78-a88f-4975-9db6-398be819e217n%40googlegroups.com.
