11:15 AM
I'm wondering how are fundamental formulas or relationships in Physics established and justified. How did Galileo justify them in the past? I'm sure the inventor did many experiments, but how can he or she generalise the finite number of observations to a Physics law? Or are these laws not necessarily an accurate description of our world?
Can anyone help me? :)

11:25 AM
2 messages moved from Problem Solving Strategies

@yh05 That's the classic problem of induction. Our "Physics laws" are not statements that we know beyond all doubt to be true forever and in all cases - in fact, we know many of them to be "wrong" (or rather, not fully accurate). You probably learned Newton's laws and classical mechanics, but since Einstein we know that's only accurate at low speeds compared to the speed of light.
But that doesn't make classical mechanics useless - it's still good enough to predict and analyze a large number of situations
All models are wrong, some are useful.

So the laws can't be justified to be true and accurate for all (infinitely many) cases. Then why do the inventor (Example, Galileo) establish such laws and we accept these laws and use them?

11:44 AM
@yh05 Because it works. We don't believe in physical laws because someone said so, but because in our experience, they actually do model the world correctly in many cases.
Sometimes they're wrong, and then we correct them after we've figured out how to.

How do we check and confirm that it works? What do you mean by in many cases?

@yh05 We use the laws to predict what will happen if we run an experiment (or operate a machine, or whatever), and compare what we observe to the prediction.
When the prediction matches the actual result (within errors), it "worked"
Take the laws of electricity: We use them to build power grids and all sorts of amazing applicances. If we had gotten the physics of electricity wrong, these things wouldn't work as we intended them to

12:02 PM
There are Physics laws that are expressed using mathematical equation. How can we check and confirm that they work? Because it will take infinitely many experiments to do so.

@yh05 Are you trying to say that in order to show that $y(x) = x$ holds for all $x$ I need to measure infinitely many pairs $(x,y)$?
If so, then you're right, but that doesn't mean that finitely many experiments cannot increase my confidence that that relationship holds. Statisticians have developed many techniques to quantify how well a particular (finite) dataset fits to such an ideal function.

@yh05 we don't try to prove laws. We try to disprove them.
@yh05 I can't think of any physical law that has been proven, but I can think of lots that haven't been disproven even after a hundred years of trying.

In what situations do we disprove a physical law? For a physical law that is expressed as a mathematical equation, how do we decide whether we should discard the law if we conduct an experiment and obtain a number different from what is expected from the law?

12:18 PM
@yh05 Well suppose you measure the gravitational force between two bodies of mass $M$ and $m$ and you find it is not equal to $F = GMm/r^2$. That disproves the law. Yes?

Hello
Fun fact in the late 19th century people tried out a variety of alternative gravitation laws
$$F(r) = \frac{GMm}{r^{2 + \alpha}}$$
That sort of stuff
Due to a variety of cosmological concerns
None of those works out great though

12:46 PM
@JohnRennie Yes.
But do we really obtain the exact equality from experiments?

No, of course not. What we obtain from experiment is that the results are consistent with that equality being true within experimental errors.

How do we decide if the results are consistent with the mathematical equality as described by the law?
And how can we be sure that all (past and future) experiments always produce consistent results as well?

@yh05 As I said, statisticians have developed many tools to analyze how well a particular dataset follows a particular mathematical relationship, called measures of goodness of fit

How is this done before Statistics is developed?

1:02 PM
E.g. if your predicted relationship is linear, then most intro physics lab will have you perform least squares regression
@yh05 Poorly :P But even without sophisticated statistical tools you can certainly compare your measured dataset against what your equation predicts, and if you're not "too far off", it's good.
The meaning of "not too far off" is of course dependent on the application domain - even with statistics. E.g. high-energy physicists use standards for "significant observations" that are much stricter than what most other fields use - but that's also because HE physicists also typically have much more data to work with.

Statistics wasn't use that much in physics until the 20ht century, IIRC
They just went with their guts :p

Today my grandma was saying, you wear black cloth, so won, t get cold, when I try it, it works, can anyone tell me why thus happen,
Sorry for grammatical errors.

2:04 PM
What is the "not too far off"? How can a finite number of "not too far off" result generalise a law to hold true in all (past and future) situation? This seems to me that the Physicist assumes what to be discovered as pre-existing and so seeing some instances of the law at work must reveal that pre-existing law (created by god or whatever superior being(?) ).

2:18 PM
Well that's how the human brain works in the end
Bayesian inference~
we try to notice patterns out of what we see

2:38 PM
A class in programming is a blueprint for making objects, which are like custom types that are made in terms of other predefined types along with functions
A universe which obeys the simulation hypothesis will mean all types are composed of some fixed collection of predefined types
Such is sufficient to enable emergence as new behaviour results from combining arrangement of these types
However, there may be types that are inherently unspecifiable in terms of code. There existence of at least one of these will disprove the simulation hypothesis

@Slereah nuuuuuuuuuuu
What will happen if I assume universe to be a simulation?
Will anything go wrong?
If any smart species answer that^
or this \/
1

I guess it's a bit related to physics, but the doubt is in the mathematical part. I was just watching some stuff on Quantum Mechanics for the solution of the Hydrogen atom. The lecture ends at.. $$\dfrac{d}{dz} \left \{ (1-z^2)P'(z) \right\} + \left\{ \beta - \dfrac{m^2}{1-z^2} \right\}p(z) =... 3:01 PM In the multiple drafts model of the brain, where "consciousness is parallel and doesn't arrive at a final Cartesian theater" is really nice but how are we not conscious of everything then? I am conscious of everything You need to step up your game #sadface I can only consciously think of one thing at a time and that should imply that there is a single linear flow of consciousness no? But it's running on parallel software? @NovaliumCompany You need medicine and some rest.. Try newer tranquilizers, they are good and no side effect, I've been prescribed... ha fun but im serious with my questions @NovaliumCompany Your brain \neq computer 3:26 PM @bolbteppa Can you help? @AbhasKumarSinha what's the problem, replace P by (1-z^2)^{m/2}G in your "closest" expression and it should work, the derivatives of P are given below equation (2) here jfoadi.me.uk/documents/lecture_mathphys2_09.pdf @ACuriousMind What is the "not too far off"? How can a finite number of "not too far off" result generalise a law to hold true in all (past and future) situation? This seems to me that the Physicist assumes what to be discovered as pre-existing and so seeing some instances of the law at work must reveal that pre-existing law (created by god or whatever superior being(?) ). @bolbteppa I tried calculating keeping$$ P(z) = (1-z^2)^{|m|/2} G(z)$$, then I calculated the first and second order of derivatives of P(z) which is insanely long, but the problem is that the power |m|/2 still remains and doesn't vanish as it should... The (1-z^2)^{m/2} term should factor out of the equation, leaving an ODE for G @bolbteppa ah, probably calculation mistake, let me check it again... 3:39 PM (1-z^2)^{m/2} \{ (1 - z^2)G'' - 2(m+1)zG' + ... \} = 0 @bolbteppa ah, okay... got it, thanks :) done... :) @bolbteppa I tried reading the Statistical Mechanics approach to Schrodinger's equation using Feynman Line integrals, it was more rigorous proof than that I've seen in L&L Why does L&L didn't add that proof too? @AbhasKumarSinha where do Feynman path integrals come from, out of thin air @bolbteppa Feynman path integrals were not given there in L&L, why they didn't add it? that's what I asked... Where can I discuss consciousness? @NovaliumCompany eternity of the universe... 3:46 PM I mean a website of a forum, where? @NovaliumCompany Quora @AbhasKumarSinha they don't need to introduce path integrals anywhere @bolbteppa But their method was more unintuitive... for example$$ \left < f \right > \stackrel{def}{=} \int \psi^* \hat f \psi \,dx  For some hermitian operator $\hat f$ is not true, rather, it can be said that it is proportional to the mean, where <> denotes mean

@AbhasKumarSinha that is wrong and not how they defined the mean in the book

@bolbteppa ...?

3:53 PM
Maybe read an easier book if it's causing too much trouble

equation 3.8

So they define the mean above 3.7 and want 3.8 to correspond to the "usual definition" above 3.7, I don't see the issue, also they do not define "Hermitian" until after (3.15)

@bolbteppa I know that... What they want some expression to correspond to some other expression, I don't get the institution behind it, it seems like they randomly made an operator just to define mean using inner product.

Not sure what the problem is

4:09 PM
@bolbteppa I don't say that there is a problem, everything fine, but they could have explained their institution a bit more...

4:21 PM
@AbhasKumarSinha you're assuming that linear operators should be relevant in QM, but before 3.7 they haven't even defined the notion of a linear operator for QM. In section 2 they have defined wave functions, and related them to the notion of probability. At the start of section 3 they are just setting up the notion of the values that a physical observable can take, and are trying to relate this to the notion of a wave function.
The notion that a wave function should encode the values that a physical system can take leads to the notion of an eigenfunction expansion as given at the start of section 3, again even before a linear operator has been defined. Before we have even defined the notion of a linear operator in QM we already see, from physical principles, that wave functions should have eigenfunction expansions,
and again without even having defined the notion of a linear operator they want to define the notion of the expected value of a physical quantity only using a wave function in an eigenfunction expansion so they have to use the definition of a mean in terms of eigenvalues times probabilities. From this they are led to defining the notion of a linear operator. Re-read the section without the words eigen, and everything would go exactly the way they say it
In other words, starting only from wave functions encoding a notion of probability, and wanting physical observables to be related to wave functions, we are forced to view wave functions as behaving in the way where the physical observable is naturally described by Hermitian operators acting on functions which can be expanded in an eigenbasis of that Hermitian operator

okay... :)
Thanks sir :)

No problem

4:47 PM
Isn't it weird that being conscious, we can notice all of the things we're doing and understand that we're doing them but it's even more weird that we understand that we're understanding the things we're doing. That's one step above... like... I can't explain it properly.
Is it possible that consciousness is related to language (communication)?
John Rennie where are you when i need ya :P
Btw I don't think having consciousness is a matter of you have it or not. I believe it's not binary. Chimps, whales and more have consciousness at some level, but it's just not developed as much as ours. Could that be a result of their undeveloped language? (they have a means of communication but it's not as sophisticated and detailed as humans)

5:28 PM
@NovaliumCompany Why would consciousness be at all related to language?
That basically says that any creature without language has no consciousness, and I'm reasonably certain that is demonstrably false

5:51 PM
@KyleKanos Why wouldn't it? I mean, it seems that we're the only species with developed language AND developed consciousness. Whales have some sort of communication and therefore less developed consciousness.

6:05 PM
Has anyone heard of global neuronal workspace theory?

@NovaliumCompany What makes you think that humans are the only species with developed consciousness?

@NovaliumCompany or perhaps start here :-)
?

6:21 PM
Hmmm, my chat is being strange.

ok
np

I was trying to quote the early paragraph of that article which suggests that consciousness as we understand it may something that arose in human culture after writing, and that the Greeks who fought the Trojan War may not have been "conscious" in the way that we understand the word today.
If you wanted to grab my attention, that's a great way to do it.

@NovaliumCompany I think you need to look at a few psychology books. There is no requirement for language to be required for consciousness

My initial reaction is that it's more likely that the complexity of writing is catching up on a kiloyear timescale to the sensation of consciousness, which seems more like a part of (my) biology than like a cultural artifact. But testing that hypothesis would require me to do an awful lot of cross-cultural reading.

6:30 PM
Literally just Google search "consciousness and language" and you'll find you are wrong
Nice highlighted text (at least it was for me, not sure if it will be for you with that link)
> Although consciousness is frequently associated with our understanding of meanings, the relation between language and consciousness is not straightforward, and it is becoming more difficult to establish this relationship because consciousness seems to be present in many species, while language is not

I mean, it's not difficult to talk out your arse, but if you're going to try defending your position, it's better to at least be right

lol

And I mean no offense by that statement, just that making ridiculous claims and then not even doing cursory searches that complete disprove your point (I imagine in hopes to further your point) is lame. Do your work

@KyleKanos Note that the concluding paragraph of your link says that the hypothesis "consciousness requires language" is implausible, not that it's wrong. This is a field that requires an awful lot of humility.

6:40 PM
Implausibility is more or less the same thing as saying it's wrong, just more polite I guess
That said, I'm reasonably certain that psychology is a bogus pseudo-science (much to my father and sister's chagrin, as they both have psych degrees)

psychometrics is trying to change that

I think that psychology, as a science, is a few hundred years behind physics in terms of separating facts from attractive-sounding fantasies. There's a lot of useful stuff in modern psychology, but there's a lot of phlogiston in the "why" behind the useful things.

::nods::

46

I have a friend who has been working on a PhD dissertation for over 3 years and he is supposed to be wrapping it up. Unfortunately, his thesis involves a complex model and populating the model with hard-to-obtain data. After having finally gathered all the data and plugged it into the model, he i...

in other news: rule 30 prize
3

6:56 PM
Surprised that hasn't been asked before

"You don't use science to show that you're right, you use science to become right." - Randall Munroe