>Relativity was first introduced to the world in 1918, just at the end of the first world war. Of course, the special theory of relativity was then quite old. It was discovered in 1905
Wow to them 13 years was "old"
It must've been incredible to have paradigm-shifting ideas coming out so frequently
does the impedance of free space say anything about space itself? or is it giving us a coefficient by which to relate the electric and magnetic fields with eachother? *(in a vacuum)
if so, ε₀/μ₀ is a proportionate measure of the same thing?
@ACuriousMind funnily i always assumed it was a property of space. it was only this afternoon i began to wonder if i was falling into a trap. since i was reading again about the Michaelson and Morley experiment. and worried i was falling for some ether trap or something hehe
what does "changing the mass to charge ratio" mean
how do you measure that the mass to charge ratio has changed
the whole point of Emilio's post is that the ambiguity comes from the fact that your measurement devices will rely on other constants, too, and in the end you can only determine that some dimensionless ratio of constants has changed unambiguously
this is a statement about what we can measure
not about what happens in any theory, so whether or not you're using Lagrangians is completely irrelevant
no one is saying you can't "change" dimensionful constants in a theory
the point is that you cannot experimentally distinguish this change from a number of changes in other dimensionful constants
I wasn't considering changes in the measurement devices. Sorry
It just occured to me that changing interaction strength would change the size of the meter sticks
So my idea doesn't work
I had been thinking that if u multiply the kinetic term of coulomb lagrangian by some constants, but leave the potential term unchanged, the theory has different predictions (assuming the standard of length and time remained unchanged)
But the standard of length and time would change too
because this is annoying, we generally think about the adjustable constants of theories in terms of the dimensionless constants so that we don't have several different values of constants that lead to the same observable physics
we're silly monkeys playing with rulers and clocks, not god-like minds that transcend reality, and our theories are for predicting what happens when we play with rulers and clocks.
If you were god, u woud just be given a chart of this ontological spacetime and you could make predictions about what any ape would observe with his ruler and stick
@ACuriousMind if you have two different universes of the same field content, how would you check whether they're equivalent universes or not ( i mean if they have equivalent local laws, initial conditions may be different)
there are various ways in which theories can be equivalent
the simplest is probably via redefinition of fields - the action of one theory turns into the action of the other under something like $\phi = \phi_1 + \mathrm{i}\phi_2$
or you might find that the theories look very different at first but it turns out the relevant quantities - like scattering amplitudes or whatever - are the same, more in the spirit of dualities like AdS/CFT
I'm not really sure what kind of answer you're fishing for here
@ACuriousMind i got this other idea : if the same local field history (same upto diffeomorphisms) is permissible in the manifolds of both universes, then the laws are equivalent in both
The field solution also includes the metric field, so we can make these statements regardless of rods and clocks
By local field history, i mean a tiny portion of field solution
that's not a difference by total derivative, and indeed two theories with different values for some parameters do not produce the same solutions to their e.o.m.!
no one is saying you can't "change" dimensionful constants in a theory
again, the point was that you can't experimentally distinguish this change from certain changes of other dimensionful parameters, not that this change isn't detectable
so, for instance, the fine structure constant is $\alpha = \frac{e^2}{4\pi \epsilon_0\hbar c}$
why do you think that this wouldn't change when "one multiplies every single dimensionful constant"?
the claim might become true in units where $\hbar = 1$ or $c=1$ but not in units with both or neither, showing the very idea of "every dimensionful constant" is ill-defined unless you fix a unit system
you can model every change in dimensional constants, whatever they are and however ambiguous they might be, by an unambiguous statement about changing a dimensionless parameter
there's really no reason to think about changing dimensionful parameters that much
Basically, if you multiply a universe's lagrangian by some constant, and then absorb this constant into a re-definition of the parameters of the lagrangian, then the new lagrangian describes the same universe
whether or not two theories describe "the same universe" is a difficult question because you might just be using different fields to describe the same thing?
and that's still purely theoretical, there's even more wiggle room when you start thinking about how the theory actually relates to what can be observed within the universe
I think the main problem is that you seem to want to argue that "the Lagrangian" or whatever is actually an intrinsic property of the universe, not just our description of it
but I don't agree with that - or, rather, I think this is an assumption science should never need to make - so I have no idea why we're discussing it
So one rule of thumb I've noticed is that if the upvotes of a question is more than the upvotes of any of the answers. Then somewhere the community feels the question was not answered satisfactorily. (This is more of an observation)
For people who like to answer questions this might be a useful f...
I don't want to get into technical details here - perhaps you could ask a question specifically about this equation, and make it less "provocative" - when you ask about temperature it attracts a lot of attention (and votes, perhaps), but it doe snot necessarily attracts people with technical expertise (and there are some people here well-versed in Cahpman-Enskog, see, e.g., this answer and this one). — Roger Vadim5 hours ago
hi, i have been trying to figure out a clarification on HOSM stack and phys stack, but to no avail. also have been searching online. i am wondering, if silver atoms are ideal for stern gerlach because of how they isolate intrinsic angular momentum effects, why were they chosen for the experiment when there was no idea of spin at that time?
@Relativisticcucumber Stern and Gerlach weren't trying to measure spin, they were trying to measure the orbital angular momentum the outer electron should have in the "old quantum theory"/Bohr-Sommerfeld model
the result was puzzling and only later explained by Pauli's and Dirac's spin
so i read that they predicted there should be quantization in direction of angular momentum. is this what you mean by "trying to measure the orbital angular momentum the outer electron should have in the "old quantum theory"/Bohr-Sommerfeld model" or am i missing something
okay and so silver is still ideal because it isolates angular momentum of one electron? but i thought this electron shouldnt have momentum according to no-spin models
they didn't know about spin at all, but the old quantum theory - the Bohr model we still get taught e.g. in basic chemistry courses - thought there were only discrete orbits the electrons could move along
interesting - yeah i was confused because sakurai and townsend describe as if silver is the perfect model for this and that's why it was chosen and ive been stuck on that for days
@Relativisticcucumber yes - these electrons in the old quantum theory literally move along orbits, so they have angular momentum, hence magnetic moments. Since the orbits are discrete, the possible magnetic momenta are, too
so they would have expected the beam to split, just as it does
@ACuriousMind suppose we have two simulations of a single particle universes under a coulomb potential, but with different charge to mass ratios. Then every single solution trajectory of the first universe is diffeomorphically equivalent to a solution of the second univeese
So i was wrong that changing the relative strengths of couplings necessarily gives a different universe
But if we do the same simulation on two universes whose time dimension have a boundary, then the two universes are different depending on the charge to mass ratio
So it is very subtle, i think. It has to be handled case by case
@RyderRude what do you mean, "single particle universe under Coulomb potential"? There's a particle moving in a potential but no source for the potential?
@RyderRude often yes, but given that there is a very general argument for why changes in dimensionful constants are not physically meaningful/unambiguous, I don't understand why you keep trying to build a "toy model" for cases where you seem to be trying to argue that it is relevant
and again, I feel you're drawing a very narrow conclusion here
a single particle universe does not meaningfully have mass or charge
effectively this is because physical measurement relies on there being stuff to compare to each other and if you just have a single particle you have no way of obtaining e.g. a length scale
but...I wasn't arguing that different mass to charge ratios give the same theory
just that you can't distinguish the change in mass to charge ratio from the change in some other dimensionful constant, and the unambiguous way to talk about this change would be in terms of dimensionless constants
I feel you're trying to remove the idea of measurement and measurement having to use actual things that are part of the universe from the picture here, but the things you're trying to remove are precisely the reason people say we should talk only about dimensionless constants changing
in the absence of measurement devices, what does it even mean to do physics
the real universe - whether it "is" a simulation or not - is not running on a computer we can access and extract measurement results from without actually doing a measurement inside the universe
so I think your attempt to argue about this in terms of simulations completely misses the original problem
But one one cant disprove that the universe is a simulation, whats the harm in using it as a personal preference. The predictions are the same either way.
I just find this to be more comfortable to think about, and it's still consistent with experiments
This way, i can talk about different universes using simulations without having to care about measurement details
But if you think that these discussions dont count as physics, then i understand your position. I just define physics more broadly, where we can also discuss simuilations
I guess then we come to the point that I in general don't understand what the point of believing or not believing in statements is that make no difference to my experience :P
Like, I understand why people believe in religions with their social and moral features. But "the universe is a simulation" doesn't directly have any such implications, it's a statement whose truth or falsity makes absolutely no difference to me
I know there's a corresponding probability distribution for electrons in particular orbitals, so let's say i measure position of electron in 1s orbital, i may have collapsed the wave function, but If i let it time evolve will it come back to the old state
@ACuriousMind i was reading about the definition of a statistical equilibrium / stationary statistical ensemble, and that def. was: "one that usually does not change over time". If an ensemble wasn't stationary, what would it change over time? The number of virtual copies in it, or the number of microstates in it?
Btw, are the microstates of an ensemble, all the possible ones, that a system can occupy or there can be other microstates, which are not included,which can be occupied by the system ?
