/sci/ - Science & Math

Anyone?

No

dude, I have no idea what you're talking about, but I think it's worthy of a bump

>>3048109
but why

>>3048086
>R and F being 3-dimensional
Dude torque would still be in the 3rd dimension. If you have two connecting vectors in free space, you can always choose a vector perpendicular to both of them.

And how the hell would you make a 4D level out of this idonteven

>>3048086
The standard, Torque = R cross F, is in three dimensions, as the standard cross product is only for 3d.

You can extend this concept in any number of ways to define a 4-d torque (or higher dimensional torque). It all depends on how you are going to redefine the cross product. You can easily extend it using tenor calculus.

None of the shit you said makes any sense though.

Anything else?

>>3048114
agreed

The problem with this sort of thing is that dimensions don't carry very well. If you try to somehow go the other way and make sense of torque in 2D, it doesn't work. Also, from 2D to 3D units and stuff all change so I don't think trying to get from 3D to 4D this easily will work.

>>3048208
what would your extra values pertaining to the extra dimensions be though?

>>3048231
It depends on how you construct your system, your metric, and all your shit.

It is purely abstract at that point and you are not producing any new physics or results, all you are doing are just cramming other equations and information into that one extra slot of freedom. This is why we don't do that shit, cause it is pointless, it is not giving us new physics or insight into anything.

>>3048086

A magnitude cannot be perpendicular to something, it does not have a direction.

Also, what is "perpendicular to an angle"?

>>3048249
i see what you are saying. and yeah that would be round about fuck stupid to do.

Torque is actually a 2-tensor (~matrix). People just ram it into a vector, because in 3 dimensions, it only has 3 independent elements that you can asociate a pseudo-vector with.

A 4^4 vector product would not lead to a 4-pseudo-vector. If i remember correctly, that would make a 6-vector.

>>3048267
It is quite easy to do though. All you need for a cross product in 4-d, is a 4-d levi-citiva symbol, which is trivial to construct.

http://en.wikipedia.org/wiki/Levi-Civita_symbol

From that wiki information, you should be able to construct cross-products of any dimension you want.

>>3048275
Let me guess, your an engineer. It is evident by all your bullshit and lack of knowledge.

>>3048275
Wow

>>3048320

No, i'm a physicist.

Now suck my dick maybe?

>>3048320
>>3048324

samefag doing it wrong

http://www.natscience.com/Uwe/Forum.aspx/physics-research/441/torque-T-r-x-F-and-basic-tensors

>>3048086
>Torque is actually a 2-tensor

>>3048320
>>3048324

lmao you both are retarded. High-school fags on my /sci/? It isn't even weekend yet.

>>3048320
>>3048324

me >>3048327 again

Whay do you even think it's wrong? You clearly lack a fundamental understanding of torque AND tensors, so how can you criticise me without providing any arguments?

That's why they should teach tensor calculus early.

People get confused every time.

>>3048347
LMFAO.

According to that website, all 3X3 objects produce a matrix. WTF? This is cause they are not summing over the proper levi-citivia indicies. Basically, they are doing math fucking wrong.

Please, use real Tensor calculus, and not this retarded shit.

>>3048365
Why aren't you properly summing over the levi-civita index's? Do you not understand Einstein summation notation?

You basically set-up the problem, but you don't actually follow through. SUM THAT SHIT YO!

>>3048383

> all 3X3 objects produce a matrix. WTF?

Example of a 3X3 object that is not actually a _tensor_?

> use real Tensor calculus, and not this retarded shit.

Real tensor calculus being?

>>3048086
R, F and Torque are all 3-dimensional, always. R and F always share a common plane, if that's what you mean by "2-dimensional".
>>3048299
I'm not very familiar with tensors, but I think you would have to chose some parameters arbitrarily and lose the "natural" aspect of it, right?

What I've been taught is that cross product can be defined in any dimension n for n-1 vectors. v1 x v2 x ... x vn-1 = vn such as for any other vector v Det(v1,...,vn-1,v) = vn.v .

>>3048394

Not him, but I don't understand you.

x_i x_j = T_{ij}

Tensor times Tensor = Tensor

r is a 1-tensor, right?
F is a 1-tensor, right?

rF therefore is a 2-tensor.

Everything else is fucked up, especially mathematically.

If you say it yields another 1-tensor, you are basically saying the right-hand direction in euclidean 3-space (or any other space at that) is a special direction.

There can't be a special direction because of isotropy.

Now what high school bitches?

>>3048398
>confuses a matrix with a tensor

A matrix is a type of tensor. Not the other way around.

That shitty website says that all 3-vectors CROSS 3-vectors produce a matrix, this is not true. A 3-vector CROSS 3-vector produces a 3-vector. If you actually use the tensor calculus, tensor notion, and the tensor notation definition of the 3-d cross product you will get a 3-vector, not a matrix.

The definition of the 3-d cross product, using tensor calculus is given @

http://en.wikipedia.org/wiki/Levi-Civita_symbol

Educate yourself.

>>3048406
>>3048406
That not the definition for the cross-product though, where the fuck are you getting this nonsense from?

The tensor definition of the 3-d cross product is the pic. It produces a vector.

\thread

>>3048442

If i'm not mistaken YOU said matrix. Which is wrong.
Are you high or something?

> A 3-vector CROSS 3-vector produces a 3-vector

That is fucking wrong as well, because it produces a 3-PSEUDO-vector. The pseudo comes from the fact it would actually be a 2-tensor (represented by a 3x3 matrix), but you can put all the independent elements into a pseudo-A 3-vector CROSS 3-vector produces a 3-vector, because there are only 3 of them.

This makes it easier for the engineers. And you apparently.

> implying the Levi-Civita symbol has anything to do with this.

>>3048460

Who the hell said i was using the cross-product?

What the fuck is wrong with all of you? Butthurt much?

The cross-product is a fucking aberation used for engineers and stupid wannabe scientists that makes, as explained, a fucking pseudo-vector out of a 2-tensor.

>>3048442

Educate yourself.

http://en.wikipedia.org/wiki/Outer_product

>>3048442

You are fucking retarded because you actually say he is true.

r_i F_j = T_{ij}, that's the general rule. Now if you are an engineer, you contract this 2-tensor with the Levi_Civita symbol, like:

T_{ij}e_{ijk} = t_k

using Einstein convention.

Y'all are fucking retarded.

>>3048466
>can't do tensor calculus
>spouts bullshit
>argues with the definition
>doesn't use levi-civitia

Please, show me the actual math, the actual tensor calculus backing up your claims.

Trollin?

>>3048497

t_k is the torque you are all talking about, by the way.

I'm 12 and what kind of math is this I don't even.

And why aren't you using the beautiful, the talented LaTeX math guys

<span class="math">r_i F_j = T_{ij}[/spoiler]
<span class="math">T_{ij} e_{ijk} = t_k[/spoiler]

>>3048497
>Engineers
>Einstein convention

Cause einstien was an engineer?

>>3048501

http://folk.uio.no/patricg/teaching/a112/levi-civita/
See bottom of the page

http://en.wikipedia.org/wiki/Tensor_calculus

I also read many books, for example
http://www.amazon.de/Space-Time-Matter-Hermann-Weyl/dp/0486602672/ref=sr_1_1?ie=UTF8&qid=1305269
498&sr=8-1

and you?

>>3048485
>You define torque using the "outer-product" and not the "cross-product".

WTF? that is not the definition!

>>3048513

> implying i said anything like that.

You should probably learn to read, asspie.

You get a 2-tensor for the torque, which is necessary because of isotropy, then you say the right-hand direction is the one you prefer, then tensor-multiply it with the Levi-Civita-tensor.
What you get is a pseudo-vector.

Are you that retarded or are you starting to get it?

Oh wow what's going on here

>Torque is actually a 2-tensor (~matrix).
Nope, if you want to have it fancy torque is <span class="math">>>3048398
-i_{r}i_{F}\mathrm{vol}^3[/spoiler], where i is the interior product, and vol the volume form. In addition, there are no 2-tensors (but (2,0)-tensors if you insist to use numbers before you say tensor), and no tensor is a matrix (there's a correspondence though).

>Example of a 3X3 object that is not actually a _tensor_?
Connection coefficients. (They are <span class="math">n\times n\times m[/spoiler] if you wanna write it like that, but if you apply them to one argument you're left with a <span class="math">n\times n[/spoiler] object that is still not a tensor)

Oh wow what's going on here

>Torque is actually a 2-tensor (~matrix).
Nope, if you want to have it fancy torque is <span class="math">-i_{r}i_{F}\mathrm{vol}^3[/spoiler], where i is the interior product, and vol the volume form. In addition, there are no 2-tensors (but (2,0)-tensors if you insist to use numbers before you say tensor), and no tensor is a matrix (there's a correspondence though).

>Example of a 3X3 object that is not actually a _tensor_?
Connection coefficients. (They are <span class="math">n\times n\times m[/spoiler] if you wanna write it like that, but if you apply them to one argument you're left with a <span class="math">n\times n[/spoiler] object that is still not a tensor)

>>3048525

I never said tensors were matrices. The "~" means they can be represented by matrices.
And yes, torque is indeed actually a matrix, or how would you explain that there's a preferred direction in space when you say it is a pseudo-vector?
One is allowed to say 2-tensor, if the space you build your tensor-calculus on is the same as your dual space. So in relativity for example, you'd be right, but in euclidean space it is perfectly fine to just say 2-tensor.

> Connection coefficients.

Are not derived by 1-tensorX1-tensor.

>>3048527

Yeah YOUR definition is, as has been said multiply the tensor by the LC-tensor, so you get a pseudo-vector.

Still, torque is a 2-tensor, that CAN be represented, in the way i showed, by a pseudo-vector, because it is a skew-tensor.

>>3048543

fucking shit, i mean

> And yes, torque is indeed actually a _tensor_

sorry.

This is what happens when /sci tries to do math intended for post-humans......

>>3048549

I'm sad. This also happens every time one talks about complex numbers, the "speed of light in matter" or "relativistic mass".

So many bullshit coming up.

>>3048529
>You get a 2-tensor for the torque

Torque is not defined as an outer-product of two vectors. Why do you keep assuming that is the standard definition of torque?

Please provide some resources for this definition you use, as it is not standard in the physics or mathematics community. I could just as well say that torque is the inner product of two vectors, if we are allowed to make up our own definitions.

>>3048559

Because it is, and as said, the pseudo-vector only comes into play when you multiply it by the LC-tensor.

it is fucking standard to do this. Your professor just didn't tell you what exactly you are doing.

I provided many sources in here. Just read.

>>3048545
>torque is a 2-tensor

Source or calling bullshit

>>3048559

> I could just as well say that torque is the inner product of two vectors

> implying that's the same as the outer product

He gave a valid definition that yields the same results.

>>3048565

Sources have been given plenty in here.

>>3048543 Are not derived by 1-tensorX1-tensor.
That's not what you were asking for.

>And yes, torque is indeed actually a _tensor_
Mathematically, all tensors are vectors (in the sense that they form a vector space), all vectors are tensors (in the sense that a (1,0)-tensor is a real tensor of the tensor space of its vector space, since <span class="math">\mathcal T^1_0:=V[/spoiler]).
Your problem is that you don't know about Hodge duality, which is as much part of torque as r and F are.

>>3048569

> That's not what you were asking for.

In that case, there was a misunderstanding. I thought he said 3-vector and 3-vector yield another 3-vector in general, and i wanted an example for something that does not give a 2-tensor when you take the outer product of two 3-vectors.

> Your problem is that you don't know about Hodge duality, which is as much part of torque as r and F are.

What? That's what i basically say the whole time.

Take two (1,0)-tensors, calculate the outer product. You get a (2,0)-tensor. That's what it is.
Then, apply the LC-tensor to it, contract over the first two indices. You get a pseudo-vector.

That's exactly what Hodge-duality states. Take a special direction that you prefer. Then you can associate anti-symmetric (2,0)-tensors (for example) with 1-tensors, as there are only 3 independent elements.

Another example would be vectors with 4 elements. Outer product yields a skew tensor with 6 independent elements. Therefore, you can associate a vector consisting of 6 elements with it.

>>3048569

Ha, thanks for that i finally found a source these idiots can maybe finally agree on:

http://en.wikipedia.org/wiki/Hodge_duality#Examples

> A common example of the star operator is the case n = 3, when it can be taken as the correspondence between the vectors and the skew-symmetric matrices of that size. This is used implicitly in vector calculus, for example to create the cross product vector from the wedge product of two vectors.

Bitches got

□ told
□ motherfucking told
■ Berthold Brecht

>>3048583 misunderstanding
I have to second this after your last post.

>Then, apply the LC-tensor to it
Levi-Civita is a symbol, not a tensor. <span class="math">\sqrt g\varepsilon_{i_1i_2\ldots}[/spoiler] is the (pseudo)tensor.

I am very disappointed in this board.

Someone comes up with something you don't know and you go all "you are fucking retarded, bullshit, wrong, stupid engineer".

How about thinking you don't know everything in this universe? You professors aren't knowing it all either.
If you want to get smart, you have to verify almost everything they tell you. Be open to someone who says "maybe you didn't quite get that right". You can refuse to accept it anyway.

Sigh, this used to be a good board.

>>3048613

> Levi-Civita is a symbol, not a tensor.

Agreed. Excuse my failure there.

My point still holds.

>>3048613

Correct, since the LC-symbol is what gives rise to the preferred direction regarding pseudo-vectors in the first place.

>>3048598
>>3048598
>>3048598
>>3048598

This.

/discussion

back to topic nao?

>>3048622 My point still holds.
And your point was? If you're one of the "cross product is a 2-tensor" guys then no, since <span class="math">-i_{r}i_{F}\mathrm{vol}^3=*(r\wedge F)\in V^*\neq V^*\otimes V^*[/spoiler].

>>3048598
wtf are you even talking about anymore?

>>3048633

Well, kind of, yes. See >>3048598
I never said the cross product yields a 2-tensor, i said torque is a 2-tensor. You get the pseudo-vector everyone uses by applying the Hodge-duality (using the Levi-Civita symbol). That's where the cross-product comes from.

Torque is actually a 2-tensor. You can represent this tensor by a pseudo-vector.

That's what i'm saying and that's what's correct, according to my professors, books and sources i and some others in here provided.

>>3048638

That article says "cross product is the reduction of the 2-tensor that you get into a vector", like that guy said in his forst post.

Basically that translates to " you are wrong, we are right".

>>3048643
Well keep believing it then, have fun generalizing angular momentum to relativity with that (double hodge for simplicity, yipee, I like my factors of -1)

>>3048654

lol

> implying it's easier to generalize angular momentum to pseudo-riemannian manifolds using the cross-product which is not even defined for 4d-spaces

My approach at 4d euclidean space:

rF = T_{ij}

where r and F are vectgors with 4 elements.

Pretty easy, huh?

>>3048654

What the fuck are you talking about? It is even mentioned in the article you brought up regarding Hodge duality.

It is always implicitly used when calculating cross products, which means that you calculate a 2-tensor, then contract it with the levi-Civita symbol so you get a vector with 3 elements.

What's your point?

All you guys just say "no you're wrong, derp" although i back up my claims in contrast to you.

>>3048583
The outer product isn't the same thing as the cross-product dumbshit. You are 100% correct about the outer-product, and all your arguments are just about the outer-product. Yes, the outerproduct would give you a matrix, WE ALL KNOW THAT SHIT!

But the torque isn't fucking defined as the outer product, it is defined as the cross product, which includes the levi-civita and summation over indcies.

Torque is a three vector, as it is a cross product, not just an outer product. All your sources either confirm this fact, or confuse the definition of the cross-product with the outer product (like you do). The CROSS-PRODUCT ISNT THE SAME THING AS THE OUTER-PRODUCT. A CROSS PRODUCT IS A PARTICULAR TYPE OF OUTER-PRODUCT, WITH CERTAIN ADDITIONAL RESTRICTIONS.

\thread

>>3048670
The cross-product isn't the same thing as an outer-product. You fail at basic logic.

>>3048519

I happen to have that book. It's in german though. It belongs to my father and i've never read it, but i looked if i could find something.

From page 40 onwards, this is pretty much what this "torque is a 2-tensor" guy says.

>>3048674
>>3048687

You still don't get it. You won't ever get it i'm afraid.

Torque MUST BE the outer product. BECAUSE YOU WOULD VIOLATE ISOTROPY IF YOU SAY THERE IS A PREFERRED DIRECTION IN SPACE.

You get it if i scream?

Torque is a 2-tensor, that can be represented by a pseudo-vector.

This is what all my sources validate. This i what i'm saying and it still is correct.

You still have failed to provide any sources against this.

Oh and yes, basically, outer product and cross-product and then applying the LC-symbol DO in fact yield the same result.

>>3048687
>>3048674

> implying he said outer product = cross product

y'all need to learn 2 read and notice when you fail and get out in time.

I'll leave this shithole, you're not worth it.

>So I was thinking, if Torque's magnitude is perpendicular to the smallest angle between it's 'R' and 'F'.

<-- if this is what you mean, then:
For a flat surface of 180 degrees (a straight line), you can determine the effect of a force applied to it by taking the sin of EITHER angle, not just the smallest. angle = A, so we have two angles: A & 180-A
Sin(x+y) = sinxcosy + cosxsiny
s(180-A) = sin(180)cos(A) - cos(180)sin(A)
0 * cos(A) - -1 * sin(A)
- -sin(A)
sin(A)

>>3048693
>torque is a 2-tensor

That is not the standard definition of torque. That book is defining torque as the outer-product of two vectors (not the standard cross-product), that is just fucking wrong.

It may help some conceptualize the idea, but it is still wrong. Sorry, bro. Your sources are shit, and will hurt you in the long run.

>>3048719

> implying it is not the cross-product definition that is "wrong"

BECAUSE IT FUCKING VIOLATES ISOTROPY

Where the fuck do you guys "learn" science?

>>3048719

> Your sources are shit, and will hurt you in the long run.

the fuck are you talking about? Generalize your definition of torque to 4 dimensions. Do it. Now.

I can do it, look:

rF = T_{ij}

Oh look, the correct definition is independent of dimensions as well as directions just like it should be.

This thread is funny.

All you guys masturbating to what you were told in school and university, you are pathetic.

The cross product is just a simplification of tensor calculus.

I learned that in my second year in a mathematics lecture specifically for physicists, so not even a real math lecture.

You guys fail at life.

>>3048707
>Torque MUST BE the outer product.

Nope

>YOU WOULD VIOLATE ISOTROPY IF YOU SAY THERE IS A PREFERRED DIRECTION IN SPACE

Wrong. The handedness of our coordinate system is arbritary. WE CHOOSE IT! We choose the direction of the cross-product, DURRRR. The choice actually doesn't matter, nor will it change our observables (as long as consistancy is maintained)

>>3048755

http://en.wikipedia.org/wiki/Cross_product#Cross_product_as_an_exterior_product

Read that. Get smart. Especially the paragraph coming after that.

> The handedness of our coordinate system is arbritary

No it is not if you want to use the cross product, fucking idiot. Refer to the linked article.

>>3048755

lol

> we break isotropy because i can do it yay

>>3048755

Does "right-hand-rule" ring any bells?

If so, why is it the right hand rule and not the left-hand rule?

That's the problem that is avoided by defining torque as a 2-tensor. It is dual to the pseudo-vector you use anyway, so they are basically the same.

>mfw still no one has provided any source backing up their claims

i suspect we're being majorly trolled in here.

>>3048775
You can use the left-hand rule and it works just as well. It is only mathematical convention, it doesn't actually change the physics.

http://en.wikipedia.org/wiki/Right-hand_rule

"When choosing three vectors that must be at right angles to each other, there are two distinct solutions, so when expressing this idea in mathematics, one must remove the ambiguity of which solution is meant."

"it may be useful to use the opposite convention, where one of the vectors is reversed and so creates a left-handed triad instead of a right-handed triad."

You can use either, left-hand rule or right-hand rule, and get the same physical results.

apart from some fundamental particle physics, handedness is a convention of our units, coordinate systems and how we sign them.

>>3048813

based on what assumption do you use one of those?

Using the tensor definition, you don't have to use one.

By choosing one, you say one is special, while they must be arbitrary.

Just read the linked article.

>>3048775
>why is it the right hand rule and not the left-hand rule?

OMFG, are you fucking serious? It is arbitrary dumbshit, just like choice of coordinate axis direction. It is a fucking gauge freedom that doesn't actually change physics whatsoever.

>>3048822
if i made electron current positive instead of negative, we'd be using a left hand rule.

>>3048823

If you fucking choose one of the definitions it is NOT arbitrary anymore.

Are you dumb or trolling? I don't really know anymore.

Look. BEFORE you choose a special direction, you have a 2-tensor torque. THEN you choose the right-hand rule, which enables you to use the Hodge duality (multiplication with the LC-symbol) to create a pseudo-vector, which describes the same goddamn thing under the assumption of a special direction.

>>3048827

Why is the righthand rule not suitable? Because you make the left-hand rule special.

Seriously, you guys are either super-retarded or tryiong to troll.

>>3048834
lol

you don't understand that arbitrary means arbitrary as a whole.

once you choose, of course it is no longer arbitrary, but the fact you can choose means as a whole, these things are conventions only.

i doubt you are but you kind of sound like an engineer. wedded to the equations rather than what they actually mean.

>>3048822
>based on what assumption do you use one of those?

None, it is fucking convention. It is a free degree of freedom, you just pick whichever one you want.....DURRRR. It won't change anything anyway. It's a gauge freedom, whatever choice you make doesn't result in any problem mathematical or physical. Either choice will result in the exact same physical results. YOUR CHOICE DOES NOT EFFECT PHYSICS!

>By choosing one, you say one is special

No, you really don't. If you want to think of it as such, knock yourself out, but the choice will not change anything. When you choose a "origin" for a coordinate system, does that mean that point is special? LMFAO

>>3048822
>By choosing one, you say one is special, while they must be arbitrary.

this is such a massive misunderstanding of reality i think you must be trolling.

the truth:

the fact of having the choice means NEITHER is special

the Greenwich meridian isn't an arbitray convention

it's a fucking fundamental physical constant

>>3048868
>>3048868
Nicely put

>>3048847
>>3048854
>>3048868

You are fucking retarded.

You called me out on sources, which i provided generously, what did you provide? Nothing but "lol that's what i learned, you are wrong, bullshit lololol".

I have also provided arguments which clearly point to torque being defined as a 2-tensor, which you were unable to refute. I also said how it came to defining a pseudo-vector perpendicular to the ones being cross-multiplied, which naturally leads to the calculus you use.
You call me an engineer, while it is you who have not provided anything of worth.

What the fuck?

Physical quantities must be independent from choosing either right-hand or left-hand rule. Therefore, torque must be the 2-tensor.

After you chose the right-hand rule, you can represent torque by a vector of 3 elements. Then, torque isn't indepenedent of a choice of direction anymore, therefore not physical.

If you still don't get it, you need to seriously get back to school.

>>3048889

Samefag assuring himself is not a valid argument.

>>3048868
>>3048889

> When measurable quantities involve cross products, the handedness of the coordinate systems used cannot be arbitrary. However, when physics laws are written as equations, it should be possible to make an arbitrary choice of the coordinate system (including handedness).

http://en.wikipedia.org/wiki/Cross_product#Cross_product_and_handedness

Who has the massive misunderstanding of reality?

Certainly i don't understand reality, but you don't even understand basic vector/tensor calculus.

>>3048898

To make this more clear:

From the point onwards you have chosen a handedness of your coordinate system you can no longer choose arbitrary coordinate systems, which is a necessity for describing physical quantities/laws.

>>3048898

Dude, you're wasting your time with retarded asspie faggots.

>>3048893
i'm actually smiling from the complement anon gave me.

>>3048890

no ones reading your sources because it is mathematically proven (not learned) that these things are convention. (except for things like CP violation).

but what is really retarded is you are actually arguing that these things are convention, without knowing it. i don't think you know what convention and arbitrary actually mean.

>>3048904

> no ones reading your sources

Then how can you say i'm wrong?

> it is mathematically proven (not learned) that these things are convention

I lol at your misunderstanding of proof and convention.

read >>3048898

>>3048868

You don't have a choice after you chose a handedness, that's the fucking point. You have to chose a handedness before you can define the cross product.

>>3048906
i lol at your misunderstanding of mathematics.

you are screaming that 1 + 1 = 3

(that's a metaphor. i understand aspies have difficulties with them)

i'll repeat the above. the laws of the universe can be written with either left or right hand rules

>>3048914
like i said

you are actually arguing it is arbitrary.

>>3048914
>after you choose a handedness

so you conceed handedness is a convention then?

>>3048918

> i lol at your misunderstanding of mathematics.

The MSc in math i will soon get says otherwise.

>you are screaming that 1 + 1 = 3

What the fuck are you talking about?

> the laws of the universe can be written with either left or right hand rules

Yeah, either. Read >>3048898
or are you afraid you might embarass yourself?

The laws of the universe must be handedness-free. That's why torque is a tensor.
There's a difference between "either left or right" and "handedness doesn't matter".

Your torque depends on the choice of a coordinate system. If you choose the left-hand rule to apply, you have to introduce a minus sign to get the correct result.

>>3048930
so if you agree with us why are you getting so worked up?

>>3048920

It is not arbitrary when you say torque is

rXF = t

because this formula will give you different results for different handednesses. What the fuck is it that you don't get?

>>3048890
>I have also provided arguments which clearly point to torque being defined as a 2-tensor

You have no arguments. You don't even define torque properly, you fail pretty hard bro.

>Physical quantities must be independent from choosing either right-hand or left-hand rule. Therefore, torque must be the 2-tensor.

Nope. There are tons of physical quantities that are coordinate system dependent, as well as handness dependent, including; momentum, angular momentum, etc. This however doesn't change the overall physics of the system. You are allowed to change view-points, coordinate systems, and handedness at fucking will. IT DOESN'T CHANGE THE PHYSICS! THE SYSTEM STILL BEHAVES THE SAME!

>>3048937

I have defined torque and i even included arguments in that specific post.

Where are you're arguments beside
"you didn't provide arguments, you are wrong"?

> There are tons of physical quantities that are coordinate system dependent

So you are a troll, i should have known that.

>>3048937

> You are allowed to change view-points, coordinate systems, and handedness at fucking will.

> implying -t = +t

because that's what your formula will give.

>>3048936
you are again having this confusion between your opponents claim "the coordinate system/handedness/equations used as a whole is arbitrary", which you keep misreading as "the individual details are arbitrary"

if i choose left handedness i choose FXr = t to be the equation, or something similar.

this is why i think you are aspie. you see details, not the whole.

Using a cross product gives you a quantity that is independent of a choice of coordinate system?

Are you fucking kidding me?

There a reason you call that PSEUDO-VECTOR.

Fucking retarded high school fags.

>>3048947

Yeah, so the formula

rXF is NOT coordinate system independent, which is my fucking point.

rF = T_{ij}


IS coordinate independent, the way it should be.

>>3048947

You just said he is right and you are wrong.

rXF and FXr are different formulas.

>>3048958
again, you are missing the argument here.

the fact that we can create a formula to suit the conventions we choose about the X product, yet the science is unchanged, means the whole system we use to model reality is full of convention and arbitrary choice.

handedness is part of that choice

>>3048936
>It is not arbitrary when you say position is
>(x,y,z)
>because this formula will give you different results for different coordinate systems (different origins)!

Do you understand how fucking retarded you sound?

>>3048970

No, you are missing the point.

Physical quantities/laws need to be defined in a coordinate-independent way. rXF is coordinate-dependent.

You still don't get it?

>>3048972

I don't understand your retarded comment, because it has no meaning.

>>3048953
>>3048953

would you agree that the choice of the letters r, F, T, i and j is arbitrary?

no, because you aren't that retarded.

well, just take a few steps further along that line of thinking and you'll get it.

sigh

define torque as t = rXF

Choose coordinate system (1,0,0), (0,1,0), (0,0,1)

you get a result. Now test this with another coordinate system (1,0,0), (0,1,0), (0,0,-1)

Now you get a different result.

Therefore, this choice of definition is not coordinate independent and therefore not physical.

>>3048972

How about you finally give some arguments.

>>3048987
you have changed the argument.

the argument was about how right handedness is arbitrary.

you now realise this is true, so are saying things everyone agrees with.

this is a common aspie compensatory behaviour.

>>3048989

I don't get what you mean, maybe use the english language to communicate?

>>3048953
>>3048953
NEWS FLASH! NEWS FLASH! NEWS FLASH!

Most quantities in physics are coordinate system dependent, including the standard definition of torque, as well as your shitty (wrong) definition of torque. Your shitty definition depends on the length scales of the coordinate axis's!

THIS DOES NOT PRESENT A PROBLEM IN THE LEAST THOUGH! IT DOES NOT CHANGE PHYSICS!

>>3048995
you keep changing the argument the moment you lose one

>>3048996

> you have changed the argument.

No.

> the argument was about how right handedness is arbitrary.
>you now realise this is true, so are saying things everyone agrees with.
>this is a common aspie compensatory behaviour.

This is a common troll post. I have always just claimed that your definition of torque is not coordinate independent. You either haven't read properly or didn't understand some things, which is more likely.

I said torque as a physical quantity is defined as a 2-tensor, which can be represented by a pseudo-vector if you chose a handedness that you can after that no longer switch (!).

Then you came up and said "bullshit" without any explanation/argument/source/whatever.

>>3048998
>claims english isn't english

you may as well just admit you have aspergers

>>3049000

> Most quantities in physics are coordinate system dependen

You still haven't provided at least a single example.

In physics, proper physics, not the high school physics you know, everything must be coordinate independent.

My definition is the correct and always used definition (be it implicitly), your's is incorrect when speaking rigorously , for the reasons i have provided.

>>3049004

Where the fuck did i change the argument?

>>3049009

Well, i'm not the one raging and not giving any arguments/sources for my claims.

I highly doubt you even know what aspie means.

>>3049005
what you have claimed isn't necessarily the argument at hand.

which was about handedness being arbitrary

if you want to come in here with different arguments, well, fine. whatever floats your boat. don't be too surprised if others continue with the original argument.

>>3049015

> which was about handedness being arbitrary

Maybe that was YOUR "argument". I never claimed it wasn't arbitrary which handedness you chose BEFORE declaring torque to be either rXF OR FXr.
I just said it is NOT arbitrary after you have provided the cross-product formula, which means torque defined in that way is not a well-defined physical quantity.

Torque as a 2-tensor is well-defined and what everyone of you uses implicitly.

>>3048993
>>3048993
>>3048993
>>3048993

This

Can we finally end this shit now?

>>3049013
>highly doubt yout know what aspie means

so you do have aspergers?

it is really fucking obvious.

because you have trouble with language as used (rather than as you wish it was used) you find yourself getting into arguments with people you would actually agree with if you could understand what they were saying (even though you'll claim your interpretation is what they are actually saying)

this combination of autistic solipsism and aspie difficulties with language is the stuff of classic pointless internet argument.

>>3048995
Arguments for what dude?
You are pretty much incoherent at this point. The fact that you keep trying to say that torque must be coordinate system independent is just wrong and fucking retarded. It is very obvious you don't know physics.

Position isn't even coordinate system independent, why would torque be? Also, being coordinate system independent isn't needed for a physical quantity.

Position, torque, momentum, energy, potential energy, kinetic energy, angular momentum, total energy, etc, Are all quantities dependent on our coordinate system and our choice of handedness. This doesn't change the physics of the system though. The physics always behaves the exact same way, regardless of our measuring scheme. THIS IS NOT A PROBLEM FOR US! The extra degrees of freedom actually exemplify that there is no perferred reference system.

>>3049033

> it is really fucking obvious.

What makes you think so?

> still doesn't know what aspie means.

> you find yourself getting into arguments with people you would actually agree with if you could understand what they were saying

But that's what you are doing. You even admitted in an earlier post.

>>3049034
WIN

\thread

>>3049034

> The fact that you keep trying to say that torque must be coordinate system independent is just wrong and fucking retarded.

http://en.wikipedia.org/wiki/Physical_quantity#Physical_quantities_as_coordinates_over_spaces_of_phy
sical_qualities

> the following question arises: Can we do physics intrinsically, i.e., can we develop physics using directly the notion of physical quality, and of metric, and without using particular coordinates (i.e., without any particular choice of physical quantities)? In fact, physics can (and must) be developed independently of any particular choice of coordinates over the quality spaces, i.e., independently of any particular choice of physical quantities to represent the measurable physical qualities.

have you ever heard of relativity by the way?

>>3048993
YOUR LOGIC:

sigh

define position as r

Choose coordinate system (1,0,0), (0,1,0), (0,0,1)

you get a result. Now test this with another coordinate system (1,0,0), (0,1,0), (0,0,-1)

Now you get a different result.

Therefore, this choice of definition is not coordinate independent and therefore position is not physical.


WTF? Serious logic fail

>>3049034

You apparently don't know what the fuck you are talking about.

>>3049042
aspie? y/n

>earlier post
>every anon is same person
aspie

>doesn't know what aspie means
you keep claiming this like i don't know what colour the sky is. it's a common condition. i'm sure everyone knows an aspie or two. when i was a student i used to tutor maths to one. i hated him.

>>3049056

Define torque as

r_i F_j = T_{ij}

Therefore, torque is independent from the choice of a coordinate system.

WTF? Serious logic fail on your side.

>>3049056

Of course it will be represented by different coordinates, but the quantity will be the same. Since position is arbitrary for the results of experiments, you only need distances to be independent from choice of coordinates.

It happens to be the case.

You feel pretty ashamed, right?

>>3049066
except that wouldn't work in non inertial coordinate systems

>>3049090

your formula wouldn't either.

We weren't talking about non-euclidean spaces here, but it is relatively easy to generalise that definition of torque to pseudo-riemannian manifolds, while it is not easy to generalise the cross-product.

>>3049050

Wow, what a shitty wiki post. Thanks for mentioning that. I deleted the shitty parts, and will make sure to keep an eye on it.

It is impossible to do physics, without any coordinate system in mind (or even switching between multiple systems, as done in relativity).

You can set-up the most abstract metric, and Lagragian, and start with pure theory and no coordinate system, but at some point you need to incoperate a coordinate system to make the connect between the physical universe. If you don't make the physical connection, you are not doing science or physics, you are just doing mathematics.

Do you not know the difference between mathematics and physics? Does your fail know no bounds?

On an observational level, how can I observe shit without a coordinate system? If I can;t observe shit, how can I verify a science?

>>3049089
Length scale is also an arbitrary choice.
Example: I can measure length in feet or meters.

It all ends up being arbitrary, even our length scales.

You can't possibly be this stupid? U trollin?

>>3049089
Must be a troll

>>3049149

Why? Because i know how to physics and you don't?

>>3049144

Relation to this discussion is?

>>3049129

> implying that is a shitty wiki article.

You disagree with it/don't understand it, therefore it is wrong?

> It is impossible to do physics, without any coordinate system in mind

Yes it is you fucking moron. That's why there is tensor calculus. It is independent of coordinate systems. Fucking idiot.

> If you don't make the physical connection, you are not doing science or physics, you are just doing mathematics.

wut?

i can't believe you believe your own stupidity.

>>3049034

Needed to get something done, so this took a while.

Position, momentum, potential energy (lol you were actually serious here?), kinetic energy, total energy

are NOT physical. What is physical is the DIFFERENCE in these things, i.e. distance, excess momentum, energy difference, difference in potential energy, difference in kinetic energy, difference in "total" energy.

torque and angular momentum ARE physical, that's why they are defined as 2-tensors.

You were basically saying that if i do an experiment in your house, i get a different result than if i do it in my house, which is fucking ridiculous.

>>3049129

wow, i just looked and you really did delete that section.

It was perfectly valid.

You are a failure to mankind.

http://folk.uio.no/patricg/teaching/a112/levi-civita/

> go to bottom

took me some seconds to google that

/thread

>>3049239

> Actually, there does not exist a cross product vector in space with more than 3 dimensions. The fact that the cross product of 3 dimensions vector gives an object which also has 3 dimensions is just pure coincidence.

>The cross product in 3 dimensions is actually a tensor of rank 2 with 3 independent coordinates.

>>3049191
>>3049196
>>3049227

>>3049271

true dat.

I'm a fucking moron.

Thanks for getting me back to reality.

>>3048086
You want a torque, which is basically a cross-product. A 4d cross product is very simple to construct, just recall the properties we need.

3D CROSS:
1) In 3d space, 3 vectors make basis
2) The cross product will take 2 vectors (a, b), and produce a perp vector (d)
3) Magnitude of d is the area of the parallelogram made by a and b.
4) d = determinate of matrix formed by unit vector, a, b (row wise)

4D CROSS:
1) In 4d space, 4 vectors make basis
2) The cross product will take 3 vectors (a, b, c), and produce a perp vector (d)
3) Magnitude of d is the volume of the parallelepiped made by a, b and c.
4) d = determinate of matrix formed by unit vector, a, b, c (row wise)

ND CROSS:
1) In nd space, n vectors make basis
2) The cross product will take n-1 vectors, and produce a perp vector (d)
3) Magnitude of d is the n-volume of the parallele-object made by original n-1 vectors.
4) d = determinate of matrix formed by unit vector, and the n-1 vectors (row wise)

Anything else?

saging cause of the trolls
>>3049191
A Troll

>>3049401

>>3049401

> 1) In 4d space, 4 vectors make basis
>2) The cross product will take 3 vectors (a, b, c), and produce a perp vector (d)

fail troll is fail

>>3049433

samefag

read

>>3049239
>>3049246

>>3049401

source?

>>3049477
Elementary Linear algebra. All you do is extend the concept for n-dimensions.

What part is troubling you?

>>3049470
>>3049470
>Implying in 4 dimensional space, the basis wouldn't be 4 different vectors

WTF? WTF? shitty troll has gotten fuckin retarded

>>3049565

The fact that the cross product is not defined for n != 3.

If you want to extend it, it is possible. In 4 dimensions you will get a 6-dimensional vector though, unlike you claimed.

Also the fact you called the person who provided a source for his claim a troll, although he is, how it appears to me, right.

>>3049596

> implying the cross-product has more than one input.
> implying you don't confuse this with the wedge product

>>3049470
OK then, please produce a basis for 4-d space with less then 4 vectors.

LMFAO

Guys I'm just passing by, but Op's pic looks like a butt in thong.

>>3049565

For me, the troubling part is that you say torque is the product of 3 vectors in 4d space, although it only has 2 vectors forming it.

fail troll is still failing.

>>3049607

> implying he said that.

Where? Please quote.

fail samefag troll is samefag troll.

>>3049602
>mfw I use \wedge for cross product because fuck \times

>>3049621

> implying corss product and wedge product are the same

> laughingwhores.jpg

>>3049628
>mfw I know they are different but don't give a fuck

Speaking of which, I've never seen a wedge product used anywhere so far in my physics experience.

>>3049633

undergrad student detected

Now i don't wonder anymore you don't see how torque and angular momentum etc. are rank 2 tensors and the cross product was only designed to teach this to engineers/make a shorter notation possible.

>>3049633

So you never had general relativity, differential geometry, topology, QM mechanics in detail etc.?

>>3049645
I just walked into this thread. What's going on here?

>>3049649
Nope.

>>3049602
That link is very very very very shitty. The reason that the author isn't capable of defining a nice cross product for 4d, is cause he makes really shitty assumptions that don't allow him to do so. He fucks up the whole thing by assuming that the cross operation is binary in a 4d system. He fails to take a moment to try and understand the meaning of the cross product, and its continuation for higher dimensions. He therefore focuses on the wrong shit, and his logical extension is invalid.

His "cross" ends up with none of the properties we associate with "cross" in any Hilbert space, all he ends up is with some shitty useless math.

The cross in an n-d system is "n-1-nary", because n vectors are needed form a basis for a n-d system. Will try and explain it more in a few minutes...hold tight buddy.

>>3049666

As far is i see it, this post
>>3048275
enraged some people. Apparently, sources and reasonable arguments were given by him, but not by the others.

>>3049682

> cross product for 4d

not possible

> cross operation is binary in a 4d system

We were talking about torque, which is the result of combining two vectors, not three.

> meaning of the cross product

which you obviously don't get (Hodge duality applied to rank 2 tensor after you have chosen a handedness).

> He therefore focuses on the wrong shit

His reasoning as well as his outcome is correct though. You have not provided a counter-example or a reason for why he is wrong.

Someone in here already said it.

Physical quantities need to be defined in a way that makes them independent from the choice of a coordinate system. This is done via using tensors. Torque is a rank 2 tensor.

Why do you guys still have a problem with this?

>>3049609
I'll start simple, since some of you seem to need it.

Every n-dimensional space has a basis. This basis is just a collection of different vectors, s.t. any vector in the space can be made as a linear combination of the basis vectors. Additionally, basis vectors are linearly independent, ie, I can't make any basis vector from linear combinations of the others.

The number of basis vectors is actually the degree of the space, n-dimensional space has n basis vectors. The cross-product for n-dimensions is designed s.t. it takes n-1 vectors (input), and finds an additional vector n (output).

We donate the total set of vectors, the n-1 vectors (input) and the n vector (output), as {n}. You can then take all possible linear combinations of these vectors, to form another set [n]. The vector n is picked by the cross operation, s.t. [n] is maximized. That is how n is picked, that is what the "cross" is defined to do. Anything that does not do that, is not the "cross" operation. It may be an outer-product, wedge-product, exterior-product, etc, but it isn't the "cross" product.

Basically, the set of {n} vectors are trying to emulate the basis vectors in a sense, and if the original n-1 vectors were already "normal", then {n} would be a basis for the space.

Hence, for a 4d space, i pick three different vectors. The cross operation then takes these three vectors and finds the additional vector, s.t. the set of vectors I form will produce the maximum amount of vectors that emulate my total space. Mathematically This is just Det [basis, n-1 vectors (row wise)].

It is all pretty simple really. Anything else?

>>3049793

> The cross-product for n-dimensions is designed s.t. it takes n-1 vectors (input), and finds an additional vector n (output).

This is where you still fuckign fail hard.

That does not compute torque from a given position vector and a force vector.

fail troll is still failing hard.

Your definition of a cross product (which is still ill-defined) gives you a basis that is postiviely oriented. Why should a positively oriented basis be preferred in reality?
It is not. That''s why physical quantities are tensors.

> Anything else?

Yeah, calculate fucking torque in 4d and see yourself fail hard.

>>3049793

Uhm yes, pretty easy, apart from you completely arguing away from the actual discussion.

>>3049717

>Physical quantities need to be defined in a way that makes them independent from the choice of a coordinate system

Some scalars maybe, but not all physical quantities. This is wrong in general.

Example, the length of an object depends on the coordinate system I view the object from. tt's basic relativity my friend.

Are you seriously trying to tell me length is not a physical quantity? What is your "definition" of physical quantity then?

>>3049793

Take a rank 1 tensor r_i
Take another rank 1 tensor F_j

Multiply, get rank 2 tensor T_{ij}.

This is a quantity that does not depend on your choice of a basis.

Now use the Hodge duality, i.e. multiply this quantity by the Levi-Civita symbol e_{ijk}, then contract over i and j.

T_{ij}e_{ijk}

and get a rank 1 tensor again, that is not independent from the choice of a basis anymore and is the quantity you get when applying the cross product to two 3-dimensional vectors.

This is what you implicitly always use when calculating the cross product in 3 dimensions, even when your teacher didn't tell you.

>>3049834

> the length of an object depends on the coordinate system I view the object from. tt's basic relativity my friend.

> implying length is a physical quantity.

So you think absolute quantities are of importance in relativity?

The physical quantity in relativity is the space-time line element/distance, i.e. x^µ x_µ, which is independent from choosing a basis.

Physical quantities are quantities that physics can be derived from. You can't derive equations of motion or conservation laws from a length. You can do this with a space-time distance though.

>>3049813

>gives you a basis that is postiviely oriented

No, it doesn't, it actually presents you with a choice. Have you never done Linear algebra?
You choose the orientation. There are two vectors perp to a plane, right? Anyway, you seem to be the troll. If you have some legit questions, then ask, else, good day sir.

>>3049829
There was really no discussion here. All there was were a few shitty trolls, or some people with very bad misconceptions who refused to listen. I am not wasting my time with that nonsense.

>>3049861

Why? You haven't answered any questions so far and just gave some LinA stuff we all knew before.

So, calculate 4d torque.

You still haven't done it after several requests to prove you know what you do. Therefore, you are the troll.

>>3049861

> No, it doesn't, it actually presents you with a choice.

Elaborate. You say your definition of the "n-d cross product" gives two results?

Back in 3d, if i take rXF, there's only one result. I smell fail again.

>length isn't a physical quantity

I think you need to look up the definition of physical, and quantity.

>>3049877

http://en.wikipedia.org/wiki/Physical_quantity

NO U

In euclidean space it is of course a physical quantity, as it is given by a spacial distance.

In relativity, it is NOT a physical quantity, as it is not independent from your choice of a coordinate system.

Fail troll is fail again.

>>3049875
>>3049875
There are two results, depending on your handedness convention. Srsly? Are you fuckin retarded?

>>3049877

context, seems to be hard to grasp that concept.

>>3049890

Ok, look, take these two vectors:

(1,0,0) , (0,1,0)

What is the cross product of those?

>>3049890

> a function that yields two results
> calls others retarded

look up the definition of function.

>>3049894

Fucking retard. You choose a convention and THEN apply the cross product.
That's ONE result, dipshit.

>>3049885
>A physical quantity is a physical property that can be quantified by measurement.

In special relativity length is a physical property that can be quantified by measurement. So why do you say it isn't a physical quantity?

> mfw still no one could deliver any approach at calculating torque in 4 dimensions

>>3049912

Because it is not independent from the coordinate system you choose.

Seriously, you don't even have a clue about relativity?

> can be quantified by measurement.

It will yield different results for different observers.

Why do you think we use tensors in relativity? Why do you think lengths can't be used for deriving equations of motion/conservation laws?
Why do you think we introduce a metric for a pseudo-riemannian distance measurement?

>>3049912

Tell me how you would measure length.

Protip: You can't come up with a consistent measurement device, which is why special relativity came up in the first place.

Before modern physics you could measure length freely because the length of a vector is invariant under coordinate transformations, but then came relativity and hell broke loose

>>3049933

Exactly.

>>3049933

correct. Everywhere in physics, only differences are physical quantities, that's why you have the freedom of gauge regarding potentials for example. In Newtonian physics, length is the spacial difference of the end points of an object, which is invariant under Galilei transformations.
In relativity, this is not the case, since lengths vary with relative speed. Therefore, the physical quantity is space-time distance, which is invariant under Lorentz-transformations.

>>3049915
>>3049915
>>3049915
>>3049915

Still nobody?

Fail troll confirmed.

This shit is even covered in the first book of the Landau-Lifschitz series, if that is known to any of you which i highly doubt.

torque is a tensor of rank 2.

>>3049852
>>3049945
>>3049933
>>3049937
>>3049926
>>3049928

Children children,

>The physical quantity

This term in nonsense and not used in physics. I think what you are trying to talk about is an a physical invariant.

Where are you getting such nonsense? One shitty wiki article?

>>3049968

> implying you know how to samefag detect

Physical quantities are properties that are invariant under coordinate transformations and therefore suitable to build up a theory on, i.e. give equations of motion/conservation laws.

You seem to lack the amount of physical knowledge necessary to grasp these concepts though.

>>3049970
Very shitty troll is shitty

Ah, path dependencies in the development of mathematics and physics. This thread is pure gold.

>>3049972

> implying i am trolling and not delivering arguments as well as sources, unlike you .

I still don't see a 4d torque delivered by you. I already have delivered it.

>>3049972

> implying you are not the one just refuting anything by "no you are dumb, that guy is dumb, stupid wikipedia

>>3048275

So this is the post that started this shitstorm?

Epic trollbait, i'll remember that.

He is definitley right though.

Still no evidence/source/arguments refuting that torque is a rank 2 tensor?

Guess i have been trolled.

http://en.wikipedia.org/wiki/Angular_momentum#Angular_momentum_in_relativistic_mechanics

> angular momentum is the 2-form Noether charge associated with rotational invariance
> 2-form
> a rank 2 tensor

/thread

Wait, let me get this straight. The torque of a system is t=r x F where r,F are vectors and x denotes the cross product. Hence the torque t is a vector and hence a tensor of rank 1. Why is everyone saying that torque is a tensor of rank 2?

>>3050132

Because that's the actual definition.

1-tensor times 1-tensor is a 2-tensor.

You can associate with this 2-tensor a 1-tensor via multiplication with the Levi-Civita symbol, which gives you a pseudo-vector (because the 2-tensor is anti-symmetric, it only has 3 independent elements).

This definition is ill though, because saying t = r x F means you have chosen a specific handedness of your coordinate system, therefore making torque not independent from coordinate system used anymore, which is required in proper physics.