/sci/ - Science & Math » Thread #13994476

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Anonymous Wed 22 Dec 06:47:29 2021 No.13994476 View Reply Original Report

Quoted By: >>13994483 >>13994501 >>13994620 >>13994630 >>13994689 >>13994866 >>13994927 >>13994998 >>13995334 >>13995378 >>13996129 >>13996168 >>13998601 >>13998673 >>13998737 >>13999072

Why is Conservation of Momentum true? I just don't get that it just is... Is it the consequence of something mathematical? And if Expiremntal, why exactly? Also, what role does Center of Mass play with it? I'm curious.

Also, fields of mathematics and science, and some good books and articles that deals with this shit and it's history would be greatly appreciated. Shit's so simple but just taken as given...

Anonymous

Anonymous Wed 22 Dec 2021 06:51:39 No.13994483 Report

Quoted By: >>13994503 >>13995320 >>13996996 >>13998558

>>13994476
>why is it true

Invalid question. It is either true or not. Having a state of existence does not have a “why”.

Anonymous

Anonymous Wed 22 Dec 2021 06:56:13 No.13994496 Report

Quoted By: >>13994503

To every transformation there is associated a physical quantity. Spatial translations are associated to momentum. Time translations are associated to energy. If a transformation doesn't change the energy then its associated physical quantity will be conserved in time. This is true for spatial translations so momentum is conserved

Anonymous

Anonymous Wed 22 Dec 2021 07:00:29 No.13994501 Report

Quoted By: >>13994526 >>13994927

>>13994476
I am not a physicist, but as far as I know, the conversation of momentum can be mathematically derived from Newton's laws of motion. On a more profound level, it can be derived from Noether's theorem about symmetries and their relationship with conservation laws.
There is a limit to how many why questions you can ask though. After some point, you just have to accept that the universe behaves the way it does,

Anonymous

Anonymous Wed 22 Dec 2021 07:00:37 No.13994503 Report

Quoted By: >>13994523

>>13994483
Why are you gay?
>>13994496
I thought Energy was derived from integrating momentum with respect to volume? Why do we assert that Energy is prior to momentum when it can be the other way around? Also, tell me more about the association of Time translations and Energy. I am really interested. Bring in the Big Maths if you can.

Anonymous

Anonymous Wed 22 Dec 2021 07:08:50 No.13994523 Report

Quoted By: >>13994538

>>13994503
Energy isn't prior to momentum, or vice versa.

If you want to know the Big Maths, in physics the state of a physical system (which you can take to be the universe if you want to extrapolate) is specified as a point in a huge multidimensional phase space where the dimensions specify the positions and velocities of all the particles (in quantum mechanics this is described by a Hilbert space instead but much of the same mathematical structure carries over).

Every function you can define on phase space can be thought of as some different physical quantity. And there is a standard way to associate a transformation on phase space to that function. You pick out one such function and call that the energy (or Hamiltonian) and its tranformations define what we mean by time. If you pick out another set of functions that translation the position dimensions in phase space, these will be your momentum.

Anonymous

Anonymous Wed 22 Dec 2021 07:10:10 No.13994526 Report

Quoted By:

>>13994501
It seems that deriving it through mass and velocity is more elementary because Aristotelian Physics made the error of assigning the properties of Force to Momentum. And prior to that I see the center of mass, because before velocity and time we have the notion of distance.

Also Conservation "Laws"-- what makes us certain of them? Has there been an instance where it was contradicted? Or is it just given that the totality of the universe is its own system? But a system has to be finite and contained, to explain away why some things disappear-- we have an idealized vision of forces with Newtonian mechanics, and everything that doesn't add up we explain away with "Frictional Forces." Even with Energy we assume it is "gone as heat."

I really want to know... Maybe somebody more advanced can tell me...

Anonymous

Anonymous Wed 22 Dec 2021 07:15:07 No.13994538 Report

Quoted By: >>13994549

>>13994523
This Phase Space stuff sounds interesting, tell me more. I am interested in more content related to this.

El Arcón

El Arcón Wed 22 Dec 2021 07:17:09 No.13994546 Report

Quoted By:

It's one of the postulates in Newton's laws. You can also get to it through Noether's theorem but then you'd have to postulate the rest of mechanics to determine that her theorem is true.

Anonymous

Anonymous Wed 22 Dec 2021 07:17:56 No.13994549 Report

Quoted By: >>13994615

>>13994538
Knock yourself out
https://en.wikipedia.org/wiki/Phase_space

It is indeed pretty interesting, in a lot of ways phase space in classical mechanics is more interesting than quantum mechanics (although the link between physical quantities and transformations exists in QM too)

Anonymous

Anonymous Wed 22 Dec 2021 07:50:33 No.13994615 Report

Quoted By:

>>13994549
Just learned about the Hamiltonian Case. Shit's really fucking interesting. I never knew of this approach.

Anonymous

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Anonymous Wed 22 Dec 2021 07:55:09 No.13994620 Report

Quoted By: >>13995274

>>13994476
>Why is Conservation of Momentum true? I just don't get that it just is... Is it the consequence of something mathematical?
Nobody knows. They just know it can be described accurately.

>Also, what role does Center of Mass play with it
Mutual "centers of mass". The "null point". Perhaps at the "null point" would be the answer/source of how these masses seemingly accelerate towards each other.

Anonymous

Anonymous Wed 22 Dec 2021 07:58:08 No.13994630 Report

Quoted By:

>>13994476
>Why is Conservation of Momentum true?
space is uniform

Anonymous

Anonymous Wed 22 Dec 2021 08:19:54 No.13994689 Report

Quoted By: >>13994791

>>13994476
You can derive it from Newton’s first law.

Anonymous

Anonymous Wed 22 Dec 2021 08:44:44 No.13994751 Report

Quoted By: >>13994791 >>13995766

its a direct mathematical consequence of newtons laws
>but why newtons laws???
you ask bad questions, maybe philosophy is more your speed

Anonymous

Anonymous Wed 22 Dec 2021 08:56:53 No.13994791 Report

Quoted By: >>13994840

>>13994689
>>13994751
the anser he is looking for is friction

Anonymous

Anonymous Wed 22 Dec 2021 09:11:31 No.13994837 Report

Quoted By:

All matter is vibrationally connected. there is your clue.

Anonymous

Anonymous Wed 22 Dec 2021 09:12:15 No.13994840 Report

Quoted By:

>>13994791
???

Anonymous

Anonymous Wed 22 Dec 2021 09:25:58 No.13994866 Report

Quoted By: >>13994871 >>13995274

>>13994476
>Is it the consequence of something mathematical?
Math can be used to describe physics in various formalisms, but never confuse it with physics itself. Math is not an empirical field. The discipline is independent of physics.
>And if Expiremntal, why exactly?
It's a physical law that has never been observed to be violated. That's really it, there's no deeper epistemological approach possible within Physics itself. All the physical laws are inherently an interpretation of physical data. Formalisms are simply refined abstractions of the physical laws.
> Also, what role does Center of Mass play with it? I'm curious.
Centre of mass should always be interpreted together with the moment integral. The reason is that you can integrate over both continuum and point particles. This allows you to model a lumped system and you can apply conservation laws (linear momentum and moment) on the system. The interpretation is simply that you capture all the sub-balances within the system which cancels out and this breaks down only when new mass crosses the boundaries of your integral.

Anonymous

Anonymous Wed 22 Dec 2021 09:27:01 No.13994871 Report

Quoted By: >>13995305

>>13994866
yawn

Anonymous

Anonymous Wed 22 Dec 2021 09:52:33 No.13994927 Report

Quoted By: >>13995071

>>13994476
>Why is Conservation of Momentum true?
because
>>13994501
>the conversation of momentum can be mathematically derived from Newton's laws of motion
which in itself comes from the Kabbalah

Anonymous

Anonymous Wed 22 Dec 2021 10:16:01 No.13994998 Report

Quoted By:

>>13994476
originally, it's newton's 3rd law. Since his 3 laws explained much of the motion of the planets (data recorded by people before him), yeah i guess it was originally an experimental observation. So, maybe like a postulate, kinda like that the speed of light is the universe speed limit, which was one of einsteins postulates.

As other said, a more modern mathematical basis for any conservation law is noether's theorem. Every symmetry or invariance has a conservation law. Linear motion -> momentum, ang motion -> ang momentum, time -> energy, phase/guage -> charge. There are a lot fancier theoretical ones but idk, im too dumb for those

Anonymous

Anonymous Wed 22 Dec 2021 10:48:12 No.13995071 Report

Quoted By:

>>13994927
>which in itself comes from the Kabbalah
You're confusing Kepler's laws with Newton's laws. The true motion of the heavens is not described by forces.

Anonymous

Anonymous Wed 22 Dec 2021 12:11:06 No.13995274 Report

Quoted By: >>13995305 >>13996526

>>13994620
>>13994866
Pseud/retard/schizo answers.

Anonymous

Anonymous Wed 22 Dec 2021 12:23:57 No.13995305 Report

Quoted By: >>13995318 >>13996526

>>13995274
>>13994871
Get fucked pseud retards. A retarded question like OP warrants a retarded answer that's how students learn.

You retards also don't even understand Noether's Theorem which only applies within the thermodynamic limit while conservation laws can be applied outside it. Noether's is used to derived coordinate independent conservation laws in a symmetric space, it is less general than the law itself.

Anonymous

Anonymous Wed 22 Dec 2021 12:27:59 No.13995318 Report

Quoted By: >>13995340

>>13995305
Wow, this pseud really looked up some big words. Noether's theorem is unrelated to thermodynamics.

Anonymous

Anonymous Wed 22 Dec 2021 12:29:39 No.13995320 Report

Quoted By:

>>13994483
stop being retarded

Anonymous

Anonymous Wed 22 Dec 2021 12:34:39 No.13995334 Report

Quoted By:

>>13994476
>Why is Conservation of Momentum true?
Because the laws of physics are the same at all locations. See Noether's theorem.

Anonymous

Anonymous Wed 22 Dec 2021 12:38:33 No.13995340 Report

Quoted By: >>13995345

>>13995318
>Noether's theorem is unrelated to thermodynamics.

>t. Retard who has never opened a Statistical Mechanics textbook

Stop posting idiot, you're embarrasing yourself.

Anonymous

Anonymous Wed 22 Dec 2021 12:40:11 No.13995345 Report

Quoted By: >>13995355

>>13995340
Yes sweetie, it's unrelated

Anonymous

Anonymous Wed 22 Dec 2021 12:42:40 No.13995355 Report

Quoted By: >>13995369

>>13995345
No sweetie, you misunderstood the wikipedia entry. Much like other B rate students.

Anonymous

Anonymous Wed 22 Dec 2021 12:47:53 No.13995369 Report

Quoted By: >>13995405

>>13995355
No honeypie, Noether's theorem can be applied to any collection of N particles, where N > 0. In particular, N can be 1, in which case thermodynamics is irrelevant

Anonymous

Anonymous Wed 22 Dec 2021 12:53:23 No.13995378 Report

Quoted By:

>>13994476
newtons laws
every force has a counter-force
force equals the derivative of momentum
so for each object that has a momentum change, there's another object with an equal but opposite momentum change, so the net change is 0

Anonymous

Anonymous Wed 22 Dec 2021 13:05:16 No.13995405 Report

Quoted By: >>13995450

>>13995369
>No honeypie, Noether's theorem can be applied to any collection of N particles, where N > 0.
No dearie, you are assuming that space time is not curved in this system in addition to a host of other assumption. Sadly this is because of your inherit genetic limitations, I know it is oh-so difficult for you to think outside the box, but keep trying!

>In particular, N can be 1, in which case
Oof, no, sorry dove, but unfortunately this is not true at all scales and we need QFT. Hint we have a nice definition that summarises the _limit_ations of Lagrangian mechanics.

>thermodynamics is irrelevant
Oh you are just adorable! So you see, the thermodynamic limit is a concept from statistical mechanics and has nothing to do with thermodynamics. I know this must be frustrating for you, all these similar sounding works are really pushing your cognitive abilities to its limits. Don't give up! The world needs more people like you, you might even make a fantastic assistant one day!

Anonymous

Anonymous Wed 22 Dec 2021 13:24:53 No.13995450 Report

Quoted By: >>13995567

>>13995405
>space time is not curved
No cupcake, you can apply Noether's theorem on any manifold not just flat ones
> but unfortunately this is not true at all scales and we need QFT. Hint we have a nice definition that summarises the _limit_ations of Lagrangian mechanics.
You have no idea what you're saying darling.
> the thermodynamic limit is a concept from statistical mechanics and has nothing to do with thermodynamics
You've hit your head my dear

Anonymous

Anonymous Wed 22 Dec 2021 14:11:28 No.13995567 Report

Quoted By: >>13995661

>>13995450
Curvature implies the existance of discontinuities in the space sweetie, that's why it doesn't work outside globally continuous space precisely because the space-time is non-manifold in the image. I'd love to hold your hand all day dearie, but wouldn't you rather go fetch us some coffee? This big boy stuff is clearly too much for you to process. I can see you have not finished your freshman year yet, come back to us when the app tells you to pick up our Starbucks delivery.

Anonymous

Anonymous Wed 22 Dec 2021 14:38:27 No.13995661 Report

Quoted By:

>>13995567
>Curvature implies the existance of discontinuities in the space, that's why it doesn't work outside globally continuous space precisely because the space-time is non-manifold in the image
Oh dear, you shouldn't put your schizophrenia on display for everyone to see like this! But I must admit I'm enjoying watching you be stupid, so I will go get some coffee for myself.

Anonymous

Anonymous Wed 22 Dec 2021 15:02:43 No.13995766 Report

Quoted By:

>>13994751
Idiot. When you make an experiment, prior to acceleration is velocity, and prior to that is the notion of displacement. You can't have the notion of velocity without the notion of time, but you can have the notion if displacement at the most elementary level.

Anonymous

Anonymous Wed 22 Dec 2021 16:37:33 No.13996129 Report

Quoted By: >>13996147 >>13999444

>>13994476
>Why is Conservation of Momentum true?

It's not true. It's an undecidable proposition.

Experimental physicists will tell you it's been empirically verified to be true.

Theoretical physicists will invoke Noether's theorem and presupose translational and rotational isotropy of the universe (which is only locally somewhat true anyways).

All of these theoretical demonstrations are just based upon the principle of uniformity, which is a belief, and has no scientific basis, just like any other religious belief.

https://en.wikipedia.org/wiki/Uniformitarianism

tl;dr you can't prove it's true, you have to believe it

Anonymous

Anonymous Wed 22 Dec 2021 16:40:53 No.13996147 Report

Quoted By:

>>13996129
Good bait, but you got some things wrong

Anonymous

Anonymous Wed 22 Dec 2021 16:45:27 No.13996168 Report

Quoted By:

>>13994476
Can someone explain Noether's theorem and how momentum conservation results?

Anonymous

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Anonymous Wed 22 Dec 2021 17:52:09 No.13996526 Report

Quoted By:

>>13995274
>>13995305
>Null point:
>In physics, the null point means the point in a field where the field quantity is zero. The field quantity is zero because the two or more opposing forces at the null point cancel each other. The field can be a tensor, scalar or a vector.

I'm sorry that physics provides you a "Pseud/retarded schizophrenic" answer, anon.

Anonymous

Anonymous Wed 22 Dec 2021 19:26:24 No.13996996 Report

Quoted By:

>>13994483
trust the science

Anonymous

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Anonymous Thu 23 Dec 2021 01:49:03 No.13998558 Report

Quoted By:

>>13994483
>>why is it true
>Invalid question. It is either true or not. Having a state of existence does not have a “why”.

Anonymous

Anonymous Thu 23 Dec 2021 02:09:08 No.13998601 Report

Quoted By: >>13998676

>>13994476
In the end, physics is an experimental science, so models and rules are used if and only if they accurately predict the results of experiments. Conservation of momentum is one thing that is observed to be true in countless experiments, so we use it. But since all laws (within a broad field of physics e.g. relativity) come from similar types of experiments, they also have to be consistent with each other. So you could look at raw data and find conservation of momentum in it, or you could infer that momentum is conserved mathematically from other laws (e.g. Newton's laws) that were deduced from the same data. New discoveries in physics may happen either way. Newton's theory of gravity was informed by astronomical observations, but Dirac predicted the existence of antiparticles from math alone.

Anonymous

Anonymous Thu 23 Dec 2021 02:19:48 No.13998633 Report

Quoted By:

>because xperiment xP
Like, yes this is true, but you are a fucking absolute physicslet if this is the only justification you can think of. You don't even need to invoke Noether's theorem or deeper symmetry. Conservation of momentum follows promptly as a result of Newton's laws.

Anonymous

Anonymous Thu 23 Dec 2021 02:29:52 No.13998673 Report

Quoted By:

>>13994476
You can derive it from the definition of force as the time derivative of momentum:

F = dP/dt = d(mv)/dt

If the force is zero, then mv = a constant, and thus the change in momentum of a system is zero.

So momentum is conserved in scenarios where moving objects collide elastically, but no external forces are applied.

Anonymous

Anonymous Thu 23 Dec 2021 02:31:12 No.13998676 Report

Quoted By:

>>13998601
Yawn

Anonymous

Anonymous Thu 23 Dec 2021 02:50:58 No.13998737 Report

Quoted By: >>13999037 >>13999444

>>13994476
Okay OP:

As the retards here have pointed out, the answer is Noether's Theorem. What is Noether's Theorem? Noether's Theorem is the fact that symmetries in the Lagrangian of a system are identical to conservation principles.

So, for each symmetry, there is a conserved quantity. The relevant symmetry for momentum is spacial translation symmetry. Spatial translation symmetry means that you can take a box full of stuff, and the physics inside the box do not depend on whether the box is at position A or 100 meters to the right of A. The direct mathematical consequence of this fact is the conservation of momentum.

Analogously, conservation of energy is the result of time-translation symmetry - the fact that the laws of physics do not change over time. Conservation of angular momentum (rotational symmetry) is another.

They start getting more abstract as you start getting away from classical mechanics, but the basic principle is the same. Conservation of charge, for example, is the result of gauge invariance of the electromagnetic field.

Anonymous

Anonymous Thu 23 Dec 2021 04:23:17 No.13999037 Report

Quoted By: >>13999042

>>13998737
You realize this was already pointed out in the second reply? Did typing this out make you feel smart?

Anonymous

Anonymous Thu 23 Dec 2021 04:24:40 No.13999042 Report

Quoted By:

>>13999037
You realize you're a nigger? Did typing this out make you feel caucasian?

Anonymous

Anonymous Thu 23 Dec 2021 04:35:49 No.13999072 Report

Quoted By: >>13999143

>>13994476
Can't destroy energy

Anonymous

Anonymous Thu 23 Dec 2021 04:56:36 No.13999143 Report

Quoted By:

>>13999072
actually yes you can in general relativity.

Anonymous

Anonymous Thu 23 Dec 2021 07:01:05 No.13999444 Report

Quoted By: >>14000335

>>13996129
Thanks
>>13998737
All good answers.

Anonymous

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Anonymous Thu 23 Dec 2021 14:12:31 No.14000335 Report

Quoted By:

>>13999444
>Thanks

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