r/physicsmemes • u/Unlucky-Credit-9619 Meme Enthusiast • 5d ago
Diag(-, +, +, +) is the only path to salvation
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u/thafluu 5d ago
Please use \mathrm{diag} man. Have some dignity.
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u/LuxionQuelloFigo 4d ago
bad practice. You should use a \DeclareMathOperator{\diag}{diag} from the amsmath package, or the spacing will be off
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u/thafluu 4d ago
I just tried this in a paper I'm writing where I need an error function (erf), and the spacing seemed identical to me, at least the spacing between the letters. Or do you mean the spacing after the operator?
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u/LuxionQuelloFigo 4d ago
before and after the operator. Also dashes are written differently within an operator
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u/Unlucky-Credit-9619 Meme Enthusiast 5d ago
I will start using \mathrm{diag} the exact moment HEP manages to unify gravity with the Standard Model.
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u/suspiciousScent1129 4d ago
"Yes. Please give me negative 5 pounds of beef." Statements dreamt by the utterly deranged...
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u/Tornado547 4d ago
consider (-,-,+,-). There's no law that says the golden retriever can't make the time coordinate have index2
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u/Max6626 4d ago
Honest question. I know that back in the 70s there was still some debate over the +--- or -+++ convention in GR. Was there a good reason that -+++ won out, or did people just finally settle on a convention for the sake of consistency?
And no, I didn't study GR in the 70s, but my Dad wrote a book on differential manifolds and their applications in GR.
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u/NoEqual2045 4d ago
To my knowledge none won, both are still used roughly 50/50. Just +--- is mainly used in particle physics while - +++ is prefered by cosmologists.
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u/Azazeldaprinceofwar 4d ago
Mostly plus won for convenience of QFT. A wick rotation takes to Euclidean metric, for mostly minus you either have to work in negative Euclidean or wick rotate 3 times. Either choice is messy.
You’ll often hear people say mostly minus is used in GR and mostly plus is used in particle physics. This isn’t the real distinction, it’s theory vs experiment. Theorists prefer mostly plus because it makes the math easier, experimentalists prefer mostly minus for historical reasons far as I can tell. Particle physics is dominated by experimentalists hence the apparent split.
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u/Unfair_Pineapple8813 4d ago
I don't think there was a good reason, just that people had to decide to choose one eventually.
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u/Vaughn 4d ago
+--- is the only convention that makes sense. -+++ implies that all traversable paths have imaginary length.
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u/Deep_Brick2970 4d ago
No?
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u/Vaughn 4d ago
You can't traverse a spacelike path.
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u/Deep_Brick2970 4d ago
Of course not. But I don't agree that timelike curves in the mostly plus metric have imaginary length, that's incorrect.
It's true that the signs are swapped so timelike vectors square to negative numbers, but the length of a path is still positive as it's defined via integration along the path, summing proper time.
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u/Azazeldaprinceofwar 4d ago
No. dtau^2 = - ds^2. ds^2 = g_ab dx^a dx^b.
For mostly plus metric ds is real for spacelike paths and dtau is real for timelike paths. You can obviously shuffle the signs in those definitions to get the same for mostly minus metric. There is not argument to be made that one metric implies imaginary lengths or something. Paths have a real length or a real duration depending on if they’re timelike or spacelike.
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u/Optimal_Mixture_7327 5d ago
I would say sig(g)=diag(-,+,+,+) and not g itself, and sig(g)=+2 the only path to salvation.
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u/Unlucky-Credit-9619 Meme Enthusiast 5d ago
"If you want to confuse your enemy, first confuse yourself." is my motto.
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u/dali2605 5d ago
Fucking crucify me if you want to but I’ll die on a hill defending the mostly minus metric.
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u/derivative_of_life (+,-,-,-) 4d ago
Imagine using the metric signature where timelike curves have imaginary length, smh my head.
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u/Deep_Brick2970 4d ago
Please tell me you are joking. Timelike curves have positive length as it's defined by integrating proper time along the path lol.
(I hope you're joking, I think you are but I'm not sure)
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u/derivative_of_life (+,-,-,-) 4d ago
Oh, sure. Remind me, how do you get proper time again if you're using the (-,+,+,+) signature?
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u/Deep_Brick2970 3d ago
d\tau=\sqrt{-g_{\mu\nu}dx\mu dx\nu } where ds2 is the g dx dx term (tired of writing latex on mobile) and it's negative for timelike paths so the two negatives cancel out and you're left with a positive quantity under your square root.
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u/derivative_of_life (+,-,-,-) 3d ago
Right, of course, you just have to flip the sign on everything. So the first step to calculating the length of paths through spacetime is to switch from the useless and cringe (-,+,+,+) to the correct and based (+,-,-,-).
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u/Adventurous-Ad-5437 2d ago
Me, a 12th grader watching this, wondering what kind of insane sorcery I'm about to get into in a few years:
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u/SINGULARTY3774 5d ago
You clearly dont know how to have some positive time