Is time the cross product of the other lower dimensions?

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Other urls found in this thread:

en.wikipedia.org/wiki/Hodge_dual
en.wikipedia.org/wiki/Exterior_algebra
twitter.com/AnonBabble

dude, what?

>it's a "freshman just learned about cross product and orthogonal bases in his linear algebra class" episode

Clearly not, or he would have known that the definition of cross product doesn't generalize to four-dimensional space.

I wasn't generalizing to four-dimensional space.

it can be roughly generalized as follows:

[eqn](u^{\mu},v^{\nu},w^{\rho}) \mapsto \varepsilon^{\alpha \beta \gamma \delta} \textbf{e}_{\alpha} u_{\beta} v_{\gamma} w_{\delta}[/eqn]

where we observe einstein summation convention, as is usual, and the e's are the basis vectors of course.

this generalization replicates one of the most important properties of the cross product, the product remains orthogonal to the space which the vectors span, we can demonstrate this with a quick calculation:

[eqn]v_{\mu}\textbf{e}^{\mu}(\varepsilon^{\alpha \beta \gamma \delta} \textbf{e}_{\alpha} u_{\beta} v_{\gamma} w_{\delta})=\varepsilon^{\alpha \beta \gamma \delta} v_{\mu}\textbf{e}^{\mu}(\textbf{e}_{\alpha}) u_{\beta} v_{\gamma} w_{\delta}= \delta^{\mu}_{\alpha} \varepsilon^{\alpha \beta \gamma \delta} v_{\mu} u_{\beta} v_{\gamma} w_{\delta}=\varepsilon^{\alpha \beta \gamma \delta} v_{\alpha} u_{\beta} v_{\gamma} w_{\delta}=-\varepsilon^{\alpha \beta \gamma \delta} v_{\alpha} u_{\beta} v_{\gamma} w_{\delta}= 0[/eqn]

where in the last step of the above chain of equations we use the skew symmetry of the levi civita system and the play a game of dummy index renaming.

witen...

of course this is a rough generalization, though the pattern should be clear. In an N dimensional vector space we can define a 'product' on (N-1) vectors which has properties similar to the cross product.

no it's chemtrails mate get your shit together man

You can write

[math] v\times w := \star \, (v\wedge w)[/math]

in any dimension, with [math] \wedge [/math] the wedge product and [math] \star [/math] the Hodge star. It's just that 3 is a special case where the result of two 3-dim vectors is again a 3-dim vector.

en.wikipedia.org/wiki/Hodge_dual
en.wikipedia.org/wiki/Exterior_algebra

I know the cartan formalism, but I prefer coordinates and ricci calculus, senpai.

Does time not exist in lower dimensions?

Does time exist?

>visit Veeky Forums after 6 years of blissful absence
>this is the top thread

time is just an idea. it's convenient.

W-what was it like?

Caltrops, OP, how do they work?

Look for people using their left hand on tests.

Did the guy in the gif die?

First of all, tell us what you think a cross product is.

A vector with magnitude equal to the area of the formed parallelogram given by the two vectors with direction that is perpendicular to the other two vectors.
It also preserves "handedness" whatever that means.

Lower dimensions are your components of a vector. They're a basis which consists of normal vectors in which the dot products of orthogonal vectors will always be zero. Therefore your theory will fail

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Time has no mass, no energy - so it can be destroyed without violating conservation of entropy.

Yeah he did. If you reverse image it a reddit post comes up with a video that includes the landing.