/sci/ - Science & Math » Thread #13523009

42KiB, 891x508, magnetic-vector-potential.jpg

View Same Google iqdb SauceNAO

mathematical garb

Anonymous Sun 15 Aug 20:26:48 2021 No.13523009 View Reply Original Report

Quoted By: >>13523021 >>13523280 >>13523698 >>13523764 >>13523765 >>13523832

Why do physicists truncate their equations due to 'them being small', writing $\approx$ but then in the next paper they switch it for = like nothing happened?

Anonymous

Anonymous Sun 15 Aug 2021 20:29:23 No.13523021 Report

Quoted By: >>13523046

>>13523009
It's called using approximations. They don't bother writing the error terms because they have better things to do.

Anonymous

View Same Google iqdb SauceNAO klein-gordon-equation.png, 208KiB, 933x788

Anonymous Sun 15 Aug 2021 20:38:31 No.13523046 Report

Quoted By: >>13523062 >>13523066 >>13523072 >>13523839

>>13523021
No its not, error is derived from uncertianty in measurement, these equations take away real momentum that aught to be conserved. Its fine when they say it approximates, but then later it gets used as a equality, like its not a simpifying assumption.

Take for example the Klein-Gorden equation. WE often hear that E = mc^2, and only find out that there is actually a first order term $E = \sqrt{p^2c^2 + m^2c^4}$ . Then even later we find out its actually defined as infinitesimally many orders in a poweer series $E = m_0c^2[1 + +\frac{1}{2}(\frac{v}{c})^2 + \frac{3}{8}(\frac{v}{c})^4)+\frac{5}{16}(\frac{v}{c})^6)+...]$ We get $\approx$ masqeurading as = for 15 years worth of education until we get the actual equality. Than attempts at finding papers that actually use the real ones is hard to find behind jargon

Anonymous

Anonymous Sun 15 Aug 2021 20:40:03 No.13523049 Report

Quoted By: >>13523059

Physishits have the shittiest notation practices. Even engineers use better notation.

Anonymous

Anonymous Sun 15 Aug 2021 20:42:54 No.13523059 Report

Quoted By: >>13523064 >>13523066

>>13523049
Well said, The theoretical physicists should be able to duck behind 'too small to matter' as they aren't physically constrained by anything like an engineer is, who don't need to be told whats too small until they have their equipment on the table. The engineers could use untruncated experiments to create new devices, especially if they want to resonate these small order effects into something meaningful at the human scale

Anonymous

Anonymous Sun 15 Aug 2021 20:43:32 No.13523062 Report

Quoted By: >>13523074

>>13523046
>No its not, error is derived from uncertianty in measurement
https://en.wikipedia.org/wiki/Truncation_error

Anonymous

Anonymous Sun 15 Aug 2021 20:43:55 No.13523064 Report

Quoted By:

>>13523059
shouldn't be able to*

Anonymous

Anonymous Sun 15 Aug 2021 20:44:14 No.13523066 Report

Quoted By:

>>13523046
>>13523059
What the fuck are you talking about? You are mad sometimes approximations are used?

Anonymous

Anonymous Sun 15 Aug 2021 20:45:03 No.13523072 Report

Quoted By: >>13523098

>>13523046
E = mc^2 is not an approximation, it holds in the rest frame of the particle.
>get ? masqeurading as = for 15 years worth of education until we get the actual equality
Your schooling is to blame for that

Anonymous

Anonymous Sun 15 Aug 2021 20:45:25 No.13523074 Report

Quoted By: >>13523078

>>13523062
>In numerical analysis and scientific computing, truncation error is the error caused by approximating a mathematical process
This is literally defined as a process in cutting off the the higher order terms, not 'error terms' themselves

Anonymous

Anonymous Sun 15 Aug 2021 20:48:36 No.13523078 Report

Quoted By: >>13523085

>>13523074
actual value - lower order terms = higher order terms. It's common to call this difference as an error.

Anonymous

Anonymous Sun 15 Aug 2021 20:50:17 No.13523085 Report

Quoted By: >>13523091 >>13523094

>>13523078
Not surprised in this Orwellian mindspace, they are far from errors in the value its expressing, I need a new language, one where root words are respected

Anonymous

Anonymous Sun 15 Aug 2021 20:51:17 No.13523091 Report

Quoted By: >>13523101

>>13523085
It's the error associated with the approximation, makes perfect sense.

Anonymous

View Same Google iqdb SauceNAO Screenshot from 2021-08-15 15-51 (...).png, 130KiB, 1117x391

Anonymous Sun 15 Aug 2021 20:52:05 No.13523094 Report

Quoted By:

>>13523085
Definition 5, with reference to a specific occurrence of definition 1

Anonymous

Anonymous Sun 15 Aug 2021 20:52:31 No.13523098 Report

Quoted By: >>13523113

>>13523072
Thats what one learns when they get upgraded to linear velocity space, and will go on assuming its the final form of the equation until they get the power series

It is totally to blame for this, I need to review if a rest frame is even technically possible

Anonymous

Anonymous Sun 15 Aug 2021 20:53:31 No.13523101 Report

Quoted By: >>13523109 >>13523119

>>13523091
"error terms" should never be physical momentum that is not an error, thats as bad as saying real numbers dont need to be real

Anonymous

Anonymous Sun 15 Aug 2021 20:54:47 No.13523109 Report

Quoted By: >>13523114

>>13523101
Lmao another schizo thread

Anonymous

Anonymous Sun 15 Aug 2021 20:55:37 No.13523113 Report

Quoted By: >>13523122

>>13523098
What the hell is a linear velocity space? The power series involving v is the energy measured by an observer moving with a velocity v wrt the object whose energy is being measured.

Anonymous

Anonymous Sun 15 Aug 2021 20:55:58 No.13523114 Report

Quoted By: >>13523123 >>13523127

>>13523109
>dont worry child anything above a rest frame in e=mc^2 is an 'error' term dont worry about it

Anonymous

Anonymous Sun 15 Aug 2021 20:56:59 No.13523119 Report

Quoted By: >>13523127

>>13523101
>semantics
Blah, this is a boring line of debate

Anonymous

Anonymous Sun 15 Aug 2021 20:58:09 No.13523122 Report

Quoted By: >>13523134

>>13523113
first order term velocity
second order term acceleration
third order term jerk
4th order term jaunt
etc etc

The space is the conceptual landscape, like defining a hilbert space. Just to accentuate that only linear velocity is allowed. "linear velocity space" is the conceptual land where only moving in linear velocity is allowed.

Anonymous

Anonymous Sun 15 Aug 2021 20:58:18 No.13523123 Report

Quoted By: >>13523132

>>13523114
The fucking klein gordon equation is not derived from the taylor series of the energy momentum relation you fucking retard it is the energy squared.

Anonymous

Anonymous Sun 15 Aug 2021 20:59:10 No.13523127 Report

Quoted By: >>13523138

>>13523114
>>13523119
this confuses the initiate and blocks questioning, did you have any intution that the first order term existed until taught?

Dont worry about those 'errors' kid, no secrets can possibly be behind there, cods whallop!

Anonymous

Anonymous Sun 15 Aug 2021 21:00:28 No.13523132 Report

Quoted By: >>13523142

>>13523123
>The fucking klein gordon equation is not derived from the taylor series of the energy momentum relation you fucking retard it is the energy squared.

This is exactly what happens when on this educations systems malware.

There is nothing stopping one from deriving a gorden-klein equation with the power series expression.

But its hard to find online- isnt it

Anonymous

Anonymous Sun 15 Aug 2021 21:00:41 No.13523134 Report

Quoted By: >>13523141

>>13523122
What on earth are you talking about lmao. Special relativity can handle acceleration without problems if that's what you're referring to.

Anonymous

Anonymous Sun 15 Aug 2021 21:01:22 No.13523138 Report

Quoted By: >>13523143 >>13523188

>>13523127
I have no idea how you're confusing the ultimate in pop culture equations with what people actually learn when studying special relativity
Not to mention the part where the "applied math not being pure math" demon raises its ugly head

Anonymous

Anonymous Sun 15 Aug 2021 21:02:18 No.13523141 Report

Quoted By: >>13523151

>>13523134
It handles it but shoving it away in 'too small to be concerned with' or in a coefficient like $\gamma$ that says nothing about the physical reality

Anonymous

Anonymous Sun 15 Aug 2021 21:02:30 No.13523142 Report

Quoted By: >>13523147

>>13523132
nigger the energy squared is a polynomial there is bo infinite series.

Anonymous

Anonymous Sun 15 Aug 2021 21:03:24 No.13523143 Report

Quoted By:

>>13523138
Pop cultures repeats the mantra E= mc^2 without mentioning rest frame 99% of the time, inducing the common belief that the position(t) function has any bearing

Anonymous

Anonymous Sun 15 Aug 2021 21:04:25 No.13523147 Report

Quoted By: >>13523165

>>13523142
see another educated fool
https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence

>For speeds much smaller than the speed of light, higher-order terms in this expression get smaller and smaller because
v
/
c
is small. For low speeds, all but the first two terms can be ignored:

ignored they say, real physical momentum, ignored, how are we to advance physics on truncated equations?

Anonymous

Anonymous Sun 15 Aug 2021 21:05:16 No.13523151 Report

Quoted By: >>13523165

>>13523141
No, you don't need to throw away any terms. No idea where you're getting this from

Anonymous

Anonymous Sun 15 Aug 2021 21:10:42 No.13523165 Report

Quoted By: >>13523172

>>13523151
Well said, there isn't any need, but look the wiki just chucks them out because lets just imagine low speeds so the higher order terms are ignored.

>>13523147

Additionally one may remember instantaneous acceleration is impossible in nature and one needs all the moments to make it to a linear velocity. These approximations that then pose as equations need to be clarified or deposed

Anonymous

Anonymous Sun 15 Aug 2021 21:12:54 No.13523172 Report

Quoted By: >>13523178

>>13523165
They're not chucking away anything. They're explaining how the classical kinetic energy mv^2 / 2 arises in the low velocity limit approximation of special relativity.

Anonymous

Anonymous Sun 15 Aug 2021 21:16:05 No.13523178 Report

Quoted By: >>13523188

>>13523172
there chucking away $\infty - 2[\math] terms because they dont like how many zeros are at the front of those numbers. Its fine when there is an <script type="math/tex">\approx[\math] sign in front of it, but than papers import these equations without substituting in an equals sign and no body actually bothers to perform their physics on the real calculations<br /><br />Even getting posters that think the idea of using the real equation is preposterous$

Anonymous

Anonymous Sun 15 Aug 2021 21:22:43 No.13523188 Report

Quoted By: >>13523199

>>13523178
I agree with this guy >>13523138
It just looks like you're upset because you mistook popsci for actual physics.

Anonymous

View Same Google iqdb SauceNAO 220px-E_equals_m_plus_c_square_a (...).jpg, 11KiB, 220x293

Anonymous Sun 15 Aug 2021 21:27:42 No.13523199 Report

Quoted By: >>13523207 >>13523224

>>13523188
I'm upset because I cant find an infinite powers expression of the klein gorden equation

I'm upset that the 4 current of the magnetic vector potential is truncated by gauge theories

I'm upset that people think its okay to represent sqrt(2) as a distance on a line

I'm upset as lazy thinking has turned approximations into equations

Anonymous

Anonymous Sun 15 Aug 2021 21:32:32 No.13523207 Report

Quoted By: >>13523232

>>13523199
Klein Gordon is exact. E^2 = p^2 c^2 + m^2 c^4 reduces to E = mc^2/sqrt(1 - v^2/c^2) (which is just the power series you posted) for a particle with mass.
>I'm upset that the 4 current of the magnetic vector potential is truncated by gauge theories
No idea what truncation you're talking about
>I'm upset that people think its okay to represent sqrt(2) as a distance on a line
This is just schizo level

Anonymous

Anonymous Sun 15 Aug 2021 21:37:48 No.13523224 Report

Quoted By: >>13523251

>>13523199
Nigga, "distance" is just ill-defined in the Euclidean plane since it requires a square root.
If $\sqrt 2$ couldn't be used as a Eucliden "distance," then you couldn't use the Euclidean algorithm on it. Proportions of measurements in the plane are inherently different to numerical approximations.

Anonymous

View Same Google iqdb SauceNAO Thoth-kepler-phi-pi.png, 376KiB, 1080x370

Anonymous Sun 15 Aug 2021 21:39:19 No.13523232 Report

Quoted By: >>13523235 >>13523265 >>13523270 >>13523311

>>13523207
exact for a magical particle that can make it to linear velocity without magically accelerating, jerking and jaunting

Gauge theory is so engrained in electrodynamics literature it would take some time to pull one out of it, If you want to try here you go
>Also, the irrotational component of the vector potential is gauged away,

https://www.researchgate.net/profile/Lee-Hively/publication/331983861_Classical_and_extended_electrodynamics/links/5d6d8458299bf1808d61b9a3/Classical-and-extended-electrodynamics.pdf

Setting the divergence in the magnetic vector potential because the maths are too big and the effects so inconsequential is a mistake

One will never be able to create a string of length sqrt(2) it has infinite precision, only schizos care, but its a factually true statement, approximation is not equality

Anonymous

Anonymous Sun 15 Aug 2021 21:39:51 No.13523235 Report

Quoted By: >>13523246

>>13523232
>kepler's triangle believer
Into the trash it goes

Anonymous

Anonymous Sun 15 Aug 2021 21:43:05 No.13523246 Report

Quoted By: >>13523249

>>13523235
Thoth just flexed palindromes, best take it out

Anonymous

Anonymous Sun 15 Aug 2021 21:44:24 No.13523249 Report

Quoted By:

>>13523246
>palindromes in base 10
lmao

Anonymous

Anonymous Sun 15 Aug 2021 21:44:59 No.13523251 Report

Quoted By: >>13523270 >>13523280

>>13523224
The potential 4-vector doesn't even arise directly in Maxwell's equations. Unless you fix the gauge you won't get a unique solution for the potential, so you choose a gauge which makes computation simpler. This is not at all an approximation or truncation.
>finitist schizophrenia
I'm done here

Anonymous

Anonymous Sun 15 Aug 2021 21:51:01 No.13523265 Report

Quoted By: >>13523286

>>13523232
>doesn't believe in $E = \sqrt{p^2c^2 + m^2c^4}$
>believes in a triangle with $\sqrt \phi$ as a base

Anonymous

Anonymous Sun 15 Aug 2021 21:52:27 No.13523270 Report

Quoted By:

>>13523251
Meant to quote >>13523232

Anonymous

View Same Google iqdb SauceNAO no-ponty-cia.jpg, 58KiB, 768x672

Anonymous Sun 15 Aug 2021 21:54:05 No.13523280 Report

Quoted By: >>13523289

>>13523251
Maxwell would've used his "heretic quaternion"
http://www.jowsey.org/physics/Dimensions.html

The truncation of the vector potential comes, as in >>13523009 pic related, come from choice. Again a situation because of Gauge cope. The maths get to hard and long so they delete real momentum and hide it by a gauge

The truncation of the 4 current becomes obvious when one reads deeper into Hivelys work. Consider
https://www.researchgate.net/publication/347844420_Implications_of_Gauge-Free_Extended_Electrodynamics

Anonymous

Anonymous Sun 15 Aug 2021 21:56:51 No.13523286 Report

Quoted By:

>>13523265
Strawman, Keplers triangle, predicting that pi is 4/sqrt(phi) =/= pi reveals the incongruencies in beleving irrational numbers can be represented as a distance of a line Its one of the most beautiful thoughts in all of math

Anonymous

Anonymous Sun 15 Aug 2021 21:57:13 No.13523289 Report

Quoted By: >>13523311

>>13523280
I'm not reading some crank you linked lmao. It's not truncation or cope or whatever as I already explained earlier. If you disagree, you should learn more physics.

Anonymous

View Same Google iqdb SauceNAO f877e48589900a97f049c07db408fb48.png, 2MiB, 1009x1703

Anonymous Sun 15 Aug 2021 22:06:38 No.13523311 Report

Quoted By:

>>13523289
>I'm not reading some crank you linked lmao
As I've said in >>13523232
>gauge theory is so engrained in electrodynamics lit it would take some time to pull one out
if your not ready, your not ready.

He's retired Oak Ridge National Labs,

Keep truncating your electrodynamics for no reason other than the math gets complicated thinking you can collect all the information as long as its invariant under the transformation of the potentials and phase

Anonymous

Anonymous Sun 15 Aug 2021 23:59:20 No.13523698 Report

Quoted By: >>13523729

>>13523009
Because you're working to the same order of magnitude

Anonymous

Anonymous Mon 16 Aug 2021 00:11:43 No.13523729 Report

Quoted By:

>>13523698
This "equals if" mentality needs to be diverted into "approximated given"

Anonymous

View Same Google iqdb SauceNAO image-66[1].jpg, 84KiB, 720x540

Anonymous Mon 16 Aug 2021 00:26:15 No.13523753 Report

Quoted By: >>13523755 >>13523801

Anonymous

View Same Google iqdb SauceNAO image-67[1].jpg, 81KiB, 720x540

Anonymous Mon 16 Aug 2021 00:27:15 No.13523755 Report

Quoted By: >>13523757 >>13523801

>>13523753

Anonymous

View Same Google iqdb SauceNAO image-70[1].jpg, 68KiB, 720x540

Anonymous Mon 16 Aug 2021 00:28:40 No.13523757 Report

Quoted By: >>13523759 >>13523801

>>13523755

Anonymous

View Same Google iqdb SauceNAO image-71[1].jpg, 58KiB, 720x540

Anonymous Mon 16 Aug 2021 00:29:42 No.13523759 Report

Quoted By: >>13523764 >>13523801

>>13523757

Anonymous

View Same Google iqdb SauceNAO image-72[1].jpg, 65KiB, 720x540

Anonymous Mon 16 Aug 2021 00:31:00 No.13523764 Report

Quoted By: >>13523801

>>13523759
>>13523009
last

Anonymous

Anonymous Mon 16 Aug 2021 00:31:26 No.13523765 Report

Quoted By:

>>13523009
same reason no one ever writes out the error term of the taylor series, its annoying. but also because many physicists are idiots, especially the women.

Anonymous

View Same Google iqdb SauceNAO proof-of-incommensurability.png, 1MiB, 724x2698

Anonymous Mon 16 Aug 2021 00:48:43 No.13523801 Report

Quoted By:

>>13523753
>>13523755
>>13523757
>>13523759
>>13523764
I dont fully understand the "It cannot be that a and h are both even numbers, because if they were , a larger unit would have fit exactly into both the diagonal and the side. But taking that as true this is based, here, to save you the trouble of printing all five again

Anonymous

Anonymous Mon 16 Aug 2021 01:02:26 No.13523832 Report

Quoted By:

>>13523009
Because theoretical physicists don't like silly formalities when something is understood from context

Anonymous

Anonymous Mon 16 Aug 2021 01:04:28 No.13523839 Report

Quoted By: >>13523859

>>13523046
You have to undergo a serious paradigm shift if you are going to make any progress understanding physics. Everything is an approximation

Anonymous

View Same Google iqdb SauceNAO 1606763691361.jpg, 63KiB, 850x400

Anonymous Mon 16 Aug 2021 01:14:18 No.13523859 Report

Quoted By: >>13524272 >>13524650

>>13523839
This is about getting those structures back closer to reality

Anonymous

Anonymous Mon 16 Aug 2021 03:45:50 No.13524272 Report

Quoted By: >>13524641

>>13523859
>engineer who got filtered by atomic theory

Anonymous

View Same Google iqdb SauceNAO tesla-keystones-abridged.png, 1MiB, 1257x855

Anonymous Mon 16 Aug 2021 06:47:06 No.13524641 Report

Quoted By: >>13524668

>>13524272
>atomic theory
positively gauged

Longitudinal EM
Charge Density waves
De gauge your mind

my "atoms" are cymatic fractals of aether

Anonymous

View Same Google iqdb SauceNAO famous science quote.jpg, 50KiB, 850x400

Anonymous Mon 16 Aug 2021 06:51:13 No.13524650 Report

Quoted By: >>13524658

>>13523859

Anonymous

View Same Google iqdb SauceNAO egypt-geometry.jpg, 4MiB, 4537x1831

Anonymous Mon 16 Aug 2021 06:55:33 No.13524658 Report

Quoted By:

>>13524650
https://www.youtube.com/watch?v=New0pTB6yDg&ab_channel=OriginalThinkingz

Anonymous

Anonymous Mon 16 Aug 2021 07:06:17 No.13524668 Report

Quoted By: >>13524688

>>13524641
Absolutely filtered

Anonymous

View Same Google iqdb SauceNAO tesla-and-the-scalar-trail-compr (...).jpg, 4MiB, 3475x4320

Anonymous Mon 16 Aug 2021 07:17:27 No.13524688 Report

Quoted By:

>>13524668
Keep setting your divergence in the magnetic vector potential cause your maths is too complex

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches