Nice Explanation my Friend.I never thought ink could be used for proving direction of time ... 😄
@marble17
Жыл бұрын
bro actually fits better to become a final boss
@jansustar4565
Жыл бұрын
I had the idea, that time didnt have to nove strictly in one direction, but we as the actors can only experience it goong forward. So the next instant could be infinitely far away or so close you dont even notice. It would be like watching a prerecorded movie, it doesnt change regardles of how you watch it
@ativjoshi1049
3 жыл бұрын
Wow, another great math channel. Loved the video!!!
@_kopcsi_
3 жыл бұрын
already the first example with the oscillating pendulum is fundamentally wrong (or rather misleading, even if it has pedagogical purposes), since that example ignores the dissipative forces and effects (which are deeply related to the concept of entropy, and entropy is -not surprisingly- related to the concept of time and its directionality). with time the pendulum loses its kinetic energy and at one point it will stop due to the mentioned dissipative forces and effects. of course if you ignore these dissipative forces and effects, you also ignore the transient aspect of dynamics. in a very simple model motion has two main aspects: stationary (periodical) and transient (non-periodical) motions. usually the former has the mathematical form of “exp(i*t)” (sinusoidal oscillation), meanwhile the latter has the mathematical form of “exp(t)” or “exp(-t)” (exponential decay). the exact functions may vary, but the essence is the same: the stationary aspect of motion has temporal symmetry/invariance, i.e. you get the same type of motion if you translate or reflect the temporal dimension (t), meanwhile the transient aspect of time has no such symmetry/invariance. ignoring the latter is an elementary fallacy. and exactly this is revealed by the end of the video (dissolution and diffusion are dissipative processes). it’s another question why and where such transient motions come from. and it’s again related to the concept of entropy (so it has combinatorial and statistical reasons). that’s where chaos and magic happens. ps.: it’s interesting that when the massflow is introduced, the formulas are perfectly analogous to the definition of action, and not surprisingly it leads to the conservation of mass (however now not energy, momentum and action are used but concentration, massflow and mass).
@kashu7691
2 жыл бұрын
speaking classically (although i’m sure this translates to quantum just as well) isn’t the whole universe a hamiltonian (thus non dissipative) and thus time reversible system? even though i can’t dispute the second law of thermo, entropy increase with time is due to the uncertainty we have of the initial micro state of the universe, ie how a small “drop” in phase space spreads out to access more and more macro states. despite this though the overall hamiltonian and thus physics is still time symmetric for a given path in phase space isn’t it? i am speaking as a beginner so i probably have misconceptions
@JohnDlugosz
Жыл бұрын
@@kashu7691 Quantum effects are probabilistic, so while the _rules_ are time symmetric (CPT symmetry) you would not un-do the passage of time if you reversed all motion and flipped all charges instantly.
@TheBlindfischLP
Жыл бұрын
All the particles etc. in the pendulum or in the glass of water follow time reversible laws though, so it's definitely not obvious, where the arrow of time comes from. And the rigorous definition of entropy alone still does not give an arrow of time.
@joyboricua3721
3 жыл бұрын
Excellent detail providing references & all. Keep it up
@williamtoner8674
2 жыл бұрын
I really like this channel, so I don't want to just be critical for no reason. This said I am not very convinced by the line of reasoning. The heavy lifting here is done by Fick's Law which is (by your own description) an 'empirical' law. Thus, the argument amounts to saying that time is not reversible because it appears not to be empirically. I don't know if a better argument exists that this but it's philosophically upsetting. It is very bizarre that physical laws which are apparently reversible manifest these irreversible behaviours at the large scale. Perhaps it's all an elaborate result of the failure of certain particle interactions to be time reversible. Who knows, not me.
@MetaMaths
2 жыл бұрын
Hi there! Thanks for the comment! The video aims to point out 2 interesting phenomena 1. Newtonian mechanics is time reversible. 2. A process can be time reversible, yet display time assymmetric properties (i.e. monotonic Dirichlet energy). To show the second point, we use the example of ink in a glass of water, whereby we make use of Fick's law. You are absolutely correct that we have not shown that Fick's law can itself be derived mathematically from a Newtonian description of the problem. Frankly speaking, I am not well read enough on Statistical Mechanics to point you to a proof of this step. If you can settle for a thermodynamic analogue (i.e. Newtonian description of ideal gas implies second law of thermodynamics), please refer to Boltzmann's H-theorem. Philosophically speaking, we felt justified in skipping this step, since all of Physics is derived through empirical laws (i.e. Fick's law is true regardless of whether or not you can prove it from Newtonian principles). Perhaps if we had made the goals of the video clearer, that would've clarified things. Hope this helped
@p07a
3 жыл бұрын
Can you talk about d’Alemberts solution to the heat equation which is a sum of functions backward and forward in time?
@BrynSCat
3 жыл бұрын
You assume time is mono directional , fundamentally 50% of fields can already be time reversed ,Now you have No matter-antimatter asymmetry problem,No Time asymmetry problem.
@somecreeep
3 жыл бұрын
I've always had a question with regard to time: What if it's not a one-dimensional concept? What if time is a two dimensional thing and we just can't perceive that it is (perhaps it's compactified, or maybe we go on a straight line through it when we don't undergo acceleration, or maybe something else)? If time wasn't one dimensional, how would it affect this math?
@StellaEFZ
3 жыл бұрын
Time is 4 dimensional bro, read up Minkowski time-space and from there get into basic quantum stuff
@somecreeep
3 жыл бұрын
@@StellaEFZ Well, spacetime is 4 dimensional, but it necessarily assumes there is one dimension of time and three of space that pour into eachother as you convert to different frames of reference. But time is assumed to be a represented by a single dimension in the spacetime fabric. I'm asking "What if we assume there's more than one?"
@MsSonali1980
3 жыл бұрын
@@somecreeep Firstly, you would have to do the maths and see if it is mathematically possible. I guess people before you had the idea and did the maths. You can google what they have to say. Or you can think in a philosophical manner, what would happen if...
@_kopcsi_
3 жыл бұрын
time is not even a dimension. if it was simply a dimension, then it wouldn’t be different from space. space and time are two very different things (even if they form together something called spacetime which is not a perfectly proper and ultimate description). time is a tricky concept and we still don’t understand it fully, but it has already become clear that it is NOT a simple dimension.
@farrankhawaja9856
Жыл бұрын
All these idiots in the replies have no idea what they’re saying. “Oh time is four dimensional” “oh time isn’t even a dimensions”
@davidsweeney111
3 жыл бұрын
what happens if we introduce entropy?
@MetaMaths
3 жыл бұрын
That's another approach ! But I decided to go with Dirichlet in this video
@JohnDlugosz
Жыл бұрын
You mean "diffuse", not "dissolve".
@marekwiton2455
Жыл бұрын
How do you get that partial derivative of u with respect to time is equal to partial derivative of q with respect to x ? I only can get that partial derivative of q with respect to x is equal minus q devided by cross sectional area
@MetaMaths
Жыл бұрын
you can write me an email and I will send you a paper
@marekwiton2455
Жыл бұрын
@@MetaMaths I can't write my email because of KZitem spam filters. Can you paste the title and names of authors of paper in comment and I will search it by Google
@kapoioBCS
3 жыл бұрын
Weak force just entered the chat.
@ourgoalisto6737
3 жыл бұрын
Entropy was never added to the chat
@hapticgamer7603
3 жыл бұрын
When is see such math problems i only can say one thing when i dont understand Every 60 Seconds a minute passes in Africa
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