I have a question: in electrostatics, when we write the generalised coulombs law, or the generalised potential field causes due to a charge distribution $\rho$ , we are intrinsically speaking about macroscopic charge density right? These densities i suppose are averaged over a small area, and hence gives us the macroscopic density?

Volume* whose radius is of order $10^{-7} m$

Today would have been Feynman's birthday

@nickbros123 Yeah densities always represent averages since real space is not known to be continuous :) What is the problem though?

@Mr.Feynman 105 birthday! :)

Y is Newton's first law prettier than Aristotle's law that moving objects come to rest?

It has nothing to do with prettier. Aristotle is just wrong. A pretty law that is wrong has to be thrown away.

Newton's laws are derived from a fundamental symmetry of spacetime while Aristotle's laws are derived from excessive faith in his own observations.

@JohnRennie lol. Yes, I meant what deeper mathematical considerations can lead to the law "moving objects keep moving with constant speed"?

Well every moving object has a rest frame. If we use that frame then an object not moving at constant speed would have to spontaneously start moving from rest.

Which seems ... unlikely :-)

@JohnRennie yes. It wud be weird

Despite it's reputation for complexity GR provides a really good way to understand this. Newton's first law is equivalent to the statement that an isolated object has a proper acceleration of zero. And it would be strange indeed if an isolated object developed a non-zero proper acceleration.

But idk. I think this already assumes that all inertial frames r "equally good". So this is assuming Galilean or Lorentz symmetry

So the deeper reason for Newton's first law cud b "galilean or Lorentz symmetry'

Yes, in fact I have seen the first law described as the statement that inertial frames exist.

That is the only meaning I can make out of the first law lol

Aha!

@JohnRennie GR also assumes a metric of a fixed signature. So this yields us the symmetries

You can also define Aristotle's theory using spacetime apparatus

Aristotle's mechanics is a 0-connection

I was just wondering how one could define Aristotle stuff using manifolds. Is the spacetime in this theory defined using a metric? @Slereah

I think once we assume a metric, we r bound to end up with Newton's first law becuz of the symmetries that come with the metric

You still have roughly the Newton-Cartan sort of structure

Or we can also apply the principle of extremum action for the metric distances. This also gives Newton's first law for curved spaces

But the connection is another matter

Yes. We can define the connection stuff so that the parallel transport and hence geodesic equation obeys Aristotle's law I guess. Is this it? @Slereah

In most theories motion is done via a connection, a map from the position and velocity to an acceleration, roughly

But this isn't true of Aristotle

You're mapping a position to a velocity

Relative positions to velocities

Becuz i wud still want translational invariance

From a spacetime point of view, this is like a "zero" connection, mapping points of the manifold to TM

Aristotle also doesn't hve translation invariance

Ooh then this is ugly. But i think we can easily make translationally invariant Aristotle formulas

This zero connection is just a vector field, and this vector field is exactly what "objects at rest" are

The flow lines are the unique paths that an object at rest follow

Oh

There's no Galilean or Lorentz trabsformation where an object can be changed to be at rest, since that would change this vector field

And velocity becomes detectable like proper acceleration

Becuz a non-zero velocity doesnt go with this flow

Any velocity that goes with this flow is defined as zero velocity

Zero velocity just means that the tangent vector is colinear to this connection

And any other velocity is "proper velocity"

@Slereah yeah

This also works the other way with n-connections

Is a metric needed in this theory? Or do we just have the connection? @Slereah

You can have connections depending on higher derivatives

It's similar to Galilean

Metric for space and metric for time

Oh

I was thinking we cud make a translationally invariant aristotle theory by using Coulomb's law formula

But we change the LHS to velocity

$\frac{dx_1}{dt}=\frac{1}{|r_1-r_2|^2}$

Or Coulomb's law is not really needed

You can make it translation invariant, though that wasn't what Aristotle had in mind certainly

We can use any translationally invariant formula

@Slereah oh

Since the center of the Earth was a preferred point

Yeah. I remember lol. Everything has a destination point

The origin of the peferred co ordinate system

Also what I'm saying is only vaguely related to Aristotle's actual mechanics

Aristotle didn't believe in "free" motion and celestial motion was entirely different

To go full Aristotle, u wud hav to define separate flows for separate elements like fire, water, dust

He said everything has a natural place

Where it gravitates

@Slereah did he believe celestial planets go round and round forever and need not come to rest?

Yes

I mean you could, but it would bear little resemblance to modern mechanics

He also thought time was literally indexed by celestial motion

@ACuriousMind but it wud b cool lol. A fire field. A water field. And a dusty field. And a preferred rest system

Our modern idea that physical theories are given as pairs of a mathematical formalism and a dictionary that connects that formalism with the physical world is very much anachronistic here. It might be interesting in some sense to see if this can be applied to pre-modern theories of nature, but we should not claim that that's "what they meant" or that this then is a faithful representation of their beliefs

@Slereah so the orbital motion is the best clock?

@ACuriousMind yeah. Becuz Aristotle did not hav a model in mind

@RyderRude it's again about precision of language: You're not going "full Aristotle", you're doing something inspired by but wholly distinct from Aristotle's philosophy.

He was just coming up with separate laws for everything instead of a reductionist model

I think at those times it wasn't important that the laws have any significant predictive power. Other things like esthetics perhaps, were more important

Well it depends

Astronomy was supposed to be predictive

That's right, they also did much better there :)

@Amit that's not necessarily true: Archimedes came up with predictive theories of buoyancy and levers, for instance!

but there was not this modern, all-encompassing scientific worldview that everything follows such mathematical laws and can in principle be described and predicted in this way

the Greeks could build machines, they understood steam power, it's not as if they didn't know things about physics and used that knowledge in practice

Right, but am I correct that there was a kind of a divide between natural philosophers and mathematicians? The mathematicians like Archimedes, Thales, etc. were often very practical, but then when they came up with very practical results, they didn't afaik associate any model with it did they? Similar to astronomy as Slereah just mentioned: when they calculated things very accurately, they didn't find it necessary to have a model that goes along with it to explain why it is so accurate

it's more that this sort of science or mathematics wasn't seen as central to the task of philosophy

it's just knowing how stuff works: when I melt this rock, iron comes out, when I construct a lever, I can move greater weights, etc. In the pre-scientific world view, this doesn't really have anything to do with what stuff is

Categories of disciplines were a bit different back then

Idk if they really had a concept of a mathematician

Mathematikoi encompassed like grammar and music

In that sense, perhaps they were on to "shut up and calculate" very early :)

"mathematics" originally literally just means "stuff you learn"

which is a bit awkward because "science" - from Latin scientia - originally also just means "stuff you know" :P

Making such things mathematical was a bit of a brand new thing and applied only to a few domains

Like astronomy and music

Aristotle had some arguments about how it's a bad idea to use in general

Mixing the sciences

Even today, people doubt reductionism

Like in that "unreasonable effectiveness of math" paper, Wigner is doubting reductionism

He says biology may be non reducible to physics

@Slereah Once we assume a metric, the metric-compatible connection is the Christoffel symbols instead of a 0-connection like Aristotle vector field. So the metric compatible connection can b a deep reason for Newton's first law, rather than Aristotle's law

@RyderRude You may be interested to read about Newton-Cartan theory

I've heard of it. But it is just a re-formulation of Newtonian gravity

So it also obeys this logic

I've seen a lecture FP Schuller gave about it (though he didn't use this name, I think it was the same subject matter) it's on YouTube

Even that theory wud hav to use Christoffel symbols I think

Well reformulating Newton in light of Einstein is already not an easy task, but I don't think you can squeeze Aristotle into all this mess :) and if you manage to, it won't bear much resemblance to what he probably had in mind

I'm not as interested in what exactly Aristotle had in mind, as I'm interested in first order laws diff eqn vs second order diff eqn laws :P

I'm just exploring deeper reason 4 second order laws and Newton's first law and stuff like y is velocity of objects maintained by the universe

The christoffels always come into the game with the second order don't they? They relate the acceleration to speed....?

The 0-connection isn't very interesting since free objects don't do much

They just move along predetermined lines

They are absolutely at rest

@Amit yea, but my point is u cud arrive at Christoffel symbols by merely assuming a metric and a compatible connection

Locally it's always first order :) I think that again because we are obsessed with predictive power we have to also put in the second order

The metric gives u a connection which is not a vector field like what Aristotle wants

When you solve an equation of motion numerically all you do is first order, suppose you're writing a simulation

@Slereah i'm interested in a modified version of this idea, which doesnt favor an origin. Like want a universe where all origins r equivalent. So i need translational invariance to make it interesting

I want this becuz usual physics treats all constant velocity frames as the same. So i want to treat all translated origins as the same or "equally good"

what is the 0 connection?

you mean connection that vanishes?

A connection is roughly a map $TM \to TTM$

@Amit it is a vector field. It gives u a first order universe becuz u only need the initial position to determine the trajectory. The vector field gives the velocity to the particle

A zero connection is $M\to TM$

@RyderRude you're just describing the notion of an affine space and many formalizations of elementary mechanics do treat space as affine (off the top of my head for example Arnold)

An n-connection being a map $T^nM \to T^{n+1}M$

That's a vector field right?

@ACuriousMind r these fictional theories?

@RyderRude The belief that everything can be mathematized is not the same as reductionism. You're mixing concepts again.

Yeah. I meant almost the same thing tho :P

It is a vector field yes

Although that's also true of connections

I need a theory which is translational and rotational invariant but not boost invariant

Just vector fields with special properties

I hav an idea : the current state is determined by initial positions of everything in the Aristotle universe. The law of physics maps this state to a 0-connection. Then the particles follow that flow. And then we rinse and repeat in small time-steps @Slereah @ACuriousMind

Generalizations of diff. geometry is a rabbit hole :)

This wud give a translationally invariant Aristotle theory

It's like how GR maps stress- energy to a metric. I'm mapping positions to a zero-connection

Technically you also need a vector field to define the foliation of the manifold, but I think the two are the same here :p

But translational invariance isn't really invariance of small time steps, if I get the hang of what you're implying

Otherwise you'd have free objects being always in motion

My real question : y is this Aristotle universe not very natural to have

Just by the principle of relativity

I think the answer is that the manifold in our umiverse has a metric. Being a metric, this doesnt yield u a 0-connection

Even the Galilean one

Objects in motion stay in motion

@Slereah this Aristotle universe has principle of relativity for rest frames

The metric isn't involved here

So it is also a "relative universe". All choices of origin r equally good

@Slereah what is the answer according 2 u? If u r god, y wud u prefer one universe design? (Assuming u work by mathematical beauty)

There's no preference, it's just not what our universe is lile

Y to prefer relatitivy of both position and velocity over relativity of just position?

@Slereah yes. This is the default answer :)

a cool god dude would put Aristotle, Galileo, Newton & Einstein each in a universe that abides by the laws they thought are correct, lol

Lol

One other answer can be ur preference of Poincaire algebra?

Is there no Aristotle algebra?

The Aristotle algebra in this case is just the Euclidian algebra and time translations

As a direct product

Maybe it's more interesting what other laws this kind of universe will mess up. Why for example QM wouldn't work any other way, and then no stars, no planets, no Physics.SE.... etc

As opposed to the Galilean algebra for Newton

Ok but Poincaire algebra does not guarantee Newton's first law. But it does guarantee that "constant velocity frames" r equivalent experimentally

So Poincaire algebra is not a reason for Newton's first law I think

@Amit this is a great point. Preference for quantisation.

Poincaré isn't for Newton for a start

You can derive the Newton equation from a few assumptions though

Yeah. But Newton's first law is valid in SR and GR too

@Slereah what r these assumptions?

You can check the work of Coleman and Korte for that

Basically inertia and constant mass

Oh

@Amit we can use stars and planets this 2 motivate y there r three dimensions!

Like, if u r God, u need inverse squared law 4 gravity

And u cook up 3 dimensions

And this is y ur Poincaire algebra has 3 generators for translation

I think planets shud b impossible without inverse squared law @Amit @Slereah

But how do we explain this from an atheist perspective? I dont want 2 assume designers with preferences

Not every choice of universe will have life, i think

Or planets

The atheist perspective cud b that there is a multiverse

I think it's called the anthropic principle or smthing

Or maybe we cud say that this is the only universe. And this is just how it is

We should not ask for y laws of physics r the way they are

These r meaningless questions

Not necessarily meaningless, it's possible that some laws are explained by deeper laws. for the case of inverse square law for example I think it's quite accepted this is just a consequence of geometry isn't it?

The area decreases as the square of the distance...

Yes. U r right. These r not meaningless questions. It is possible that some answers may b found in future. But even if there r no answers, it is ok @Amit

@Amit yea. This reason was found for inverse squared law

Logically there has to come a point where there are no answers right? :)

Yes. I think it is a categorical error to expect reasons for everything

Reasons should be expected for things within the universe in terms of other things within the universe. That's the right category for "reason"

There's no reason for the universe itself

Self evident truth.

Stop asking "why?"

Shut up and speculate! lol

:D

What do you all like most about physics, the discipline?

Is it any of philosophical answers, technological advances, math of physics, deeper laws etc, or something else @ACuriousMind @Amit @Slereah @user223626865 @naturallyInconsistent

I can answer this only in a roundabout way: as a kid when I realized you can write computer programs, I was most interested in learning how to program in assembly language because that's the closest one to the machine level as far as I understood, lol

So u like deeper laws

I'm a Fundamentalist! lol

Yeah that's one way of putting it

I also love deeper laws. But I don't like that they just get more and more complicated lol

There is no philosophical answers in deeper laws cuz they keep getting more complicated

But i still love deeper laws the most about physics

Yes, I was also quite disappointed when I realized it ain't gonna be as easy as learning machine language... but the mystery is also part of the fun... as Einstein put more eloquently

U can program in 1s and 0s? :P

Oh u said assembly language

I think you also know you need to separate the complication of the calculations from those of the concepts, it's more the former we have trouble with right?

Yeah, assembly / machine are corresponding. ASM is just giving nice names to the strings of bits that the CPU can perform

Oh

@Amit yes. The concepts r still pretty

But sometimes they can get arbitrary. Like spontaneous symmetry breaking

I dont like arbitrariness in deeper laws. QFT is very much arbitrary in that the Lagrangian is just this particular complicated object @Amit

@RyderRude I don't think I "like" physics like one likes a hobby. I just cannot imagine a version of myself that would be disinterested in physics and still be me: the desire to comprehend what is going on in the world I find myself in is fundamental to my identity.

Well said.

Thermodynamics / Stat mech is a bit different in that regard, it is a bit higher level than the fundamental laws (in relation to spontaneous processes in general @RyderRude)

@ACuriousMind I also think I am this way. But lately I've been growing very disinterested in physics becuz deeepr laws look arbitrary :P

Idk I feel apathetic to physics sometimes

Disinterest can have many causes, but if you know that in general you like a subject but find yourself disinterested, it may be due to no focused goals for example. I think we need some constant feedback that gives us a sense of achievement to stay interested. Like "I understood this chapter of that book" or "I solved this equation for the first time" or "Now I understand from the model why I can't see stars during the day time" (stole that last one from Feynman, lol)

@Amit i dont like stat mech stuff becuz its just fundamental laws plus ignorance :P

Some people say entropy is the reason time exists. That is so cringe.

The definition of entropy involves ur level of ingorance. How can that underlie time lol

Yes. But even there, I bet that if you see how beautifully stat mech can be used to predict some actual systems, especially if you do it yourself, you will feel a bit differently (or not, just guessing)

@RyderRude Sorry, but I don't think we are alike: You seem extremely focused on "fundamental laws" and naturalness and such things. I don't really care about any of these. I don't want science to explain "why" the world is the way it is, I want science to provide me a framework for making sense of the world around me. To not have to label the phenomena around me as "magic idk" but understand how they are related to each other, how technology works, how my body works.

@ACuriousMind yeah. My interest is very different then. I rarely care about the phenomena I observe

e.g. I wud be more interested in the equation for light rather than actually seeing light lol @Amit

I think practical phenomena r always too complicated

lmao... weren't you fascinated by reflections as a kid? I remember if I happened to have something shiny and a source of light I could play with that for a long time. like the old fashioned way of playing with a laser pointer today

I have a similar constitution as ACuriousMind. I do not have to know everything, but I must know enough of the basic workings of the universe, at least enough to understand the stuff for modern life.

@Amit same

I think all kids are kind of natural born scientists... but then there's school... lol

@naturallyInconsistent so u also r interested in phenomena u observe

I am also interested in possibilities of time travel tech

@Amit agree

Would be cool if GR allows time travel

@RyderRude I don't think you quite understood me: I don't need to know how a modern semiconductor fab works, but it is important to me that I at least in principle understand what semiconduction is. I don't need to know the details of the statics that keep a high-rise from collapsing, but it is important to me that I have some idea of the mechanical principles at work and how someone would go about solving this problem.

I don't need to know every chemical reaction but it is important to me that I know the essential ones involved in keeping me alive.

Not all phenomena. Most phenomena, definitely, but not every minor detail. General principles to understand most things at once is more interesting to me than random trivia.

@ACuriousMind i also have these interests. To have an idea of the fundamental interactions at play

Like,. I can, in principle, relate Chemistry and Biology to physics

Evolution also comes down to physics eventually

About real world phenomena, the cosmos are extremely interesting

Imagine beautiful star systems existing but no one's there to see it

It's so terrifying

There is a scene in Guardians of the Galaxy where they visit a skull-type star system

It was called Knowhere iirc

It's so terrifying that completely devoid of life places exist for billions of light years

Maybe there is also something religious about the attraction to Physics. Religion I think in many cases was a quest to connect the personal with the universal. Physics is a way to create a connection to laws which we always try to extend as universally as possible

I mean "something religious" as a sort of a religious impulse which we may have inherited genetically, or are prone to naturally by the nature of human existence

@RyderRude Again, to me this is not about reductionism. My interest in biology is not "how can I reduce this to physics"

you will never in a million years derive what happens in a single cell from "fundamental physics"

Oh. U just want to have a basic understanding of these processes. Reducing this to physics wud give u no progress

even though in principle you could, this "knowledge in principle" is completely useless

I also hav basic knowledge about cancer and evolution. I dont reduce it to physics.

But my knowledge is school-level lol

Oh yeah, while I am very interested in GR, quantum gravity, origins of universe and so forth, and like the look of astronomical pictures, I am not interested in endless pretty pictures of galaxies. I want to know the evolution of stars and basic cosmology, but not the details of inflation.

There could be some terrifying looking star systems. I would be interested in them. It would be like an entire galaxy of horror movie setting

What can be so terrifying about a star system?

It could be a terrifying combination of red and black

lol, would be pretty as long as you're not too close

I had seen one of them in a pic

@Amit it looked like hell lol

it wouldn't do as a well designed hell, a good hell needs to be able to torture you for eons... lol

But maybe it wasnt a star system. U r right. It was cosmic dust cloud or smthing

hell is just pain porn... like human beings try to extend pleasure indefinitely they do the same with suffering

Like Devil's anus

lol

I think Annulus is the technical term here: en.wikipedia.org/wiki/Annulus_(mathematics)

I don't even really care if the theories I study are true

let engineers worry

Why do loyalties lie, but for example, "things" stand?? :)

Is it emphasizing that loyalties are more permanent? "Things" on the other hand, may more easily start moving from where they stand?

Hello hello

Welcome to $\hbar$

@Amit I will have some superfluid beer

You're in luck! We just received a new phase transition

Oh no, phase transitions are my current nightmare

I can't stand these Ising models anymore aaaaaaaaaaa

Ah, is it a condensed matter course?

@RyderRude it is abstract enough to be simpler (in the sense that at least in textbook physics things are consequences of very few principles with absolutely 0 counterexamples) than chemistry or biology, but it is concrete enough to be directly tied to reality (as opposed to math qua math)

this is the regime my brain can function in best i think heh

although an alternate explanation is that perhaps what i really enjoy is particular types of mathematics. and physics allows me to dabble and justify learning and using said mathematics :P

@Amit Kind of

I chose it to learn about the renormalization group and it's held by a hep-th guy who makes a lot of references to QFT

Sounds like a ball. Or at least an ellipsoid

Hey everyone! I'm trying to understand why wires that are carrying current in the same direction attract each other.

I have one particular question. Suppose I have two wires that are far away from each other, and they're carrying a certain amount of current. The magnetic field surrounding those wires contains a certain amount of energy. If I bring those wires closer together, does that amount of energy increase or decrease?

@CassieSwett I think that the potential energy must be greater when they are far apart. Since as you bring them together, you can see that some energy is converted to motion and they either attract or repel each other (depending on the direction of the current)

That seems to jive with the fact that things attract each other if moving them away from each other would increase their potential energy.

You know, it just occurred to me that my question is ambiguous.

As I bring the wires together, am I holding the current through the wires constant, or am I holding their end-to-end voltages constant?

I was assuming constant currents, it's easier to assume we're dealing with "magnetostatic" energy :)

That makes sense.

But I'm trying to figure out how all this is compatible with the fact that if we have two parallel wires next to each other, it's "easy" to induce currents through them in opposite directions, and "hard" to induce currents through them in the same direction.

If my understanding were correct, we could make a perpetual motion machine out of this. But we can't make a perpetual motion machine out of this, so my understanding must be wrong.

It has something to do with the magnetic dipole moment, but I'm really rusty in all this jazz :)

Actually no, if it is a magnetostatic case there can't be induction anyway

Here's how the machine would work. Take two long parallel wires, separated by a great distance, and charge them up (so to speak) so that they're both carrying 1 A; this requires some amount of energy E. Now bring the wires close together; they attract each other, so you get some amount of energy from this action.

Now that the wires are together, they have more inductance than they did when they were apart, so when you discharge them back to 0 A, the amount of energy you get back is more than the initial charging energy E.

inductance is something you get from an oscillating magnetic field, but if the current is stable it won't oscillate

Or, I'm not sure about the "more inductance" thing, but now you effectively have one inductor carrying 2 A, so when you discharge it, you get 4 times as much energy as the amount you put into each of the two wires to begin with.

But obviously I'm wrong about something.

I suspect that where I'm going wrong is in assuming that it's possible to maintain that current of 1 A through each wire without supplying additional energy.

This is black magic to me I'm not an electronics person lol. But first, I think you need to realize that actually the fact that the wires moved means you already lost some energy to motion. And secondly, inductance only occurs when there is a change in the magnetic field

I'm not sure what you mean by "lost some energy to motion." If I have two objects that are attracting each other, and I allow them to move closer together, I've taken energy from the objects; I haven't given energy to them.

And yes, steps 1 and 3 of my "perpetual motion machine" involve changing the current, and thereby changing the magnetic field, and so inductance comes into play.

Now it's true that the magnetic field will change slightly when the wires move, as the field is dragged along with the wires, but I don't see how that helps you. In a stable current case, they will move some fixed distance apart (or together) and stay there

Yeah, my assumption is that I have some kind of handle or something that I can manipulate in order to move the wires closer or farther from each other.

Handle means you need to apply energy :)

Not if I'm a robot and the handle is pushing my hand!

lol

Energy conservation for better or worse works... perpetual motion machines are actually quite terrifying. If someone built one and forgot to shut it down, it could create a black hole

Heck, let's assume that the handle is oriented vertically, so that when the wires attract each other, it lifts the handle. Obviously the handle now has more potential energy, since it's higher up.

lol

Oh yeah what I wrote is correct for the case $E_{out} > E_{in}$ , if it's an equality it's not terrifying, just a bit weird (and again, impossible)

You can't build anything that doesn't lose some energy to heat, noise, etc.

Yup.

Even the Beatles codified that in a song: "and in the end, the love you take is equal to the love you make" -- replace love with energy and it's the same principle

add to that, we always make some noise, heat, and unavoidably useless stuff additionally to what we really wanted to do. probably also a similar thing happens in love, lol

gee, I now realize that "Maxwell's silver hammer" is on the same album. Were the Beatles sending us secret messages about Electromagnetism?? lol

All right, I think I've figured it all out. I know exactly what the paradox is, as well as the resolution to the paradox.

Suppose I have two loops of wire, far away from each other, both carrying current in the same direction. Then I bring them together. Does the energy in the magnetic field decrease? I had two answers to this question which contradicted each other.

Has to decrease as far as I understand it

Answer 1: the loops attract each other, so the energy they carry must decrease as they are moved together. Answer 2: the total inductance of the loops increases as they are moved together, and E = 1/2 * L * I^2, and since L is increasing, the energy must increase.

But when you say decrease I am assuming that you are computing $E_1+E_2$ regardless of where each energy field is located

So there's the paradox, but what's the resolution?

Both are true? $L$ increases but $I$ decreases? $E$ is constant?

It depends on what's held constant. If no voltage is applied to the wires, then answer 1 is correct; the formula E = 1/2 * L * I^2 holds true, but the current must decrease. If sufficient voltage is applied to the wires to maintain a constant current, then answer 2 is correct, and that voltage supplies the additional energy.

need a sanity check. the Wiki page for the electromagnetic tensor writes the Faraday 2-form as $$F=(E_{x}/c)\ dx\wedge dt+(E_{y}/c)\ dy\wedge dt+(E_{z}/c)\ dz\wedge dt+B_{x}\ dy\wedge dz+B_{y}\ dz\wedge dx+B_{z}\ dx\wedge dy$$

@CassieSwett Sort of makes sense